Phase-Field Model for Unidirectional Composite Materials

The phase-field model (PFM) was implemented in Abaqus via a user element (UEL) subroutine to investigate crack propagation in a 2D domain. First the PFM implementation was verified for isotropic materials considering several problems: a square plate with a horizontal edge crack and square plate with a 45° inclined crack at its middle. The PFM results were compared to linear elastic fracture mechanics (LEFM) results and the influence of the regularization parameter ℓ and characteristic element size h on the accuracy of the results was investigated. It was found that as ℓ increases the crack is smoothed over a wider area and a lower force to fracture is obtained compared to LEFM. By decreasing ℓ the difference between PFM and LEFM predictions decreases. The influence of the pseudo time increment ∆t on the force-displacement curve was investigated and it was observed that for the smaller ∆t the PFM results approached the LEFM results. The PFM was then extended to unidirectional fiber-reinforced polymer composites (FRPs). The problem of a rectangular plate with a horizontal edge crack was analyzed for three different cases of boundary conditions (BCs). Each case was conducted for several fiber angles, and it was observed that the crack propagation direction followed the fiber orientation. The PFM was found to be a convenient and effective method for predicting crack propagation in unidirectional composites in 2D domains, without having to change the mesh as a result of an evolving crack.