A METHODOLOGY TO DERIVE THE IMPLICIT EQUATION OF FAILURE CRITERIA FORFIBROUS COMPOSITE LAMINATES

Strength failure criteria of fibrous composite laminates have been pro posed up till now in two different forms: (1) parametric formulations, in which the failure envelope is described by a parametric equation i n the stress or strain space and (2) implicit formulations, when the f ailure surface is defined by an implicit equation between failure stre sses and strains. A systematic connection between these two types of f ormulations has not yet been elaborated. Such a connection would permi t the combination of the flexibility of the parametric formulation wit h 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 prop osed to calculate the equivalent implicit equation of a criterion from its parametric expression. Although different failure modes may be de scribed simultaneously by the failure criterion, with dual kriging onl y 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 tensoria l failure criteria is also exposed. Finally, the methodology is applie d to a unidirectional graphite-epoxy and to [0/90] graphite-epoxy fabr ics.