Fiber waviness in textile composites and its stochastic modeling

Abstract

A generic stochastic theory of composite materials with continuous, randomly curved (imperfect) fiber reinforcements, recently developed by the present authors, enables one to quantify the effect of fiber deviations from the assumed “perfect” paths. The theory of random functions and stochastic extension of the orientational averaging approach are utilized to evaluate the mean values and standard deviations of the full set of anisotropic stiffness characteristics. The major advantage of this novel stochastic approach is its applicability to practically any fiber reinforcement architecture, from unidirectional to multidirectional, 3-D woven, and braided composites. Importantly, the approach does not ask for exact quantification of the reinforcement imperfections, but needs only a limited knowledge of the mean path of the reinforcement and standard deviation of the local tangent. Numerical examples illustrating applications of the stochastic theory developed consider three types of composites having (i) unidirectional, (ii) biaxial, 2-D braided, and (iii) 3-D orthogonally woven reinforcements. The first example concerns validation of the model. The second example is selected due to the commonly observed significant randomness of the fiber architecture in biaxially braided composite shell elements. The third example illustrates the effect of Z-yarn waviness (illustrated by optical microscopy) in orthogonally woven composites on their elastic characteristics.