# chapter 2: plasticity

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```CHAPTER 2: PLASTICITY
CHAPTER 2: PLASTICITY
AISI 1040 Steel
True stress-true strain curves are obtained by
converting the tensile stress and its
corresponding strain values into true stress
and extending the curve.
Yield stress varies 250-1100MPa
Total Strain varies between 0.38-0.1
Properties of steel depend on heat
treatment and quenching produces a hard
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.
CHAPTER 2: PLASTICITY
Volume stays constant
The incremental longitudinal strain:
CHAPTER 2: PLASTICITY
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.
CHAPTER 2: PLASTICITY
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.
CHAPTER 2: PLASTICITY
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
CHAPTER 2: PLASTICITY
CHAPTER 2: PLASTICITY
CHAPTER 2: PLASTICITY
CHAPTER 2: PLASTICITY
CHAPTER 2: PLASTICITY
CHAPTER 2: PLASTICITY
```