A Modified Strain-Energy Density Criterion Applied to Crack Propagation

An exact solution is presented to the problem of the crack-initiation direction by applying the minimum strain-energy density criterion in the case of a slant crack loaded uniaxially. The exact expressions of stresses, obtained from Muskhelishvili’s complex functions, are used in evaluating strain energy. Although the position of direction of the minimum density (ϑ_m) was accepted as the probable direction of the next kink of a propagating crack, the mean value of the strain-energy density is also introduced, instead of its minimum value, in the role of the critical quantity for crack initiation. Interesting results were derived for the behavior of this quantity concerning the phenomenon of bifurcation. The ratio of the mean-energy densities above and below the expected path of propagation is introduced as a second factor influencing the exact value of angle ϑ_m of propagation.