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International Journal of Fracture, January 2014, Volume 185, Issue 1-2, pp 97-114.
Noel N. Nemeth.
National Aeronautics and Space Administration, Glenn Research Center, 21000 Brookpark Rd. MS 49–7, Cleveland, OH, 44135, USA.
Abstract
Models that predict the failure probability of monolithic glass and ceramic components under multiaxial loading have been developed by authors such as Batdorf, Evans, and Matsuo. These “unit-sphere” failure models assume that the strength-controlling flaws are randomly oriented, noninteracting planar microcracks of specified geometry but of variable size. The purpose of this paper is to describe a formulation of the probability density distribution of the orientation of critical strength-controlling flaws that results from an applied load. This distribution is a function of the multiaxial stress state, the shear sensitivity of the flaws, the Weibull modulus, and the strength anisotropy. Examples are provided showing the predicted response on the unit sphere for various stress states for isotropic and transversely isotropic (anisotropic) materials—including the most probable orientation of critical flaws for offset uniaxial loads with strength anisotropy. The author anticipates that this information could be used to determine anisotropic stiffness degradation or anisotropic damage evolution for individual brittle (or quasi-brittle) composite material constituents within finite element or micromechanics-based software.
Significance Statement:
Models that predict the failure probability of monolithic glass and ceramic components under multiaxial loading have been developed by authors such as Batdorf, Evans, and Matsuo. These “unit-sphere” failure models assume that the strength-controlling flaws are randomly oriented, noninteracting planar microcracks of specified geometry but of variable size. This “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. The purpose of this paper is to describe a formulation of the probability density distribution of the orientation of critical strength-controlling flaws that results from an applied load.
A companion paper on this topic, titled “Unit sphere multiaxial stochastic-strength model applied to a composite material” will be published in the Journal of Composite Materials. In that paper, results from finite element analysis of a fiber-reinforced matrix unit cell are 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. This methodology is mechanistic in that it is based on the physical characteristics of brittle fracture, and morphological in that it considers the size, shape, and orientation distribution of strength controlling defects or flaws. On that basis, it can also account for a material’s failure modes and direction of damage initiation from loading. It is capable of predicting an anisotropic material’s probability of failure under transient and cyclic loading. This innovation can be applied to materials such as graphite, coatings, or the individual brittle constituents of composite materials. It is intended for aerospace applications where trade-offs must be performed regarding safety, durability, and weight. The developed software will be used with finite element and micromechanics-based codes describing the behavior of composite materials. This incorporation will allow the full exercise of the new methodology, including incremental time/load steps, and fatigue of composite laminates and woven composite structures.
New paper by the authors can be found on this link : http://jcm.sagepub.com/content/early/2013/11/20/0021998313509865.abstract
