Porous materials reinforced with short fibers: Unbiased full-field assessment of several homogenization strategies in elasticity

Abstract

This work is concerned with the micromechanical modeling of porous short fiber-reinforced composites considered as three-phase microstructures: cavities and short fibers embedded in a matrix phase. Several homogenization strategies are evaluated in isothermal linear elasticity: two-level, two-step and direct Mori-Tanaka (MT) models. Unbiased evaluation of the methods is conducted based on full-field finite element (FE) analyses. No Eshelby-based analytical mean-field models are used. A parametric study for a porous thermoplastic polymer matrix reinforced with short glass fibers is carried out, for both fixed and distributed fiber orientations. The predictions of the various homogenization strategies are compared against reference FE results of the original three-phase composites. The reported numerical simulations are in 2D plane stress, but provide nevertheless insight into 3D situations. There are three main findings. (1) The best predictions are obtained with a two-level strategy, where in the lower level the actual porous matrix is homogenized, and in the upper level, fibers are embedded in the homogenized matrix. (2) The direct MT model can generate nonphysical predictions: effective properties outside the Voigt and Reuss estimates, and non-symmetric effective stiffness matrix. (3) For misaligned fibers, two-step homogenization methods can be used at the upper level in combination with the recommended two-level strategy. Acronyms and abbreviations: FE: finite element, BC: boundary condition, PBC: periodic BC, MF: mean-field, MT: Mori-Tanaka, ODF: orientation distribution function, OT: orientation tensor, RVE: representative volume element, SFRC: short fiber-reinforced composite, UC: unit cell, UD: unidirectional.