  In this paper, two improvements to the theory of transition from brittle to
ductile fracture developed by Langer 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 shows good agreement.
