Mechanism of yielding in dislocation-free crystals at finite temperatures—Part I. Theory

Abstract

A new mechanism of dislocation generation that can be activated suddenly above a critical temperature is proposed. Unlike dislocation generation by Frank-Read type sources, this process is a thermally driven, stress-assisted cooperative instability of many dislocation loops (dipoles in two dimensions). The dislocation loops are formed by thermal fluctuations and are sub-critical in size at low temperatures. The small plastic strain associated with the loops invokes an effective decrease in the moduli that describe the linear relation between the applied stress and the total strain. The self-energy of a loop which forms in the presence of other loops is proportional to these effective moduli and, consequently, it is lower than the energy of an isolated loop. As the temperature increases, the density of thermally generated loops increases and the concomitant lowering of the effective moduli and the self-energy provides a feedback for its further increase. Ultimately, above a critical temperature, the free energy of the loops becomes negative and a collective unstable expansion of many loops occurs. In a solid which is not loaded, this instability corresponds to the Kosterlitz-Thouless model of a defect-mediated phase transition that occurs just below the melting temperature. However, under large applied loads, the instability appears well below the melting temperature. Above the critical temperature, the density of glissile dislocations increases precipitously and extensive yielding occurs. This paper analyzes this mechanism in two dimensions where dislocation loops are replaced by dipoles.