A Framework for Phase-Field Modeling of Damage Evaluation in Heterogeneous Materials


Student thesis: Doctoral Thesis

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Awarding Institution
Award date4 Aug 2021


Fiber-reinforced composites have been extensively employed in engineering applications owing to their remarkable specific mechanical properties such as lightweight nature, enhanced durability, stiffness, strength, and fracture toughness, and fairly adequate performance under high temperature. However, it is extremely challenging to describe their complex mechanical behaviors and uncover their failure mechanisms. The experimental investigation of fiber-reinforced composites entails high economic costs and is time-consuming, thereby making modeling techniques indispensable. In the last few decades, some phenomenological and physically based damage and fracture models have been developed to evaluate the mechanical performance of fiber-reinforced composites. Unfortunately, because of their high microstructural heterogeneity and complex failure modes, only few modeling frameworks can provide a comprehensive and detailed insight into the failure mechanisms.

We first implemented the phase-field model based on the variational principle to simulate crack initiation and propagation in composites. An efficient and robust staggered scheme is adopted by separating the fracture phase-field and displacement field. Within this framework, the mixed-mode crack propagation and fracture process of fiber-reinforced composites can be captured with a fair precision. Parametric studies indicate that the mechanical properties and crack propagation are influenced by the direction of defects with respect to the load, interaction among defects, and damageable layer. The simulation results successfully predict crack initiation from a damageable layer, crack propagation in the matrix, and crack branching when it encounters a stiffer material and propagates along the interface.

Subsequent to that, this thesis presents a newly coupled phase-field cohesive-modeling framework that can precisely capture interfacial damage and matrix cracking behavior of fiber-reinforced composites. Here, the phase-field method is used to capture crack evolution in the matrix, and a coupled cohesive-zone model is introduced to characterize interfacial debonding. It should be accentuated that a newly developed scalar indicator that directly extracts inelastic strain from the total strain field and couples the cohesive traction-separation law is implemented to determine the regularized interfacial displacement jump. The fracture process, not only the computational contour of the phase field and displacement but also the theoretical kinking and debonding angles, can be accurately characterized.

The proposed methodology is further applied to modeling progressive damage and failure behaviors of multiphase microstructures in multifiber systems, wherein the periodic boundary conditions in the coupled phase-field cohesive framework are incorporated to characterize crack evolution in random fiber systems. A comprehensive set of failure modes, namely crack initiation, propagation, kinking, and coalescence are characterized in highly heterogeneous solids. Parametric studies of the novel framework yield numerical results markedly congruous with the experimental findings and reveal the effects of fiber distributions, fiber volume fractions, and boundary conditions on the nonlinear mechanical behaviors of fiber-reinforced composites.

In the next stage of this thesis, we present an efficacious numerical framework for evaluating the impacts of stochastic interface properties on the transverse tensile response of fiber-reinforced composites. The Weibull distribution is employed to characterize the stochastic fiber-matrix interface properties. Several numerical examples are implemented to display different failure mechanisms and the key findings of this study. It is demonstrated that a dispersive distribution of weak interfaces leads to a larger composite failure strain by avoiding the clustering of weak interfaces where crack tends to initiate and coalescence. Moreover, the cracks tend to initiate along weak but not always the weakest interfaces due to the stress concentration induced by the variation in fiber spacing.

Lastly, we introduce a novel machine learning-assisted approach to determine the interfacial mechanical properties based on previous micro-bond tests. Through the comparison between the pullout test results and prediction results, the effectiveness of the proposed model in the prediction of the maximum load force and the interfacial shear strength is validated. The relationship between influencing attributes and these interfacial properties can be reasonably captured. Meanwhile, it can be referred from mean impact value analysis that the interfacial properties are conspicuously dependent on the fiber’s diameters. This work reveals that gradient boosting regressor (GBR) and artificial neural network (ANN) exhibit outstanding generalization and interpretation abilities. Besides, both ANN and GBR with small datasets have tremendous potential for extensive applications in predicting the shear resistance properties in fiber-reinforced composites.

The computational framework has been validated to possess superlative potential to evaluate the mechanical performances of composite materials in engineering applications, which can provide a more realistic material behavior description and accelerate the material enhancement and design based on the microfracture evolution predictions.