Some results on crack propagation in media with spatially varying elastic moduli

TLDR: In this article, energy release rates for cracks propagating in media with spatially varying elastic moduli, this variation being in a direction perpendicular to the crack growth direction, are derived for transient problems of semi-infinite cracks in infinite media for certain special forms of the variation in shear modulus.

Abstract: Energy release rates are calculated for cracks propagating in media with spatially varying elastic moduli, this variation being in a direction perpendicular to the crack growth direction. Results are given for transient problems of semi-infinite cracks in infinite media for certain special forms of the variation in shear modulus. Steady state crack propagation in a displacement loaded strip is also considered and it is shown by the use of a certain path independent integral that a simple formula for the energy release rate can be obtained for quite general variations in clastic moduli provided these variations are in a direction perpendicular to the crack. Other path independent integrals are derived which may be of use for transient crack tip stress analysis in strips in a similar way to that used in [4] for the homogeneous elastic problem.