Environmental Engineering Reference
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of the material prior to deformation. Curve A is a typical creep curve
observed in several materials. The curve consists of a normal primary stage
characterized by a decreasing strain rate, a secondary stage where defor-
mation proceeds at a constant rate and a tertiary stage where the material
deforms at increasing strain rates with time/strain leading to eventual fail-
ure. Such creep curves are usually exhibited by annealed metals and cer-
tain alloys (known as class-M or class-II type). In comparison to curve A,
curve B depicts a very small primary creep stage. In fact, it appears as if
the material enters the steady state immediately. Such a type of curve is
obtained when the substructure pertaining to creep remains constant such
as in some alloys (known as class-A or class-I type). Curves of type C are
obtained from materials that have been previously crept at a higher stress.
The increasing creep rate over the primary creep stage is due to the recov-
ery of the substructure corresponding to the previous steady-state condi-
tion. The sigmoidal type of creep curve (curve D) suggests the nucleation
and spread of slip zones until a steady state is achieved. Such creep behavior
has been exhibited by certain dispersed phase alloys.
In certain cases, it is possible that the total creep curve is in the primary
stage, and the secondary and tertiary creep stages are not attained at all.
Such a curve has been seen for materials tested at low temperatures (
T
< 0.3
T
M
) where effects due to diffusion are suppressed (no annealing or recov-
ery) and the entire deformation is due to work hardening (dislocation con-
trolled). The primary creep strain rate tends towards a value of zero at long
periods. The strain hardening due to long range dislocation interactions pre-
cludes a constant rate of creep deformation. The absence of recovery pro-
cesses due to the low test temperatures allows the strain hardening process
to be the creep-controlling mechanism. This eventually leads to an increase
in strength of the material to a value greater than the applied stress value.
Further deformation can only occur under the application of a higher stress
or in the presence of a higher temperature. Such a behavior is described as
an exhaustion creep behavior and the creep curve can be described by a
logarithmic creep equation.
4
3.2
Standard creep equations
On the basis of his studies, Andrade
1
proposed that the creep curve could be
described by an equation of the form
(
)
13
t
,
[3.1]
κ
t
0
1
β
t
13
)
e
εε
=
ε
+
where
are constants. The transient
creep, that is the primary creep stage, is described by
ε
is the strain,
t
is the time and
β
and
κ
rep-
resenting the secondary stage describes an extension per unit length that
β
; the constant
κ
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