Invariant integrals of crack interaction with an inhomogeneity

The crack growth can be shielded or anti-shielded by a specific inhomogeneity occurring in materials. This can be estimated from the change of the crack tip invariant Jk-, M-, L-integrals due to the presence of inhomogeneity. The closed-form solutions of the change of invariant integrals are derived for a crack interacting with the near crack-tip inhomogeneity by using the concept of material configurational forces. Two simple problems such as a phase transformation or an inhomogeneous inclusion interacting with a main crack in two-dimensional solids are solved in explicit form. The present formulations and methods are validated by the alternative weight functions or finite element analysis. It is concluded that the total components of configurational forces given by integration over the inhomogeneity can be used to evaluating the shielding or anti-shielding effect of various inhomogeneities e.g., inclusion, plasticity, dislocation, phase transformation, residual strain, on the crack growth in fracture mechanics.