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2. CHAPTER 2: PLASTICITY AISI 1040 Steel Yield stress varies 250-1100MPa
Total Strain varies between
Properties of steel depend on heat treatment and quenching produces a hard martensitic structure which is gradually softened by tempering at higher temperatures. The annealed structure is ductile but has low yield stress.
The ultimate tensile stresses are marked by arrows.
After these points plastic deformation becomes localized (called necking) and the engineering stresses drop because of the localized reduction in the cross sectional area. However true stress continues to rise because the cross sectional area decreases and material work hardens in the neck region.
True stress-true strain curves are obtained by converting the tensile stress and its corresponding strain values into true stress and extending the curve.

3. CHAPTER 2: PLASTICITY Volume stays constant
The incremental longitudinal strain:

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5. CHAPTER 2: PLASTICITY n<1 Parabolic hardening
Translate it upward by assuming yield stress is equal to σ0 then equation becomes:
n is called strain hardening exponent and depends on the nature of the material, the temperature at which it is work hardened and strain.
n varies between 0.2 and 0.5 and K is in between G/100 and G/1000.
The equations predict a slope of infinity for ε=0 which does not conform experimental results.
The equations imply that σ→∞ when ε→∞ ( We know this is not correct and that experimentally a saturation of stress occurs at higher strains.

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The fact that some equations reasonably approximate the stress-strain curves does not imply that they are capable of describing the curves in a physically satisfactory way. There are two reasons for this: (1) In the different position of stress-strain curves, different microscopic processes predominate. (2) Plastic deformation is a complex physical process that depends on the path taken; it is a thermodynamic state function. The accumulated is not uniquely related to the dislocation structure of the material.
Ludwik-Hollomon is the most common representation of plastic response. When n=0, it represents ideal plastic behavior (no work-hardening). More general forms of this equation, incorporating both strain rate and thermal effects, are often used to represent the response of metals; in that case they are called constitutive equations. The flow stress of metals increases with increasing strain rate and decreasing temperature because thermally activated dislocation motion is inhibited.

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8. CHAPTER 2: PLASTICITY A=0.2% offset yield stress
B and C= upper and lower yield point
D=proportional limit (stress at which the curve deviates from linearity)
D’=UTS
E=rupture stress
F=Uniform Strain
Beyond F necking starts
G is strain to failure.
Elastic energy absorbed=Resilience=area under elastic portion of the curve
Work of fracture= Total area under the curve

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BAUSCHINGER EFFECT

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