Geology Reference
In-Depth Information
twinning if sufficiently penetratively distributed (Paterson
1969
) but often it is
probably better viewed as a special type of heterogeneity of deformation
associated with the slip system on which it is based, contributing somewhat to a
reduction in the number of slip systems required.
5. Minor accommodation requirements may be met by elastic strains accompa-
nying variations in stress within the grains.
In the discussion, so far it has been implicit that the crystallographic orientation
distribution of the grains is more or less random and the shape roughly equiaxed.
When strong preferred orientation is introduced, such as through large strain or
recrystallization, the accommodation requirements are relaxed gradually as the
single crystal limit is approached. Also accommodation requirements become
somewhat less stringent as the grain shape becomes highly anisotropic, another
factor that may be significant in highly deformed, foliated or lineated materials
(Kocks and Canova
1981
; Mecking
1981b
).
6.8.3 Grain Boundary Effects and Grain Size Dependence
In a homogeneously deforming polycrystalline aggregate or in an aggregate in
which the heterogeneity scales with the grain size, there would not necessarily be
any grain size dependence of the flow stress. Even the presence of the geometri-
cally necessary dislocations need not lead to a grain size dependence (Mecking
1981b
). However, in practice, it is widely observed that the flow stress tends to be
higher for small grain sizes in aggregates deforming by intragranular crystal
plasticity, especially in the athermal regime. This effect indicates that the presence
of the grain boundaries has itself a strengthening influence, apart from any effect
associated with the occurrence of multiple slip.
The grain boundary strengthening effect is usually attributed in some way to the
accumulation of dislocations in the neighborhood of the boundary, presumably due
to there being an impediment to the accommodation of the dislocations in this
region because of the influence of the contiguous grain or to there being interaction
with
other
dislocations
already
accumulated
there.
The
effect
is
commonly
expressed through an additive term in the flow stress r
;
as follows:
r
¼
r
0
þ
kd
m
where r
0
is the contribution to the flow stress of the aggregate purely from the
multiple slip within the grains, d the grain size, and k, v constants. The value of v is
commonly put as
2
;
following Hall (
1951
) and Petch (
1953
); see other references in
Friedel (
1964
, p. 267). However, this value is often not well defined experimen-
tally owing to the practical difficulty of keeping other factors constant while
preparing specimens of different grain size, and a value of m
¼
1issaidtobe
equally valid in many cases (for example, Dollar and Gorczyca
1981
; for example,
Kocks
1970
; Mecking
1981b
).
