metallurgical basics

7/31/2019 metallurgical basics

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Equivalent Plastic Strain

The equivalent plastic strain gives a measure of the amount of permanent strain in an

engineering body. The equivalent plastic strain is calculated from the component plastic

strain as defined in theEquivalentstress/strain section.

Most common engineering materials exhibit a linear stress-strain relationship up to a stress

level known as theproportional limit. Beyond this limit, the stress-strain relationship will

become nonlinear, but will not necessarily become inelastic. Plastic behavior, characterized

by nonrecoverable strain or plastic strain, begins when stresses exceed the material'syield

point. Because there is usually little difference between the yield point and the proportional

limit, the ANSYS program assumes that these two points are coincident in plasticity analyses.

In order to develop plastic strain, plastic material properties must be defined. You may define

plastic material properties bydefining either of the followingin theEngineering Data:

Bilinear Stress/Strain curve. Mulitlinear Stress/Strain curve.

As has been already mentioned in the previous section, there are two differentapproaches for

the synthesis of UFG (Zhu and Liao, 2004), in the present section weattempt to illustrate

these approaches in detail. A schematic representation of processingroutes and their effect on

final grain size refinement is given in figure 1.1. It is obviousfrom the figure that

accumulative roll bonding (ARB) and ECAP, variants of severe plastic deformation, can be

effectively used to produce UFG materials. Nanomaterialsfind numerous applications

depending upon the structure and property variation obtainedduring processing. A summary

of the possible variation in the specific properties of nanomaterials is shown in figure 1.2.

This describes the variation when the materialreaches in nanoscale regime. The synthesis

route of nanomaterials can be divided intotwo broad approaches which are described in thefollowing sections.
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1.1.1 Bottom up approachIn the bottom-up approach of synthesis, atoms, molecules and evennanoparticles can be

used as the building blocks for the creation of complex structures.Most of the bottom-up

approaches emphasize use of nanopowders for the synthesis of nanostructured materials. Forstructural applications, the nanopowders need to beconsolidated into bulk nanostructured

materials. Examples of these techniques includeinert gas condensation(Gleiter, 1981 and

1989),electrodeposition (Erb et al.,1993), ball milling with subsequent consolidation (Koch

and Cho, 1992)and cryomilling with hot isostatic pressing (Luton et al.,1989 and Witkin and

Lavernia, 2006).In practice, these

techniques are often limited to the production of fairly small samples that may be usefulfor

applications in fields such as electronic devices but are generally not appropriate for large-

scale structural applications. Furthermore, the finished products from thesetechniquesinvariably contain some degree of residual porosity and a low level of contamination, which

is introduced during the fabrication procedure. Recent research hasshown that large bulk

solids, in an essentially fully-dense state, may be produced bycombining cryomilling and hot

isostatic pressing with subsequent extrusion (Han et al.,2004) but the operation of this

combined procedure is expensive and at present it is noteasily adapted for the production and

utilization of structural alloys in large-scaleindustrial applications.

1.1.2 Top-down approachThe top-down processes are effective examples of solid-state processing of materials. In

this synthesis approach, coarse-grained materials are refined intonanostructured materialsthrough heavy straining or shock loading. This approachobviates the limitation of small

product sizes and also the contamination that is inherentfeatures of materials produced using

the bottom-up approach. This has an additionaladvantage that it can be readily applied to a

wide range of pre-selected alloys. The firstobservations of the production of UFG

microstructures using this approach appeared inthe scientific literature in the early 1990s.

(Valiev et al., 1990 and Valiev et al., 1991). Itis important to note that these early

publications provided a direct demonstration of theability to employ heavy plastic straining in

the production of bulk materials having fairlyhomogeneous and equiaxed microstructures

with grain sizes in the submicrometer range.

1.2 Severe plastic deformation

Severe plastic deformation term (SPD) is a modified form of intensive plasticdeformation.

The term severe plastic deformation was first introduced by Musalimoveand Valiev in 1992,

where they described the deformation of an Al-4% Cu-0.5%Zr alloy[R.S. Musalimove and

R.Z. Valiev (1992)]. In the last decade, this process established- 2 -

itself very well as an effective method for the production of bulk ultra fine-grained

(UFG)metallic materials (Valiev et al., 1993; Valiev et al., 2000; Valiev,

2004).Severalmethods of SPD are now available for refining the microstructure in order to

achievesuperior strength and other properties


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Top-down Approach

In top-down approach, nano-scale objects are made by processing larger objects in size.

Integrated circuit fabrication is an example for top down nanotechnology. Now it has been

grown to the level of fabricating nano electromechanical systems (NEMS) where tiny

mechanical components such as levers, springs and fluid channels along with electroniccircuits are embedded to a tiny chip. The starting materials in these fabrications are relatively

large structures such as silicon crystals. Lithography is the technology which has enabled

making such tiny chips and there are many types of them such as photo, electron beam and

ion beam lithography.

In someapplicationslarger scale materials are grinded to the nanometer scale to increase the

surface area to volume aspect ratio for more reactivity. Nano gold, nano silver and nano

titanium dioxide are such nano materials used in different applications. Carbon nanotube

manufacturing process using graphite in an arc oven is another example for top-down

approach nanotechnology.

Bottomup Approach

Bottom-up approach in nanotechnology is making larger nanostructures from smaller

building blocks such as atoms and molecules. Self assembly in which desired nano structures

are self assembled without any external manipulation. When the object size is getting smaller

in nanofabrication, bottom-up approach is an increasingly important complement to top-down

techniques.

Bottom-up approach nanotechnology can be found from nature, where biological systems

have exploited chemical forces to create structures for cells needed for life. Scientists and

engineers perform research to imitate this quality of nature to produce small clusters of

specific atoms, which can then self assemble into more complex structures. Manufacturing of

carbon nanotubes using metal catalyzed polymerization method is a good example for

bottom-up approach nanotechnology.

Difference between Top-down and Bottom-up approach in nanotechnology

1. Manufacturing process starts from larger structures in top-down approach where starting

building blocks are smaller than the final design in bottom-up approach

2. Bottom-up manufacturing can produce structures with perfect surfaces and edges (not

wrinkly and does not contain cavities etc.) though surfaces and edges resulted by top-down

manufacturing are not perfect as they are wrinkly or containing cavities.

3. Bottom-up approach manufacturing technologies are newer than top-down manufacturing

and expected to be an alternative for it in some applications (example: transistors).

4. Bottom-up approach products have a higher precision accuracy (more control over the

material dimensions) and therefore can manufacture smaller structures compared to top-down

approach.
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5. In top-down approach there is a certain amount of wasted material as some parts are

removed from the original structure contrast to bottom-up approach where no material part is

removed.

The von Mises yield criterion[1]

suggests that theyieldingof materials begins when thesecond deviatoric stress invariantJ2 reaches a critical value k. For this reason, it is sometimes

called theJ2-plasticity orJ2 flow theory. It is part of a plasticity theory that applies best to

ductilematerials, such as metals. Prior to yield, material response is assumed to beelastic.

Inmaterials scienceandengineeringthe von Mises yield criterion can be also formulated in

terms of the von Mises stress or equivalent tensile stress, v, a scalar stress value that can

be computed from thestress tensor. In this case, a material is said to start yielding when its

von Mises stress reaches a critical value known as theyield strength,y

Deformation incontinuum mechanicsis the transformation of a body from a reference

configuration to a currentconfiguration.[1]

A configuration is a set containing the positions of

all particles of the body. Contrary to the common definition of deformation, which implies

distortionor change in shape, the continuum mechanics definition includes rigid body

motions where shape changes do not take place ([1]

footnote 4, p. 48).

The cause of a deformation is not pertinent to the definition of the term. However, it is

usually assumed that a deformation is caused by external loads,[2]

body forces (such as

gravity or electromagnetic forces), or temperature changes within the body.

Strain is a description of deformation in terms ofrelative displacement of particles in the

body.

Different equivalent choices may be made for the expression of a strain field depending on

whether it is defined in the initial or in the final placement and on whether the metric tensor

or its dual is considered.

In a continuous body, a deformation field results from astressfield induced by appliedforces

or is due to changes in the temperature field inside the body. The relation between stresses

and induced strains is expressed byconstitutive equations, e.g.,Hooke's lawforlinear elastic

materials. Deformations which are recovered after the stress field has been removed are

called elastic deformations. In this case, the continuum completely recovers its original

configuration. On the other hand, irreversible deformations remain even after stresses have

been removed. One type of irreversible deformation isplastic deformation, which occurs in

material bodies after stresses have attained a certain threshold value known as the elastic limit

oryield stress, and are the result ofslip, or dislocationmechanisms at the atomic level.

Another type of irreversible deformation is viscous deformation, which is the irreversible part

of viscoelastic deformation.
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In the case of elastic deformations, the response function linking strain to the deforming

stress is the compliance tensor of the material.

Continuum mechanics

[show]Laws

[show]Solid mechanics

[show]Fluid mechanics

[show]Rheology

[show]Scientists

vde

[edit] Strain

A strain is a normalized measure of deformation representing the displacement between

particles in the body relative to a reference length.

A general deformation of a body can be expressed in the form where is the

reference position of material points in the body. Such a measure does not distinguishbetween rigid body motions (translations and rotations) and changes in shape (and size) of the

body. A deformation has units of length.

We could, for example, define strain to be

.

Hence strains are dimensionless and are usually expressed as adecimal fraction, apercentage

or inparts-per notation. Strains measure how much a given deformation differs locally from arigid-body deformation.

[3]
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A strain is in general atensorquantity. Physical insight into strains can be gained by

observing that a given strain can be decomposed into normal and shear components. The

amount of stretch or compression along a material line elements or fibers is the normal strain,

and the amount of distortion associated with the sliding of plane layers over each other is the

shear strain, within a deforming body.[4]

This could be applied by elongation, shortening, or

volume changes, or angular distortion.[5]

The state of strain at amaterial pointof a continuum body is defined as the totality of all the

changes in length of material lines or fibers, the normal strain, which pass through that point

and also the totality of all the changes in the angle between pairs of lines initially

perpendicular to each other, the shear strain, radiating from this point. However, it is

sufficient to know the normal and shear components of strain on a set of three mutually

perpendicular directions.

If there is an increase in length of the material line, the normal strain is called tensile strain,

otherwise, if there is reduction or compression in the length of the material line, it is called

compressive strain.

[edit] Strain measures

Depending on the amount of strain, or local deformation, the analysis of deformation is

subdivided into three deformation theories:

Finite strain theory, also called large strain theory, large deformation theory, dealswith deformations in which both rotations and strains are arbitrarily large. In this

case, the undeformed and deformed configurations of thecontinuumare

significantly different and a clear distinction has to be made between them. This iscommonly the case withelastomers,plastically-deformingmaterials and otherfluids

and biologicalsoft tissue.

Infinitesimal strain theory, also called small strain theory, small deformation theory,small displacement theory, or small displacement-gradient theorywhere strains and

rotations are both small. In this case, the undeformed and deformed configurations

of the body can be assumed identical. The infinitesimal strain theory is used in the

analysis of deformations of materials exhibitingelasticbehavior, such as materials

found in mechanical and civil engineering applications, e.g. concrete and steel.

Large-displacementor large-rotation theory, which assumes small strains but largerotations and displacements.

In each of these theories the strain is then defined differently. The engineering strain is the

most common definition applied to materials used in mechanical and structural engineering,

which are subjected to very small deformations. On the other hand, for some materials, e.g.

elastomersand polymers, subjected to large deformations, the engineering definition of strain

is not applicable, e.g. typical engineering strains greater than 1%,[6]

thus other more complex

definitions of strain are required, such as stretch, logarithmic strain, Green strain, and

Almansi strain.
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[edit]Engineering strain

The Cauchy strain or engineering strain is expressed as the ratio of total deformation to the

initial dimension of the material body in which the forces are being applied. The engineering

normal strain or engineering extensional strain or nominal straine of a material line element

or fiber axially loaded is expressed as the change in length L per unit of the original lengthL of the line element or fibers. The normal strain is positive if the material fibers are stretched

or negative if they are compressed. Thus, we have

where is the engineering normal strain,L is the original length of the fiber and is the final

length of the fiber.

The true shear strain is defined as the change in the angle (in radians) between two materialline elements initially perpendicular to each other in the undeformed or initial configuration.

The engineering shear strain is defined as the tangent of that angle, and is equal to the length

of deformation at its maximum divided by the perpendicular length in the plane of force

application which sometimes makes it easier to calculate.

[edit]Stretch ratio

The stretch ratio or extension ratio is a measure of the extensional or normal strain of a

differential line element, which can be defined at either the undeformed configuration or the

deformed configuration. It is defined as the ratio between the final length and the initial

lengthL of the material line.

The extension ratio is approximately related to the engineering strain by

This equation implies that the normal strain is zero, so that there is no deformation when thestretch is equal to unity.

The stretch ratio is used in the analysis of materials that exhibit large deformations, such as

elastomers, which can sustain stretch ratios of 3 or 4 before they fail. On the other hand,

traditional engineering materials, such as concrete or steel, fail at much lower stretch ratios.

[edit]True strain

The logarithmic strain, also called natural strain, true strain orHencky strain.

Considering an incremental strain (Ludwik)
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the logarithmic strain is obtained by integrating this incremental strain:

where e is the engineering strain. The logarithmic strain provides the correct measure of thefinal strain when deformation takes place in a series of increments, taking into account the

influence of the strain path.[4]

[edit]Green strain

Main article:Finite strain theory

The Green strain is defined as:

[edit]Almansi strain

Main article:Finite strain theory

The Euler-Almansi strain is defined as

[edit] Normal strain

Two-dimensional geometric deformation of an infinitesimal material element.

As withstresses, strains may also be classified as 'normal strain' and 'shear strain' (i.e. acting

perpendicular to or along the face of an element respectively). For anisotropicmaterial that

obeysHooke's law, anormal stresswill cause a normal strain. Normal strains produce

dilations.
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Consider a two-dimensional infinitesimal rectangular material element with dimensions

, which after deformation, takes the form of a rhombus. From the geometry of theadjacent figure we have

Superplasticity the ability of a material to sustain large plastic deformation has been

demonstrated in a number of metallic, intermetallic and ceramic systems. Conditions

considered necessary for superplasticity are a stable fine-grained microstructure and a

temperature higher than 0.5 Tm (where Tm is the melting point of the matrix). Superplastic

behaviour is of industrial interest, as it forms the basis of a fabrication method that can be

used to produce components having complex shapes from materials that are hard to machine,

such as metal matrix composites and intermetallics. Use of superplastic forming may become

even more widespread if lower deformation temperatures can be attained.

In order to improve the fracture toughness in ultrafine-grained metals, we investigate the

interactions among crack tips, dislocations, and grain boundaries in aluminum bicrystal

models containing a crack and 112 tilt grain boundaries using molecular dynamics

simulations. The results of previous computer simulations showed that grain refinement

makes materials brittle if grain boundaries behave as obstacles to dislocation movement.

However, it is actually well known that grain refinement increases fracture toughness of

materials. Thus, the role of grain boundaries as dislocation sources should be essential to

elucidate fracture phenomena in ultrafine-grained metals. A proposed mechanism to express

the improved fracture toughness in ultrafine-grained metals is the disclination shielding effect

on the crack tip mechanical field. Disclination shielding can be activated when twoconditions are present. First, a transition of dislocation sources from crack tips to grain

boundaries must occur. Second, the transformation of grain-boundary structure into a

neighboring energetically stable boundary must occur as dislocations are emitted from the

grain boundary. The disclination shielding effect becomes more pronounced as antishielding

dislocations are continuously emitted from the grain boundary without dislocation emissions

from crack tips, and then ultrafine-grained metals can sustain large plastic deformation

without fracture with the drastic increase of the mobile dislocation density. Consequently, it

can be expected that the disclination shielding effect can improve the fracture toughness in

ultrafine-grained metals.

metallurgical basics

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