  We study the effects realistic fracture criteria have on crack morphology
obtained in numerical simulations with a stochastic discrete element method.
Results are obtained with two criteria which are consistent with the theory of
elasticity and compared with previous results using the original criterion,
chosen when the method was first published, The conventional choice has been to
consider the combined loading as an interaction between bending and tensile
forces only, leaving out shear forces altogether. Moreover the combination of
bending and tension used in the old criterion is correct only for plastic
deformations. Our results show that the inclusion of shear forces have a
profound effect on crack morphology. We consider two types of external loading,
torsion applied to a circular cylinder and tension applied to a cube. In the
tensile case, the exponent which characterises scaling of crack roughness with
system size is found to be very close to the experimental value zeta = 0:5 when
realistic fracture criteria are used. In the present calculations we obtain
zeta = 0.52, a value which remains constant for all disorders. It is proposed
that the small-scale exponent zeta = 0.8 appears as a consequence of cleavage
between crystal planes and consequently requires a different fracture criterion
than that which is used on larger scales.
