Phenomenological Theories
Phenomenological theories of creep have to take account of the flow of materials in four stages, which are generally designated in the following manner: 1. An immediate extension, which is elastic. 2. A stage during which the rate of flow decreases, whic
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PART II I
1. lntroduction
Phenomenological theories of creep have to take account of the flow of materials in four stages, which are
gene~
ally designated in the following manner: 1. An immediate extension, which is elastic. 2. A stage during which the rate of flow decreases, which is transient. 3. A stage during which it is constant, called stationary. 4. A final stage in which it accelerates,called rupture. The passage from stage three to four is through a point of inflection in the strain-rate curve. This has received very little attention. The difficulties, particularly the ambiguity in the interpretation of experimental data and that involved in the choice of a suitable constitutive equation for the three states of creep, excepting the first are pointed out by Rabotnov[l]. Each of these states is characterised by two parameters- one for the measure and the other for irreversibility. Also, since the creep strain rate depends on the stress and temperature at a given structural state, it is not the total strain, but the
B. R. Seth, Transition Problems of Aelotropic Yield and Creep Rupture © Springer-Verlag Wien 1970
Cha.p.." l i I - Creep Rupture
26
total rate of creep strain, which is significant. It can therefore, be expected that a generalised
measure~concept,
in which
the two parameters are experimentally determined, may give a better insight into creep behaviour. The nature of strain in the four stages described above is different in each case. But for the elastic part the remaining three are essentially non-linear in character.We should therefore have a form of the strain measure which can be used for all the stages. The generalized measure, developed and utilized in a num ber of recent papers [2,3] , can be profitably used for such a global representation of creep, particularly in view of a recent paper by R. Hill
[4] ,
in which he shows that the constitutive
inequalities for elastic and plastic deformations depend upon the strain measure used.
2. Oeneralized Strafn Measures It has been shown that for the uni-axial case a generalized measure, which includes all the known measures of Cauchy, Green, Almansi, Hencky and others is given by [2]
1
(3.2.1) when
n
JJ.=
is the measure, m
n
[~ {-t-(y) I]
m
the irreversibili ty index and
1
0 ,
l
are the initial and strained length of the rod respectively. These can be positive, negative or zero, integral or fractional. For the zero value we get
Hencky, or the logarithmic
meas-
Generalized Strain Measures
27
sure, (3.2.2)
n
is positive or negative according as
~
is referred to the
strained or unstrained framework. Since for actual measurements in an experiment the initial length is the reference frame we can put
n
=- q., q..
being positive, and get (3.2.3)
In the cartesian framework we can readily write down the generalized measure in terms of any other measure. For example, in terms of the principle Almansi strain components ~~L the generalized principal strain components (3.2.4)
Having known the principal measures the com
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