A crack initiation and two debondings development at the interface of a circular rigid inclusion under uniform loading

Competition of a crack and two debondings 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 these debondings develop along the interface of the inclusion from the initial debondings and where 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 debondings develop and the crack occurs are determined. The magnitude of the load is also determined. As the criterion for debonding development and crack occurrence, 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 stress intensity factor of mode I just after crack occurrence is positive. As for the load, the constant load and the gradually increasing load from zero are considered. The stress analysis is carried out as a mixed boundary value problem with two stress and two displacement boundaries of plane elasticity. The rational mapping function of a sum of fractional expressions and complex stress functions are used for the stress analysis.