The interaction of the plane stress mode i crack with an inhomogeneity undergoing a stress-free transformation strain

Thin composite films containing inclusions are commonly being developed as corrosion resistant, wear resistant coatings and so forth. For systems where the composite film is under residual stresses properly designed, a controlled debonding process of the inclusions can be used to reduce the stress levels in the film lowering the risk of through cracks in the film as well as the risk for the film's delamination from the substrate. In this paper, on the basis of the Eshelby equivalent inclusion theory, a general solution is derived by treating an inhomogeneous inclusion as a homogeneous one with transformation strain for the configuration force (CF) and stress intensity factor (SIF) between mode I crack and an inhomogeneous inclusion of arbitrary shape which undergoes some degree of stress-free transformation strain under plane stress loading conditions. Then the CF associated with the transformation is calculated from the work done during the transformation, from which some simplified approximate formulae are also presented for common inclusion shapes in order to provide a quick estimate for the effects of inclusion shape, location and size on the CF of plane stress model I crack. In comparison to conventional numerical approaches, the present solution provides a novel approach to explain the behavior of crack deflection/penetration and can be used for the optimization design of the composite films.