Analytic model for the line tension of a bowing dislocation segment

The resistance of a dislocation to bowing under stress governs the strength of the gamut of metallic material systems. This resistance is commonly referred to as the dislocation line tension (Γ) and is employed ubiquitously within continuum scale models of metal plasticity. Despite its significance, a unifying model for the line tension of a bowing dislocation segment, which has been analytically derived and independently reproduces simulation results, remains lacking. Here, we report a model for Γ of a curved, semicircular bowing dislocation segment. Upon applying our model to the operative stress of a Frank–Read dislocation source, we predict a prelogarithmic scaling of the Frank–Read source strength in agreement with existing simulation results. Moreover, in the limit of infinitesimal bowout we predict a prelogarithmic line tension factor which also agrees with theoretical analyses. Our model provides insight into the evolution of an arbitrarily oriented, stressed dislocation segment without resorting to numerical methods.