A Study of Crack-Inclusion Interaction Using Moiré Interferometry and Finite Element Analysis

Abstract

Failure of composite materials is intrinsically linked to the fundamental problem of a matrix crack interacting with a second phase inclusion. In this work, the critical issue of matrix-inclusion debonding in the presence of a nearby crack is addressed experimentally and numerically. Optical measurement of surface deformations in the vicinity of a crack-inclusion pair is carried out using moiré interferometry. The measurements are used to validate an approach for simulating evolution of inclusion-matrix debonding. The numerical model is subsequently used to parametrically study crack-inclusion interactions. In the first phase of this work, a process based on microlithography is developed for creating master gratings on silicon wafers. Two methods are then developed to transfer gratings to polymeric specimens. Edge cracked epoxy beams, each with a cylindrical glass inclusion ahead of the crack tip, are fabricated to experimentally model crack-inclusion interactions. A moiré interferometer for mapping displacement fields in the crack-inclusion vicinity is developed. Debonding of an inclusion from the surrounding matrix is detected successfully by the interferometer. The measured displacements are analyzed to estimate surface strains and study the evolution of strain fields associated with crack-inclusion debonding phenomenon. The associated effects on fracture parameters namely, crack mouth opening displacements (CMOD), crack mouth compliance, mode – I stress intensity factors (SIF) and energy release rates (ERR), are extracted. A sharp rise in crack mouth compliance values and strains in the close vicinity of the inclusion due to debonding is observed. Next, a finite element model is developed to simulate the experimentally observed behavior. Interfacial debonding between the matrix and the inclusion is simulated using the element stiffness deactivation method. A failure criterion based on a critical radial stress is shown to capture the onset and progression of debonding and finite element results are in good agreement with measurements. A follow up parametric study is performed to examine effects of inclusion size and inclusion proximity to the crack tip. The results show that debonding is delayed as the inclusion size increases for a constant L/d ratio where L and d are crack tip-inclusion distance and inclusion diameter, respectively. For a constant L, debonding occurs at lower loads for larger inclusions along with higher crack mouth compliance following inclusion-matrix debonding.