Theory of transition from brittle to ductile fracture

In this paper, two improvements to the theory of transition from brittle to ductile fracture developed by Langer [J. S. Langer, Phys. Rev. E 103, 063004 (2021)2470-004510.1103/PhysRevE.103.063004] are proposed. First, considering the drastic temperature rise near the crack tip, the temperature dependence of the shear modulus is included to better quantify the thermally sensitive dislocation entanglement. Second, the parameters of the improved theory are identified by the large-scale least-squares method. The comparison between the fracture toughness predicted by the theory and the values obtained in Gumbsch's experiments for tungsten at different temperatures [P. Gumbsch et al., Science 282, 1293 (1998)10.1126/science.282.5392.1293] shows good agreement.