Micromechanical failure analysis of thin plain weave textile composites using the finite element method

A micromechanical analysis of the representative volume element (RYE) of a plain weave textile composite has been performed using the finite element method. A previous study by the authors extended a method, known as the Direct Micromechanics Method (DMM), to develop failure envelopes for a plain-weave textile composite under plane stress in terms of applied macroscopic stresses (σ_x,σ_y, ι_xy). In the current study, stress gradient effects are investigated, and it is assumed that the stress state is not uniform across the RYE. This is unlike most stiffness and strength models, which start with this premise that there exists an RVE, which is subjected to a uniform stress or strain. However, for textile geometries, nonuniform stress considerations are important, as the size of a textile RYE will typically be several orders of magnitude larger than that of a unidirectional RYE, for which many analysis techniques are developed. Thus a gradient across this dimension could be appreciable. The stress state is defined in terms of the well-known laminate theory load matrices [N], [M], i.e. applied loads and applied moments. Furthermore, structural stiffness coefficients analogous to the [A], [B], [D] matrices are defined. In this approach, these structural stiffness coefficients are computed directly from the micromechanical models, rather than making estimations based upon the homogeneous Young's modulus and plate thickness. Assuming that micro level failure criteria for the yarn and matrix are known, failure envelopes for a plain-weave textile composite have been constructed using microstresses from finite element analysis of the RVE. The predicted values of stiffness and strength compare well to expectable magnitudes. Failure of the fiber tow was the dominant mode of initial failure. The DMM failure envelope compared closely to the Tsai-Wu failure theory, but was more conservative in some areas.