Brittle versus ductile behavior

Formulating a criterion to discriminate between brittle and ductile response based on atomistic features of the solid has been a long sought after goal in the mechanics of solids. At the phenomenological level, theories have been developed that characterize the two types of behavior in terms of cleavage of the crystal or the nucleation and motion of dislocations[138, 139], We review here the basic elements of these notions. 

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Chip Formation (Abrasive Process), Fig. 2 Brittle material behavior versus ductile material behavior in grinding (based on Salje and Mohlen 1987 Klocke 2009)... 

To begin, assume the stress-versus-strain behaviors for fiber and matrix phases that are represented schematically in Figure 16.9a in this treatment we consider the fiber to be totally brittle and the matrix phase to be reasonably ductile. Also indicated in this figure are fracture strengths in tension for fiber and matrix, o-f, and a-, respectively, and their corresponding fracture strains, and e, furthermore, it is assumed that eln > /, which is normally the case. 

Several cautions are, however, in order. Polymers are notorious for their time dependent behavior. Slow but persistent relaxation processes can result in glass transition type behavior (under stress) at temperatures well below the commonly quoted dilatometric or DTA glass transition temperature. Under such a condition the polymer is ductile, not brittle. Thus, the question of a brittle-ductile transition arises, a subject which this writer has discussed on occasion. It is then necessary to compare the propensity of a sample to fail by brittle crack propagation versus its tendency to fail (in service) by excessive creep. The use of linear elastic fracture mechanics addresses the first failure mode and not the second. If the brittle-ductile transition is kinetic in origin then at some stress a time always exists at which large strains will develop, provided that brittle failure does not intervene. 

Rice, J. R. and Thomson, R. (1973), Ductile versus brittle behavior of crystals,, , 73-97. 

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