PLASTIC DEFORMATION ï± Mechanisms of Plastic Deformation ï± The Uniaxial...
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- Slide 1
- PLASTIC DEFORMATION Mechanisms of Plastic Deformation The Uniaxial Tension Test Mechanisms of Plastic Deformation Mechanical Metallurgy George E Dieter McGraw-Hill Book Company, London (1988)
- Slide 2
- Plastic deformation Mechanisms / Methods by which a can Material can FAIL Fracture Fatigue Creep Chemical / Electro-chemical degradation Physical degradation Wear Erosion Microstructural changes Phase transformations Twinning Grain growth Elastic deformation Particle coarsening If failure is considered as change in desired performance*- which could involve changes in properties and/or shape; then failure can occur by many mechanisms as below. * Beyond a certain limit Corrosion Oxidation Slip Twinning
- Slide 3
- Slip (Dislocation motion) Plastic Deformation in Crystalline Materials TwinningPhase Transformation Creep Mechanisms Grain boundary sliding Vacancy diffusion Dislocation climb + Other Mechanisms Note: Plastic deformation in amorphous materials occur by other mechanisms including flow (~viscous fluid) and shear banding Plastic 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 (T g ) and by flow above T g. 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 rotation
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- Tension/Compression Bending Shear Torsion Common types of deformation TensionCompression Shear Torsion Deformed configuration Bending Note: modes of deformation in other contexts will be defined in the topic on plasticity Review
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- Mode I Mode III Modes of Deformation Mode II In 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
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- One of the simplest test which can performed to evaluate the mechanical properties of a material is the Uniaxial Tension Test. This is typically performed on a cylindrical specimen with a standard gauge length. (At constant temperature and strain rate). 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 (A 0 and L 0 ). 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 and 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 initial i instantaneous Subscript Note: quantities obtained by performing an Uniaxial Tension Test are valid only under uniaxial state of stress
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- The Tensile Stress-Strain Curve Stroke Load e s Gauge Length L 0 Possible axes Tensile specimen Initial cross sectional area A 0 Important Note We shall assume cylindrical specimens (unless otherwise stated)
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- Problem with engineering Stress (s) and Strain (e)!! Consider the following sequence of deformations: L0L0 2L 0 L0L0 e 12 = 1 e 23 = e 13 = 0 1 2 3 [e 12 + e 23 ] = It is clear that from stage 1 3 there is no strain But 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 Hence, a quantity known as True Strain is preferred (along with True Stress) as defined in the next slide.
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- True Stress ( ) and Strain ( ) A i instantaneous area The definitions of true stress and true strain are based on instantaneous values of area (A i ) and length (L i ).
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- Same sequence of deformations considered before: L0L0 2L 0 L0L0 12 = Ln(2) 23 = Ln(2) 13 = 0 1 2 3 [ 12 + 23 ] = 0 With true strain things turn out the way they should!
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- Schematic s-e and - curves Information gained from the test: (i)Youngs modulus (ii)Yield stress (or proof stress) (iii)Ultimate Tensile Stress (UTS) (iv)Fracture stress UTS- Ultimate Tensile Strength Subscripts: y- yield, F,f- fracture, u- uniform (for strain)/ultimate (for stress) Points and regions of the curves are explained in the next slide 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 (e elastic ~10 3 ) [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 e fracture and e elastic is drawn to the same scale). Schematics: not to scale Note the increasing stress required for continued plastic deformation Neck
- Slide 12
- O unloaded specimen OY 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. 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 length N 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 stress F Fracture of specimen (many polycrystalline materials like Al show cup and cone fracture) Sequence of events during the tension test Notes: 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
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- Comparison between true strain and engineering strain True strain ( ) 0.010.100.200.501.02.03.04.0 Engineering strain (e)0.010.1050.220.651.726.3919.0953.6 Comparison between Engineering and True quantities: Note that for strains of about 0.4, true and engineering strains can be assumed to be equal. At large strains the deviations between the values are large. In engineering stress since we are dividing by a constant number A 0 (and there is a local reduction in area around the neck) Engineering and true values are related by the equations as below. At low strains (in the uniaxial tension test) either of the values work fine. As we shall see that during the tension test localized plastic deformation occurs after some strain (called necking). This leads to inhomogeneity in the stress across the length of the sample and under such circumstances true stress should be used. Valid till necking starts
- Slide 14
- Yielding can be defined in many contexts. Truly speaking (microscopically) it is point at which dislocations leave the crystal (grain) and cause microscopic plastic deformation (of unit b) this is best determined from microstrain (~10 6 ) experiments on single crystals. However, in practical terms it is determined from the stress-strain plot (by say an offset as described below). True elastic limit (microscopically and macroscopically elastic where in there is not even microscopic yielding) ~10 6 [OA portion of the curve] Microscopically plastic but macroscopically elastic [AY portion of the curve] Proportional limit the point at which there is a deviation from the straight line elastic regime Offset Yield Strength (proof stress) A curve is drawn parallel to the elastic line at a given strain like 0.2% (= 0.002) to determine the yield strength. Where does Yielding start? In some materials (e.g. pure