Failure Criteria for Reinforced Materials

Failure of materials is often characterized as ductile yielding, brittle fracture, creep rupture, etc., and different criteria given in terms of different parameters have been used to describe different types of failure. Only criteria expressing failure in terms of stress are considered in what follows. The reinforcement here consists of long bars or fibres and complete bond between matrix and reinforcement is assumed so that no problems arising from incomplete transfer of adhesive and frictional forces are discussed. During loading, the reinforcement may yield, but total failure does not take place until the matrix, the continuous component of the composite, fails. When an isotropic matrix is reinforced as described above, the result is an anisotropic composite material. Even if the material is anisotropic, it usually exhibits a rather high degree of symmetry and such symmetries place certain restrictions on the form of the failure criteria for anisotropic materials. In section 2, some failure criteria for homogenous materials are reviewed. Both isotropic and anisotropic materials are described, and in particular the constraints imposed on the criteria from the symmetries orthotropy, transverse isotropy, and isotropy is considered. A flow rule for anisotropic materials is discussed in order to make it possible to distinguish between stress-states and strain-states. Failure criteria for reinforced materials are developed in section 3. While a composite consisting of matrix and reinforcement is inhomogenous, the introduction of some special assumptions concerning the behaviour of the reinforcement makes is possible to express failure criteria for reinforced materials as homogenous criteria. It is not necessary to compute the stress in both matrix and reinforcement, only the total stress in the composite are needed. Finally, in section 4, some of the criteria in sections 2 and 3 are compared with each other