Computational micro-mechanics for probabilistic failure of fiber composites in tension

Abstract

The design of a composite from fiber and matrix properties requires micro-mechanics modeling of strength. The strength of a composite has an inherent variability which is a manifestation of the underlying stochastic failure processes of the constituent fiber and matrix. For fiber-dominated tensile composite failures, the failure process starts with the breaking of weak fibers. The initial failure sites are isolated by micro-redundancy provided by local load-sharing of the neighboring fibers. Higher applied load leads to progressive clustering of fiber breaks which ultimately cause macroscopic failure. Probability modeling of the failure sequences of the fiber breaks and the spatial geometry of the clustering of the sites resulted in the local load-sharing model. This model requires numerical evaluation because it contains an extremely large matrix of the transitional probability of the occurrences of the cluster sites. This paper provides an accessible computational implementation of this model for computer platforms ranging from personal computers to supercomputers. The computational algorithm was made general by a three-section piecewise-linear, tri-modal model for fiber statistics. This tri-modal local load-sharing software numerically computes the cumulative distribution function (CDF) of the composite strength by using a very wide range of fiber statistics as input. This CDF can be used to analyze composite strength data in testing, to predict size effects in design, to monitor processing quality, and to quantify the reliability of composite structures.