PSI - Issue 43

Jelena M. Djoković et al. / Procedia Structural Integrity 43 (2023) 95– 100 Author name / StructuralIntegrity Procedia 00 (2022) 000 – 000

96 2

1. Introduction The interface is a feature of the composite materials – reinforced and layered materials and systems. It is defined as "the area between the two different materials that has the characteristics of both materials". The structural properties of composite materials depend on behavior of the interface. The fracture mechanics phenomena at the interface between the two materials can be identified with a large number of problems in several areas such as: protective coatings, multilayer capacitors, thin layer systems/base for electronic packages, structural layered composites of various types and glued joints. In composite materials the interface plays an essential role, since it causes the discontinuity in materials' elastic and thermal characteristics. The interface crack problems, within the fracture mechanics, have been studied since the middle of the twentieth century, Williams (1959), Zak and Williams (1963), Erdogan (1965), England (1965), Malyshev and Salganik (1965), Rice and Sih (1965). Various analytical and numerical solutions were presented, which are in a very good agreement with results of experimental investigations, Comninou (1977), Comninou and Dundurs (1980). Resurgence of the interface crack research occurred with intensifying use and research of composite materials (CM) in the eighties of the last century, with special contribution by Banks-Sills and her several papers on the issue, summarized in a book, Banks-Sills (2018). Problems of a crack behavior at the interface between the substrate and the reinforcement were not the only ones considered, the behavior of a crack in the bulk (substrate - matrix) approaching the interface was studied, as well as delamination of the layered materials, Hutchinson, Mear and Rice (1987), He and Hutchinson (1989), Suo and Hutchinson (1990), Rice, Suo and Wang (1990), Hutchinson and Suo (1992). The fundamental contribution for development of this research was Rice (1988) paper, where the linear elastic fracture mechanics (LEFM) concept for the interface cracks was formulated. Comninou (1990) presented a review of papers on interface crack solutions, dividing them in three categories: the LEFM concept solutions, nonlinear and elasto-plastic considerations and experimental programs. It became extremely interesting and important to study how the interface influences the behavior of a crack propagating in its vicinity (the sub-interface crack). Such a crack can behave in several ways – it can cross the interface and continue to propagate in the material across it; the crack can deflect into the interface and continue to propagate along it; the crack can bounce back from the interface or it can even arrest at the contact with the interface. From the point of view of preserving the carrying capacity of a composite material, it is preferable for a crack to deflect into the interface than to penetrate it, since the latter would mean that the reinforcing component (e.g. fiber) was fractured. For the crack at the interface there are two possible manners of propagation - to continue to propagate along the interface, or to kink away from the interface in one of the materials constituting it. The danger of the latter case is that such a crack can impinge on the near reinforcement component and even fracture it. Which of all the mentioned cases of the crack behavior would occur depends on numerous factors, the most important ones are the characteristics of the two materials, the fracture toughness of the interface itself, the energy release rate(s) necessary for either of the mentioned cases of the crack behavior. Some researches were devoted to the so-called designing of the interface, by selecting the characteristics of the two materials constituting the interface in such a way that it would be possible to control the crack behavior and prevent the undesired case of the interface crack propagation. Attention of authors in this paper is devoted to the problem of a crack attacking the interface at an arbitrary angle. The prediction of the crack behavior, i.e. possible directions of the crack propagation, is based on application of the linear elastic fracture mechanics (LEFM) concept, where the stress intensity factor and the energy release rate are the two most significant parameters that characterize the material behavior around the crack tip. 2. Problem formulation The considered problem is presented in Figure 1. The interface lies between the material 1, which occupies the upper half-plane and material 2, which is in the lower half-plane. Elastic characteristics of the two materials are E m - the Young's moduli of elasticity,  m - the Poisson's ratios and  m - the shear moduli, m = 1, 2. When both materials are elastic and isotropic, the stress field for the problem of this type depends on the elastic constants, via the two Dundurs parameters, Dundurs (1969):