A methodology to derive the implicit equation of failure criteria for fibrous composite laminates

Strength failure criteria of fibrous composite laminates have been proposed up till now in two different forms: (1) parametric formulations, in which the failure envelope is described by a parametric equation in the stress or strain space and (2) implicit formulations, when the failure surface is defined by an implicit equation between failure stresses and strains. A systematic connection between these two types of formulations has not yet been elaborated. Such a connection would permit the combination of the flexibility of the parametric formulation with the simplicity of the implicit criterion. In previous papers [8,10] a methodology to derive failure envelopes of composite laminates based on uniaxial failure stresses, physical considerations and/or failure modes has been elaborated. Up till now, only the parametric expression of the criterion has been derived. In this paper, a procedure is proposed to calculate the equivalent implicit equation of a criterion from its parametric expression. Although different failure modes may be described simultaneously by the failure criterion, with dual kriging only one analytical equation is necessary in the stress or in the strain space. This procedure is general and describes the failure of various kinds of composite laminates. The practical relationship with tensorial failure criteria is also exposed. Finally, the methodology is applied to a unidirectional graphite-epoxy and to [0/90] graphite-epoxy fabrics.