The theoretical conditions for brittle rupture were found with one single normal stress as the only mechanical variable. But, for the conditions of ductile rupture, experi-mental facts demand the specification of some stress states instead of a single stress and certain arbitrary stress functions were taken for this purpose. A theoretical formulation of the conditions for ductile rupture has not been made up to this date. Fundamentally, such problem would be approached from the dislocation theory, but quantitative treatment is difficult in the present state of this theory. Alternatively it may be possible to approach this problem from the view point of relaxation, should the basic phenomenon of strain hardening associated with ductile fracturing be well interrepted from this view point. It is believed that future studies along such lines will throw more light on the understanding of this problem. Yet, it was thought that if one considers the thermodynamic relation among various types of energy involved in ductile fracture instead of simply taking some arbitrary stress functions as criterion, the conclusions thus obtained would be helpful in understanding this problem, Thus this paper was written.
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