Interface Plasticity and Micro-Crack Extension in an Inclusion Reinforced Solid

Abstract

The transfer of stress between embedded fibres, inclusion type reinforcements and the surrounding matrix is achieved either by means of a bonding mechanism which can include chemical bonding and mechanical interlock or by means of a slip mechanism which can include friction between the matrix and the fibre inclusion. In many classical studies involving multiphase materials it is invariably assumed that the interface between the reinforcing inclusion and the surrounding matrix exhibits complete continuity (Eshelby, 1957; Hill, 1961; Willis, 1981; Mura, 1982). Such interfaces can, however, experience damage and delamination due to a variety of factors including thermoelastic mismatch between the matrix and the reinforcing fibre inclusion, moisture migration and accumulation at the interface, chemical incompatibility between the fibre inclusion and the matrix and amplification of interfacial stresses due to dynamic loads. The mechanical response of the resulting damaged interface can be influenced by the micro-mechanical behaviour of the contact. In this paper we examine the problem where the fibre inclusion-matrix interface exhibits non-linear interface effects characterized by processes such as Coulomb friction and dilatant plasticity with degradation of dilatancy which depends on plastic energy dissipation at the interface. The methodology is applied to investigate the manner in which matrix crack extension occurs at the boundary of a penny-shaped crack which is bridged by a cylindrical elastic fibre inclusion. In many classical studies involving multiphase materials it is invariably assumed that the interface between the reinforcing inclusion and the surrounding matrix exhibits complete continuity (Eshelby, 1957; Hill, 1961; Willis, 1981; Mura, 1982). Such interfaces can, however, experience damage and delamination due to a variety of factors including thermoelastic mismatch between the matrix and the reinforcing fibre inclusion, moisture migration and accumulation at the interface, chemical incompatibility between the fibre inclusion and the matrix and amplification of interfacial stresses due to dynamic loads. The mechanical response of the resulting damaged interface can be influenced by the micro-mechanical behaviour of the contact. In this paper we examine the problem where the fibre inclusion-matrix interface exhibits non-linear interface effects characterized by processes such as Coulomb friction and dilatant plasticity with degradation of dilatancy which depends on plastic energy dissipation at the interface. The methodology is applied to investigate the manner in which matrix crack extension occurs at the boundary of a penny-shaped crack which is bridged by a cylindrical elastic fibre inclusion. The analysis of the problem is approached via an incremental boundary element technique which accommodates both non-linear effects at the fibre inclusion-elastic medium interface and singular behaviour of the stress field at the crack tip.