  We address analytically and numerically the problem of crack path prediction
in the model system of a crack propagating under thermal loading. We show that
one can explain the instability from a straight to a wavy crack propagation by
using only the principle of local symmetry and the Griffith criterion. We then
argue that the calculations of the stress intensity factors can be combined
with the standard crack propagation criteria to obtain the evolution equation
for the crack tip within any loading configuration. The theoretical results of
the thermal crack problem agree with the numerical simulations we performed
using a phase field model. Moreover, it turns out that the phase-field model
allows to clarify the nature of the transition between straight and oscillatory
cracks which is shown to be supercritical.
