A Tow-Level Progressive Damage for Simulating Carbon-Fiber Textile Composites: Interim Report

A numerical approach to model the elasto-plastic and tensile damage response of tri-axially braided carbon-fiber polymeric-matrix composites is developed. It is micromechanically based and consists of a simplified unit cell geometry, a plane-stress tow-level constitutive relationship, a one-dimensional undulation constitutive law, and a non-traditional shell element integration rule. The braided composite lamina is idealized as periodic in the plane, and a simplified three-layer representative volume (RV) is assembled from axial and braider tows and pure resin regions. The constituents in each layer are homogenized with an iso-strain assumption in the fiber-direction and an iso-stress condition in the other directions. In the upper and lower layers, the fiber-direction strain is additively decomposed into an undulation and a tow portion. A finite-deformation tow model predicts the plane-stress tow response and is coupled to the undulation constitutive relationship. The overall braid model is implemented in DYNA3D and works with traditional shell elements. The finite-deformation tow constitutive relationship is derived from the fiber elasticity and the isotropic elasto-plastic power-law hardening matrix response using a thermodynamic framework and simple homogenization assumptions. The model replicates tensile damage evolution, in a smeared sense, parallel and perpendicular to the fiber axis and is regularized to yield mesh independent results. The tow-level model demonstrates reasonable agreement, prior to damage, with detailed three-dimensional FE (finite element) elasto-plastic simulations of aligned, periodically arranged, uni-directional composites. The 3-layer braid model response is compared with predictions obtained from detailed micromechanical simulations of the braid's unit cell in uni-axial extension, shear, and flexure for three braid angles. The elastic properties show good agreement as does the non-linear response for loadings dominated by the axial tows. In loadings dominated by the braider tow response, the absence of a non-linear undulation model deteriorates the agreement. Nonetheless, the present approach is applicable to a broad range of tri-axially braided composites as well as for unidirectional composites, but presently lacks any compressive failure mechanisms and an adequate non-linear undulation model