A numerical framework is presented for simulating fracture and fatigue in a T-section, cut from an overmolded thermoplastic composite panel made of CF/PEEK. The framework combines a cohesive zone model for the overmolded interface with an anisotropic viscoplasticity model for the laminate and accounts for processing effects. For high-cycle fatigue analyses, a two-scale time-homogenized version of the viscoplasticity model is derived. The numerical framework is applied to the analysis of a rib pull-off test and is used to gain insights into the influence on the short- and long-term response of two typical processing effects: out-of-plane deformations of the laminate that occur during thermoforming and non-uniform healing profiles resulting from spatially varying thermal histories. Furthermore, the effects of various modeling assumptions are studied, such as modeling the local fiber orientations of each ply in the laminate with a mesoscopic ply-by-ply approach, the effect of viscoplastic deformations in the laminate, the influence of non-uniform local stress ratios, and the effect of the boundary conditions. The analyses demonstrate that the framework is capable of efficiently simulating a large number of cycles. The simulation results show that the local wrinkles in the laminate as a result of thermoforming have a significant effect on the mechanical response, especially under cyclic loading. Moreover, accounting for viscoplastic deformations appears more important when high degrees of bonding of the overmolded interface are achieved. Finally, it is shown that changes to the boundary conditions have a significant effect on the short and long-term response of the T-section, challenging the validity of the test for characterizing fracture and fatigue properties of the overmolded interface.

A micromechanical model for simulating failure of unidirectional composites under cyclic loading has been developed and tested. To efficiently pass through the loading signal, a two-scale temporal framework with adaptive stepping is proposed, with a varying step size between macro time steps, and a fixed number of equally spaced micro time steps in between. With the focus on matrix dominated failure under off-axis loading, viscoplasticity and microcracking are included in the model for the polymer matrix, while carbon fibers are modeled as elastic. For a proper representation of viscous deformation in the matrix under cyclic loading, a two-scale version of the Eindhoven Glassy Polymer constitutive model is formulated, that is based on time homogenization with an effective time increment. The failure state of the representative volume element is reached by the initiation and damaging of cohesive microcracks. Cyclic and static degradation are represented by using Dávila's fatigue damage function, which is built on top of Turon's quasi-static cohesive model. The model results are compared with available experimental data on unidirectional carbon/PEEK composites tested at different stress levels, load ratios, frequencies and off-axis angles. Plasticity controlled and crack growth controlled failure mechanisms, characteristic of the long-term response of polymeric composites, are captured by the model, as well as their distinct frequency dependence. As a limit case, the model is able to reproduce the time to failure in creep loading, where the heterogeneous microstructure and viscoplastic flow of the matrix trigger the evolution of quasi-static damage. However, for the studied material system, the present model does not accurately reproduce the load ratio dependence and the off-axis angle dependence of the crack growth controlled failure mechanism.

In this work, a recently proposed high-cycle fatigue cohesive zone model, which covers crack initiation and propagation with limited input parameters, is embedded in a robust and efficient numerical framework for simulating progressive failure in composite laminates under fatigue loading. The fatigue cohesive zone model is enhanced with an implicit time integration scheme of the fatigue damage variable which allows for larger cycle increments and more efficient analyses. The method is combined with an adaptive strategy for determining the cycle increment based on global convergence rates. Moreover, a consistent material tangent stiffness matrix has been derived by fully linearizing the underlying mixed-mode quasi-static model and the fatigue damage update. The enhanced fatigue cohesive zone model is used to describe matrix cracking and delamination in laminates. In order to allow for matrix cracks to initiate at arbitrary locations and to avoid complex and costly mesh generation, the phantom node version of the eXtended finite element method (XFEM) is employed. For the insertion of new crack segments, an XFEM fatigue crack insertion criterion is presented, which is consistent with the fatigue cohesive zone formulation. It is shown with numerical examples that the improved fatigue damage update enhances the accuracy, efficiency and robustness of the numerical simulations significantly. The numerical framework is applied to the simulation of progressive fatigue failure in an open-hole [±45]-laminate. It is demonstrated that the numerical model is capable of accurately and efficiently simulating the complete failure process from distributed damage to localized failure.

A common choice for multiscale modeling of the mechanical response of composites is to use periodic boundary conditions (PBCs) on square and cubical representative volume elements (RVEs). However, when strain localization occurs in the micromodel, these PBCs are unable to reproduce the transverse isotropy of composite materials with a random microstructure. Existing remedies to alleviate this issue have been proposed in literature by either rotating or shifting the periodicity constraints. However, this results in a mismatch of the microstructure on opposing edges which may prevent cracks to cross the boundary and consequently limit the supported localization angles. Furthermore, in absence of a strategy that ensures a single localization band to arise in a fracturing RVE, it is difficult to formulate a generic expression for the length scale parameter that is used to regulate the energy dissipation, which plays an important role in obtaining RVE-size objective results. As an alternative to square (or cubical) RVEs, circular (or spherical) RVEs have been proposed in literature since they provide a response which is independent of the orientation due to shape of the RVE. However, it is shown in this work that the existing formulation with straightforward application of PBCs on a circular RVE fails to predict the correct softening behavior, due to over-constraining when cracks reach the boundary. Therefore, a new formulation of PBCs on a circular RVE is proposed, which allows for a single fully developed localization band under arbitrary angle. The performance of the new formulation is tested with a series of simulations where macroscopic strains are imposed under varying orientations. It is demonstrated that the circular RVE with the new formulation of PBCs successfully predicts a transversely isotropic response with full softening without the issue of mismatching microstructure as with previously developed remedies for the square RVE. In addition, it is shown that the length scale parameter is well-defined and independent of the orientation of the circular RVE.