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compressed parallel to a unique slip plane. The latter effects can be described
without reference to the boundaries of the specimen or system while the bound-
aries are involved in an essential way in describing the former.
In mechanical testing, one can generally regard the combination of specimen
and loading rams as a system subject to prescribed displacements or loads applied
at certain boundaries. The precise behavior within this system may involve either
of the types of instability just distinguished. Thus, in compression tests there is, on
the one hand, the possibility of a shape instability in which the initial alignment of
loading ram and specimen is replaced by a buckled configuration (for creep
buckling, see Hoff 1958 ) and, on the other hand, even if the gross alignment is
preserved, the distribution of deformation within the specimen itself may become
heterogeneous due to material instability, as in the formation of localized shear
zones. In extension testing, there is no question of buckling instability but necking
can occur when the loss of strength due to a virtual reduction in cross-sectional
area locally is less than the gain due to strain hardening associated with the locally
increased strain or strain rate. The corresponding shape instability in compression
is local bulging (Jonas and Luton 1978 ), (Jonas et al. 1976 ) but it tends to be less
important than buckling, especially when the deformation is strain-rate sensitive,
and it is less frequently observed than shearing instability in the material itself. The
analysis of the necking or bulging instability has been developed by many writers
since the classical paper of Considère ( 1885 ), especially in recent years in con-
nection with ''superplasticity'', the phenomenon that is defined macroscopically by
the ability of a specimen to undergo exceptionally large elongations without
failure resulting from excessive necking (see, for example, Hart et al. 1995 );
(Jonas et al. 1976 ; Reid 1973 , pp. 38-43). Of particular, interest in the latter
connection is the role of the strain rate dependence in determining the rate at which
necking develops; superplasticity depends more on the slowness of development
of a neck than on inherent instability against any necking at all.
Shearing instability within a deforming body is of potential importance in all
types of mechanical testing as well as in natural situations involving complex
stresses. It involves the localization of strain within a zone parallel to a surface of
pure shear or zero extensional strain, that is, to a characteristic or slip surface in the
sense of the mathematical theory of plasticity (Hill 1950 ); (Prager and Hodge
1951 ); (Hoffman and Sachs 1953 ). There have been many analyses of instability
based on the work done on a deforming specimen (Argon 1973 ; Backhofen 1972 ;
Evans and Wong 1985 ; Poirier 1980 ). However, such analyses do not take into
account the development of local heterogeneity of deformation during the onset of
instability and can fail to account for observations in torsion tests (Paterson 2007 ).
A full analysis needs to be based on continuum mechanics and perturbation theory,
such as set out by Fressengeas and Molinari ( 1987 ) and Shawki and Clifton ( 1989 ).
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