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(a)
(b)
True stress-strain curve
Hooke's
law region
x f
Engineering
stress-strain curve
UTS
U
x F
σ Y
L
Lüders
strain
Work
hardening
Necking
{ σ = k ε
m
}
-
σ
ε
s-e
σ LY
Extrapolation
σ s
σ i
Strain
Strain
1. 13 (a) Typical stress vs strain curve depicting yield point such as is
observed in steels 20 and (b) extrapolation of the plastic curve to elastic
line delineating the source ( σ s ) and friction ( σ i ) hardening terms. 22
constant strain-rate resulting in the observed load or stress drop. The stress
maximum known as the upper yield point is followed by deformation tak-
ing place within a relatively small region of the specimen (Luders band),
with continued elongation of the specimen by the propagation of the band
along the gauge section wherein the deformation is inhomogeneous. Once
the entire gauge section is traversed by the band, normal strain hardening
occurs with stress increasing and further deformation taking place. This dis-
tinct yield points (
￿ ￿ ￿ ￿ ￿ ￿
y ) in stress-strain curves can be represented as a sum of
a non-zero source hardening term (
σ
s ) and a friction hardening term which
represents the resistance experienced by the mobile dislocation (
σ
σ
i ) ,
,
[1.20a ]
=+
σ i
σ
σ
σ
σσ
s
y
i
similar to the well-known Hall-Petch equation:
k
y
,
[1.20b ]
σ y
=+
σ i
σ
σσ
i
d
 
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