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which depends on the elastic modulus of the material and, in a simple uni-
axial loading case,
σ
,
[1.2 ]
ε
=
E
E
is the stress (load per unit area), E the modulus of elasticity (also
known as Young's modulus) and
where
σ
E is the instantaneous elastic strain (change
in length per unit length). Anelastic strain is time dependent, completely
reversible and generally small in magnitude - albeit non-negligible in some
cases - as will be discussed in detail in Chapter 3. On the contrary, plas-
tic strain is permanent and remains even after removal of the stresses; it is
generally time- and rate-dependent. A typical stress vs strain curve under
uniaxial loading is shown in Fig. 1.2a 8 and the important design parameters
are the yield strength, tensile strength, uniform elongation and ductility or
total elongation to fracture. The deformation beyond the elastic limit obeys
a power relation between the true stress (
ε
σ
) and the true plastic strain (
ε
p ) :
σ
=
K (
ε
p ) n ,
[1.3 ]
where K is the strength coeffi cient and n is the strain-hardening exponent.
The area under the stress-strain curve represents the energy to deformation
and fracture (referred to as resilience and toughness in the elastic and plastic
regime, respectively), and this grades a material as brittle or ductile (Fig. 1.2b).
The various mechanical properties of a material are also rate dependent and
the fl ow stress is often characterized by the strain-rate sensitivity ( m ):
m
.
[1.4 ]
A
σ
ε
T
ε
,
￿ ￿ ￿ ￿ ￿ ￿
The higher the n value, the higher is the uniform elongation, while a higher
m value means a higher total elongation to fracture. The maximum possible
value for m is unity which corresponds to viscous fl ow as seen in fl uids, and
this is generally noted in metals and ceramics at relatively high tempera-
tures and at low strain-rates (or stresses).
Time dependent plastic deformation that occurs under constant load or
stress (creep) becomes important above homologous temperature ( T / T M >
0.4, where T M is the melting point in absolute temperature). The reader is
referred to Chapter 3 for more detail on the underlying creep mechanisms
and phenomenological descriptions of the creep rupture life. A typical creep
curve is illustrated in Fig. 1.3 and design allowances are limited to the total
strain accumulation in the primary and secondary regimes. Thus the strain at
any instant of time is given by the sum of instantaneous recoverable elastic
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