Competition of crack and debonding at the interface of a circular rigid inclusion under uniform loading

Abstract

Competition of a crack and a debonding at the interface of a circular rigid inclusion in an infinite elastic body is analyzed under uniaxial loading in the x and y directions, respectively, and under biaxial uniform loading. It is investigated how the debonding develops along the interface of the inclusion from the initial debonding and where the debonding stops and a crack occurs from the tip of debonding. Particularly when there are both possibilities of the debonding development and of the crack occurrence from the tip of the debonding, it can be decided which phenomenon actually occurs. The angles at which the debonding develops and the crack occurs are determined. As the criterion for debonding development and crack occurrence at the debonding tip, strain energy release rates are used. Moreover, the restricting condition is that the normal stress at the interface ahead of the debonding tip is positive and the Mode I stress intensity factor just after crack occurrence is positive. As the loading, the constant load and the gradually increasing load from zero are considered. The stress analysis is carried out as a mixed boundary value problem of plane elasticity. As the stress analysis, the rational mapping function of a sum of fractional expressions and complex stress functions are used and closed form stress functions are derived.