PLASTIC DEFORMATION ï± Modes of Deformation ï± The Uniaxial Tension Test...

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  • PLASTIC DEFORMATIONModes of DeformationThe Uniaxial Tension TestMechanisms underlying Plastic DeformationStrengthening mechanismsMechanical MetallurgyGeorge E Dieter McGraw-Hill Book Company, London (1988)

  • An Al rod when bent through a large angle does not come back to its original shape.Steel is more difficult to deform as compared to Al.A steel piece is easier to deform when heated (as compared to when it is cold).Chinese Clay when deformed does not regain its original shape.Silly putty deforms like Chinese clay when slowly deformed. However, when one bounces a ball of silly putty it bounces like a rubber ball.Let us start with some observationsRevise: the mechanisms by which materials fail There is no volume change during plastic deformation (by slip/twinning).Shear stresses lead to plastic deformation in metallic materials Pure hydrostatic stresses cannot cause plastic deformation (metals).Fracture strain is strongly influenced by hydrostatic stresses.Plastic deformation by slip (motion of dislocations leaving the crystal/grain) involves shear stresses at the level of the slip plane (i.e. even if we apply tensile forces, certain planes may feel shear stresses, which can lead to slip).Amorphous materials can deform by flow (e.g. glass blowing of heated glass), etc. these are not the focus of the current chapter. Important points to be kept in mind

  • Slip (Dislocation motion)Plastic Deformation in Crystalline MaterialsTwinningPhase TransformationCreep MechanismsGrain boundary slidingVacancy diffusionDislocation climb+ Other MechanismsNote: Plastic deformation in amorphous materials occur by other mechanisms including flow (~viscous fluid) and shear bandingPlastic deformation in the broadest sense means permanent deformation in the absence of external constraints (forces, displacements) (i.e. external constraints are removed).Plastic deformation of crystalline materials takes place by mechanisms which are very different from that for amorphous materials (glasses). The current chapter will focus on plastic deformation of crystalline materials. Glasses deform by shear banding etc. below the glass transition temperature (Tg) and by flow above Tg.Though plasticity by slip is the most important mechanism of plastic deformation, there are other mechanisms as well. Many of these mechanisms may act in conjunction/parallel to give rise to the observed plastic deformation.Grain rotationPhenomenological terms

  • A body can be deformed using many modes:Tension/CompressionBendingShearTorsion It is important to note that these are macroscopically defined with respect to a body of given geometry (even in tensile loading inclined planes will be subjected to shear stress)Common types of deformationTensionCompressionShearTorsionDeformed configurationBendingNote: modes of deformation in other contexts will be defined in the topic on plasticityReview

  • Mode IMode IIIModes of DeformationMode IIIn addition to the modes of deformation considered before the following modes can be defined w.r.t fracture.Fracture can be cause by the propagation of a pre-existing crack (e.g. the notches shown in the figures below) or by the nucleation of a crack during deformation followed by its propagation.In fracture the elastic energy stored in the material is used for the creation of new surfaces (when the crack nucleates/propagates).Peak ahead

  • The following aspects need to be understood to comprehend plasticity*: External process parameters (Temperature, strain rate, etc.) Macroscopic and Microscopic aspects of plasticity Continuum and Discrete views of plasticity Plasticity in single crystals Plasticity in polycrystals Plasticity in multiphase materials Plasticity in nanomaterialsPath to understanding plasticity* Some of these aspects will be covered in the current chapter

  • One of the simplest test which can performed to evaluate the mechanical properties of a material is the Uniaxial Tension Test. The force/load applied is uniaxial.This is typically performed on a cylindrical specimen with a standard gauge length. (At constant temperature and strain rate). Other types of specimens are also used. Usually the specimen is polycrystalline.The test involves pulling a material with increasing load (force) and noting the elongation (displacement) of the specimen.Data acquired from such a test can be plotted as: (i) load-stroke (raw data), (ii) engineering stress- engineering strain, (iii) true stress- true strain. (next slide).It is convenient to use Engineering Stress (s) and Engineering Strain (e) as defined below as we can divide the load and change in length by constant quantities (A0 and L0). Subscripts 0 refer to initial values and i to instantaneous values.But there are problems with the use of s and e (as outlined in the coming slides) and hence we define True Stress () and True Strain () (wherein we use instantaneous values of length and area).Though this is simple test to conduct, a wealth of information about the mechanical behaviour of a material can be obtained (Modulus of elasticity, ductility etc.) However, it must be cautioned that this data should be used with caution under other states of stress.The Uniaxial Tension Test (UTT)0 initiali instantaneousSubscriptNote: quantities obtained by performing an Uniaxial Tension Test are valid only under uniaxial state of stress

  • The Tensile Stress-Strain CurveGauge Length L0Possible axesTensile specimenInitial cross sectional area A0Important NoteWe shall assume cylindrical polycrystalline specimens (unless otherwise stated)Note that L0 is NOT the length of the specimen, but the gauge length

  • Problem with engineering Stress (s) and Strain (e)!!Consider the following sequence of deformations:L02L0L0e12 = 1e23 = e13 = 0123[e12 + e23] = It is clear that from stage 1 3 there is no strainBut the decomposition of the process into 1 2 & 2 3 gives a net strain of . Clearly there is a problem with the use (definition) of Engineering strain (for large strains as in the example above). Hence, a quantity known as True Strain is preferred (along with True Stress) as defined in the next slide.

  • True Stress () and Strain ()The definitions of true stress and true strain are based on instantaneous values of area (Ai) and length (Li) and not on the original measures (as for engineering stress and strain). Ai instantaneous areaSame sequence of deformations considered before:L02L0L0 12 = Ln(2) 23 = Ln(2)13 = 0123[ 12 + 23] = 0With true strain things turn out the way they should!True strains are additive, engineering strains are not.

  • Schematic s-e and - curvesPoints and regions of the curves are explained in the next slide * It is better to determine the Youngs modulus from sound propagation experiments, than from UTT experiments.These are simplified schematics which are close to the curves obtained for some metallic materials like Al, Cu etc. (polycrystalline materials at room temperature).Many materials (e.g. steel) may have curves which are qualitatively very different from these schematics.Most ceramics are brittle with very little plastic deformation.Even these diagrams are not to scale as the strain at yield is ~0.001 (eelastic ~103) [E is measured in GPa and y in MPa thus giving this small strains] the linear portion is practically vertical and stuck to the Y-axis (when efracture and eelastic are drawn to the same scale).Schematics: not to scaleNote the increasing stress required for continued plastic deformation(the stress to cause continued plastic deformation is called flow stress)NeckPolycrystalline SpecimenLinear elastic material (obeys Hooks law)UTS- Ultimate Tensile Strength Subscripts: y- yield F, f- fracture u- uniform (for strain)/ultimate (for stress)

  • O unloaded specimenOY Elastic Linear Region in the plot (macroscopic linear elastic region)Y macroscopic yield point (there are many measures of yielding as discussed later) Occurs due to collective motion of many dislocations finally leaving the grain boundary or crystal surface. The stress at this point is called yield strength. [i.e. stress strength]YF Elastic + Plastic regime If specimen is unloaded from any point in this region, it will unload parallel to OY and the elastic strain would be recovered. Actually, more strain will be recovered than unloading from Y (and hence in some sense in the region YF the sample is more elastic than in the elastic region OY). In this region the material strain hardens flow stress increases with strain. This region can further be split into YN and NF as below.YN Stable region with uniform deformation along the gauge lengthN Plastic Instability in tension Onset of necking True condition of uniaxiality broken onset of triaxial state of stress (loading remains uniaxial but the state of stress in the cylindrical specimen is not).NF most of the deformation is localized at the neck Specimen in a triaxial state of stressF Fracture of specimen (many polycrystalline materials like Al show cup and cone fracture)Sequence of events during the tension testNotes:In the - plot there is no distinct point N and there is no drop in load (as instantaneous area has been taken into account in the definition of ) in the elastic + plastic regime (YF).The stress is monotonically increasing in the region YF true indicator of strain hardening.

  • Youngs modulus* slope of the OY (elastic part of the curve).Yield stress (or proof stress) stress corresponding to point Y.Ultimate Tensile Stress (UTS) point N (maximum) in s-e plot.Fracture stress stress corresponding to point F.Ductility measured as: (a) strain at fracture (in %), (b) % reduction in area. Resilience (area under the curve elastic portion- OY). Toughness (area under the curve total) has unit of Energy/volume [J/m3]. Strain hardening exponent (from