Geology Reference
In-Depth Information
In these expressions the symbols are as used in Sect. 6.4.1 and Fig. 6.19 . The
relation ( 6.40a ) leads to a creep rate
vc 0 e tr
1 þ vs r
c ¼
ð 6 : 41 Þ
e tr 1
The initial creep rate (t ¼ 0) is therefore again c 0 v and the creep rate approa-
ches c 0 = s r ¼ r = h as t !1: The latter result,
c s ¼ r
h
ð 6 : 42 Þ
for the steady-state strain rate c s in recovery-controlled creep is the well-known
Bailey-Orowan equation (Bailey 1926 ; Orowan 1946 ). It is usually derived more
directly by equating hDc and rDt in the steady state. It should be reiterated here
that the Bailey-Orowan equation for the steady-state creep rate rests on the view
that the strain hardening or dislocation multiplication aspect is dependent only on
the strain and the recovery or dislocation elimination aspect dependent only on the
elapsed time through thermal activation; this extreme view has been criticized as
overlooking the possibility of strain-driven recovery or strain softening effects, the
incorporation of which would require a different approach (see summary of these
views in Roberts ( 1984 )).
The quantity s r can be viewed as a sort of relaxation time for primary creep.
When t s r ; ( 6.40a ) approximates the form
c tot ¼ c inst þ c 0 ln vs r þ r
h t
ð 6 : 43 Þ
where the term c 0 ln vs r represents an additional contribution to the strain during
primary creep above what would have been contributed in steady-state creep
alone. In principle, the evaluation of this term, of the initial creep rate c 0 v ; and of
the steady state creep rate c 0 = s r enables the three parameters c 0 ; v and s r in Eqs.
( 6.40a ) and ( 6.41 ) to be determined experimentally. However, it must be borne in
mind that the underlying theoretical model of a deformation controlled primarily
by mutual dislocation interaction is one in which the concepts of strain hardening,
recovery, and the thermally activated surmounting of the dislocation interaction
barriers have been incorporated in a more or less phenomenological way. Attempts
to interpret these concepts more mechanistically have been largely confined to the
case of steady-state creep, ( 6.42 ), to which the remaining discussion here will be
restricted, concentrating on the quantity r while assuming the form of ( 6.32 ) for h,
that is, h ¼ bG with b constant.
On the mutual dislocation interaction model the flow stress s is taken to be
equal to s d ¼ aGbq 2 and so r is given by
r ¼ o s
ot
¼ 1
2
s
q
o q
ot
ð 6 : 44 Þ
c
c
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