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Lehrstuhl für Technologie der Fertigungsverfahren

Prof. Dr.-Ing. Dr.-Ing. E.h. Dr. h.c. Dr. h.c. Fritz Klocke

Master thesis

Cand.-Ing.: Ashwin Moris Devotta

Matr.-Nr.: 298960

Kurzthema: Development and validation of a 3D multiphase

finite element model for micro drilling of ferritic

pearlitic steel AISI 1045

Betreuender Assistent: Dr.-Ing. Mustapha Abouridouane

Aachen, den 10.07.2012

Inhalt und Ergebnis dieser Arbeit sind ausschließlich zum internen Gebrauch be-

stimmt. Alle Urheberrechte liegen bei der RWTH Aachen. Ohne ausdrückliche Ge-

nehmigung des betreuenden Lehrstuhls ist es nicht gestattet, diese Arbeit oder Teile

daraus an Dritte weiterzugeben.

Lehrstuhl für Technologie der Fertigungsverfahren


Aachen, 10. Juli 2012

M. Abouridouane - Tel. 0241-8028176

Master thesis

für Herrn Cand..-Ing.

Ashwin Moris Devotta

Matrikelnummer: 298960

Thema: Development and validation of a 3D multiphase finite element model for micro

drilling of ferritic pearlitic steel AISI 1045

For the simulation of micro cutting processes, where the chip thickness is in the same order

of work piece material’s grain size, the resulting size and scaling effects has to be taken into

account for an accurate estimation of the cutting forces, temperature development during

cutting and chip formation. Within the scope of this research work, a new 3D multiphase FE

computational model is to be developed based on the concept of representative volume

element (RVE) and constitutive material modelling to simulate explicitly micro drilling ferritic

pearlitic carbon steels. First, a material characterization which includes the analysis of micro-

structure and constitutive equations for each phase ferrite, pearlite and composite ferritic

pearlitic carbon steel is to be carried out. Then, the two phase 3D FE material model for steel

AISI 1045 is to be developed and verified using tension, compression and shear tests. Finally

the developed multiphase FE model is to be validated by simulating the micro drilling process

using the Lagrangian formulation proposed in the implicit FE code DEFORM 3DTM.

The following subtasks need to be solved:

Material Characterization and Material modelling

- The microstructure of the ferritic pearlitic steel AISI 1045 has to be character-ized based on grain size.

- The constitutive equations for each phase ferrite, pearlite and composite ferrit-ic pearlitic steel AISI 1045 has to be developed.

Representative volume element (RVE) development and validation

- The RVE for the steel AISI 1045 has to be developed.

- The developed RVE has to be verified based on tension, compression and shear tests.

The multiphase finite element model has to be validated by simulating the micro drill-ing process using the Lagrangian formulation proposed in the implicit FE code DE-FORM 3DTM.


I Table of Contents i

I Table of Contents

I Table of Contents ......................................................................................................... i

II Table of symbols and abbreviations ........................................................................... i

III List of Figures .............................................................................................................. ii

IV List of tables ................................................................................................................. i

1 Introduction .................................................................................................................. 2

2 State of the art ............................................................................................................. 4

2.1 Mechanical micro cutting process .......................................................................... 5

2.1.1 Micro drill geometry and material .................................................................... 6

2.2 Simulation of cutting process ................................................................................. 7

2.2.1 Empirical modeling of cutting forces in metal cutting ...................................... 8

2.2.2 Analytical modeling of chip formation in metal cutting ..................................... 9

2.2.3 Finite element simulation of chip formation in metal cutting ...........................11

2.2.4 Molecular dynamics simulation of chip formation in metal cutting ..................24

2.2.5 Artificial neural network modeling of metal cutting process ............................25

2.3 Microstructure based finite element mesh model development .............................25

2.3.1 Image based FE mesh construction for material microstructure ....................25

2.3.2 Voronoi tessellation based FE mesh .............................................................26

2.4 Conclusion and derivation of the problem .............................................................27

3 Objectives and approach ...........................................................................................28

4 Development of 3D multiphase FE model for micro-cutting ....................................29

4.1 Microstructure based FE material model development ..........................................29

4.1.1 Microstructure characterization and constitutive material modelling ..............30

4.1.2 New methodology for multiphase material based FE mesh development ......33

4.1.3 Algorithm to develop a 3D microstructure based FE mesh ............................36

4.1.4 Implementation of algorithm into DEFORM 3D ..............................................39

4.1.5 Preliminary validation of 3D multiphase FE model using tension, compression

and shearing tests ........................................................................................................41

4.2 Johnson-Cook (JC) model development methodology for all carbon steels ...........43

4.2.1 JC model development methodology for ferritic pearlitic steels......................44

4.2.2 Validation of the JC model development methodology ..................................47

I Table of Contents ii

5 Validation of 3D multiphase FE model using micro drilling process simulation ...49

5.1 Experimental setup for micro drilling & results .......................................................49

5.2 Cutting process simulation set up in DEFORM 3D ................................................53

5.2.1 Simulation set up ...........................................................................................55

5.2.2 Object definition & object positioning: Cutting tool & work piece ....................56

5.2.3 Mixture material modelling .............................................................................60

5.2.4 Inter-object data ............................................................................................62

5.2.5 Drill modelling ................................................................................................63

5.2.6 Work piece modelling ....................................................................................65

5.2.7 Remeshing strategy ......................................................................................66

5.3 Simulation of drilling process .................................................................................69

5.3.1 Prediction of feed forces & torque .................................................................69

5.3.2 Prediction of chip form ...................................................................................70

5.3.3 Prediction of chip morphology .......................................................................71

6 Future Directions ........................................................................................................74

7 Conclusion ..................................................................................................................75

V Index of literature ........................................................................................................77

II Table of symbols and abbreviations i

II Table of symbols and abbreviations

Symbol Unit Description

α mm Rake angle

β degree Friction angle

mm Yield strength

φ mm Shear angle

d mm Cutting diameter

Fc degree Force along the rake surface

Fp N Cutting force along the direction of cut

Fs N Force along the shear plane

fX mm Volume percentage of phase X

Np N Cutting force perpendicular to the direction of cut

Ns N Force perpendicular to shear plane

t1 N Uncut chip thickness

t2 N Chip width

Abbreviation Description

AISI American Iron and Steel Institute

HSS High speed steel

HSCO Cobalt High speed steel

RVE Representative volume element

CAD Computer aided design

III List of Figures ii

III List of Figures

Figure 1-1: Components employing mechanical micro drilling process ............................. 2

Figure 2-1: Mechanical drilling with process parameters, cutting speed and feed velocity 6

Figure 2-2: Micro drill geometries (1) twist drill (2) spade drill (3) D shape drill ................. 7

Figure 2-3: Merchant’s single shear plane theory ............................................................10

Figure 2-4: Lee & Schaffer’s theory using slip line field theory .........................................10

Figure 2-5: Oxley’s predictive machining theory ..............................................................11

Figure 2-6: Finite element simulation of chip formation in metal cutting ...........................12

Figure 2-7: Basic material modeling approaches in FE simulation of plastic deformation

process ..........................................................................................................15

Figure 2-8: Flow curve modeling with influence of strain, strain rate and temperature on

flow stress of work piece material ..................................................................15

Figure 2-9: Split Hopkinson pressure bar test setup ........................................................16

Figure 2-10: Material modeling using machining tests and Oxley’s predictive machining

theory ............................................................................................................19

Figure 2-11: Microstructure incorporated FE mesh in metal cutting by Simoneau et al

[SIMO06] (A-pearlite & B-ferrite) ....................................................................22

Figure 2-12: Microstructure based FE mesh for AISI 1045 steel with the influence of grain

shape ............................................................................................................22

Figure 2-13: Chip formation at various uncut chip thickness to microstructure size ratio is

simulated using microstructure based FE model ............................................23

Figure 2-14: Microstructure based FE mesh using hexagon based grain cell ....................23

Figure 2-15: Microstructure material level model for chip formation simulation in Ti-6Al-4V ..

..................................................................................................................24

Figure 4-1: Line intercept measurement method for grains size in ferritic pearlitic steel

microstructure ................................................................................................31

III List of Figures iii

Figure 4-2: Microstructural representation of C05, C45, C53 and C75 ferritic pearlitic steel

......................................................................................................................32

Figure 4-3: Microstructure based FE simulation of micro-cutting overview.......................34

Figure 4-4: DEFORM key file predefined structure ..........................................................35

Figure 4-5: Microstructure based FE mesh development algorithm part 1 .......................36

Figure 4-6: Microstructure based FE mesh development algorithm part 2 .......................38

Figure 4-7: Pictorial representation of microstructure based FE mesh development

algorithm ........................................................................................................40

Figure 4-8: Two phase 3D FE model developed for simulation of ferritic pearlitic steel

plastic loading ................................................................................................41

Figure 4-9: Variable loading of different microstructural constituents, pearlite and ferrite on

tension loading ..............................................................................................42

Figure 4-10: Validation of flow curve modelling methodology using law of mixtures ...........48

Figure 5-1: Machine tool setup for micro drilling experiments and microdrill geometry

employed .......................................................................................................50

Figure 5-2: Measurement set up for micro drilling experiments ........................................51

Figure 5-3: Experimental related feed force and related torque in micro drilling process .53

Figure 5-4: Plunging of the work piece and initiation of chip formation with consideration of

cutting edge rounding ....................................................................................56

Figure 5-5: Application of mesh density window to reduce remeshing during simulation run

......................................................................................................................57

Figure 5-6: Boundary conditions for velocity and heat transfer in work piece ...................58

Figure 5-7: Meshing of twist drill geoemtery ....................................................................59

Figure 5-8: Mixture material modelling for microstructure based FE mesh.......................60

Figure 5-9: Preliminary mixture material based FE mesh development ...........................61

Figure 5-10: Volume fraction information format in DEFORM 3D key file ...........................61

III List of Figures iv

Figure 5-11: Twist drill geometry used in experiments and simulation ...............................63

Figure 5-12: Drill geometry variation with drill diameter in micro drilling range ...................64

Figure 5-13: Work piece modelling using drill cutting edge geometry basis .......................65

Figure 5-14: Work piece geometry employed in micro drilling process simulation ..............66

Figure 5-15: Influence of remeshing methodology (global remeshing and local remeshing)

on mesh size .................................................................................................67

Figure 5-16: Chip form during micro drilling of AISI 1045 microstructure steel using 3D two

phase FE model ............................................................................................69

Figure 5-17: Prediction of feed force and torque using 3D two phase FE model, isotropic

FE model in comparison with the experimental results ..................................70

Figure 5-18: Chip form prediction using isotropic FE model and 3D two phase for a drill

diameter of 100 µm ........................................................................................71

Figure 5-19: Chip form prediction using isotropic FE model for a drill diameter of 100 µm ....

......................................................................................................................72

Figure 5-20: Chip shape during micro drilling in AISI 1045 steel ........................................72

Figure 5-21: Chip form and the presence of micro holed during micro drilling of AISI 1045

steel using 1 mm micro twist drill ...................................................................73

Figure 6-1: New local remeshing methodology for multiphase FE model .........................74

IV List of tables i

IV List of tables

Table 4-1: Microstructural characterization of ferritic pearlitic steel .................................32

Table 4-2: Test parameters for material modelling of ferritic pearlitic steel family ...........33

Table 4-3: Johnson Cook parameters for ferrite phase and pearlite phase .....................33

Table 4-4: Flow curve data for a constant strain of 0.1 for various strain rates at room

temperature ...................................................................................................47

Table 5-1: Cutting parameters, measured feed force and torque in micro drilling ...........52

Table 5-2: Parameters involved in the FEM simulation of metal cutting using DEFORM

3D ..................................................................................................................54

Table 5-3: Time step parameter for various drill diameters in DEFORM 3D ...................55

Table 5-4: Time step parameter for various drill diameters in DEFORM 3D ...................57

Table 5-5: Friction modelling and heat transfer modelling for chip, work piece and cutting

tool ................................................................................................................62

1 Introduction 2

1 Introduction

Product miniaturization is considered a key technology in the 21st century due to its inherent

advantages. The foray of metal cutting processes into micro scale manufacturing as an

alternative to material additive and removal process is on the rise and compete with other

micro-manufacturing technologies [DECH03]. A major advantage of the metal cutting pro-

cess is its ability to be employed in a wide array of work piece materials, at different size

scales, complex geometries and at lower economic order quantity. The study of metal cutting

process was of primary importance due to its application in the manufacturing of precision

engineered products of the 20th century in areas like automotive manufacturing, general

engineering and aerospace engineering. In the 21st century, new fields of application like

biomedical engineering, instrumentation, precision mechanics, lightweight design etc. are

probed and pursued (Figure 1-1). Advanced levels of control and predictability of machining

process has been reached due to decades of research effort that took place in different

aspects of machining process. Research in machining focusses on different aspects like

process mechanics, process tooling, work piece material metallurgy optimization, control

strategy, process simulation, process parameter optimization, tool path programming etc.

[DORN06]. This advanced level of knowledge gathered over several decades from different

parts of the world has led to application of the machining process into the micro scale.

Figure 1-1: Components employing mechanical micro drilling process

DIXI

DATRON 5 mm DATRON

1 Introduction 3

Miniaturization in different aspects of product development has seen giant leaps in counts of

improvement in the past two decades. This strategy of miniaturization of products started

primarily within the electronics community where the miniaturization of the circuits and elec-

tronic devices were directly related to its improved efficiency and performance. In the field of

printed circuits, Moore’s law predicted that the number of transistors that would be accom-

modated within the integrated circuit would be doubled every two years. This would indirectly

mean the manufacturing technologies deployed there within would have to improve their

capability in the same pace. This led to the development of a number of manufacturing tech-

nologies that are divided into deposition process, removal process, lithography process and

modification process. These processes were work piece material specific and primarily

worked in the 2D scale.

Since, the manufacturing processes that were developed within the semiconductor manufac-

turing community were material specific, it was not possible for them to be extended to new

areas of materials, geometries and applications. Hence, new manufacturing technologies or

scaling down of existing manufacturing technologies had to be pursued to meet these chal-

lenges. The miniaturization of products in fields other than semiconductor processing needed

processes which were generic and material independent. Material removal process that was

predominantly developed within the realms of general manufacturing is being studied today

to be employed in the micro scale. Micro forming, micro machining, micro injection molding

are a few areas that are pursued with vigor. Challenges that are specifically of interest when

the material processes are scaled into the micro scale are termed as scaling and size effects

[LIU04].

For e.g. in machining with geometrically defined cutting tools at microscale, when the cutting

tool is scaled down from the macro scale into the micro scale, the cutting edge dimensions

reach the dimensions of the phases present in the work piece microstructure leading to an

increase in the specific cutting energy [VOLL03]. Change in cutting tool dimensions for need

of rigidity also leads to specific cutting energy as the mechanics of material removal moves

from shearing of the work piece material into ploughing [KOPA84]. The understanding of the

metal cutting mechanics at the microscale is required to deploy the process in critical engi-

neering applications. These aspects of scaling in metal cutting are better studied through

finite element simulation [KOTS03].

In this work, the scaling and size effects in material removal process in general and micro

drilling process in particular are studied using FE simulation method. A new methodology to

generate a finite element mesh based on microstructure is developed. The newly developed

microstructure based FE mesh is then incorporated into the DEFORM FEM package. Using

the FE mesh, micro-drilling process has been simulated in AISI 1045 steel. The process

output parameters, feed forces and torque are predicted with improved accuracy in compari-

son to isotropic FE mesh and the influence of microstructure on the chip formation process is

ascertained.

2 State of the art 4

2 State of the art

The miniaturization of a number of products into micro range has put a great stress on manu-

facturing technology research to focus on micro manufacturing technologies [WEUL04].

Micro component manufacturing started in the field of electronics where the circuits and other

electronic component size continue to shrink according to the Moore’s law [ROBI05].

With the deployment of micro components primarily within the electronics industry, the manu-

facturing technologies associated with it were silicon based manufacturing technologies.

These silicon based manufacturing technologies were very specific in respect to the geomet-

rical capability and the choice of material on which they can act upon. In due course, different

work piece materials also had to be employed in addition to silicon. This called for the need

to use other manufacturing technologies. The classification of micro manufacturing technolo-

gies has been provided by different research groups based on different classification meth-

odologies. One classification methodology proposed by Brinksmeier [BRIN02] is used here

for it encompasses a wide variety of the manufacturing technologies that are at the disposal

for micro component manufacturing.

Micro manufacturing technologies

1. MEMS processes.

E.g. UV lithography, silicon micro machining, LIGA

2. Energy assisted processes.

E.g. Laser Beam machining, Focused Ion Beam machining, Electron beam machin-

ing, micro electro discharge machining

3. Mechanical processes.

E.g. turning, milling, drilling, polishing, grinding

4. Replication techniques.

E.g. forming, injection molding, casting

5. Technological aids for micro manufacturing technologies.

E.g. handling, assembly, metrology

These technologies are used in both Microsystem Technologies (i.e. technologies used for

the manufacture of micro-electronic mechanical systems and Micro optic-electro mechanical

systems (MOEMS)) and micro-engineering technologies (manufacture of highly precise

mechanical components, molds and micro structured surfaces).

The macro mechanical material removal processes refer to the use of geometrically defined

and undefined cutting tools to remove parts of work piece material with energy input leading

to the removal of material through plastic deformation in the form of chips. The application of

macro mechanical material removal processes in the micro range leads to a number of spe-


cific challenges which are to be understood at the fundamental level for its success in the

long run. These specific challenges are termed size effects in metal cutting and are con-

cerned with the influence of different input parameters at the micro scale.

2.1 Mechanical micro cutting process

The mechanical micro cutting process includes a wide variety of processes within itself and

includes turning, drilling, milling, sawing etc. This work is concerned with the drilling process

in particular and more specifically into the application of drilling process into the micro range.

The micro drilling process falls within the mechanical machining process and in general

encompasses a wide variety of processes depending on the source of energy used to re-

move the material. In general, the micro drilling process is either laser based or mechanical

drill based and each process has its own advantage and disadvantage. The tool based micro

drilling process is a scaled down version of the macro drilling process utilizing the twist drill.

This scaling brings in a new set of challenges with it.

The twist drilling process is a widely used material removal process for the manufacture of

blind and through holes and is by design used at the tail end of the manufacturing of a prod-

uct. The positioning of the twist drilling process in the later stage of the manufacture increas-

es the need for increased reliability of the process because an error during the drilling pro-

cess would lead to the loss of material, process energy, time and human effort. Unfortunate-

ly, twist drilling process is one of the least understood of all the material removal process

using geometrically defined cutting edges as the material removal takes place hidden from

the view of an engineer. The twist drilling process is carried out using different varieties of

drill geometry. The variation of the drill geometry depends on the work piece material in

which the drilling process takes place, the work piece geometry and the process capability in

relation to machine tool.

The term mechanical micro drilling process is not well defined with respect to the drill diame-

ter. But the general classification of drill diameter of less than 1 mm is satisfactorily accurate

where the process parameters are in the micron range.

The process parameters in the drilling process (Figure 2-1) are

1. Speed (m/min)

2. Feed (mm/ rev)

The process parameters are highly dependent on the work piece material, the cutting tool

geometry, cutting tool material and process conditions. The process parameter feed (mm/

rev) is a derivation of the more fundamental parameter of chip thickness. The chip formation

process in micro drilling in addition to the influence of flow behavior of work piece material

and process parameter as in the macro scale, also depends on the work piece microstruc-

ture.


Figure 2-1: Mechanical drilling with process parameters, cutting speed and feed velocity

The cutting speed is dependent on the work piece material’s behavior during chip formation.

This includes the chip form and heat transfer between the cutting tool and the work piece.

The heat generated during the chip formation is directly related to the material deformation

rate. This heat generated is transferred to the cutting tool material and this heat accumulated

reduces the tool’s strength exponentially. Taking all these into account, the cutting speed for

a work piece-cutting tool combination is decided upon. Further, the cutting speed also de-

pends on the application of coolant, the nature of the process etc., the ability of the coolant to

reach the primary shear area.

The scaling of the micro drilling process comprises of scaling down of the micro drill geome-

try and micro drilling process parameters. Linear scaling of the drill geometry leads to non-

linear reduction in the rigidity and makes the process highly unstable. The minimum chip

thickness which is one of the important process parameter depends on the micro drill edge

rounding geometry. The micro drill edge geometry depends on the size of the carbide particle

employed in the manufacture of the particular drill, grinding of the drill geometry and em-

ployment of various post-processing operations. The inter relationship between the different

drill geometry parameters leads to a situation requiring the study of different parameters on

process stability and capability.

2.1.1 Micro drill geometry and material

The micro drill geometry primarily depends on the micro drill diameter. The primary reason

for micro drill geometry to depend on the drill diameter is the method of manufacture of the

micro drill geometry and the increase in cutting load to diameter ratio as the diameter of the

drill reduces. The commonly available drill geometry can be differentiated approximately as

follows although variations occur with each manufacturer.


The drilling geometries that are used in micro drilling are the following (Figure 2-2)

1. Twist drill geometry (0.2 mm < d < 1 mm)

a. Twist drill geometry without undercut ( 0.3 mm < d < 1 mm)

b. Twist drill geometry without margin (0.1 mm < d < 0.3 mm)

2. Spade drill geometry ( d < 0.1 mm )

3. D shape drill geometry ( d < 0.05 mm )

Figure 2-2: Micro drill geometries (1) twist drill (2) spade drill (3) D shape drill

With the continuous improvement in the manufacturing capability of the micro drill geometry,

it is becoming possible for complex geometries to be manufactured for micro drills.

The choice of materials for the manufacture of micro drills falls primarily with HSS and car-

bide material. HSS (Cr4W6Mo5V2) and HSCO (Cr4W6Mo5Co5V2) are two varieties of the

High speed steel family that are employed in the manufacture of micro drills. The carbide

used in the manufacture of micro cutting tools in general fall under the high cobalt content

micro- and nano- grain size family. Cobalt content in tungsten carbide material increases its

toughness which is a prerequisite in micro machining regime.

2.2 Simulation of cutting process

The chip formation process directly or indirectly influences all the different aspects of metal

cutting like temperature distribution in cutting tool and work piece, tool wear, tool deflection,

surface integrity of the machined work piece, machine tool vibration, chatter marks on work

piece surface, surface roughness etc. [LUTT98]. With the increased importance attributed to

the control of the metal cutting process in modern day manufacture, a wide variety of re-

search approaches are pursued to understand the chip formation process. This includes

experimental techniques, numerical techniques and analytical techniques to name a few. The


chip formation process due to its complexity has to date has not lent itself to a successful

theoretical investigation. The primary theoretical investigation started with works of Piispanen

and Merchant and has led to a basic understanding of the chip formation process. The ex-

perimental technique provides the best understanding of the chip formation process in the

metal cutting although the cost involved is enormous and in addition calls for a highly sophis-

ticated technology availability requirement. This has lead naturally for the world’s research

community to embrace numerical simulation approach. The numerical simulation of chip

formation process is itself widely spread depending on the scale of the machining process

under study. Finite element simulation, finite volume method, Boundary value approach, slip

line field modeling, hydrodynamic particle approach and molecular dynamics are some of the

numerical technique approaches that are employed in the simulation of chip formation in

metal cutting. A few of the research approaches in metal cutting are described below in

detail.

2.2.1 Empirical modeling of cutting forces in metal cutting

Empirical relationships have been employed over a long period of time for the prediction of a

number of outcomes in metal cutting. Empirical relations are developed with the enormous

amount of data obtained through experimental investigation. The validity of the empirical

relationship depends heavily on the quantity of data employed to develop the empirical rela-

tion and predict the relationship between input and output parameters within the experi-

mental space. Two categories within the empirical modeling of cutting forces in metal cutting

are linear approximation and the potential approximation. The linear approximation is partly

based on the shear plane model and is easy to calculate. But it leads to a larger percentage

of error compared to the potential approximation method.

The general form of the linear approximation method is given by

(1)

Where A & B are constants of proportionality and b & h represent the cross section of un-cut

chip thickness.

The potential approximation method is a result of curve fitting done to a large value of exper-

imental values and is statistically verified. The drawback with this method is the absence of a

theoretical basis and its non-extendibility to predict the other cutting force components. One

of the most widely used potential approximation method in the field of metal cutting is the

Taylors formula relating the tool life (T) to the cutting velocity (Vc) through material related

constants (C & n).

(2)

Another important empirical formula for the prediction of cutting forces in metal cutting is

given by Victor-Kienzle. It is used to predict the cutting forces based on chip thickness and

chip width as input parameters and hence it is partially based on a theoretical basis.


(3)

Where is the cutting force per unit area, b & h represent the chip cross section area, m

represents the slope of the cutting force curve against chip thickness and K stands for the

material constant.

The empirical relations are best suited for the prediction of parameters in metal cutting. But

the major disadvantage lies in their inability to predict or explain the underlying mechanisms

of material removal in metal cutting.

2.2.2 Analytical modeling of chip formation in metal cutting

With chip formation being the primary source of force generation in metal cutting, various

analytical models of chip formation have been proposed over a period of time with varying

levels of complexity although most of them deal with the simple orthogonal cutting process.

An analytical model is a mathematical model which provides the solution to the equations

which describe the physical state using a closed formed analytical function. Several analyti-

cal models have been developed over a period of several decades. Some of the well-known

analytical model are Merchant’s single shear plane theory, the slip line field modeling of

metal cutting by Lee & Schaffer and Oxley’s predictive machining theory.

Merchant’s single shear plane model is concerned within the purview of orthogonal cutting

with a sharp cutting edge and the un-deformed chip thickness is significantly larger than the

cutting edge corner. This theory assumes that the work piece material is strained in a single

shear plane that extends from the main cutting edge to the free surface of the work piece

material and the friction between the cutting tool and the work piece is concentrated only on

the rake face and the relief face is free from friction. Tool wear, deflection of cutting tool and

nose radius are some of the parameters that are avoided. With all these assumptions made,

the chip is considered to be in equilibrium due to force by the cutting tool on one hand and

work piece on the other hand. The resulting cutting force is measured using a dynamometer

in both the directions. Using the circle of Thales, a circle is constructed whose diameter is

equal to the length of the resultant force vector. This resultant force vector is resolved along

different directions: Along and normal to the shear plane; in the machine coordinate system;

along and normal to the rake face (Figure 2-3).

The simplicity of the Merchant’s theory in explaining the chip formation was widely accepted

to understand the preliminary concepts of metal cutting without getting deep into the fields of

plasticity, metallurgy and mathematics. Naturally a number of shortcomings accompany the

theory which is the assumptions that are made in the first place. The shearing of the material

when it reaches the shear strength of the material without consideration of the strain harden-

ing, the presence of a single shear plane with unit thickness, the shear plane angle remain-

ing constant throughout the cutting process are some of the errors associated with it. Still

with all these assumptions as errors, this theory has provided some critical points in under-

standing chip formation.


Figure 2-3: Merchant’s single shear plane theory

To overcome the above said shortcomings, Lee & Schaffer proposed their solution to the

problem of metal cutting using the slip line field analysis (Figure 2-4). The slip line field solu-

tions include the determination of a system of orthogonal curvilinear trajectories of the maxi-

mum shear stress called slip lines.

Figure 2-4: Lee & Schaffer’s theory using slip line field theory

tool chip

Work piece

φ

β-α

β

Fp

F q

α

chip Shear plane

𝜋

4

𝜋

4− 𝜃

t2

𝛾

t1

Area bounded by slip lines

𝜑


Slip lines bounds the area within which the plastic deformation takes place. But the consider-

ation of a single shear plane and a plastic material behavior without the consideration of

strain, strain rate and temperature on the flow stress of the material made the Lee & Schaffer

model not to predict the cutting forces with reasonable accuracy. Moreover the consideration

of a sharp cutting edge is still void.

Figure 2-5: Oxley’s predictive machining theory

The latest among the well-known analytical models is Oxley’s predictive machining theory.

Oxley’s theory primarily was also concerned with the orthogonal cutting condition

(Figure 2-5). The theory is based on a model of chip formation from slip line field analyses of

experimental flow fields. Stress distributions along the primary shearing plane and the tool

chip interface are analyzed and then the shearing angle is selected so that the stress distri-

butions are in equilibrium. Using the temperature prediction from a compilation of experi-

mental data made by Boothroyd, the temperature along the primary shear plane and along

the interface is calculated.

In addition, the chip thickness which is calculated by taking moments about the tool edge and

the chip thickness is used to calculate the maximum shear strain rate at the tool/ chip inter-

face. The shear stresses are finally calculated and compared to the shear flow stress of the

chip. When the shear stresses and the shear flow stresses are in equilibrium, the corre-

sponding shear angle is ascertained as the correct shear angle. This theory was later devel-

oped for oblique cutting with a nose radius.

2.2.3 Finite element simulation of chip formation in metal cutting

The finite element method is a numerical modeling approach used in varied fields of engi-

neering and increasingly in manufacturing process simulation. The finite element method has

been developed over the past few decades to the extent that they are now capable of solving

industrial problems with high level of accuracy. This leads to improved productivity at a much

lower cost. Within manufacturing, the finite element method has been applied with high levels

of accuracy in small deformation type problems like forming, bending etc. [LORO06].

t1

Work piece

Fs

FN

Fc F

t

𝜃

𝜆 F

N

chip plastic zone

𝛼


Solving of physical problems with large deformation and processes with fracture phenomena

are still not fully developed to the required levels of accuracy. Still, finite element method is

regularly used in the analysis of large deformation type manufacturing process mainly within

the forming process simulation. The simulation of the chip formation process in metal cutting

using finite element method also falls within the large scale deformation process category

[SUH01, MOVA00] (Figure 2-6). In addition to the large scale deformation categorization, the

non-linear material behavior modeling, chip separation criteria, friction modeling between tool

and work piece and between work piece and chip influences the process output parameter

simulation [FILI08].

Figure 2-6: Finite element simulation of chip formation in metal cutting

In the finite element method, the geometry is divided into finite elements. Each element is

considered as a spring element and is described by the stiffness constant. With the increase

in the complexity of process mechanics to be studied, the complexity of finite element chosen

to simulate them also grows, from a single degree of freedom bar element to the more com-

plex tetrahedral element. A given three dimensional geometry is converted into a finite ele-

ment mesh and the stiffness matrix of the complete FE model is built using the stiffness

matrix of each finite element. The resulting stiffness matrix is termed as the global stiffness

matrix. The Lagrangian formulation and the Eulerian formulation are two methods that were

primarily employed. This leads to the development of a generalized formulation, the Arbitrary

Lagrangian-Eulerian formulation.

2.2.3.1 Lagrangian Formulation, Eulerian Formulation & ALE formulation

The Lagrangian formulation attaches the mesh to the material. This leads to large scale

mesh distortion with the progress of deformation in the work piece material [BORO05]. This

formulation is primarily used in solid mechanic problems for small scale deformation problem

analysis. The Eulerian formulation attaches the mesh to the space and the material is al-

lowed to flow through the mesh and is naturally used in fluid mechanics problems.

Cutting Tool (fixed in space) chip

Work piece

Mesh refinement

Chip-work piece contact

Chip-tool contact

Vc


The application of the Lagrangian formulation in the chip formation simulation necessitates

the very fine mesh size in absence of the remeshing capability due to the enormous amount

of material deformation in the process. Since the FE mesh is linked to the material, as the

material is deformed, the mesh shape gets distorted with the increase in the deformation of

material. The main advantage of the Lagrangian simulation approach is its ability to simulate

the initial penetration of the tool into the work piece, the plunging of the tool, the chip for-

mation process and the reaching of steady state chip formation process. The main ad-

vantage lies in the extreme deformation of the mesh.

The Eulerian formulation is fundamentally applicable to fluid mechanics problems as the

usage of control volume is well defined. The FE mesh is not attached to the material. Rather

the material is allowed to flow through the mesh. This approach completely avoids the main

disadvantage of the Lagrangian formulation, the mesh deformation. On the other side, the

control volume has to be defined. The definition of control volume in a metal forming simula-

tion would imply the volume within the die to be defined accurately and is possible in most

cases with the required accuracy. In the simulation of chip formation, the definition of control

volume means the prediction of the chip shape. Since the chip shape depends on the pro-

cess itself, the prediction of control volume is not possible. This leads to the development of

Arbitrary Lagrangian-Eulerian Formulation. The Arbitrary Lagrangian-Eulerian formulation

combines the merits of both the Lagrangian formulation and Eulerian formulation and is built

from the principle of virtual work.

The Arbitrary Lagrangian-Eulerian formulation uses one mesh which is fixed to the material

and another mesh which is fixed to the global space. A one to one mapping scheme is used

to relate the material mesh and global space mesh. This formulation can be simplified to two

different cases, the Lagrangian formulation and Eulerian formulation.

2.2.3.2 Material modeling in chip formation

A very important aspect for the FE simulation of chip formation in metal cutting is the incorpo-

ration of the work piece material’s thermo-mechanical behavior and cutting tool’s thermo-

mechanical behavior modeling [DENK06]. The effort undertaken to incorporate this thermo-

mechanical behavior depends on the results of the simulation that are of interest to the engi-

neer and the assumptions made thereof. The finite element simulation can be carried to

predict a number of different output parameters like cutting forces, temperature at the cutting

tool edge, chip form, shear angle prediction etc. A comprehensive model to predict all these

output parameters simultaneously with the highest level of accuracy is still not available for

the simplest of cutting condition: the orthogonal cutting model.For e.g. the cutting tool mate-

rial behavior is not given the highest importance when compared to the work piece material

behavior when the aim of the simulation is to study the chip formation and not the cutting tool

deflection, cutting tool wear or temperature at the cutting edge. Under these conditions, the

cutting tool is modeled as a rigid type material [ÖZEL07]. A rigid model does not undergo

elastic or plastic deformation. This significantly reduces the computational power require-

ments which can be the deciding factor in many cases. But the cutting tool material behavior


should incorporate the thermal properties of the cutting tool like thermal conductivity, emis-

sivity when the temperature distribution during cutting process is of prime interest.

In chip formation simulation, the work piece material behavior description plays a very im-

portant role in the prediction of cutting forces, chip morphology and temperature develop-

ment [FILI08]. The stresses experienced by the work piece material at high strain, high strain

rate and temperature, termed as flow stress is to be determined. In chip formation simulation,

the deformation of the work piece is described with increasing levels of complexity as shown

(Figure 2-7).

1. Ideal plastic with no strain hardening.

2. Plastic with strain hardening.

3. Elasto-plastic with strain hardening.

An ideal plastic material yields at a constant rate independent of the strain applied. This

assumption leads to a linear equation and grossly deviates from the physical reality in terms

of work hardening. The concept of work hardening is incorporated into the material modeling

using a model of plastic deformation with strain hardening. Strain hardening in a material is

due to the dislocation movement in the material under applied load.

Modeling of plastic deformation incorporating the strain hardening effect simulates the work

piece material behavior during metal cutting with better accuracy and the important output

parameters of cutting forces, chip form and temperature is predicted well. Hence this model

is used extensively in the material modeling of work piece material. The elastic-plastic mate-

rial model is required to predict the elastic deformation of the work piece when the load is

removed. The plastic material with strain hardening can be defined by the equation,

(4)

Where


Figure 2-7: Basic material modeling approaches in FE simulation of plastic deformation

process

The elastic recovery modeling is required during metal cutting simulation to predict the resid-

ual stresses and work piece material deformation during machining of thin walled compo-

nents.

Figure 2-8: Flow curve modeling with influence of strain, strain rate and temperature on

flow stress of work piece material

The thermo-mechanical behavior of the work piece material defined by flow stress’s depend-

ence on strain, strain rate and temperature is defined in Figure 2-8. In a multiphase material,

the dislocation movement along the grain boundaries is the primary reason for the plastic

deformation when external load applied on the work piece is beyond the elastic limit. This

dislocation movement is restricted with increases in the strain rate and is reflected in the

increase in flow stress with increase in strain rate. With the increase in temperature, the

dislocation movement is greatly activated and leads to reduction in flow stress. When the

material is deformed in the plastic range, heat is generated at the shearing surface, this

leads to reduction in flow stress.

Ideal plastic Plastic with strain

hardening

Elastic-plastic with

strain hardening

σ σ σ

ε ε ε

𝜀 −

𝑤𝑖𝑡 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒 𝑖𝑛 𝑠𝑡𝑟𝑎𝑖𝑛 𝑟𝑎𝑡𝑒

𝑤𝑖𝑡 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒 𝑖𝑛 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒

𝜎 𝑁

/𝑚𝑚

2


To model this flow curve in FEM simulation of chip formation process in metal cutting, the

constitutive equations of this flow stress are used. A wide variety of constitutive equations

are developed by different researchers. Some of the common constitutive equations for steel

are Litonski-Batra model, power law, Johnson-Cook [JOHN83] and Bodner Partom model.

To develop these constitutive equations, material testing is to be carried out in similar condi-

tions to metal cutting. The deformation mode during the material testing experiments will also

have to replicate the material deformation during metal cutting. With the metal under the

cutting edge undergoing a large compressive load before shearing, the compression test is

chosen to obtain the flow curves for FE simulation of metal cutting process. To obtain the

flow curves without these material testing other methods like practical machining tests and

reverse engineering using FEM technique are also used by few researchers.

The compression tests are used in place of tension test because the necking phenomena

during strain under tensile loading are not applicable for material under deformation during

cutting. Also the compression tests are easier to be conducted and have a higher level of

repeatability. The compression tests are carried out under quasi-static conditions and for

lower strains. The material behavior under high strain, high strain rate modeling is mainly

carried out using the Hopkinson’s pressure bar test (Figure 2-9). The Hopkinson’s pressure

bar test consists of an incident bar, a transmitted bar and a striker bar. The striker bar is

being operated using a pressure chamber. With an initial velocity applied, the pressure bar

hits the incident bar. The incident bar is thus provided by the incident stress wave and the

incident stress wave passes through the incident bar. The incident bar is kept long enough to

allow the disturbances to die out leaving only a single wave of specified wave length to pass

through the other end of the incident bar. The specimen is placed between the incident bar

and the transmitted bar. At the end of the incident bar, the stress wave is divided into the

transmitted wave and the reflected wave. The transmitted wave is transmitted to the speci-

men. The reflected wave is transmitted back into the incident bar. The transmitted wave

passes through the specimen.

Figure 2-9: Split Hopkinson pressure bar test setup

This transmitted wave is used for the loading of the specimen and results in a homogeneous

straining of the specimen. A part of the wave that is transmitted through the specimen is

transmitted to the transmitted bar and the other part is reflected back to the specimen. Strain

gauges are placed on both the incident bar and the transmitted bar. The influence of temper-

Projectile mass: m = 0.64 / 2.01 kg

Projectile velocity: v = 8 – 50 m/s

Deformation rate: de/dt = 103 – 104 s-1

bearing bearing

specimen

temperature control

output barinput bar

tube

compressed-air unit

projectile

damping unit

bearing bearing

specimen

temperature control

output barinput bar

tube

compressed-air unit

projectile

damping unit

Split-Hopkinson-Pressure-Bar


ature is accounted for by conducting a series of tests where the specimens are heated using

an induction based heating system. The specimen is heated using this heating system out-

side the experimental setup and immediately placed inside the temperature controlled enclo-

sure in the experimental set up. To obtain the flow stress behavior at different strain rates,

the incident bar velocity is modified for different strain rates. From the strains that are meas-

ured using the strain gauges, the flow stress is obtained for different strain and strain rate.

The work piece constitutive behavior is also obtained using a combination of orthogonal

machining tests, Oxley’s parallel sided shear zone theory and SHPB tests. One example for

the development of the flow curves using machining tests is the method developed by

Sartkulvanich et al [SART03].

In this method, for a given set of cutting parameters, i.e. cutting speed, uncut chip thickness,

chip width and rake angle, two cutting tests are conducted. The two cutting tests that are

done are slot milling tests and quick stop test. The cutting forces and cutting torque are

measured from the slot milling test. In addition, the ratio of the average deformed plastic

zone thickness in the primary zone to the length of the shear plane from the slot milling test

and the ratio of the deformed plastic zone thickness to the cut chip thickness from the quick

stop test is calculated.

In parallel, a computer program is developed that utilizes Oxley’s machining theory to predict

the cutting forces. An initial set of flow stress parameters, basic material properties of the

work piece material, thermal conductivity, specific heat and melting temperature are provided

as input. The flow stress curves are modified in an iterative procedure in comparison to the

cutting forces measured using the experimental set up (Figure 2-10).

The cutting forces, tangential forces and chip thickness are measured from the cutting tests.

The average shear strain, average shear stress are calculated from the cutting test outputs.

The equivalent stress and strain are calculated using Von Mises criterion. These values and

the flow curves obtained using the SHPB tests are inserted in the JC model. Non-linear

regression method is used to calculate the values of JC parameters, A, B, C, n and m with an

initial value of C0 as input. The hydrostatic stress values at the two ends of the primary shear

zone are calculated based on Oxley’s theory. The optimization of the parameters leads to the

identification of the Johnson-Cook parameters.


The Johnson Cook Model is a visco-plastic material model empirical equation and is de-

scribed as follows, [JOHN83]

(

) ( − (

− −

)

) (5)

-

- -

-

- -

-

-

-

It is divided into three different parts, the strain component, strain rate component and ther-

mal component. The strain component is built using a power function with the strain as the

variable. The constant value in the strain component corresponds to the yield stress. The

constant in the power function (n) is used to depict the strain hardening in the material. The

parameter identification of Johnson Cook model is carried out using different methods by

different researchers. This includes various optimization techniques like regression analysis,

evolutionary algorithm, Monte-Carlo simulation and various other techniques. Simpler tech-

niques including fitting of curves are also employed successfully.

-Thermal Component

-Strain Rate Component

-Strain Component


Figure 2-10: Material modeling using machining tests and Oxley’s predictive machining

theory

2.2.3.3 FE simulation of macro cutting process

The simulation of macro cutting process using the FE method has been researched over a

period spanning more than four decades and this has resulted today in the ability to predict

number of outcomes in a machining process. This ranges from the residual stresses in the

work piece and work piece distortion after its removal from the machine tool, the crater wear

in a tool during cutting process to the prediction of machine tool vibration during the cutting

process. The influence of the cutting tool geometry and the work piece response during the

chip formation process are critical factors that are to be included in the simulation of cutting

process [DENK12, ÖZEL07]. In the macro scale, the influence of work piece response in the

chip formation process is considered to depend on the strain undergone by the work piece

material, strain rate at which the strain take place and the temperature generated due to

plastic work.

This indirectly implies that the work piece material is assumed isotropic. This isotropic mate-

rial behavior assumption has been justified by the predicting capability of the FE simulation in


chip formation to near realistic proportions. The influence of the work piece material behavior

is included into the FE simulation by appropriate material behavior modeling.

Several specific FE models have been developed for various manufacturing processes like

turning, milling, drilling, sawing, grinding, broaching etc. The development of specific cutting

models have also been extended to other non-conventional or specific cutting processes like

ultrasonic machining, electro chemical machining, electro discharge machining, plasma hot

machining, laser cutting, laser assisted machining etc. Development of these processes has

been called for based on its criticality in the product manufacture and economics concerned

with the development of the specific machining process in specific applications.

A review of the finite element simulation in cutting process has been published by Jaroslav

Mackerle, (Finite element analysis and simulation of machining: a bibliography (1976-1996)

and Finite element analysis and simulation of machining: an addendum: A bibliography

(1996-2002)). The finite element simulation of cutting process for different work piece materi-

al behavior has also been carried out to a large extent. The simulation of work hardening

materials like nickel based alloys; titanium alloys call for as they demand specific material

behavior modeling to incorporate the work hardening properties.

2.2.3.4 FE simulation of micro cutting process

The finite element simulation of micro cutting process brings in new challenges in addition to

the ones found in the FE simulation of macro cutting process. In micro cutting, the cutting

edge’ radius is in the same scale as the un-deformed chip thickness. This is believed to lead

to a fundamental shift in the chip formation process. When the un-deformed chip thickness is

less than the cutting edge’ radius, a non-proportional increase in the cutting forces is ob-

served. The chip formation mechanics under these conditions falls under the ploughing

mechanism instead of the normal shearing mechanism and is termed under a group under

size effect in metal cutting.

In addition to the effect of un-deformed chip thickness in the cutting edge radius, the effect of

the different phases of the work piece material, their grain size and shape also is found to

have an important influence in the metal cutting process. Hence, the simulation of micro

cutting process has led to the need for inclusion of scaling and size effects. To simulate the

micro cutting process with the finite element method, the incorporation of grain volume, grain

shape and the volume fraction of the corresponding phases has to be incorporated. This

geometrical inclusion calls for new techniques of mesh generation. In addition to the inclu-

sion of geometrical variation within the FE mesh, the flow curve behavior of the different

phases will also have to be incorporated in the simulation. To incorporate the phase material

behavior, the mixture material models are employed where the different phases of the mate-

rial, their interaction, heat transfer and transformation properties can be incorporated.

The inclusion of the different phases in a multiphase material like steel calls for a great effort

in the mesh generation methodology. The Voronoi cell Finite element method is specifically

developed for the representation of the microstructure using meshes in 3D. The maturity of

the VC FE method is not yet developed to simulate the chip formation process in metal cut-


ting. In the present stage, this has led to limitation of the chip formation simulation in the

micro scale in 2 dimensions as they do not need the use of complex algorithms to be incor-

porated.

The chip formation process in the micro-cutting of multi-phase material is simulated using a 2

dimensional cutting model using ABAQUS explicit version 6.4 finite element software by

Simoneau et al [SIMO06, SIMO07, MOHA11] (Figure 2-11). The simulation is carried out for

the micro scale, meso-scale and macro-scale cutting of AISI 1045 Steel. The two phases of

the AISI 1045, ferrite and pearlite have a grain size of 10µm and 100 µm respectively. The

un cut chip thickness is used as a criteria to differentiate among the different scales of cut-

ting: Un cut chip thickness of 5 µm, (uncut chip thickness < ferrite grain size, 50 µm (uncut

chip thickness > ferrite grain size & uncut chip thickness < pearlite grain size) and 100 µm

(uncut chip thickness ≈ pearlite grain size).The cutting edge radius is considered to be sharp

and the edge rounding influence is neglected.

This model was used to understand the variation in chip formation mechanics across scales

of metal cutting. The increased specific cutting forces as the scale of cutting moves from

macro scale cutting into micro scale cutting is explained using the larger plastic deformation

and shear extrusion that takes place in cutting. The larger plastic deformation and the addi-

tional shear localization which is predominantly present in the micro scale cutting are better

captured using the heterogeneous finite element model. The chip shape during micro cutting

is termed as a quasi-shear-extrusion chip whereas under the same cutting conditions, the

chip shape in the macro scale is a continuous chip form and the chip shape in the meso-

scale is a transition between the quasi-shear-extrusion chips to continuous chip shape.

The heterogeneous FE model’s advantage in predicting the surface defects during the micro

cutting of a multiphase material is also simulated. The chip formation process varies as the

primary shearing zone is varied from softer material, ferrite towards the grain boundaries

between ferrite and into pearlite and lastly into the harder pearlite phase and the continuation

till the length of cut is reached. This variation is explained with the change in the shear plane

angle in the different phases, the amount of plastic deformation that the different phases

undergo to keep the cutting energy in equilibrium.


Figure 2-11: Microstructure incorporated FE mesh in metal cutting by Simoneau et al [SI-

MO06] (A-pearlite & B-ferrite)

Another microstructure based FE mesh is developed by Simoneau et al (Figure 2-12). This

model incorporates the shape of the microstructural constituents instead of a cubic structure.

This microstructure based FE mesh is employed to simulate the chip formation process in

AISI 1045 steel.

Figure 2-12: Microstructure based FE mesh for AISI 1045 steel with the influence of grain

shape

The steel’s constituents, ferrite and pearlite are modeled in 2D scale with the cutting edge

considered to be infinitely sharp, i.e. the effect of cutting edge radius is not taken into ac-

count. This model is reported to predict the chip shape with different levels of uncut chip


thickness in a better way . The cutting at different uncut chip thickness in relation to the grain

size is shown to affect the chip shape and the mechanisms that lead to it (Figure 2-13).

Figure 2-13: Chip formation at various uncut chip thickness to microstructure size ratio is

simulated using microstructure based FE model

The influence of the microstructural composition, grain size and distribution of pearlite,

graphite and ferrite in ductile machining is also simulated using a hexagonal shaped grain

structured FE mesh was developed by L.Chuzhoy et al [CHUZ03, PARK04] (Figure 2-14).

This (two dimensional) plane strain model modeled the work piece using a rectangular block

consisting of a single microstructure meshed with bilinear quadrilateral elements. An internal

state variable model called the BCJ model is used to model the material behavior.

Figure 2-14: Microstructure based FE mesh using hexagon based grain cell

The friction modeling is done using a sticking of the chip with the cutting tool. The mesh

distortion using repetitive remeshing instead of adaptive remeshing as the mesh element

size reduction beyond a limit also reduces the stiffness of the mesh. The ferrite, pearlite and

ductile iron were simulated separately. The model’s ability to simulate strain localization, the

local deformation of the softer ferrite particle by the harder pearlite particle was studied. The


segmented chip formation was predicted by the microstructure level model and was con-

firmed by experimental test results.

A microstructure material level FE mesh is developed for the simulation of chip formation of

Ti-6Al-4V by Zhang et al (Figure 2-15). The FE mesh is developed employing the cohesive

element model in ABAQUS. The FE mesh is developed does not incorporate two phases, but

only the influence of one phase with the grain boundary. The effect of grain orientation on the

chip formation is studied with this model. This model includes the cutting edge rounding and

simulates the pull out of the grain predicting the burr formation in the newly formed surfaces.

Figure 2-15: Microstructure material level model for chip formation simulation in Ti-6Al-4V

2.2.4 Molecular dynamics simulation of chip formation in metal cutting

The process of metal cutting has been applied in varied fields of application. A relatively

recent application of metal cutting is in the nanometer scale. Two applications of metal cut-

ting in the nanometer scale are single point diamond turning and ultra-precision diamond

grinding. The nanometric cutting process is used to study the material deformation process

at the nanometer scale [PROM10]. The uncut chip thickness is at the scale of 1 nm. The

simulation of the nanometric cutting is carried out using molecular dynamics simulation. At

this scale, the material deformation is not based on the grain boundary displacement, dislo-

cation movement in the material etc. The material movement is at the atomic scale. Material

at the uncut chip thickness contains only few layers of atoms. The interaction of the atoms is

analyzed using the potential energy function. Simulation of nanometric cutting is a relatively

new arena in metal cutting research which requires huge amount of computational power for

the simulation of industrial scale implementation.The material behavior in nanometric cutting

is incorporated using potential energy function. For e.g. in the nanometric cutting of copper,

the embedded atom model (EAM) potential function is used to relate the interaction between

two atoms of copper. Due to the absence of an EAM potential function for the interaction

between the diamond cutting tool and the copper work piece, the Morse potential function is

used. The trajectories of the chip, the cutting forces on the tool, energy of the system, tem-


perature generated during cutting are some of the outputs in the simulation of metal cutting.

Computational power is the main criteria for the non-usability of this simulation technique to

be used in industrial scale micro machining applications.

2.2.5 Artificial neural network modeling of metal cutting process

The metal cutting process due to a large number of input parameters and the interactions

among them lead itself as a candidate to be modeled using artificial neural network method-

ology. The main advantage of artificial neural network methodology is its ability to perform

the modeling process with missing input data and unknown interaction between the input

parameters. Some of the output parameters that are predicted using ANN are forces, torque,

power, tool failure, deformation, surface integrity, noise, acoustic emission, vibration, chip

formation and temperature. Neural networks use a minimum of three steps, or in the ANN

terminology, three layers. These are the input layer, hidden layer and the output layer. Neural

networks are massive parallel systems made up of simple processing units termed as neu-

rons and are linked with weighted connections. These weighted connections represent the

knowledge possessed by the networks. The input parameters are provided to the neurons in

the input layer which converts them into normalized functions, multiply them with the

weighted connections and transferred to the hidden layer. The transfer of the neurons to the

hidden layer is done after scaling of the input layer using a function called bias. The neurons

are further transferred to the next layer using a transfer function termed the activation func-

tion. Finally the output parameters that are present in the neurons of output layer are com-

pared to the experimental values. The difference between the output parameters from the

experiment or learning values and the ANN model is reduced by changing the weights of the

connections between the neurons using a wide variety of back propagation learning algo-

rithm, conjugate gradient algorithms, quasi newton algorithms and Levenberg-Marquardt

method.

2.3 Microstructure based finite element mesh model development

Currently various methods are available for the generation of representative volume element

with different levels of complexity that are employed for different applications. The frequently

used representative volume element methodologies in FEM are

1. Image based FE mesh construction for material microstructure

2. Voronoi tessellation based FE mesh

2.3.1 Image based FE mesh construction for material microstructure

The image based FE mesh construction for material microstructure used to develop a repre-

sentative volume element of a multiphase material [WOJN04]. Direct method and indirect

method are two variations that are available within this methodology. The microstructural

image from a standard metallographic examination is used as the basic for FE mesh devel-

opment.


In the direct method, a pixel of the image is used to represent each phase of a material. The

pixel fineness is directly related to the accuracy of the mesh developed. The image’s each

pixel is identified as a distinct element and each pixel is recognized. Consequently at the end

a single grain can contain a large number of pixels. Each microstructure grain is depicted by

a number of pixels. This leads to a computationally inefficient method. To be used in the

finite element simulation, the mesh obtained from the direct method is to be modified to make

it more computationally efficient. The mesh developed using the direct method is also report-

ed to exhibit false stress concentration geometry.

The indirect method uses the image to develop a FE mesh without only the direct conversion

of pixel into element. An image is initially defined by the pixel and the mesh is generated.

Different algorithms are then employed to improve the efficiency with the FE mesh before

being used in a simulation. The boundary of the elements is identified, modified to reduce the

unnecessary elements within a grain. This results in a computationally efficient FE mesh

which represents the microstructure.

The methodology in obtaining the image from the microstructure is also critical to the accura-

cy of the developed FE mesh. The basic procedure is the serial sectioning of the material

using a standardized metallographic technique. This image segmentation technique results

in a series of images of a microstructure in two dimensions [WEJR08]. This is then used to

develop the FE mesh. The different phases are represented by their boundaries and color.

This methodology provides the best representation of microstructure in the FE mesh. But the

time required to create a mesh is enormous and tedious. One another disadvantage of the

image based FE mesh is the need for process of RVE development to be carried out for

each steel microstructure.

2.3.2 Voronoi tessellation based FE mesh

The Voronoi tessellation scheme is used in 2D space and 3D space. In two dimensional

spaces, a set of points are distributed in the given space initially. Next, the position of the

points is adjusted using Delaunay triangulation algorithm.

In the Delaunay triangulation, the points lying near to each other are used to construct trian-

gles. The Delaunay triangulation then positions the points, such that no point lies inside the

circumcircle of the triangles. These triangles form the grains in a 2 dimensional space. This

tessellation when applied in 3D, leads to the Voronoi tessellation representing microstruc-

ture. The triangles in 2D are converted into tetrahedral elements in 3 D space. The incorpo-

ration of the grain size, grain volume and grain shape has to be taken into account to convert

the Voronoi tessellation into a representative volume element [LASC10].

The Voronoi tessellation is considered a very good approach to model 3D microstructures

[FRIT09, GHOS04]. The challenge in the application of the Voronoi tessellation based mesh

in the finite element simulation of chip formation process lies in the capability of the simula-

tion engine to accept the Voronoi mesh. A major challenge is the regeneration of the mesh

that is of primary importance in the metal cutting simulation. The currently employed FE

simulation package, DEFORM 3D V10.2 does not contain the ability to generate the mesh


based on Voronoi tessellation. This methodology can be probed in the future, when the

capability to incorporate Voronoi tessellation based mesh into the simulation package is

achieved.

2.4 Conclusion and derivation of the problem

The above review of the state of the art clearly shows the importance attached to the devel-

opment of new micro-manufacturing technologies. The importance of material removal pro-

cesses in micro-manufacturing technologies also grows as new work piece materials are to

be processed. The micro-drilling process is a critical process in the manufacturing sequence

of complex engineering products. The micro-drilling process using a twist drill is a scaled

down version of the macro drilling process. The scaling down brings in additional challenges

to those already present in the macro drilling process.

The drilling process carried out using the twist drill in the macro scale includes the extrusion

of the material under the chisel edge due to the highly negative rake angle and the material

removal through shearing under the main cutting edge. The influence of the cutting edge’s

macro geometry like the chisel edge width, cutting edge shape, clearance profile geometry is

significant in relation to the cutting forces generated, the temperature generated at the prima-

ry and secondary shear area. At the micro scale, the influence of the cutting edge rounding

on the mechanics of material removal is significant as proved from previous research for

simple orthogonal cutting. In addition, the work piece microstructure is also proved to be an

influencing factor in the chip formation mechanism under orthogonal cutting. The micro cut-

ting process is so far studied in the 2D scale as the generation of microstructure based FE

mesh is still not completely developed for cutting process simulation. The three dimensional

microstructure based finite element mesh based on Voronoi cell methodology needs other

aspects of cutting process simulation like remeshing, chip separation criteria are to be devel-

oped. To carry forward the application of micro cutting process into industrial applications

with higher level of accuracy, 3 dimensional cutting processes like micro drilling is to be

studied with all its influencing factors taken into consideration.

The study of micro- machining process is carried out using a wide variety of research ap-

proaches which includes experimental approaches, analytical approaches and numerical

simulations approach. One important numerical simulation technique that is used in the study

of cutting process simulation is the finite element simulation method. The finite element

simulation method is developed to the extent to be used for the realistic prediction of cutting

forces, chip form and heat transfer to the cutting tool. The finite element mesh of the work

piece has so far been modeled as isotropic. Since the work piece microstructure is proved to

be an important factor in the micro cutting process, the need for a heterogeneous microstruc-

ture based finite element mesh is warranted. The generation of heterogeneous finite element

mesh and the simulation of microstructure based finite element modeling of chip formation in

micro cutting process would be a step further in understanding of the micro cutting process.

3 Objectives and approach 28

3 Objectives and approach

From the previous discussion on the state of the art in chip formation simulation in the micro

scale, the need for a multiphase FE Model development methodology in the micro scale is

clearly warranted. This model development would enhance the understanding of the chip

formation mechanics in the micro scale and could be developed further for the process moni-

toring of micro-cutting process.

The main aim of this work is the development of a new 3D multiphase FE computational

model for the incorporation of different phases of the work piece material. The developed

model is to be validated by its ability to predict the process output parameters with improved

accuracy in comparison to the isotropic FE model at micro scale plastic deformation pro-

cesses, specifically micro cutting with defined cutting edges. The flow behavior of the differ-

ent phases of the work piece material will also have to be incorporated separately into the

simulation. DEFORM 3D is a FE software developed by Scientific Corporation, Ohio, USA

primarily used for the simulation of metal forming process. Continuous development in the

process capability of the software has led to the possibility to simulate metal cutting process

and hence DEFORM 3D is employed in this work for the simulation of micro cutting process.

The work is divided into three parts and are grouped based on the objective and the ap-

proach thereof pursued.

1. To develop a representative volume element generation strategy for multiphase material.

This strategy should incorporate the microstructure parameters, grain size, grain shape and

phase volume percentage of each phase. The developed representative volume element will

be subjected to different loading conditions like tension, compression and shear loading and

compared with the corresponding experimental result and to validate in the preliminary stage

the ability of the developed RVE to simulate plastic deformation at the micro scale. The AISI

1045 microstructure is used to validate the RVE development strategy.

2. The flow curves of each microstructural phase have to be ascertained through material

testing and modeled using Johnson-Cook model for incorporation into the multiphase materi-

al FE model. A methodology to predict the flow curve behavior of a steel family is also devel-

oped which utilizes the flow curve of its individual constituents. This can be utilized for the

flow curve modelling with reasonable accuracy without conducting extensive material tests.

The two constituents of ferritic pearlitic steel: ferrite and pearlite are modeled using C05 and

C75 microstructure.

3. The RVE developed for AISI 1045 is used in the FE mesh generation for the work piece

used in the chip formation simulation in micro drilling process. Feed forces and torque are

the primary output parameters that are used to evaluate the developed FE model. In addi-

tion, the chip shape and morphology are also compared with the real chip morphology. The

influence of different parameters like uncut chip thickness, cutting edge radius are also stud-

ied. The validity of the generated FE mesh is compared with the results of experimental

investigation.

4 Development of 3D multiphase FE model for micro-cutting 29

4 Development of 3D multiphase FE model for micro-

cutting

As discussed in the state of the art, the need for a methodology to develop a 3D multiphase

material based finite element model for the simulation of micro manufacturing process exists.

To cater to this need, a new methodology which generates a multiphase material based FE

model built on the concept of representative volume element is developed. This FE model

incorporates microstructural parameters such as phase volume percentage, grain volume

and grain shape of the different phases of a multiphase material.

The development of a 3D multiphase FE model for micro cutting involves the generation of a

multiphase material based FE mesh and constitutive material modelling of the microstructural

phases. In addition as part of this work, a general methodology for the constitutive material

modelling for the carbon steel family is also carried out by employing the constitutive material

models of ferrite phase and pearlite phase in the law of mixtures.

4.1 Microstructure based FE material model development

The microstructure based FE material model development involves the development of a

multiphase FE model that is built on the concept of a representative volume element. This

multiphase FE model contains the different phases of the microstructure. The different phas-

es of the microstructure are represented distinctly in terms of geometry, distribution and

material behavior.

A representative volume element of a microstructure as explained by R.Hill is structurally

entirely typical of the whole microstructure on average and the material behavior is macro-

scopically uniform, i.e. the fluctuation of a mean value of a material parameter is small. This

reduction in fluctuation is made by making the representative volume element larger.

The incorporation of the microstructure geometry in the finite element is important and the

complexity level increases multifold compared to a isotropic FE mesh. The microstructural

phases’ geometric shape is highly varied. A common shape cannot be assumed as it leads

to erroneous results. The 3 dimensional geometrical classification of microstructure is a large

area to explore in itself. The effort to be exerted to incorporate the exact geometry of a single

grain into a finite element simulation depends on the scale of the process and also requires

large scale computing power even to today’s standards. For modelling the microstructure’s

geometry in carbon steel family, spheroidal shape has been shown to yield good results in

comparison to experimental investigation. In addition to the geometrical shape, the distribu-

tion of the phases will also have to be taken into account for the finite element mesh to be-

have as a representative volume element of a multiphase material.

The geometry of the grain is specified by its size in addition to its shape. The influence of the

grain size on the material properties is established by Hall-Petch effect. The mechanical

properties of multiphase materials depend on the grain boundaries to a large extent as they


impede the movement of dislocations when a material applied. Therefore, with variation in

grain size the dislocation movement is influenced and the yield strength is varied.

(6)

Where is the yield strength, d is the grain size and k is the strengthening coefficient. x and k

are material specific parameters.

In addition, the microstructure’s phase distribution can be uniform or non-uniform as in the

case of special heat treated steels. The carbon steel under consideration contains uniform

distribution of the microstructure. The minor variation in the microstructural distribution from

the center of a cylindrical specimen to the outer surface of the cylindrical specimen is ne-

glected without significant loss in accuracy.

In order to use the developed multiphase material based FE model, material behaviors of

each phase has to be independently described in the finite element simulation. For e.g. the

presence of a harder microstructural phase in a softer matrix has to be differentiated on

material level to study the influence of each separate phase during simulation. With the

material models for the different phases being separately considered the deformation re-

sponse of the harder microstructural phase finite element is distinct compared to the defor-

mation response of the softer matrix phase. In addition to the material behavior of phase, the

influence of grain boundaries also plays an important role. The incorporation of the grain

boundaries and their influence needs a completely new upcoming methodology in FEM

called the crystal plasticity based FEM and hence is not considered in this work.

4.1.1 Microstructure characterization and constitutive material modelling

To incorporate the microstructure geometry specifications of grain size, grain shape and

phase volume percentage into the finite element simulation, the material has to be character-

ized. As part of this work, the material characterization is done using standard metallography

technique [WOJN04]. The information obtained from a metallography procedure primarily

includes grain size and the phase volume percentage of the microstructure [BADD02]. For

the ferritic pearlitic steel family, the phase volume percentage of pearlite & ferrite and grain

size of ferrite is to be obtained. To reduce the complexity, the inter-lamellar spacing and the

aspect ratio of pearlite are assumed constant for ferritic pearlitic steel family.

The material characterization is carried out for C05, C45 and C75 steel microstructure. The

standard quantitative metallographic investigation is carried out by polishing and etching the

steel specimen. The microstructure is analyzed under magnifications of 100X, 200X and

500X. The phase percentage is calculated by its area and in the case of ferritic pearlitic

steels; the ferrite area is calculated in µm2. A total of 3 samples are measured to obtain a

statistically accurate estimation.

In addition to the phase volume percentage, the grain size is also to be measured for model-

ling the microstructure with reasonable accuracy. The grain size measurement is carried out

using the intercept method. The grain size to be measured in all its complexity will have to be


measured using a 3 dimensional irregular structure. To measure the 3 dimensional ferrite

particles which is or arbitrary shape, the integral of the areas of its plane sections is sufficient

by Fubini’s Theorem. Based on this, Delesse, a French geologist, proposed that the plane

section of a microstructure can be regarded as representative of the 3 dimensional irregular

structures. This falls under the idea that the constituent phases that is present in the planar

scale is to be present in the same proportion in which they occur throughout the microstruc-

ture.

This was further simplified by Rosiwal to one dimension by drawing lines across the steel

microstructure image and then calculating the length of the lines that overlap the constituent

of interest under study, in this case the ferrite constituent.

This assumption in simplified terms is represented by

Figure 4-1: Line intercept measurement method for grains size in ferritic pearlitic steel

microstructure

A simple representation of the line intercept method for the C45 steel microstructure in nor-

malized condition is shown here (Figure 4-1). The black lines are drawn at equally spaced

intervals over an image of the C45 steel microstructure. The red lines represent the overlap-

ping of the black lines with the microstructural constituent of interest, ferrite. The measure-

ment of the line’s length is used as a measurement of the microstructure’s grain size.

The carbon percentage in a ferritic pearlitic steel increases from C05 to C75. This increase in

carbon implies the increase in pearlite phase percentage from 1% to 99%. The iron-carbon

diagram clearly depicts this increase in carbon percentage from C05 to C75.

100 µm


Table 4-1: Microstructural characterization of ferritic pearlitic steel

Steel Carbon

/ w%

Pearlite

/ %

Ferrite

/ %

Ferrite grain size

/ µm

C05 0.05 1 99 30

C45 0.45 60 40 15

C75 0.75 99 1 45

This increase in the pearlite volume percentage takes place at the expense of reduction in

ferrite volume percentage. The variation in the volume percentage directly influences the

grain size variation. Therefore, with the increase in the pearlite percentage, the ferrite grain

size reduces from 30µm in C05 steel microstructure to 15µm in C45 steel microstructure.

Figure 4-2: Microstructural representation of C05, C45, C53 and C75 ferritic pearlitic steel

A representative image of the microstructure of ferritic pearlitic steel is provided for C05 to

C75 (Figure 4-2). This shows the complex microstructural shapes that has to be incorpo-

rated into the microstructure based finite element mesh. The grain size is an approximation

as the grain size is not constant. For the sake of simplicity in microstructural representation in

finite element mesh generation, the mean value of the grain is used. The grain shape, grain

size and volume percentage as shown should be reflected in the finite element mesh that is

developed for the simulation of ferritic pearlitic steel.

To model the micro drilling process using a multiphase finite element model, in addition to

the multiphase finite element mesh, the work piece material behavior will also have to take in

to consideration the two different phases present in the work piece microstructure instead of

modelling the work piece behavior in the model of a single isotropic material model. Hence

C05

C53 C75

C45


for the multiphase simulation of carbon steels, the two important phases, pearlite and ferrite

are required [ALLA08, RAMA12, SUH01]. In order to obtain the different phases of the work

piece material’s flow curve behavior, a material microstructure in which one of the work

piece’s phases is present in an absolute majority can be used as a reference for the phase.

Hence, to obtain the material models of the AISI 1045 microstructure’s phases separately

two specific steel microstructures, C05 steel and C75 are used. The C05 steel microstructure

contains 1 % of pearlite and 99 % of ferrite and its flow curve model is considered to be

representative of the ferrite phase. The C75 steel microstructure on the other hand contains

99 % of pearlite and 1 % of ferrite and is considered representative of the pearlite phase. The

change of pearlite grain volume with the change in the carbon weight percentage is evident

and its influence is not considered in the current work. The grain boundary variation, inter-

lamellar spacing and aspect ratio of pearlite’s influence on the mechanical behavior is also

not taken into account.

The material testing for the carbon steel family is carried out by a quasi-static compression

loading and a series of high strain, high strain rate compression loading using a split Hopkin-

son pressure bar tests at various temperatures (Table 4.2).

Table 4-2: Test parameters for material modelling of ferritic pearlitic steel family

Microstructure tested C05, C15, C45, C53, C75

Strain ε / - < 0.4

Strain rate έ / (1/s) 0.002, 0.07, 0.35, 3285, 3464,

3713, 3950, 3963, 4050, 4373,

4455, 4994, 5153 Temperature / °C 20, 200, 400, 600, 800

The material testing is carried out for all the microstructures listed in the table under the

conditions specified there within. The constants for the Johnson Cook model are obtained

from these curves.

Table 4-3: Johnson Cook parameters for ferrite phase and pearlite phase

Phase/Microstructure A / MPa B / MPa n / - C / - m / -

Ferrite 175 571 0.35 0.034 1.86

Pearlite 546 487 0.25 0.015 1.22

The Johnson Cook model constants for the ferrite phase are obtained from the flow curves of

C05 steel and the constants for the pearlite phase are obtained from the C75 steel flow

curves as tabulated (Table 4.3).

4.1.2 New methodology for multiphase material based FE mesh development

To incorporate the geometric details of grain size, grain shape and volume percentage of the

ferrite phase and pearlite phase obtained from the metallographic characterization of the

ferritic pearlitic steels in the 3D finite element simulation of the plastic deformation process in

the micro scale, a new methodology for mesh development is established. The advantages


of this methodology lie in its simplicity and its ability to be integrated into any commercial

finite element software package. An overview of the new 3D multiphase Finite element model

development is provided in this section (figure 4-1). In the subsequent sections, each aspect

of this model development procedure is explained in detail. The overview is provided initially

to provide a better understanding of the structure of model development procedure. The new

methodology is explained is described in this section using generic terms without specific

reference to ferritic pearlitic steel to underline its applicability to general microstructure based

FE mesh development.

Figure 4-3: Microstructure based FE simulation of micro-cutting overview

The micro drilling process is chosen to validate the multiphase finite element material model.

DEFORM 3D is the finite element software chosen to simulate this process. The micro drill

and the work piece geometry is required to simulate the micro drilling process in DEFORM

3D. The work piece geometry is converted into a multiphase material based FE mesh instead

of the usual isotropic FE mesh. DEFORM 3D software has capability to provide different

material behavior modelling for different elements of a finite element mesh. This capability is

employed to generate a FE mesh which is termed as mixture material based FE mesh.

This mixture material based FE mesh does not reflect the microstructure geometry parame-

ters. A new algorithm to model the microstructure geometry parameters in three dimensions

to be used in the FE mesh. A program based on the new algorithm converts the mixture

material based FE mesh into a microstructure based FE mesh. This microstructure based FE

mesh is then employed by DEFORM 3D to simulate the micro drilling process in ferritic pearl-

itic steel.

Micro cutting process simulation

Microstructure based FE model with consideration of grain size, grain volume and phase volume percentage

mixture material based FE model without consideration of grain size, grain volume and phase volume percentage

Work piece CAD modelling (STL format) Solidworks

2010

WZL program

DEFORM 3D V10.2

DEFORM 3D V10.1


The modelling of the micro drill, work piece and the setting up of the chip formation simula-

tion in DEFORM 3D is explained in the subsequent sections. Specific aspects of the micro-

structure based FE mesh is alone explained here. In DEFORM 3D, all the user input data

required for the simulation are present in a file created by DEFORM 3D preprocessor called

the key file. The work piece and cutting tool are termed as objects in a key file. The object

details that are contained in the DEFORM key file include geometry details, material behavior

and process parameters. This DEFORM3D key file contains the mixture material based FE

mesh of the work piece and is provided as an input to WZL program. In addition the geome-

try details of the microstructure is provided to the WZL program as input and the output is

the multiphase material based FE mesh. The WZL program requires the volume of each

element of the work piece and this is provided by a file called EVOL.txt. The EVOL.txt file is

created by modifying the DEFORM 3D FEM Engine. The EVOL.txt file is explained in the

subsequent sections.

The DEFORM key file contains all the information needed by the DEFORM FEM engine to

run the simulation and its structure is described here for better clarity (Figure 4-4). The struc-

ture of the key file can be read by any text editing software. The key file structure is studied

in detail in order to obtain all the relevant information for the development of the microstruc-

ture based FE mesh.

Figure 4-4: DEFORM key file predefined structure

The element information contains the nodes of each element. In the case of chip formation

simulation using DEFORM 3D software, the tetrahedral element is the default option for the

user. Hence each tetrahedral element is represented by four nodes.

The volume fraction of each element is available only when the work piece material is de-

scribed using the mixture material model. The mixture material model can contain n number

of phases. In this work, for the simulation of two phase carbon steels, the work piece material

is described as a mixture material, with ferrite and pearlite as its constituents.

DEFORM 3D KEY FILE STRUCTURE

• Process definition • Stopping & Step controls • Iteration controls • Processing conditions • User defined variables • Property data of material 1 • Property data of material 2 • Inter-material data • Data for object#1 • Data for object#2 • Inter-object data


4.1.3 Algorithm to develop a 3D microstructure based FE mesh

To convert the 3D mixture material based FE mesh developed using DEFORM 3D V10.1 into

a microstructure based FE mesh using a standalone computer program based on given

parameters an algorithm was developed as part of this work (figure 4-5 and figure 4-6).

The inputs to this algorithm are the 3D geometry whose FE mesh is to be converted into a

multiphase material mesh, the grain volume and the volume percentage of the phase. This

particular algorithm is developed to convert a FE mesh into a two phase FE mesh. But the

approach can be extended to multiphase FE mesh generation easily.

Initially, points in 3D space are distributed in the given work piece geometry. The number of

points to be distributed in the 3D work piece geometry is equal to the number of grains of the

secondary phase. The number of grains present within the work piece geometry is calculated

from the phase volume percentage of the secondary phase. Given the volume percentage of

the secondary phase, grain volume and the 3D work piece geometry,

is calculated.

Figure 4-5: Microstructure based FE mesh development algorithm part 1

KEY *

gv → grain volume

Pvp → phase volume percentage

fmsh → FE mesh

evol → element volume file

tev → total volume of selected elements

sgp → selected gaussian point p → p(x,y,z) gp → gaussian point sp → seed point se → selected element mp=2 → material parameter of element =2

fe → finite element ev → element volume

* → Abbreviations arranged in order of appearance

obtain 3D geometry from the fmsh

gv, pvp,fmsh,evol

Disperse seed points in the 3D geometry based on gv and pvp

i=1; j=1;tev=0;

start

A


With grains being represented by points and the number of grains being distributed inside the

3D geometry based on volume fraction of the microstructure phase (pvp), the points are to

be distributed using a Delanuay triangulation algorithm. This distributes the given points in a

random fashion representing the distribution of phases in a microstructure.Once these points

are uniformly distributed, each point is considered as a seed point (sp) and each seed point

represents the centroid of a grain. The points are stored in a separate array.

The procedure to represent one grain in the mesh is described as follows.To generate the

multiphase mesh, the mixture material model based FE mesh (fmsh) is imported and the FE

mesh nodes are read as 3D points (gp). The point (sgp) nearest to the first seed point is

identified. The DEFORM key file contains an array which relates each finite element (fe) to

their corresponding node points. Using this array, the associated finite element to the point is

selected. This selected finite element’s element number is stored in a seperate list.The

volume of the selected finite element (se) is obtained from EVOL.txt (evol) file. The selected

element’s volume (ev) is compared with the grain’s volume. When the selected element’s

volume is less than the grain’s volume (gv), the next element is selected and added to the

list. The newly selected element’s element number is also added to the list of element

numbers created with the selection of the first element.


Figure 4-6: Microstructure based FE mesh development algorithm part 2

The combined volume (tev) of the two elements is calculated and compared with the grain

volume. This process is repeated till the combined volume increases the grain’s volume.

The material data of all the elements (mp) whose element number is present in the list is now

converted into phase 2. The procedure so far described creates one grain within the finite

eleemnt mesh whose grain volume is equal to or slightly greater than the average grain

volume which is provided as an input to the algorithm. This procedure is repeated for all the

seed points. The list of elements selected is cleared and the list is made empty and the

procedure repeated. When the procedure is completed for all the seed points, the finite

element mesh is converted from a simple mixture material model based FE mesh into a two

phase material based FE mesh.

sgp= min( p(gp)-p(sp (i)))

se=fe (j) ∈ sgp; mp(se)=2;

tev = tev + ev (se) if j+1 < te, se=fe (j+1) ∈ sgp

mp(se)=2

else

se = (gp+1) ∈ fe(j); mp(se)=2;

tev>gv

yes

sp≥nsp

no

i=i+1;

yes

j=1;tev=0;

end

A

no


This algorithm can be extended to multiphase FE mesh generation by modifying the seed

point creation algorithm to accommodate separate seed point creation for different phases.

4.1.4 Implementation of algorithm into DEFORM 3D

The implementation of the algorithm developed has been done through a computer program

written in JAVA which converts the mixture material based DEFORM key file into a multi-

phase material model based FE mesh. The structure of the program developed is given in

the Figure 4-7. The DEFORM key file contains all the necessary data required by the FEM

engine to solve the problem. In addition to the above said parameters, one important param-

eter, the element volume has to be generated. The volume of a tetrahedral element is given

by

| − ∙ − − |

6 (7)

Where

a,b,c,d → Gaussian points described in 3 D coordinate system

V → element volume

Elements’ volumes are stored in a separate file called the EVOL.txt file. Since the elements’

volumes are available during the equation solving routine, the FEM engine is modified to

obtain these values and store them in a separate file.

The program flow is explained in the figure (Figure 4-7). The program calculates the number

of grains that will be accommodated in the given 3D volume based on the grain volume and

phase volume percentage. When the number of grains is calculated, these grains are distrib-

uted within the 3D volume using a particle dispersion algorithm. Each grain is described

using a point in Euclidean space. The Gaussian points in the 3D FE mesh is obtained from

the key file. Using the developed algorithm, the 3D FE mesh is converted into a multiphase

FE mesh. The developed algorithm can be used to generate n phase FE mesh although; the

implementation currently supports only a 2 phase material model.


Figure 4-7: Pictorial representation of microstructure based FE mesh development algo-

rithm

Grain size (GS)

Phase volume % (PV)

DEFORM 3D V10.1

Work piece geometry

Key file with mixture material model FE mesh

All grain points are incorpo-rated

END

NO

YES

EV>GS

Adjacent elements are added to reach grain size

Each point represents a ferrite grain and is termed as grain point

Points distributed within the work piece geometry based on grain size and phase volume percent-age

geometrical comparison

DEFORM 3D

A finite element attached to the node is selected to represent a ferrite microstructure-and the element‘s volume is termed as EV.

FE node closest to grain point is selected

WZL Program


4.1.5 Preliminary validation of 3D multiphase FE model using tension, com-

pression and shearing tests

The developed 3D multiphase FE model’s ability to simulate large deformation process is

tested primarily by simulation of individual loading conditions of tension, compression and

shear carried out using DEFORM 3D V10.2 and the efficacy of the 3D multiphase FE model

in comparison to the experiment is tested. To simulate the 3D multiphase FE model’s ability,

a two phase 3D FE model for the ferritic pearlitic steel from the micrographs shown and grain

geometry data obtained using the line intercept method. To perform this preliminary valida-

tion, since the multiphase FE model is developed on the basis of representative volume

element, a representative volume element of 0.1 mm3 is selected and tension, compression

and shear loading test simulations are carried out on it (Figure 4-8). From the figure, it is

clear that a FE mesh developed using the newly developed methodology is able to replicate

the microstructure geometry. The pearlite and the ferrite phase’s shape are being clearly

captured in the finite element mesh.

Figure 4-8: Two phase 3D FE model developed for simulation of ferritic pearlitic steel plas-

tic loading

The tensile test specimen’s necking area is meshed using a mesh density window and rep-

resents the representative volume element. The tensile tests were conducted experimentally

and the newly developed multiphase finite element mesh methodology’s ability to capture the

deformation process is established. The time step parameter is set at 10-7 sec and the veloci-

ty of the top plate is set at 10000 mm/sec. The step parameter is selected so that the steady

state is reached well in advance before the deformation of the material. This is carried out

using a trial and error method. The load along the axis of the specimen is obtained using

DEFORM post processor. The bottom surface of the tensile test specimen is fixed in space

and the top surface is fixed with the top plate. The interface between the top plate and the

contact surface of the tensile test specimen is inseparable.

The compression loading simulation and the shear loading simulation is similarly carried out

in a similar fashion in DEFORM 3D. The compression loading is carried out using a cylinder

specimen and the shear loading is carried out using a cube shaped specimen. The compres-

Pearlite

Cross section Longitudinal section

Two-phase 3D FE model(0.1 x 0.1 x 0.1 mm)

Ferrite


sion load specimen is a cylinder with the diameter of 0.1 mm and length of 0.1 mm. The

cylinder is fitted with two plates on the flat faces. The bottom plate is fixed in space and the

top plate moves along the cylinder’s axis at a speed of 0.0002 mm/sec. The friction contact

between the two faces of the cylinders and the plates is defined by columbic friction with a

constant value of 10-5. The friction is required to keep the cylinder moving perpendicular to

the direction of cylinder’s axis. The contact between the two faces and the plates are sepa-

rable as the inseparable contact condition leads to the bulging of cylinder which is avoided

during experimentation.

The experimental investigation was carried out using a hut probe test. The shearing model-

ling using a hut probe test required extremely large number of elements that would make

simulation to stop abruptly. Hence, the modelling of the shearing loading is carried out using

a cube with dimensions of 0.1 mm X 0.1 mm X 0.1 mm. This corresponds to the unit volume

of the shearing volume of the hut probe specimen. This provided a reliable way to simulate

the shearing loading without increased computational efforts. The right hand side face of the

cube is fixed and the left hand side face of the cube is attached using a plate and the plate is

set with a velocity of 0.01732 mm/sec corresponding to the experimental values.

Figure 4-9: Variable loading of different microstructural constituents, pearlite and ferrite on

tension loading

The finite element simulations performed using DEFORM 3D for similar geometries. The true

stress and true plastic strain curves predicted by the 3D two phase FE model is compared

with the experimental results (Figure 4-9).

0

300

600

900

1200

0 0.5 1.0 1.5 2.0

True plastic strain e, , -

Tru

e s

tre

ss M

Pa

CompressionTension

Ø 0.1x0.1 mm

Shear

0.1x0.1x0.1 mmQuasi-static

FE model

Experiment

Tension stress

Compression stress

Shear stress


The finite element simulation of the tensile loading clearly predicts the loading of the harder

pearlite phase and the earlier yielding of the ferrite phase. This clearly indicates the ability of

the multiphase FE model to differentiate between the different phases present in the micro-

structure and the yielding of the softer pearlite phase as displacement increases. In the

developed FE model, the behavior of both the ferrite and pearlite phase are considered to be

plastic with no fracture as the main aim is not complete simulation of the tensile loading.

In a similar way, the finite element simulation for compression loading is carried out similar to

the case of tensile loading. The ability to simulate the work piece behavior under compres-

sion loading is more important compared to tensile loading as plastic deformation during chip

formation in micro cutting process involves the compressive loading of the work piece mate-

rial which lies ahead of the cutting edge before reaching the shear plane. The finite element

simulation of the compression loading of AISI 1045 microstructure is in good agreement with

the experimental values. The simulation is able to predict the larger load bearing capability of

the harder pearlite microstructure phase compared to the softer ferrite phase. The stress

path traced under compression loading is in very good to experimental curve fitting.

The FE simulation of the AISI 1045 microstructure using the multiphase FE model is im-

portant to prove its capability in modelling the plastic deformation taking place in the primary

shear area in micro cutting. The true stress – true strain curve obtained under shear loading

through experiments is very well reproduced by the 3D two phase FE model.

These simulations prove that the 3D multiphase FE methodology is able to model the AISI

1045 microstructure under simple cases of tensile loading, compression loading and shear

loading. With the simple cases of loading being simulated with good accuracy, the more

complex loading of chip formation in AISI 1045 microstructure is carried out.

4.2 Johnson-Cook (JC) model development methodology for all

carbon steels

As part of this work, a methodology to obtain the Johnson Cook parameters for a given mi-

crostructure composition is developed. In general, Johnson Cook model is developed for

each specific microstructure. This involves extensive material testing for each microstructure.

In the newly developed methodology, the Johnson Cook model for the different phases pre-

sent in a composite microstructure is utilized to develop the Johnson Cook model. In this

methodology, the rule of linear mixtures is employed to relate the different phases to the

required microstructural composition [WILLI08]. The composite microstructure is considered

as the sum of its individual microstructure phases. For the family of carbon steels, the ferrite

and pearlite are considered the two important microstructure phases which sums up close to

99% volume. This in turn, leads to the conclusion that the carbon steel’s thermo-mechanical

behavior can be ascertained from the thermo-mechanical behavior of its constituent micro-

structural phases, ferrite and pearlite which are obtained from the thermo-mechanical behav-

ior of C05 steel and C75 steel.


4.2.1 JC model development methodology for ferritic pearlitic steels

The rule of mixtures is used to relate the properties of a composite whose constituents are A

and B. According to the law of mixtures, eq. 8,

(8)

-

-

-

-

-

The rule of mixture states that the property of a composite can be broken down into the

properties of its constituents. The influence of each phase depends on the phase’s fraction in

the composite. An additional condition applies that the phases fA and fB constitute the 100 %

weightage of the composite (Equation 9).

(9)

This formulation is used to calculate the values of the constants of the Johnson Cook Model

for various compositions of the ferritic pearlitic steel.

In ferritic pearlitic steel, the fraction of the ferrite phase fF and pearlite phase fP is obtained

from the Iron-Iron carbide diagram. As an example the fraction of ferrite phase and pearlite

phase in AISI1045 carbon steel is calculated as follows. The carbon percentage in AISI 1045

carbon steel is 0.45 weight %. The C75 carbon steel (carbon wt. %=0.75) is considered as

100% pearlite and C05 carbon steel (carbon wt. %=0.05) is considered as 100% ferrite.

Applying the lever rule in the Iron-Iron carbide diagram,

6 − 4

6 −

4 4

− 4

The Johnson Cook model for the ferrite phase is obtained from the flow curve of C05 steel

composition and the Johnson Cook model for the pearlite phase is obtained from the flow

curve of C75 microstructure composition. Other influences, such as the shape of the phases,

the interphase relationship are not considered in this work.

The flow curve of ferrite phase is written as follows, eq. 10,

( ) (

) ( − (

− −

)

) (10)

Where the subscript ‘ ’ represent ferrite phase.

The Johnson Cook model for the pearlite phased is written as follows, eq. 11,


( ) (

) ( − (

− −

)

) (11)

Where the subscript ‘ ’ represent pearlite phase.

To calculate the constants of the Johnson Cook model for any composition of ferritic pearlitic

steel, the linear law of mixtures is applied as follows, eq. 12,

− (12)

Where represent the flow stress of the ferritic pearlitic steel composition with percent-

age of ferrite and percentage of pearlite.

To calculate the value of the constant, the yield stress of the composite, the yield stress of

the constituent phases is to be added according to the linear rule of mixtures. The yield

stress is obtained by applying the following conditions.

to the flow stress equations of ferrite phase and pearlite phase.

Applying the above conditions to equation for and leads to

Applying the above equations in the rule of mixtures leads to

−

( − )

To calculate the value of the constant the following conditions are applied to the flow

stress equations.

This leads to

( ) ( )

Applying the above equations to the rule of mixtures provides

− ( ) ( )

Subtracting the above equation by the Ac equation,

−

( − )

To calculate the value of n, the conditions,


are applied to obtain

Differentiating on both sides with respect to strain,

− [ ( )] [ ( ( ))]

When ,

− [ ] [ ]

( ) (( ) − ( ))

To calculate the value of C, the conditions

are applied.

This result in

(

)

(

) ( − ( (

))) ( ( (

)))

(

) (( − ( (

))) ( ( (

))))

When

(( − ( ( ))) ( ( ( ))))

(( − ( ( ))) ( ( ( ))))

( ) ( ( ) − ( ))

To calculate the value of the constant m, the conditions

Is applied which leads to the equation

( − (

)

)


Differentiating on both sides

(

)

(

)

When

− (

− )

(

) ( − ) (

) (

)

( − ) ( ) ( )

( ) (( ) − ( ))

Thus the flow curves of any ferritic pearlitic steel can be obtained from the flow curves of its

constituent phases as follows, eq.13 - eq.17,

( − ) (13)

( − ) (14)

( ) (( ) − ( )) (15)

( ) ( ( ) − ( )) (16)

( ) (( ) − ( )) (17)

This methodology provides an easy approach to calculate the Johnson Cook model parame-

ters for all any microstructure when the phase constituents of the microstructure are known.

4.2.2 Validation of the JC model development methodology

The developed model is validated using the high speed compression test results. The values

of the flow stress for C45 composition in normalized conditions are provided for a constant

strain of 0.1(Table 4.4).

Table 4-4: Flow curve data for a constant strain of 0.1 for various strain rates at room

temperature

Strain rate 0.003 0.08 0.72 3409 3745 3980 4214 4527

Flow stress 808.82 818.73 831.53 939.31 964.92 994.66 1024.63 1025.23

For a constant strain of 0.1 at room temperature

The flow stress curves are provided in a log-log graph to accommodate the range of strain

rate which ranges from o.03 to ~4500. The graph clearly shows the validity of the newly


developed methodology for obtaining the flow stress curves of a multiphase material by

applying the law of mixtures to the constituents of the multiphase material (Figure 4-10).

Figure 4-10: Validation of flow curve modelling methodology using law of mixtures

Using this methodology, the Johnson Cook parameters for any composition can be obtained

from the Johnson Cook parameters of its constituents. The deviation at higher strain rates is

explained with the reference to the grain boundaries. If the grain boundaries are included into

the formulation, the methodology can be improved further to give accurate results.

0

200

400

600

800

1000

1200

1400

0.001 0.1 10 1000

Strain rate de/dt, 1/s

Tru

e co

mpre

ssio

n s

tres

s, M

Pa

5 Validation of 3D multiphase FE model using micro drilling process simulation 49

5 Validation of 3D multiphase FE model using micro drill-

ing process simulation

The 3D multiphase FE material model in this work is validated by testing its capability to

simulate the effect of microstructure during plastic deformation analysis of ferritic pearlitic

steels. Plastic deformation in multiphase materials is orthotropic and takes place primarily in

the grain boundaries. Since the plastic deformation of materials for manufacturing purposes

for all practical reasons takes place in the macro-scale, work piece material behavior in

manufacturing process simulation have so far been considered isotropic. With the venture of

traditional manufacturing process technologies into the micro scale, the isotropic material

behavior assumption does not hold good anymore. Hence the newly developed 3D multi-

phase FE model would be a better candidate to simulate the manufacturing process and

validate its efficacy.in simulating the plastic deformation.

In this work, the 3D multiphase FE model is used for the simulation of chip formation process

during micro drilling process. This chip formation process simulation is carried out using

DEFORM 3D V10.2 finite element simulation package. DEFORM 3D is a finite element simu-

lation package specifically used for the simulation of plastic deformation during various man-

ufacturing processes like forming and machining. In this FEM software, the chip formation

process is simulated using an updated Lagrangian formulation.

The chip formation simulation process using DEFORM 3D can be segregated into micro twist

drill geometry modelling, the work piece geometry modelling, work piece material modelling,

cutting tool material modelling, process parameter setting, boundary condition setting, simu-

lation set up and inter object interaction modelling . The 3D CAD modelling of cutting tool is

done as part of a previous work. The work piece geometry modelling is carried out using

Solid works 2010 employing the cutting tool model’s geometry as a reference. The material

flow behavior for the work piece is defined using the Johnson Cook model. For the micro

drilling process, the work piece material is considered anisotropic and hence the Johnson

Cook model for the phase constituents, pearlite and ferrite is employed in mixture material

model. Feed forces and torque predicted during the micro drilling chip formation simulation

process is compared with the isotropic finite element model and experimental investigation

results.

In the following section, the micro drilling experiments and the micro drilling simulation using

the 3D multiphase FE material model with focus on cutting tool modelling, work piece model-

ling, material behavior modelling and setting up of the simulation is presented.

5.1 Experimental setup for micro drilling & results

The micro drilling process is carried out using a high precision KERN Evolution machine tool.

This machine tool has a positioning accuracy of ±0.5 µm as the drive for these high precision

systems are provided by direct digital drives with AC Servo motors and Heidenhein glass

measuring scales with a resolution of ±0.1 µm. The maximum spindle speed is 160,000 rpm


using HSK 25 adaptor. The machine tool built using special high tech material provides the

maximum rigidity under static and dynamic conditions, higher vibration absorption compared

to cast iron and lower sensitivity to temperature fluctuations. The machine tool comes with a

a laser based non-contact measuring system for the measurement of the cutting tool geome-

try for offsetting and accurate positioning. This system is able to measure the length, radius

and concentric accuracy even at high speeds. The data obtained using the laser based

measuring system is directly transferred to the Heidenhein contouring control and are taken

into consideration in the active program. These characteristics make the KERN Evolution

machine tool the best option for carrying out the micro drilling experiments.

Figure 5-1: Machine tool setup for micro drilling experiments and microdrill geometry em-

ployed

To calculate the feed forces and the torque generated during the micro-drilling process,

special cutting force measurement systems are used. Although a large number of research

has been conducted in the field of monitoring of cutting operations using different types of

measurement techniques, direct dynamometer based cutting force measurement systems

are still considered the most reliable for high frequency cutting operations like micro milling

and micro cutting. In micro milling, the tool contact frequency is the primary reason for the

higher frequencies during the cutting process whereas during the micro drilling process, run

out deviation present in the micro drills lead to a similar high frequency cutting tools. There-

fore dynamometer based cutting force measurement used in micro milling process would

best suit the micro drilling process. A specific dynamometer based measurement system

depicted by Klocke et al [KLOC11] is used in the present study. This measurement system

will also have to exhibit high dynamical behavior to be able to capture the torque generated

during micro drilling experiments.


Figure 5-2: Measurement set up for micro drilling experiments

In this measurement setup, two sensors, one for cutting force measurement and the other for

torque measurement are used. A Kistler dynamometer 9256B is used for the cutting force

measurement. This dynamometer consists of four 3-component piezoelectric sensors and is

able to measure forces in 3 directions with a range of ±250N. The Kistler dynamometer

9256B are insensitive to temperature measurement and is best suited for measurement in

machining process study because of its small size with low response threshold, high sensitiv-

ity and high natural frequency. In addition to the measurement of cutting forces, it is also able

to measure the torque generated using single sensor signals and the geometrical distance

between the sensor location and the point of torque application. But the dependence on this

single dynamometer for the measurement of cutting torque is not justified due to its low

quality of torque results compared to measurements using specific torque measuring sen-

sors.

Therefore to measure the torque generated during cutting with the highest level of accuracy,

an additional Kistler 9329A type torque sensor is employed. This torque sensor because of

its low weight of 50 grams can be loaded directly on the 9256B dynamometer. The dyna-

mometer also exhibits higher natural frequency, lower threshold and acceptable cross talk

behavior. It exhibits a natural frequency larger than 53 KHz and leads to accurate measure-

ments at 160000 rpm of the cutting tool. With a low threshold of 0.03Nmm and a high sensi-

tivity of >2000 ρC/Nm, these torque sensors can be used for torque measurement of cutting

tool diameter of 100 µm. In addition with a lower influence of axial forces onto the torque

signal with a maximum cross talk of 0.01 Nmm / N, it exhibits a maximum cross talk of 0.35

Nmm / N, which is less than 3% for a measurement of a 1 mm drilling process. The output

from these sensor are in Coulombs of charge and are converted into standard voltage sig-

nals using charge amplifiers with a 16 bit National instruments data acquisition card which is

realized using NI LabVIEW. The data obtained thereof is analyzed using NI DIAdem.

The micro twist drills from SPHINX cutting tools are manufactured using ultra-fine grain

carbide (HW-K20). The cutting speeds suggested by the manufacturer for these cutting tools

Workpiece

Force measuring dynamometer

Kistler 9256B

Torque sensor Kistler 9329


lie in the range of 35-95 m / min. The drilling depth is maintained at a constant value of 2xd

and the cutting is performed in the dry conditions. The experimental results are tabulated in

Table 5.1. In addition to the feed forces and torque, the chips are also collected and ob-

served.

Table 5-1: Cutting parameters, measured feed force and torque in micro drilling

Diameter

/ µm

RPM

/ 1/min

Feed

/ µm

Feed force

/ N

Torque

/ Nmm

50 160000 0.6 0.27 Not measurable

100 111410 1.2 0.65 0.027

200 55704 2.4 2.0 0.202

300 37136 3.6 4.5 0.553

400 27852 4.8 7.3 1.196

500 22282 6.0 11.3 1.446

600 18568 7.2 14.3 2.811

800 13926 9.6 21.4 5.850

1000 11141 12 35.0 11.650

To compare the feed forces and torque during micro drilling process, the feed forces and

torque obtained from the micro drilling experiments are converted into related feed force and

related torque. The related feed force and related torque are obtained by dividing the feed

forces and torque by the cross sectional area of the chip. The cross sectional area of the chip

is calculated by multiplying by the drill’s cutting edge length with the feed per cutting edge.

( )

( )

Where

Related feed force (kN/mm2)

Maximum feed force (kN)

Related torque (kNmm/mm2)

Maximum torque (kNmm)

Drill diameter (mm)

Feed rate per revolution (mm/ rev)


Figure 5-3: Experimental related feed force and related torque in micro drilling process

The experimental results clearly show the scaling effect in micro drilling process

(Figure 5-3). In micro drilling process using a twist drill, as the diameter is reduced from

1000 µm to 50 µm, the related feed force increases. This increase in related feed force is

directly related with the increase in chisel edge width in the micro drill geometry family em-

ployed for the micro drilling experiments. The increase in the chisel edge width with reduction

in the drill diameter is warranted due to the need for the increase in rigidity of the drill. With

the increase in the chisel edge width, the ratio of the cutting area under the main cutting

edge proportionally reduces leading and leads to less uncut chip width under the main cut-

ting edges and the remaining area under the chisel edge width being ploughed. This is

proved as the torque generated during the micro drilling process show a linear trend as the

cutting diameter increases.

5.2 Cutting process simulation set up in DEFORM 3D

The simulation of micro drilling process is carried out using DEFORM 3D employing the

updated Lagrangian formulation. The DEFORM 3D simulation package contains three main

divisions namely Preprocessor, FEM engine and post processor. The preprocessor is used

to build the FE model and the output of the preprocessor is the key file. The preprocessor

builds the key file employing the geometry data, constitutive material models, cutting process

parameters and the simulation specific parameters. In addition to the key file, the preproces-

sor builds the data base file, which is machine readable and is used to store the simulation

output parameters.

0

4

8

12

16

20

0 1 2 30

2

4

6

8

10

12

Experiment

tr

kf

Workpiece material: C45 normalized # Cutting material: HW-20Cutting speed: v

c = 35 m/min # Feed: f = 0.012*d # Cooling: dry

Drill diameter d, mm

Re

late

d f

ee

d f

orc

e k

f ,

(kN

/mm

2)

Re

late

d t

orq

ue

tr ,

(kN

mm

/mm

2)


The work piece geometry and the micro drill geometry are modeled using Solidworks 2010

and imported using the standard .STL Format. The constitutive material models of the pearl-

ite phase and ferrite phase are used in this multiphase material FE model. The general pro-

cedure for setting up the simulation of metal cutting process in DEFORM 3D preprocessor is

outlined (Table 5.2). The simulation procedure is divided into simulation set up, object defini-

tion, Material, Object definition and inter object relationship. These subdivisions are detailed

in the following section with reference to the micro twist drilling process on AISI 1045 normal-

ized steel.

Table 5-2: Parameters involved in the FEM simulation of metal cutting using DEFORM 3D

Sim

ula

tio

n

set

up

Type of simulation Updated Lagrangian formulation

Mode Deformation, heat transfer

Step definition Time increment

Ob

ject

defi

nit

ion

Object Work piece Cutting tool

Object type definiti-on Plastic Rigid

Geometry import Work piece 3D CAD model Micro twist drill 3D CAD model

Mesh ~100000 elements ~30000 elements

Remesh criteria Local remeshing No remeshing

Movement None Translation & Rotation

Boundary conditions

- Velocity in X,Y & Z direc-tions of outer surface & bot-tom surface is zero

- Heat transfer

Heat transfer

Material

AISI 1045

mixture material model -Pearlite -Ferrite

Tungsten carbide

Object positioning Contact between cutting edge and work piece cut surface

Inter object relationship Friction Interface heat (N/sec/mm/C)

Work piece-Work piece Coulomb friction factor Constant

Top die-Work piece Coulomb friction factor constant


5.2.1 Simulation set up

As the simulation of the chip formation process in micro twist drilling falls under the large

scale plastic deformation mechanics the updated Lagrangian formulation is selected in addi-

tion to heat transfer module. The heat generated during the chip formation process influ-

ences the process to a large extent and hence the equations of deformation and heat trans-

fer are solved simultaneously.

In updated Lagrangian simulation, the time step is crucial to keep the computational error at

a minimum thereby ensuring a stable simulation. An approximate value for the time step is

given by DEFORM as

To optimize the simulation for faster computation, the time step for simulation is divided into

time step during plunging and time step during cutting. The time step for the different drill

diameters are provided in the following table for a comparison (Table 5.3).

Table 5-3: Time step parameter for various drill diameters in DEFORM 3D

Drill diameter

/ µm

Time step during

plunging

/ sec

Time step during

cutting

/ sec

100 5xe-6

1xe-6

500 2xe-6

1xe-6

1000 1xe-5

2xe-5

The time step for the plunging step is kept smaller compared to the time step during cutting

as the mesh under the main cutting edge is deformed to take the shape of the cutting edge

with consideration of the edge rounding. The edge rounding of the cutting edge influences

the number of steps to replicate the subtracted surface of the rounded cutting edge

(Figure 5-4). The number of steps required for the plunging of the drill into the work piece

depends on the drill’s cutting edge radius. With the cutting edge radius getting larger, depth

to which the cutting edge has to be plunged is increased for constant mesh size. This in turn

increases the number of time steps for the plunging and in turn the simulation has to be run

for more than one revolution when the plunge depth increases above the feed rate during

cutting.

The plunging of the cutting tool is carried out by translation of the cutting tool along the cut-

ting tool axis in the direction of the work piece. During the penetration, the cutting edge inter-

feres with the work piece mesh. The mesh penetration leads to remeshing to be initiated.

With remeshing, the work piece mesh takes the shape of the twist drill edge and leads to

chip formation. The speed of the cutting tool is usually higher by an order of 2 compared to

the cutting tool feed velocity for a faster computation.


Figure 5-4: Plunging of the work piece and initiation of chip formation with consideration of

cutting edge rounding

5.2.2 Object definition & object positioning: Cutting tool & work piece

The cutting tool and the work piece are defined as Objects in DEFORM 3D. The object defi-

nition includes all aspects of the cutting tool and work piece that are required for the solver to

solve the finite element equations.The object definition includes deformation mode of the

material, geometry, mesh definition, translational and rotational movement and boundary

conditions. The object definition and object positioning of the work piece is defined in this

subsection. The work piece is defined as plastic neglecting the elastic deformation to reduce

the complexity of the simulation and as the main priorities of simulation are the cutting force

generation and chip form prediction during chip formation. The geometry of the work piece is

generated with reference to the specific micro twist drill. The geometry is imported into DE-

FORM through the .stl format. The .stl format stands for Standard tessellation language and

describes the geometry using raw unstructured triangulated surfaces by the unit normal and

vertices of the triangles using a three dimensional Cartesian coordinate system. In this work,

the 3D Coordinate system is defined with the origin at the point of contact of the work piece

with the micro twist drill’s center.

The tetrahedral element is used for the meshing of a 3 dimensional geometry in DEFORM.

The mesh definition takes place in three stages. The first stage of mesh definition is the

number of elements and size ratio. The number of elements for a work piece range from

100000 to 150000. The size ratio is defined as the ratio between the maximum element size

and minimum element size. A size ratio of 10 is recommended by DEFORM to mesh the

work piece during chip formation simulation. The second stage of mesh definition is the

weighting factors. The weighting factors are based on surface curvature, temperature defini-

1 2 3

4 5


tion, strain distribution, strain rate distribution and mesh density window. The mesh density

window is a geometry based factor for refining the mesh. The mesh density window is pro-

vided as shown (Figure 5-5). The mesh density window increases the number of elements

on the cut volume. This reduces the need for frequent remeshing and the associated loss of

microstructure details of the associated remeshed element. The meshing parameters are

used throughout the simulation during every remesh and hence has to be given due

importance. Different meshing parameters are employed during the initial mesh creation and

during remeshing (Table 5.4).

Figure 5-5: Application of mesh density window to reduce remeshing during simulation run

During the initial mesh creation, the aim is to concentrate large number of meshes within the

work piece cut volume. To achieve this, the weighting parameters are provided with maxi-

mum weighting percentage to the mesh density window and a lower value to the surface

curvature to take into account the cut surface reproducibility. The other parameters of strain,

strain rate and temperature are set to zero. During remeshing, the aim is to reduce the

remeshing on the whole work piece volume and concentrate the remeshing only on the work

piece mesh under the cutting edge which undergoes deformation. This reduces to a larger

extent the loss of microstructure details of each finite element when the work piece mesh is

microstructure based instead of an isotropic FE mesh.

Table 5-4: Time step parameter for various drill diameters in DEFORM 3D

Meshing weighting

parameters

Surface

curvature

Temperature

distribution

Strain

distribution

Strain rate

distribution

Mesh densi-

ty window

During initial mesh

creation

0.1 0 0 0 1

During remeshing 0.375 0.250 0.5 0.375 0.8

Mesh density


A challenge with the microstructure based finite element creation is the need for an extreme-

ly large mesh number to accommodate simultaneously the work piece geometry and the

sufficient number of meshes for one single grain. This is possible to a certain extent using

the above mesh weighting parameters.

The work piece is fixed to the coordinate system. This is done by fixing the velocity of the

outer surface of the work piece and the bottom surface to zero in x, y and z direction. The

boundary condition for the heat transfer is given in two steps (Figure 5-6).

The heat transfer of all the nodes within the work piece is provided as heat conductive and

the outer and bottom surfaces act as heat sink. Hence the temperature of the outer surface

and the bottom surface is kept at a constant of 20oC.

A new origin is created on the cut surface at the center of the work piece in the Solid works

CAD model and this origin is specified during the .stl file creation. This origin is brought to the

DEFORM 3D coordinate system origin using the rotation and drag method within the object

positioning dialog box.

Figure 5-6: Boundary conditions for velocity and heat transfer in work piece

The object positioning of the cutting tool is defined as follows in reference to work piece

positioning. The cutting tool object is defined as a rigid object. The rigid object type is used

as the simulation does not aim to simulate the cutting tool deflection but only the cutting tool

temperature is to be ascertained. The geometry of the micro twist drill is also modeled using

Solid works 2010 and .stl format is used for the import of the micro twist drill into DEFORM

3D.

The meshing of the micro twist drill is done in a single step and is relatively simple compared

to the meshing of the work piece as the rigid material does not need remeshing during the

simulation run. The micro twist drill is meshed with approximately 30000-50000 elements

with the mesh density window concentrated near to the cutting edge (Figure 5-7). The

weighting parameters are set with highest weightage to mesh density window and other

weighting parameters set to zero during initial mesh generation.


The cutting tool movement is defined within the object movement controls. The feed rate and

cutting speed are used to define completely the motion of the cutting tool. The feed rate is

defined in mm/sec and directed in the –Z direction in accordance with the work piece posi-

tion. The cutting tool movement is defined for translational direction for the initial plunging

step and the rotational movement is added during chip formation simulation. The cutting

tool’s translational movement is set at two times the feed rate during cutting to reduce the

number of steps required for plunging. The cutting speed is specified after the required

plunging is reached.

The feed rate of the drill into the work piece is given as axial velocity in mm/min and is de-

rived from the concept of minimum chip thickness.

(

) (18)

The value of feed rate is given in the form of

and is termed as feed velocity.

Figure 5-7: Meshing of twist drill geoemtery

The cutting speed is converted into revolutions per minute and provided in the rotation com-

ponent of the cutting tool. The drill’s cutting speed is given by

(19)

Fine mesh near to

the cutting edge


The boundary conditions associated with the cutting tool object is heat transfer as the cutting

tool movement is defined using the object movement control. The complete cutting tool is

heat conductive.

5.2.3 Mixture material modelling

The mixture material modelling is used in DEFORM 3D to incorporate the different phases of

a material microstructure when the FE mesh is to correspond to multiphase FE model

(Figure 5-8).

Figure 5-8: Mixture material modelling for microstructure based FE mesh

In general, the material modelling in a finite element simulation considers the material behav-

ior as homogeneous, i.e. all the elements in a finite element mesh have the same defor-

mation characteristics without any consideration for the different phases of the material. An

additional capability of DEFORM 3D to model the work piece material behavior as a mixture

of n phases is useful for microstructure modelling. In this work, the model is used to accom-

modate the two phase microstructure, ferrite and pearlite. The first step in the modelling of

the mixture material model is the selection of mixture model under the material tab where the

different phases of the material microstructure are specified. This creates a mixture material

with a single phase. Additional phases are added using the phases tab. For the modelling of

AISI 1045 steel, the two phases, ferrite and pearlite are added. The Johnson Cook material

model parameters for the ferrite and pearlite phases are added under the Flow stress

→Plastic tab for ferrite and pearlite phase.


The second step in the modelling of the mixture material model is the incorporation of the

phase volume percentage for each phase. In addition the grain volume is also to be incorpo-

rated. The ability to incorporate both the phase volume percentage and grain volume is not

available within the capability of DEFORM 3D V10.2. This has been done using the newly

developed methodology. Initially to add the volume fraction details to the simulation key file,

the volume fraction of the mixture material model is defined by Element data under the ad-

vanced tab in the work piece object (Figure 5-9).

Figure 5-9: Preliminary mixture material based FE mesh development

The volume fraction detail of the mixture material model is incorporated into the simulation

key file (Figure 5-10). The volume fraction of one phase, for e.g. pearlite is made 100 % and

a group of elements without consideration of phase volume percentage and grain volume is

selected. The volume fraction is the parameter that is modified using the algorithm and pro-

gram developed in the previous section.

Figure 5-10: Volume fraction information format in DEFORM 3D key file

The next step in the mixture material modelling is the incorporation of the phase volume

percentage and the grain volume. This is carried out using the program developed as part of

VOLFC 1 859102 2 0.0000000E+000

1 0.0000000E+000 1.0000000E+000

2 1.0000000E+000 0.0000000E+000

… ……. …….

… ……. …….

Object

Number of elements

Number of phases


this work. Figure 5-10 shows the format of the volume fraction in key file which is modified

according to phase volume percentage and the grain volume. The volume fraction section

contains the number of phases in the mixture material, the number of finite elements in the

FE model and the phase volume fraction of each element.

5.2.4 Inter-object data

The finite element simulation of metal cutting involves the interaction between the cutting tool

mesh and the work piece mesh and this interaction is defined in the inter-object data section

in DEFORM 3D. The inter object interaction in the case of chip formation simulation involves

the interaction between a rigid body and a deformable body and the interaction between two

deformable bodies (Table 5.5).

Table 5-5: Friction modelling and heat transfer modelling for chip, work piece and cutting

tool

No Master Slave Seperation

Friction

coefficient

µ

Interface heat trans-

fer

N/sec/mm/C

1 Cutting tool Work piece Separable Coulomb –

0.2 10000

2 Work piece

(chip

Work piece

(bulk material) separable

Coulomb –

0.2 10000

The modelling of the inter-object data is important and its influence on the cutting force mod-

elling during chip formation process is significant [ÖZEL05]. The inter object data definition in

DEFORM 3D is provided in the format of master-slave relationship. In a master slave rela-

tionship, the master object will be able to penetrate the slave object and not vice versa. Since

the penetration of the cutting tool into the work piece is a realistic option, the cutting tool is

defined as master and the work piece as slave. This leads to the deformation of the work

piece without the cutting tool being cut leading to a realistic simulation of chip formation. The

second factor is the interaction between the bulk work piece surface and the work piece

surface converted into chip. This leads to the formed chip not interfering with the bulk work

piece surface as the chip curls with the tool movement. This is carried out by the work piece

being termed as both master and slave which does not allow the penetration of the work

piece into itself. In the case of chip formation simulation, this penetration turns out to be the

chip not cutting into the work piece.

The inter object data definition is defined by two parameters in this work, the deformation

parameter and the thermal parameter. The deformation parameter is concerned with the

forces related to the interaction between the objects. This parameter is defined by separation

parameter and friction parameter. In the case of the cutting tool - work piece interaction, the

two objects are provided as separable as the cutting tool movement by its very nature leads


to a relative motion between the cutting tool mesh and the work piece mesh. The friction

parameter assigned in this work is Coulomb among the choices of Coulomb, Shear and

Hybrid friction factors. The Coulomb friction factor has been employed in a number of chip

formation simulation studies and is known to better predict cutting forces and torque during

cutting process compared to other models. In the case of work piece - work piece interaction,

the chip being formed has a relative motion with the work piece and also changes in geome-

try as time progresses. Hence the bulk work piece surface and the formed chip are designat-

ed as separable and the friction factor is provided with a constant Coulomb factor with a

value of 0.2.

The thermal parameter of the inter object data definition in the case of cutting tool – work

piece interaction is concerned with the heat transfer between the nodes of the work piece

surface and the cutting tool. This heat transfer is very important in predicting the heat that is

being conducted away from the main cutting zone from the main cutting edge into the cutting

tool. This indirectly influences the flow stress of the deforming work piece mesh and conse-

quently cutting forces and chip form. The thermal parameter for the work piece – work piece

interaction is also provided with a constant heat transfer parameter with the value of 10000

Nsec-1mm-1C-1.

The final step in the setting up of simulation is the generation of the database file. The data-

base file is a machine readable file. The simulation output parameters are saved to the data-

base file. This file can be opened using DEFORM Preprocessor and Postprocessor.

5.2.5 Drill modelling

The geometric modelling of the cutting tool and work piece are the primary data required for

the FEM simulation. The modelling of the micro drill geometry has been carried out using

Solid works 2010. As part of a previous project, the modelling of the drill geometry is auto-

mated using API Programming.

Figure 5-11: Twist drill geometry used in experiments and simulation

The drill geometry was measured using a Keyence digital microscope. The micro drill geom-

etry details are not available either from literature or from the cutting tool manufacturer with

reasonable accuracy and clarity. Hence the modelling of drill is to be made based on meas-

flute geometry

clearance geometry

chisel edge geometry

main cutting edge


urement of the actual drills. The drills used in the micro drilling process falls under the four

planar facet point drill geometry type. The facet point drill geometry developed by Armarego

et al [ARMA90] is widely used for its simplicity in the grinding axis movement during drill

grinding. This results in a stable and reliable process. The drill geometry is measured and

classified into three main divisions (Figure 5-11)

The four planar facet point drill geometry is primarily divided into

1. Chisel edge geometry

2. Flute geometry

3. Clearance geometry

The chisel edge geometry is defined by the chisel edge angle, chisel edge width and the

point angle. The chisel edge angle is defined by two clearance planes present in the face of

the cutting tool. These two clearance planes are defined as the primary clearance plane and

the secondary clearance plane. The chisel edge directly contributes to the axial forces expe-

rienced by the micro twist drill. The chip formation under the chisel edge angle is predomi-

nantly by ploughing due to the larger negative rake angle created by the point angle and

clearance planes.

The flute geometry acts as the rake surface and the rake angle at each point from the center

of the drill is defined by the helix angle.

Figure 5-12: Drill geometry variation with drill diameter in micro drilling range

The flute geometry is defined using a closed curve and the helix curve. The flute geometry in

addition to acting as the rake face also acts as the chip clearance passage. The flute geome-

try is designed using the sweep operation with the curve as the profile and the helix angle

acting as the path. The clearance geometry is provided on the body of the drill. This body

clearance reduces the friction caused by the rubbing of the drill to the finished work piece.

The drill geometry is modified with the reduction in diameter as the strength of the drill has to

be increased with reduction in cutting diameter (Figure 5-12). This can be done by increas-

ing the contact between the drill’s surface and the work piece. This increases the contact and

indirectly guides the drill through the work piece reducing the wandering of the drill The

clearance geometry is absent for all diameters measured below the diameter of 300 micron.

D > 300 micron D < 300 micron


The major variation in the drill geometry with scaling down of drill diameters is depicted as

follows.

As the diameter is reduced, the drill’s strength is severely reduced due to the scaling effect.

The grinding of the clearance surface also poses a challenge. The challenge of grinding the

outer surface of the drill body is overcome by providing the clearance surface by providing a

continuous reduction of diameter as in the case of drill diameters less than 300 µm. For drills

above diameter of 300 µm, the drill’s body clearance surface contains a padding surface to

improve the rigidity of the drill. This design provides better stability with reduced friction com-

pared to the continuous body clearance geometry.

5.2.6 Work piece modelling

The modelling of the work piece plays an important role in regard to the quickness with which

the chip formation process during the steady state cutting process can be simulated. The

modelling of the work piece is carried out using Solid works 2010. The work piece geometry

is to be modeled based on the specific tool geometry for the drill diameter that is used for the

simulation (Figure 5-13).

Figure 5-13: Work piece modelling using drill cutting edge geometry basis

The geometrical parameters of the cut surface are obtained from the corresponding drill

geometry. The drill’s main cutting edge and its corresponding chisel edge are obtained from

the drill geometry model. These curves are utilized to obtain the surface generated during the

drilling process. These surfaces which represent the surface generated in the work piece for

one rotation of the drill are then knitted to generate one single surface model. Subsequently,

the drill surface is used to remove material from the solid work piece body. The resulting

solid body is used to represent the work piece in the finite element simulation. The basic

geometry of the micro drill work piece geometry that is used in this work is provided

(Figure 5-14). The work piece diameter is 20 % larger than the drill diameter. This is done to

ensure that the finite element mesh on the work piece surface is stable enough to avoid


unrealistic distortion during cutting. The work piece thickness is also made to a constant ratio

of 50 % of drill diameter.

Figure 5-14: Work piece geometry employed in micro drilling process simulation

5.2.7 Remeshing strategy

The remeshing of the elements is a very important aspect for the finite element simulation of

a plastic deformation process. The element deformation during loading leads to highly dis-

torted element shape and results in the simulation to stop prematurely with increase in time

step. To avoid this, in the updated Lagrangian simulation, the plastic object’ mesh is regen-

erated based on predefined remesh initiation criteria. The highly distorted elements are

modified to improve the shape of the element. The remeshing strategy in DEFORM 3D is

completely handled without much of user interference.

The initiation of remeshing can be controlled in a number of ways in DEFORM 3D and is

contained within the remesh criteria. This includes

1. Maximum Stroke increment

2. Maximum time increment

3. Maximum step increment.

4. Interference depth

The interference depth is a parameter that is used to specify when the remeshing is to be

triggered. The interference depth is defined by the penetration of the rigid body’s mesh into

the plastic object’ mesh.


Figure 5-15: Influence of remeshing methodology (global remeshing and local remeshing) on

mesh size

The depth can be given in absolute mode or relative mode. In the absolute mode, the inter-

ference depth is given in millimeters and the relative mode specifies the interference depth in

the form of fraction. A fraction value of 0.7 is recommended for the simulation of chip for-

mation process. The absolute method is easier for simulations where the interference is

highly predictable like forming simulation. During the chip formation simulation, due to the

complexity of the cutting tool geometry and the high level of mesh deformation, the absolute

method is not advisable. In this work, the relative mode is utilized for the remeshing of the

work piece mesh. The remeshing in this work is to be reduced to the extent possible so that

the microstructure phase information of the element is not lost. The remeshing algorithms so

far developed are used only for isotropic finite element mesh. The consideration of the mi-

crostructural phase during the remeshing is not available within the DEFORM 3D capability.

To avoid the number of remeshing during the chip formation simulation of microstructure

based FE mesh, the mesh size is reduced on the work piece cut surface to the extent possi-

ble. Two different remeshing methodology are available in DEFORM 3D namely global

remeshing method and local remeshing method (Figure 5-15).

Initial condition

Number of meshes : ~100000

After global meshing


After local meshing


Increase in number of meshes com-

pared to global remeshing


The diagram shows the difference between the global remeshing method and the local

remeshing method. In general, the global remeshing, remeshes the complete work piece

geometry. This method leads to highly efficient remeshing of the work piece with the number

of meshes being approximately constant throughout the simulation run. This remeshing

methodology works very well when the work piece mesh is considered homogeneous from a

material point of view. The remeshing process takes into account the mesh weighting pa-

rameters provided in the work piece object definition. The strain, strain rate and temperature

are given higher weightage compared to geometry and mesh density window. This approach

is best suited to simulate the chip formation process as the elements near to the cutting edge

in which deformation reaches high levels of strains at larger strain rates accompanied by

rising temperature due to plastic work. But the global remeshing algorithm does not take into

account the phase of the element during remeshing and hence does not suit the microstruc-

ture based FE mesh. Hence during remeshing, the element’s phase information is lost. This

leads to the resulting mesh to be homogeneous and to erroneous results. The modification of

the mesh weighting factors to higher weightage did not prove successful as the remeshing

halted abruptly due to the inability of the DEFORM automatic mesh generator. Irrespective of

the mesh weighting factor settings, the global remeshing approach on initial trial lost all the

microstructure information within 50 simulation steps and proved futile with respect to micro-

structural phase information retain ability.

The local remeshing methodology suits better for the microstructure based FE mesh. In this

approach, the remeshing is highly restricted to the mesh distorted by the deformation. The

mesh in the rest of the work piece geometry is not altered. This greatly improves the retain-

ing ability of the microstructure phase information in the finite element mesh.

The local remeshing methodology contains two options for the selection of the element to be

remeshed and is termed as size control. The two options for size control are ‘average of

neighbors’ and ‘scaling factor’. The average of neighbors uses the adjacent elements to be

remeshed. This leads to a maximum probability of only 50% for the elements to lose their

phase information instead of 100% as in the case of global remeshing methodology. The

scaling factor option within the local remeshing methodology uses the elements to be

remeshed in the form of scaling of the element size. Upon initial study this methodology does

not provide a stable chip formation simulation in heterogeneous material model. The local

remeshing strategy allows the simulation to be run to steady state without considerable loss

of phase information loss. Although this process does not prove to be the best option for the

remeshing of a multiphase material mesh, it proves sufficient for the chip formation simula-

tion.

In addition to all the above said factors, the finite elements with good shape and good sur-

face are eliminated from remeshing. This is employed to reduce the loss of phase infor-

mation of the individual elements.


5.3 Simulation of drilling process

The simulation of the drilling process is carried out for two different diameters of 100 µm,

500µm and 1 mm. The simulation is carried out with the isotropic finite element mesh and

the 3D two phase finite element mesh to validate the use of this multiphase FE model devel-

opment approach in simulating the chip formation process in micro cutting process. The

experiments are carried out for diameters from 0.05 mm to 1 mm and 3mm. The finite ele-

ment simulation of micro drilling process performed using DEFORM 3D is able to simulate

the chip formation process using the microstructure based multiphase FE model developed

as part of this work.

Figure 5-16: Chip form during micro drilling of AISI 1045 microstructure steel using 3D two

phase FE model

The modelling of the work piece using the microstructure based finite element model makes

it possible to study the influence of the microstructure geometry in the chip formation process

in micro drilling. Figure 5-16 clearly shows the plastic deformation of the microstructure

based finite element mesh of the work piece into a chip. The two phases, pearlite and ferrite

is being represented by grey and white color respectively.

5.3.1 Prediction of feed forces & torque

The prediction of cutting forces, torque generated during drilling and the chip form in micro-

drilling compared to isotropic FE mesh are carried out for validating the multiphase FE model

development approach.

Feed force and torque are the output parameters plotted for comparison with the simulation.

The maximum feed force and maximum torque obtained during the drilling process simula-

tion is used for comparison.

Chip

Drill

Workpiece

Microstructure


Figure 5-17: Prediction of feed force and torque using 3D two phase FE model, isotropic FE

model in comparison with the experimental results

The prediction of the feed forces by the 3D two phase FE model is better compared to the

isotropic FE model and it proves that as the drilling diameter reduces, need for multiphase

FE model is more pronounced (Figure 5-17). As the drill diameter reduces, the influence of

the phase’s geometry in feed force generation increases. The 3D two phase FE model in-

cludes the geometry of the microstructural phases and therefore its ability to predict the feed

forces increases in micro drilling. In addition, as explained in the previous section, the in-

crease in related feed force and torque in cutting operation is due to the corresponding in-

crease in the chisel edge width to diameter ratio. The 3D two phase FE model is able to

predict this influence better compared to the isotropic FE model.

5.3.2 Prediction of chip form

The chip formation during micro drilling process is highly influenced by the ratio of the cutting

edge radius to the uncut chip thickness. When the uncut chip thickness is less than the cut-

ting edge radius, the plastic deformation of the work piece material happens because of

ploughing of the material instead of shearing of the material. When the uncut chip thickness

is larger than the cutting edge radius, the plastic deformation of the work piece material takes

place by shear deformation. This dependence of chip formation on the cutting edge radius is

simulated using two different cutting edge radiuses for a drill diameter of 100 µm. The cutting

edge radiuses chosen are 0 µm (sharp cutting edge) and 0.2 µm (rounded cutting edge).

Simulations are carried out using these two cutting edge rounding values. The results clearly

shows that with a cutting edge radius of 0.2 µm the chip form is better predicted for a drill

0

4

8

12

16

20

0 1 2 30

2

4

6

8

10

12

Simulation(isotropic FE macro model)

tr

kf

Simulation (isotropic FE model, d = 100 µm)

Experiment

Simulation (mixture FE model, d = 100 µm)

Workpiece material: C45 normalized # Cutting material: HW-20Cutting speed: v

c = 35 m/min # Feed: f = 0.012*d # Cooling: dry

Drill diameter d, mm

Re

late

d f

ee

d f

orc

e k

f ,

(kN

/mm

2)

Re

late

d t

orq

ue

tr ,

(kN

mm

/mm

2)


diameter of 100 µm and indirectly the mode of cutting during the micro drilling of normalized

steel AISI 1045 using a 100 µm, ploughing (Figure 5-18).

Figure 5-18: Chip form prediction using isotropic FE model and 3D two phase for a drill

diameter of 100 µm

5.3.3 Prediction of chip morphology

The chip form is an important criterion to validate the capability of a FE model to simulate the

intricacies to form chip during the cutting process. During micro-drilling of AISI 1045 steel

under normalized state, the material undergoes severe plastic deformation before the chip

formation. The harder particles are also pulled out during the chip form.

This is not reflected during the chip form simulation using an isotropic FE model as the mate-

rial model does not differentiate between a harder phase and a softer phase. When the chip

shape is compared to the experimental chips obtained using SEM images, the multiphase FE

model chip formation simulation proves to be beneficial compared to the isotropic FE model

chip formation (Figure 5-19 & Figure 5-20). The micro drilling using 1 mm diameter micro

drill is shown here to predict in addition to the chip form, the presence of micro holes in the

chip.

Simulation

Experiment


Figure 5-19: Chip form prediction using isotropic FE model for a drill diameter of 100 µm

When micro drilling AISI 1045 steel, the harder particles (pearlite) are pulled out of the chip

as they do not undergo yielding like the softer matrix (ferrite). This pull out of the harder

particles is clearly depicted by the presence of micro holes in the chip. The presence of these

chips is captured better using the 3D two phase FE model in comparison to the isotropic FE

model. The ability of the 3D two phase FE model to predict the micro holes is due to the

deletion of the very small elements during the course of remesh in FEM simulation.

Figure 5-20: Chip shape during micro drilling in AISI 1045 steel

In DEFORM 3D during the simulation of chip formation process in micro drilling; the remesh-

ing of the work piece is to be restricted to the extent possible for the want of reduction in loss

of microstructural information. In addition, remeshing is also restricted to local area where

required using local remeshing option and avoiding meshes with a good surface area being

avoided from remeshing. The above two steps leads to very fine meshing of the chip surface

as the mesh shape gets distorted with the progression of chip formation.

Isotropic FE model

Multiphase FE model

Rough edges

Rough edges


Figure 5-21: Chip form and the presence of micro holed during micro drilling of AISI 1045

steel using 1 mm micro twist drill

DEFORM 3D removes very fine meshes in the work piece and this leads to the prediction of

cracks on the edges of the machined chip and micro holes in the chips internal surfaces

(Figure 5-21). This prediction of holes and rough edges present in the work piece is better

with the multiphase FE model. In the 3D two phase finite element model, the elements which

represent the harder pearlite particle are remeshed more often compared to the elements

which represent the softer ferrite particles. This leads to the harder pearlite particle finite

elements to become fine earlier compared to the soft ferrite particle finite elements. This

corresponding leads to the deletion of the elements in the chip and the prediction of holes

during micro drilling of AISI 1045 microstructure steel.

Chip form

Holes

6 Future Directions 74

6 Future Directions

The developed multiphase Finite element model is the first attempt in this direction with the

DEFORM simulation package. The developed model can be improved further to an extent as

outlined here.

The finite element software package DEFORM 3D recognizes the different phases in a mate-

rial, but does not take into consideration the grain size and grain geometry as a whole. This

has been overcome in this work by the developed algorithm and program. In addition, the

DEFORM 3D remeshing module can be improved to recognize the grain shape and geome-

try during remeshing. This will highly retain the phase information during the course of

remeshing and hence improve the efficiency of the simulation of micro cutting processes in

general using multiphase finite element mesh.

Figure 6-1: New local remeshing methodology for multiphase FE model

During the course of the simulation, it has been observed that local remeshing leads to

enormous increase in the number of meshes and this leads to abrupt termination of the

simulation. This can be improved if the remeshing methodology takes into account grain

shape and reverts back the refined mesh under the cutting edge to coarse mesh. This will

reduce the overall increase in mesh size over the course of simulation and in turn increase

the computational efficiency of multiphase finite element modelling of 3D micro cutting pro-

cess.

Area selected to remesh

Present local remeshing methodology

Proposed local remeshing methodology

7 Conclusion 75

7 Conclusion

This work primarily is concerned with the development of a multiphase finite element model

to analyze the micro cutting process in ferritic pearlitic steel. The micro cutting process war-

rants the phases present in the work piece microstructure to be included in the finite element

model to understand the mechanics of material removal. The study of micro cutting process

with isotropic finite element model does not predict the process output parameters with the

required accuracy due to a lot of specific aspects of cutting at the micro scale termed in

general as size effects in micro cutting. The micro cutting process has so far been studied

through finite element model in two dimensions. The two dimensional multiphase finite ele-

ment models are used for the study of chip formation in orthogonal metal cutting. For the

study of industrially relevant metal cutting processes like drilling, a reliable 3D multiphase

finite element model is developed.

The details of microstructural phases present in the work piece that are needed for the 3D

multiphase FE model development include phase volume percentage, grain size and grain

shape of each constituent. These details are obtained through standard metallographic ex-

aminations of the work piece specimens. To incorporate the obtained work piece microstruc-

ture information into a 3D FE mesh, an algorithm is developed which distributes points in

correspondence to the number of grains of a microstructure phase present in the given geo-

metrical volume separately. Once the points are distributed, these points represent geomet-

rical location of grains in a microstructure. These points are then compared in geometrical

coordinates with the finite element nodes. The node present closest to a point is selected to

represent a microstructural phase and is called seed node. To incorporate the grain volume

information in the finite element model, the first element corresponding to the seed node is

selected. The seed node’s volume is calculated and compared to the grain volume. When

the element’s volume is less than the grain volume, additional adjacent nodes and corre-

sponding elements are selected to reach the grain volume. This procedure is carried out for

all the seed points in the geometrical volume.

With the multiphase finite element mesh generated using the above mentioned methodology,

the material modelling of the work piece also has to consider the different phases present in

the material microstructure. Hence the material behavior modelling for the multiphase finite

element model is carried out using the mixture material model present in DEFORM 3D. The

ferritic pearlitic steel is modeled as a mixture material with ferrite and pearlite as its constitu-

ents. The ferrite phase is modeled using C05 microstructure’s flow curve model and the

pearlite phase is modeled using C75 microstructure.

This new multiphase finite element model development methodology is validated through

finite element simulation of AISI 1045 steel microstructure under tensile loading, compres-

sion loading, shear loading and finally micro twist drilling process. The geometry for the

tensile loading are modeled using Solidworks 2010 and imported into the finite element

package. The compression and shear geometries are modeled within the finite element

package itself. From the simulation results under tensile, compression and shear loading, the

developed finite element model’s efficacy is proved for simple loading conditions.

7 Conclusion 76

Finally, micro drilling is employed to validate the developed multiphase finite element model’s

ability to simulate the influence of microstructure during large scale plastic deformation prob-

lems at the micro scale. The micro drilling process experiments are carried out for a variety

of diameters ranging from 50 micron to 1 mm in AISI 1045 steel. The feed forces, torque and

the chip form are selected as the process output parameters that are to be compared with

the finite element simulation results.

For the finite element simulation of the micro drilling process, the micro twist drill geometry is

studied using Keyence digital microscope and geometrical parameters like chisel edge angle,

chisel edge width, cutting diameter, main cutting edge length, main cutting edge angle,

clearance geometry along the axis, primary clearance angle and secondary clearance angle

on the face of the cutting edge is measured. With the measured geometrical details the micro

twist drill geometry is modeled using Solidworks 2010 and imported into DEFORM 3D.

The micro drilling simulation is carried out for drill diameters 100 µm, 500 µm and 1000 µm.

The finite element simulations are carried out with isotropic finite element models and multi-

phase finite element models. The process output parameters, feed force, torque and chip

forms are compared. As the cutting diameter is reduced from 1000 µm to 50 µm, the related

feed force calculated from the experimental results is shown to increase which is explained

with the increase in chisel edge width increase as the cutting diameter is reduced. The chip

formation simulation results are validated by the micro drilling experiments conducted on

AISI 1045 microstructure steel using the same parameters as employed in FE simulations.

From the simulation results, it is proved that the multiphase FE model is able to predict better

the feed forces and torque better compared to the isotropic FE model. This shows the influ-

ence of the microstructure in chip formation mechanics in addition to the macro geometry

variations like chisel edge width increase. The chip form is also better predicted using the

multiphase FE model when compared to the isotropic FE model. In micro drilling, the influ-

ence of the micro drill’s cutting edge radius parameter is also studied using FE simulation.

When the micro drilling process is simulated using a sharp cutting edge micro drill, a smooth

chip edge is simulated whereas the experimental investigation shows the chip to have a

rough edge. This is better simulated using a micro twist drill with a cutting edge radius of 0.2

µm. Thus the size effect due to the ratio of uncut chip thickness to the cutting edge radius

parameter is explained. The multiphase FE model is also able to predict the holes present in

the chips generated during micro drilling whereas the isotropic FE model predicts a smooth

chip without the presence of the micro holes. When the uncut chip thickness, is in the same

range of the microstructure phase size, the chip generated during the cutting process is

shown to have micro holes which correspond to the harder phase present in the work piece

microstructure.

The chip formation in micro drilling process is therefore better simulated using a multiphase

FE model compared to an isotropic FE model. Using this simulation, the new multiphase

material FE model development methodology’s ability to study large scale plastic defor-

mation at the micro scale is proved.

V Index of literature 77

V Index of literature

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