Thermodynamics of dislocations and shock compression of solids

A thermodynamic theory of dislocations is developed to provide a unified account of adiabatic shear and melting observed in metals and minerals under shock-wave compression. The theory contains two significant features. The first is the differentiation of irreversible energy changes from those of equilibrium energy functions. The second is the inclusion of dislocation dilatation. When applied to shock compression, it reveals a thermodynamic condition of instability based upon a principle of positive-entropy production for irreversible processes. This instability may be identified as adiabatic shearing or heterogeneous melting in the plane of maximum shear. The numerical results for selected materials from metals and minerals are in agreement with experimental observations, and show that the shear yielding becomes critical at about half the melting temperature and the dislocation density of about ${10}^{15}$/${\mathrm{m}}^2$.