An anisotropic cohesive phase field model for quasi-brittle fractures in thin fibre-reinforced composites

Abstract

Thin unidirectional-tape and woven-fabric composites are widely utilized in the aerospace and automotive industries due to their enhanced fatigue life and damage resistance. Providing high-fidelity simulations of intra-laminar damage in such laminates is a challenging task both from a physics and a computational standpoint, due to their complex and largely quasi-brittle fracture response. This is manifested by matrix cracking and fibre breakage, which result in a sudden loss of strength with minimum crack openings; subsequent fibre pull-outs result in a further, although gradual, strength loss. To effectively model this response, it is necessary to account for the cohesive forces evolving within the fracture process zone. Furthermore, the interaction of the failure mechanisms pertinent to both the fibres and the matrix necessitate the definition of anisotropic damage models.We propose a cohesive phase-field model to simulate intra-laminar fracture in fibre reinforced composites. To capture damage anisotropy, distinct energetic crack driving forces are defined for each pertinent composite damage mode together with a structural tensor that accounts for material orientation dependent fracture properties. The material degradation is governed by a 3-parameter quasi-quadratic degradation function, which can be calibrated to experimentally derived strain softening curves. The proposed damage model is implemented in Abaqus and is validated against experimental results.

Phase-field modeling of fracture in heterogeneous materials: jump conditions, convergence and crack propagation

“…is a quadratic degradation function to account for previously introduced phase-field cracks. Various other degradation functions are proposed in [28,29], including multiple functions for isotropic and anisotropic contributions [30] and compared for example in [31,32]. The residual stiffness η 1 prevents numerical problems for fully degraded material c = 0.…”

Phase field fracture predictions of microscopic bridging behaviour of composite materials

“…The coupled system is solved using a staggered solution scheme [24]. This modelling methodology has proven to be very useful in capturing complex cracking phenomena in composites and multi-phase materials, such as crack branching, intricate crack trajectories and merging of multiple defects [44][45][46]. As shown below (Section 3), both matrix and fibre cracking can be captured.…”

Computing the effective crack energy of heterogeneous and anisotropic microstructures via anisotropic minimal surfaces

“…As a resulting of to the manufacturing process, they show higher Young's modulus and higher strength in fiber direction compared to the plane perpendicular to it. We use a crack resistance tensor for a fiber oriented in (unit) direction p as G = 25 γ p ⊗ p + 0.5 γ (Id − p ⊗ p), assuming an internal contrast of 50 for the crack resistance, as suggested by Pillai et al [35]. Furthermore, we model the matrix material in our composite with the isotropic crack resistance γ , assuming that the fibers transverse crack resistance is lower than that of the matrix material.…”

“…More general approaches were proposed using a multi phase-field setting, see Nguyen et al [30], or a higher order phase-field method, using fourth order tensors [31][32][33][34], to study polycrystalline materials. Pillai et al [35] proposed an anisotropic cohesive phase-field model to simulate the behavior of anisotropic fiber structures. Incorporating weak interfaces via cohesive elements was proposed by Rezaei et al [36].…”