asad_intercut2008

7/31/2019 Asad_Intercut2008

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Intercut 2008 Cluny, October 22-23

2nd

International Conference Innovative Cutting Processes & Smart Machining

1

NUMERICAL AND EXPERIMENTAL APPROACH FORAN ALUMINIUMALLOY MICRO-MILLING

Muhammad Asad, Clement Hignette, Tarek Mabrouki, Jean-Franois RigalLaMCoS, INSA-Lyon, CNRS UMR5259, F69621, France,

Asad.muhammad /Clement.hignette / Tarek.mabrouki / Jean-Francois.Rigal @insa-lyon.fr

Abstract: This study put forwards a numerical approach to investigate macro- and micro-scale down cutmilling process for an aeronautic aluminium alloy A2024-T351. The global aim is the physical

comprehension of chip formation phenomena at macro- and micro- scale, with variable conditions of

cutting speed and tool edge radius. Johnson-Cook material model is used as material behaviour law. A

failure model is developed with material fracture energy dissipation coupling. Results concerning chip

morphology, temperature and specific cutting energy evolution along chip section for the case of

orthogonal down-cut peripheral milling are presented. Simultaneously an experimental methodology is

developed to validate the numerical results. The proposed fracture energy coupling approach; based on

FE-methodology, put forwards a good comprehension of micro-HSM for an aluminium alloy.

Keywords: Numerical model, progressive damage, aluminium alloy A2024-T351, micro-millingexperiment

1 Introduction

Today, in aeronautic and automobile manufacturing industries the interest in micro-high speed machiningof materials with high strength to weight ratio, for example aluminium alloys, is increasing. To improve theproduct finish, cutting conditions need to be optimised. In this context, the present study proposes a FE -based methodology; with experimental validation, to explain multi-physical phenomena involved in

orthogonal milling process. As chip morphology directly affects surface finish and residual stresses patternon machined workpiece, so the present study targets to develop an optimised numerical approach to predicta realistic chip formation. Increase in material strength [1, 2] associated with decrease in cuttingtemperature due to reduction in the uncut chip width (macro to micro-scale milling) and affect of tool edgeradius (size effect) is also highlighted in this work.

2 Experimentation: Equipments and Results

Micro milling tests were realized with micro end mill, 0.5 mm (fig.1) on a High Speed Machining Center(maximum allowable rotation speed: 24000 RPM).Best efforts had been made to reproduce orthogonalcutting case. So that, the tool cutting edge was orthogonal with the feed rate and cutting speed (which wasquite difficult to ensure, especially for micro-mills). Workpiece (A2024-T351) was prepared with uni-axialgrooves as shown in fig. 2.

Fig.1: SEM picture of micro end mill

0.5mm


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Fig.2: SEM picture of groove and burr a) total machined workpiece b) zoom on a single

groove (top view)

The measuring equipment was consisted of a standard dynamometer (Kistler 9257B, with the threshold

force registration and the first natural frequency: 0.01 N and 2.3 kHz respectively), scanning electronicmicroscope (SEM) and a profile-meter. Taguchi method for orthogonal design of experiments was used.Cutting forces (in cartesian directions) registered by dynamometer; compatible with the measure range ofdynamometer (1N and less than 1 kHz), for ap =0.1mm,fz =0.005mm,N=24000rpm are shown in fig.3.

Fig.3: Force registration in cartesian directions

A series of tests had been performed, and chip morphology was observed with SEM. For comparison with

the numerical model (detailed in section 3) cutting force and chip shape obtained for N=24000RPM, fz=0.005mm, Rn=2m (measured with SEM) is presented (fig.8b, fig.9). In addition groove shape, burrformation (fig. 2) and the surface roughness of the machined part were also observed.

3 Numerical Modelling

3.1 Geometrical model, Hypothesis and Meshing

A 2-D orthogonal down-cut peripheral milling cutting model was developed in commercial softwareAbaqus/Explicit. Tool-workpiece geometrical model conceived is shown in fig.4. To overcome contactdifficulties; workpiece was initially modelled in three parts, chip, cutter path, and machined part. As valueof feed ratefzis very less than that of axial cutting depth aP, therefore plane strain hypothesis was assumed.Also, as heat generated by plastification work and friction has very less time to propagate in the material.Therefore, adiabatic hypothesis are valid for machining in general and high speed machining in particular[3].

Forc

e(N)

Cutting time (sec)

Total cutting time=0,03 sec

Fx Fy Fz

Groove

Burr

Vf

N

a b


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Interaction between contacting bodies was defined with Coulombs friction law[3, 4]. Boundary conditionswere applied to tool center of rotation. It can advance with feed velocity Vf m/min; this actually replicate

the table feed rate in x-axis direction, and can rotate withNrev/min in anti-clockwise direction. Thus cutterrotates with constant cutting speed (measured at cutter edge, tangential to tool diameter). For workpiece alldegree of freedom were blocked. For numerical simulation, two cutting speeds 400m/min; for macro-micromilling (with Rn=20m) and 37 m/min; for micro milling (with Rn=2m) had been used. For cuttingspeeds of 400m/min; 25mm tool (with 2 cutters ) with a feed rate of 0.4mm/rotation was used .Where asfor cutting speed of 37 m/min speed a 0.5mm tool (with 2 cutters) with a feed rate of 0.01 mm/rotationwas used. As the tool rotates and advances horizontally, so the path traced by the cutter is not a simplecircular path but it follows a trochoidal path in ideal case (not considering the affects of toolchatter) .Therefore trochoidal path equations were used to model the chip section geometry. To obtain thephysical results, sensitivity tests; to acquire optimal elements dimensions, had been performed. For variousworkpiece parts, elements sizes of the order of 30m-3m had been conceived.

Fig. 4: Tool-workpiece boundary conditions

3.2 Material behaviour and chip formation criterion

The numerical approach is the same that had been used in our previous published work [5]. Nevertheless,some necessary details have to be mentioned in the present contribution. The constitutive model used in the

, 2m,0.2

4mm

Edge radius, Rn=20, 2m


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present study is that proposed by Johnson-Cook [6]. This model is presented by the expression ofequivalent stress (eq.1)

( )m

n

mElasto-plastic term

Viscosity term Softening term

room

o room

T - T = A + B 1+Cln 1-

T - T

(1)

Where A, B, n, C, m are JC-model constants. In the numerical model, chip formation is realised by ductilefailure phenomenon that occurs in two steps. The first step concerns the damage initiation, whereas thesecond one concerns damage evolution based on fracture energy approach [7].1

Ststep- damage initiation:The Johnson-Cook shear failure model is used as a damage initiation criterion.

Where D1 to D5 are JC-model constants.

T TP roomD D exp D 1 D ln 1 D51 2 3 4 T Tm room

ioo

= + + +

(2)

Damage in a finite element is initiated when a scalar damage parameter exceeds 1. This parameter isbased on a cumulative law and is defined as:

oi

= (3)

2nd

step- damage evolution: Once the ductile material damage has been initiated, the stress-strainrelationship no longer accurately represents the material behaviour. Continuing to use the stress-strain

relation introduces a strong mesh dependency based on strain localization. Hillerborgs fracture energyproposal [7] is used to reduce mesh dependency by creating a stress-displacement response after damageinitiation. Hillerborg defines the energy Gf; required to open a unit area of crack as a material parameter.With this approach, the softening response after damage initiation is characterized by a stress-displacementresponse rather than a stress-strain response. According to this law, the damage evolution law can bespecified in terms of terms of fracture energy dissipation Gf. The law defines that; ductile material damagecan evolve linearly (eq. 4) or exponentially (eq.6). This can be described in the form a damage parameterD.

f f

L uD

u u

= = (4)

Where the equivalent plastic displacement at failure, fu is computed as:

2Gf

uf

y= (5)

01 expu

D duG

f

=

(6)

In Abaqus, an element is removed from the mesh if all of the section points at any one integrationlocation have lost their load-carrying capacity (D=1). So, all the stress components will be set to zero andthat material point fails (cutter path elements). Thus chip detachment is realised from workpiece. In the


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model, Gf is provided as an input parameter which is a function of fracture toughness, Youngs modulusand Poisson's Ratio. Johnson-Cook laws material entities used in the numerical model are shown in chart

1. Thermo-mechanical properties of materialare shown in chart 2.

A (MPa) B (MPa) n C m D1 D2 D3 D4 D5

352 440 0.42 0.0083 1 0.13 0.13 -1.5 0.011 0

Chart1: Johnson-Cook parameter used to simulate the behaviour of A2024-T351 [8]

Physical parameters Workpiece (A2024-T351)Density, (Kg/m3) 2700

Elastic modulus,E(GPa) 73Poissons ratio, 0.33Specific heat, Cp

(Jkg-1

C-1

)

0.557 877.6C TP

= +

Expansion, d(m.m

-1C

-1)

38.910 22.2Td

= +

Tm, (C) 520

Fracture energy,fG (N/mm) 18

Troom, (C) 25

Chart 2: Workpiece physical parameters [9]

3.3 Results and discussionThe present section deals with the results regarding chip morphology as function of material fracture

energyf

G and chip thickness. Evolution of specific cutting energy as a function of uncut chip thickness and

t/Rn ratio (chip thickness to cutter edge ratio) is also presented. Micro milling simulation had beenperformed for two cases:

a) with a macro tool (25mm, Rn 20m), feed rate 0.4mm/rot for cutting speed of 400m/min.b) with a micro tool (0.5mm, Rn 2m), feed rate 0.01mm/rot for cutting speed of 37m/min.

For case a): variable section continuous chip for an input value off

G =18N/mm [9] was obtained (fig.5a).

However with a slight decrease in material fracture resistance (f

G =16N/mm), segmented chip morphology

was obtained (fig.5b). The latter is because of the higher strains, which increases temperatures. Thisenhances thermal softening phenomenon and thus segmented chip is obtained. However as the chipthickness decreases and approaches to tool edge radius dimensions; wider plastic shear zones (w.r.t tooledge radius) require higher energy dissipation. Consequently, there will be lesser deformation on chipsection, because of size effect [2]. Therefore continuous chip is obtained. Fig.7 shows this effect in terms ofan increase in specific cutting energy for decrease in uncut chip thickness. Nevertheless, it can be noted thatas chip thickness reduces to almost 110m, chip section is distorted and not continuous(fig.5b).Temperature calculated on middle of chip section; plotted in fig.6, explains the reason of chipsection distortion. During simulation, as chip section width approaches to 110m there is a remarkabledecrease in temperature. That is due to the size effect discussed previously. This decrease in temperatureintends to decrease material thermal softening and consequently material strength had been increased

(fig.7). However, in the numerical simulation material strength; in terms of input value off

G had not been

increased. Incessant use of lowerf

G value may result in the brittle chip fracture. Therefore,f

G value was

increased upto 36N/mm (from 110m to onward chip section), to get a realistic chip (fig.5c). Chipmorphology thus obtained was comparable with experimental one (fig.5d). Figure 7, shows an increasing


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trend in specific cutting energy with a decrease in uncut chip thickness due to size effect. It can also be seen

that an increase inf

G value also increases specific cutting energy.

Fig. 5: Chip morphology a)f

G =18N/mm, b)f

G =16 N/mm, c)f

G =16 N/mm (macro-

section), 36N/mm (micro section), d) experimental chip ( Vc=400m/min, Rn=20m)

Figure 6: Temperature evolution calculated on middle of chip section along length

X

Y

Tool

Cutting velocity33728019511025

Temp (C)Avg : 75%

1mm

a b

c d

Width 110m

Macro zoneMicro zone

0

50

100

150

200

250

300

350

0 2 4 6 8 10 12 14 16 18

(10.8mm

Chip width 110m

Distance along chip length (mm)

Tempera

ture


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Figure 7: Specific cutting energy ~ uncut chip

Figure 8: chip morphology a) numerical chip b) experimental chip

Figure 9: specific cutting energy ~ uncut chip thickness to cutter edge ratio (t/Rn)

For case b): at very low cutting speed; Vc=37m/min, lower is the material strain hardening. Simultaneously,though cutter radius Rn, had been decreased to 2m, but well known tool radius edge effect [2] is not the

t/Rn ratio

Spec

ificcu

ttingenergy

(MPa

) Experimental ResultNumerical Result

25%

13%

Spec

ificcu

ttingenergy

(MP

a)

Micro

0

200

400

600

800

1000

1200

1400

0 50 100 150 200

Macro

Uncut chip thickness (m)

Gf=16 N/mm

Gf=16 N/mm (macro section),36 N/mm (micro section)

a 10m b


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dominant factor to increase material strength for theses cutting conditions. Consequently, a decrease inmaterial strength was marked, as shown in fig.9.

On the other hand, fG value was decreased (8 N/mm) for this case, so that numerically obtained chip

(fig8a), was comparable with that obtained experimentally (fig.8b). This notable decrease in material

strength (in terms off

G ) had increased chip section strains and temperatures. Temperature in chip section

has been increased to 506C (melting temperature for this material is in the range of 520C~560C) atsome regions in chip (fig8a). It means that, chip material might have been melted at some regions; asconfirmed by the highly distorted chip obtained experimentally (fig.8b) and abnormal burr formation(dimensions of the order of chip section) on edges of micro machined surface (fig.2b).Fig.9 shows specific cutting energy and t/Rn ratio plot .Since at smaller chip thickness values cutter edgeeffect/size effect is higher. Therefore, an increasing trend in specific cutting energy can be seen with adecrease in t/Rn ratio. Numerically calculated specific cutting energy values were lesser than experimentalmeasured values (13% to 25%).This is may be due to the non consideration of strain gradient plasticityaffect [2]. This affect is usually considered as governing factor to increase material strength at micron level

deformations.

4 Conclusion and Perspective

The global aim of this contribution concerns the comprehension of the physical phenomenonaccompanying the chip formation during micro milling operations. The studied material is an aeronauticaluminium alloy referenced as A2024-T351.From practical point of view, it is difficult to optimize working parameters for micro machining operations.At the same time accurate measurement of very low cutting forces, machined surface roughness, micro chipmorphology analysis and to reproduce orthogonal cutting case is not an easy task.A numerical model was developed to understand micro milling process. The model put forwards theimportance of material damage and fracture energy coupling for a realistic chip morphology. Materialstrength was found to be increased at micro dimensions at higher cutting speed, because of the decrease in

tool-workpiece interaction temperature. However decrease in material strength was noted for low cuttingspeed. This was because of the simultaneous effects of, decrease in material strain hardening and increasein temperature due to lower fracture energy value. Calculated specific cutting energy values were lowerthan experimental ones. This might be due to strain gradient plasticity affects, which is considered asprevailing factor in increasing material strength at micro level cutting. In future strain gradient plasticitywill be introduced in material model for efficient prediction of results at micron level.

References

[1] J.E Campbell, J. L. Shannon, W. F. Brown, 1974, Fracture toughness of high-strength alloys at lowtemperature, ASTM special technical publication, N 556, p.3-25.

[2] Kia liu, Shreyes N. Melkote, 2007, Finite element analysis of the influence of tool edge radius onsize effect in orthogonal micro-cutting process, International Journal of Mechanical Sciences N 29

p. 650660[3] T. Mabrouki, J.-F. Rigal, 2006, A contribution to a qualitative understanding of thermo-mechanicaleffects during chip formation in hard turning, J. Mat. Proc. Techn., N 176, p.214221.

[4] K. Li, X.-L. Gao, J.W. Sutherland, 2002, Finite element simulation of the orthogonal metal cuttingprocess for qualitative understanding of the effects of crater wear on the chip formation process, J.Mater. Proc. Techn. N 127/3 p. 309324.

[5] T. Mabrouki, F. Girardin, M. Asad, J.-F. Rigal,Numerical and Experimental study of dry cutting foran aeronautic aluminium alloy (A2024-T351), Int. J. Mach. Tools. Manuf. N48 p.1187-1197.

[6] G.R. Johnson, W.H. Cook, 1985, Fracture characteristics of three metals subjected to variousstrains, strain rates, temperatures and pressures, Eng. Fract. Mech. N 21/1 p. 3148.

[7] A. Hillerborg, M. Modeer, P. E. Petersson, 1976, Analysis of Crack Formation and Crack Growthin Concrete by Means of Fracture Mechanics and Finite Elements, Cement and Concrete Research,N 6, p. 773782.

[8]

X. Teng, T. Wierzbicki, 2006, Evaluation of six fracture models in high velocity perforation,Engineering Fracture Mechanics, N 73 p. 16531678.[9] www.knovel.com

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