Damage modelling in fibre-reinforced composite laminates using phase field approach

Thin unidirectional-tape and woven fabric-reinforced composites are widely utilized in the aerospace and automotive industries due to their enhanced fatigue life and impact damage resistance. The increasing industrial applications of such composites warrants a need for high-fidelity computational models to assess their structural integrity and ensure robust and reliable designs. Damage detection and modelling is an important aspect of overall design and manufacturing lifecycle of composite structures. In particular, in thin-ply composites, the damage evolves as a result of coupled in-plane (membrane) and out-of-plane (bending) deformations that often arise during critical events, e.g., bird strike/ hail impact or under in-flight service loads. Contrary to metallic structures, failure in composites involves complex and mutually interacting damage patterns, e.g., fibre breakage/ pullout/ bridging, matrix cracking, debonding and delamination. Providing high-fidelity simulations of intra-laminar damage is a challenging task both from a physics and a computational perspective, 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. In addition, the failure in composites extends across multiple scales; it initiates at the fibre/ matrix-level (micro-scale) and accumulates into larger cracks at the component/ structural level (macro-scale). From a simulation standpoint, accurate prediction of the structure’s critical load bearing capacity and its associated damage thresholds becomes a challenging task; accuracy necessitates a fine level of resolution, which renders the corresponding numerical model computationally expensive. To this point, most damage models are applied at the meso-scale based on local stress-strain estimates, and considering material heterogeneity. Such damage models are often computationally expensive and practically inefficient to simulate the failure behaviour in real-life composite structures. Moreover at the macro-scale, the effect of local stresses is largely minimised, which necessitates definition of a homogenised failure criterion based on global macro-scale stresses. This thesis presents a phase field based MITC4+ (Mixed Interpolation of Tensorial Components) shell element formulation to simulate fracture propagation in thin shell structures under coupled membrane and bending deformations. The employed MITC4+ approach renders the element shear- and membrane- locking free, hence providing high-fidelity fracture simulations in planar and curved topologies. To capture the mechanical response under bending-dominated fracture, a crack-driving force description based on the maximum strain energy density through the shell-thickness is considered. Several numerical examples simulating fracture in flat and curved shell structures which display significant transverse shear and membrane locking are presented. The accuracy of the proposed formulation is examined by comparing the predicted critical fracture loads against analytical estimates. To simulate diverse intra-laminar fracture modes in fibre reinforced composites, an anisotropic cohesive phase field model is proposed. The damage anisotropy is captured via distinct energetic crack driving forces, which are defined for each pertinent composite damage mode together with a structural tensor that accounts for material orientation dependent fracture properties. Distinct 3-parameter quasi-quadratic degradation functions based on fracture properties pertinent to each failure mode are used, which result in delaying or suppressing pre-mature failure initiation in all modes simultaneously. The degradation functions can be calibrated to experimentally derived strain softening curves corresponding to relevant failure modes. The proposed damage model is implemented in Abaqus and is validated against experimental results for woven fabric-reinforced and unidirectional composite laminates. Furthermore, a dynamic explicit cohesive phase field model is proposed to capture the significantly nonlinear damage evolution behaviour pertinent to impact scenarios. A strategy is presented to combine the phase field and the cohesive zone models to perform full composite-laminate simulations involving both intra-laminar and inter-laminar damage modes. Finally, the developed phase field model is employed within the framework of a multiscale surrogate modelling technique. The latter is proposed to perform fast and efficient damage simulation involving different inherent scales in composites. The technique is based on a multiscale FE2 (Finite Element squared) homogenisation approach, however the computationally expensive procedure of solving the meso- and macro-scale models simultaneously is avoided by using a robust surrogate model. The meso-scale is defined as a unit-cell representative volume element (RVE) model, which is analysed under a large number of statistically randomised mixed-mode macro-strains, applied with periodic boundary conditions. The complex damage mechanisms occurring at the meso-scale are captured using the anisotropic cohesive phase field model, and the homogenised stress-strain responses post-damage evolution are obtained. These anisotropic meso-scale fracture responses are used to train the Polynomial Chaos Expansion (PCE) and Artificial Neural Network (ANN) based surrogate models, which are interrogated at the macro-scale using arbitrary macro-strain combinations. The accuracy of the surrogate model is validated against high-fidelity phase field simulations for a set of benchmarks