Progressive failure of a unidirectional fiber-reinforced composite using the method of cells: Discretization objective computational results

摘要

The smeared crack band theory is implemented within the high-fidelity generalized method of cells micromechanics model to capture progressive failure within the constituents of a composite material while retaining objectivity with respect to the size of the discretization elements used in the model. Orientation of the crack band is determined using the maximum principal stress. When oriented perpendicular to the maximum principle stress the faces of the cracks in the crack band are subjected to only normal tractions and grow under pure mode I conditions. The traction-separation law governing the behavior of the crack band is related to the mode I fracture toughness, and formation of the crack band is initiated with a maximum stress criterion. Conversely, if the direction of the principal stress with the largest magnitude is compressive, it is assumed that the cracks within the crack band are constrained from growing in mode I. Instead, it is assumed that mode II cracks form within the crack band oriented along the plane of maximum shear stress. A Mohr-Coulomb initiation criterion is utilized to incorporate the effects of the normal tractions acting on the crack faces, and an effective shear traction is defined accordingly. The effective shear traction versus mode II separation law is a function of the mode II fracture toughness. A repeating unit cell containing 13 randomly arranged fibers is modeled and subjected to a combination of transverse tension/compression and transverse shear loading. The implementation is verified against experimental data and an equivalent finite element model that utilizes the same implementation of the crack band theory. Additionally, a sensitivity study is also performed on the effect of the size of the RUC on the stiffness and strength of the RUC.