Structuresmade of fiber-reinforced polymer (FRP) composites are usually considered lightweight. On account of this feature, polymeric composites find their application in many engineering disciplines, where the expected service lifetimemay extend to decades. The advent of thermoplastics has brought about cost-effective processing and the possibility to recycle structural components, among other features. However, the viscous nature of the polymer matrix poses a challenge to the straightforward application of FRP composites in load-bearing situations: the material response is a function of time and temperature. In addition, structural components may be subjected to long-term cyclic loading, that may lead to failure irrespective of the viscous nature of the material constituents. Hence, for an optimal application of (thermoplastic) FRP composites in load-bearing situations, it is necessary to understand, and eventually to predict their long-termperformance....@en

In this work, a hybrid physics-based data-driven surrogate model for the microscale analysis of heterogeneous material is investigated. The proposed model benefits from the physics-based knowledge contained in the constitutive models used in the full-order micromodel by embedding the material models in a neural network. Following previous developments, this paper extends the applicability of the physically recurrent neural network (PRNN) by introducing an architecture suitable for rate-dependent materials in a finite strain framework. In this model, the homogenized deformation gradient of the micromodel is encoded into a set of deformation gradients serving as input to the embedded constitutive models. These constitutive models compute stresses, which are combined in a decoder to predict the homogenized stress, such that the internal variables of the history-dependent constitutive models naturally provide physics-based memory for the network. To demonstrate the capabilities of the surrogate model, we consider a unidirectional composite micromodel with transversely isotropic elastic fibers and elasto-viscoplastic matrix material. The extrapolation properties of the surrogate model trained to replace such micromodel are tested on loading scenarios unseen during training, ranging from different strain-rates to cyclic loading and relaxation. Speed-ups of three orders of magnitude with respect to the runtime of the original micromodel are obtained.

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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.

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A microscale numerical framework for modeling creep rupture in unidirectional composites under off-axis loading is presented, building on recent work on imposing off-axis loading on a representative volume element. Creep deformation of the thermoplastic polymer matrix is accounted for by means of the Eindhoven Glassy Polymer material model. Creep rupture is represented with cohesive cracks, combining an energy-based initiation criterion with a time-dependent cohesive law and a global failure criterion based on the minimum in homogenized creep strain-rate. The model is compared against experiments on carbon/PEEK composite material tested at different off-axis angles, stress levels and temperatures. Creep deformation is accurately reproduced by the model, except for small off-axis angles, where the observed difference is ascribed to macroscopic variations in the experiment. Trends in rupture time are also reproduced although quantitative rupture time predictions are not for all test cases accurate.@en

A micromechanical framework for modeling failure in unidirectional (UD) thermoplastic composites under rate-dependent off-axis loading is presented, with the aim to predict and analyze transverse matrix cracking under various load conditions. The onset of global softening in the micromodel corresponds to macroscopic matrix crack initiation. The problem addressed in this study is to include matrix plasticity and microcracking in the failure analysis of UD composites. A thin slice representative volume element (RVE) with periodic boundary conditions is used, which enables representation of 3D stress states. The testing conditions of a constant prescribed strain-rate and an off-axis uniaxial stress state are reproduced in the model with a dedicated arclength control method. The studied material system is carbon/PEEK composite material, where plasticity in the matrix is represented with the Eindhoven Glassy Polymer (EGP) constitutive law, while the fibers are modeled as transversely isotropic elastic material. In order to account for microcracking in the matrix, a cohesive surface methodology is applied. Cohesive elements are added on the fly with a stress-based initiation criterion. For this purpose, a power law microcrack initiation criterion is proposed. After initiation, the microcracking process is governed by a mixed-mode damage cohesive law. Geometric nonlinear effects are also included in the cohesive model, such that cohesive forces include material as well as geometric contributions. The model is validated with experimental data from tensile tests on UD material at different off-axis angles and strain-rates. The obtained maximum stress levels are used to generate Tsai-Hill failure envelopes for macroscopic transverse crack initiation. Additional capabilities of the model are demonstrated through examples with different fiber-volume ratios and temperature conditions. @en

In this paper we develop a finite deformation micromechanical framework for modeling rate-dependent failure in unidirectional composites under off-axis loading. The model performance is compared with original experiments on thermoplastic carbon/PEEK composites tested at different strain-rates and off-axis angles. To achieve quantitative agreement with the experiments, a microcrack initiation criterion based on the local stress and the local rate of deformation state in the polymer matrix is proposed. Microcracking is represented by a cohesive zone model, with special attention to the inclusion of geometric nonlinearity in the formulation. In this regard, the cohesive geometric nonlinearity is based on extension of an existing formulation to three-dimensional space. Beside microcracking, the Representative Volume Element (RVE) also accounts for viscoplasticity in the polymer matrix. A recently introduced dedicated arclength control method is utilized to impose a strain-rate on the micromodel. Accordingly, kinematic relations governing the RVE deformation allow for the change in orientation of the micromodel in the loading process. This change in orientation of the microstructure has an important implication on the apparent material strength.

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In this paper, a micromechanical framework for modeling the rate-dependent response of unidirectional composites subjected to off-axis loading is introduced. The model is intended for a thin slice representative volume element that is oriented perpendicular to the reinforcement of the composite material. The testing conditions from a uniaxial off-axis test are achieved by a dedicated strain-rate based arclength formulation. The constraint equation of the arclength model is constructed such that the deformation state of the micromodel, as imposed in its local coordinate system, corresponds to the strain-rate applied on the material in global frame of reference. The kinematic description allows for finite strains in the material, meaning that the micromodel changes orientation during the deformation process. This geometric nonlinear effect is also included in the evaluation of external loading, ensuring that the external forces are equivalent to the applied off-axis stress in global coordinate system. Several examples are considered in order to show that the model resolves rate-dependency of the material, accounts for different off-axis loading, and captures finite strains exactly. Additionally, a small strain version of the model is derived from the general nonlinear framework. Results obtained with this simplified approach are compared to results of the large deformation framework.@en