Progressive damage analysis of realistic woven composites using an automated conformal finite element mesh model

Abstract

An automated procedure for generating conformal finite element volume meshes of woven composite micro-geometries is developed in order to improve micro-mechanics analysis of woven composites. The Digital Element Approach (DEA) facilitates the generation of realistic fiber-level micro-geometries of woven composite unit cells using a dynamic relaxation technique. A triangular surface mesh is then created to represent the fiber-level unit cell at the meso-scale, or yarn-level. The unit cell domain is first discretized into a uniform cuboid element mesh using 8-node hexahedron elements. Numerical imperfections such as yarn interpenetrations or narrow gaps between yarns are then removed by an efficient intersection search algorithm. A sequential process of nodal rearrangement and element splitting at the yarn-yarn and yarn-matrix interface is employed to transform the initial mesh domain into a conformal finite element mesh. The conformal meshing ensures that the element boundaries match the meso-scale geometry boundaries perfectly and that the shape functions across shared element faces are compatible. The quality of each element is examined and a mesh repair algorithm is employed to improve element quality if required. The mesh generation strategy uses realistic micro-geometries with irregular cross sections and yarn paths, and hence no idealized assumptions are made, which does not limit its application – it can be used for any general woven architecture or geometry. Next, the stress and failure response of the unit cell meshed models is studied using a progressive damage model that is implemented using a user-defined material subroutine. The yarns in the woven composite domain are assumed to be comprised transversely isotropic elements while the surrounding polymeric matrix is assumed to be purely isotropic. Hence the yarn elements can be modeled as unidirectional composite laminates using this meso-scale idealization. The local orientations of the yarn elements are determined according to the yarn central path from their micro-geometry. A recursive stiffness degradation method is employed to model damage evolution in yarns, while damage initiation is governed by the maximum strain criteria. This damage evolution model also takes into account combined failure modes. In case of the matrix, the maximum stress criterion is used with the instant stiffness degradation method. The validity of the model is established by comparing the results with available experimental and numerical data for two very different unit cells. Finally, a purpose-driven design study is performed. A comparative analysis is presented where three different woven architectures – 3D-woven layer-to-layer, 3D-woven orthogonal and multi-layer 2D-woven unit cells – with similar overall fiber volume fraction and yarn fiber volume fraction are analyzed. The in-plane stiffness and strength results are compared and discussed. Failure mechanisms are discussed in detail and validated using experimental observations in literature.