Unit-sphere multiaxial stochastic-strength model applied to a composite material

Abstract

The Batdorf “unit-sphere” methodology has been extended to predict the multiaxial stochastic strength response of anisotropic (specifically transversely isotropic) brittle materials, including polymer matrix composites, by considering (1) nonrandom orientation of intrinsic flaws and (2) critical strength or fracture toughness changing with flaw orientation relative to the material microstructure. The equations developed to characterize these properties are general and can model tightly defined or more diffuse material anisotropy textures describing flaw populations. In this paper, results from finite element analysis of a fiber-reinforced matrix unit cell were used with the unit-sphere model to predict the biaxial strength response of a unidirectional polymer matrix composite previously reported from the World-Wide Failure Exercise. Findings regarding stress–state interactions, thermal residual stresses, and failure modes are also provided. The unit-sphere methodology is an attempt to provide an improved mechanistic basis to the problem of predicting strength response of an anisotropic and composite material under multiaxial loading as compared to polynomial interaction equation formulations. The methodology includes consideration of strength scatter to predict material probability of failure, shear sensitivity of flaws, and accounting for multiple failure modes regarding overall failure response.