Near Tip Field for Quasi-Static Crack Grouth along the Interface between a Porous-Ductile Material and a Rigid Substrate

A numerical asymptotic solution is provided for stress and velocity fields near the tip of an interface crack steadily propagating between a porous elastic-plastic material and a rigid substrate, under plane strain conditions. The constitutive description of the ductile material is defined by the Gurson model with constant and uniform porosity, both for isotropic hardening and for perfectly plastic behavior as a limit case. Solutions are obtained by numerically integrating the field equations within elastic and plastic asymptotic sectors and by imposing full stress and velocity continuity. If the hardening coefficient is lower than a critical value two distinct kinds of solution can be found in variable-separable form, corresponding to predominantly tensile or shear mixed mode. The elastic-perfectly plastic solution is constructed by means of an appropriate assembly of generalized centered fan and non-singular plastic sectors and an elastic unloading sector. The results show that the porosity mainly influences the stress fields of the tensile mode rather than the shear mode, due to the higher hydrostatic stress level. In particular, for high porosities the maximum of the hoop stress deviates from the interface line ahead of the crack-tip, causing possible kinking of the crack trajectory. The performed analysis of the debonding process of this kind of interface is essential for the determination of the overall strength, toughness and reliability of many advanced composite materials and structural components.