  This paper describes an attempt to construct a first-principles theory of the
fracture toughness of crystalline solids. It is based on the thermodynamic
dislocation theory (TDT), which starts with the assertion that dislocations in
solids must obey the second law of thermodynamics. A second starting assumption
is that fracture is initiated when the tip of a notch is driven to undergo a
sharpening instability. The results of this analysis are developed in
comparison with measurements by Gumbsch and colleagues of the notch toughness
of both predeformed and non-predeformed tungsten crystals. The theory includes
a mathematical conjecture regarding tip dynamics at small dislocation
densities. Nevertheless, its predictions agree quantitatively with the
experimental data, including both brittle and ductile fracture, over a wide
range of temperatures, loading rates, and initial conditions.
