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Micromechanical Damage Models for Continuous Fiber Reinforced Composite Materials


The primary objective of this research work is to investigate the effective mechanical responses of continuous fiber reinforced composites by modifying and extending the available micromechanical framework. A major part of the work conducted involves the investigation of the effective damage responses due to damage evolutions of matrix microcracks and fiber breakages.

Chapter 3 presents the effective elastic damage behavior of continuous fiber reinforced composites with evolutionary matrix microcracks. A cohesive penny-shape microcrack model is proposed within a two-step homogenization framework to achieve the effective elastic damage behavior of continuous fiber reinforced composites. In the proposed model, the size and the number density of microcracks are defined as two damage parameters to control the matrix microcrack evolution. In addition, the thermal effect is taken into account by taking advantage of the thermal eigenstrain and the Eshelby's equivalent inclusion principle. The overall coefficient of thermal expansion (CTE) of the composite is systematically derived under the framework of micromechanics to describe the overall damage behavior of composites due to matrix microcrack evolution under temperature changes.

Chapter 4 proposes a micromechanical evolutionary damage framework capable of predicting the overall mechanical behavior of and damage evolution in continuous fiber reinforced composites. In the framework, the effective stress fields in a single fiber due to an embedded penny-shaped fiber breakage are systematically derived by applying the double-inclusion theory. The notion of effective length denoting the distance between two adjacent breakages is introduced as a damage parameter while determining the damage evolution within a single fiber. This enables the modeling of the effective damage behavior of a single-fiber reinforced composite. As an application of the proposed framework, a micromechanical damage model is further proposed to simulate the fiber-dominated failure mechanism within a multi-fiber composite. A Weibull probability function is adopted to estimate the varying volume fractions of damaged fibers and intact fibers. Numerical simulations are presented to demonstrate the effectiveness of the proposed methodology.

In Chapter 5, based on the linear elastic fracture mechanics (LEFM) and ensemble-volume averaging technique, an effective eigenstrain is newly proposed to quantify the homogenized stress fields in a single fiber due to multiple fiber breakages. In the proposed model, the number density evolution of fiber breakages is characterized by a two-parameter Weibull statistic with the temperature effect implicitly enclosed by properly adjusting the Weibull parameters. The damage criterion in the evolutionary damage model is theoretically derived. Utilization of the proposed damage framework, a homogeneous damage evolution model capable of simulating the material behavior of multi-fiber reinforced composite materials is developed.

Chapter 6 presents two stochastic risk-competing models to simulate the fiber breakage evolution in a multi-fiber composite with an inhomogeneous fashion by considering different load sharing mechanisms. A unit cell model is adopted with each cell being assigned an initial weakness based on a normal distribution. Damage evolution inside each cell structure follows the micromechanical model presented in Chapter 5. Two risk-competing models are introduced subsequently to determine the damage sequence within the multi-fiber composite by computing the fracture probability based on the weakness of cells at each time step. It is observed that one risk-competing model tends to generate a concentrated damage pattern with broken fibers clustering in a T-shape or a cross-shape, while the other model yields a more diffused damage pattern. Finally, the overall stress-strain responses and the fiber breakage evolution are predicted and verified against experimental data.

Chapter 7 examines the effective elastoplastic behavior of metal matrix composites (MMCs) containing unidirectionally aligned continuous fibers. A homogenization procedure is utilized to derive the overall yield function for the composite based on the probabilistic spatial distribution of aligned inclusions. Based on continuum plasticity, a plastic flow rule and a hardening law are postulated. These laws together with the proposed overall yield function then characterized the macroscopic elastoplastic behavior of the composite under three-dimensional arbitrary loading/unloading histories. The overall uniaxial elastoplastic stress-strain behavior of MMCs with aligned continuous fibers is investigated. Comparisons between theoretical predictions and experimental data for the composite are performed to illustrate the capability of the proposed method.

Chapter 8 concludes the present research on micromechanics and effective elastic and elastoplastic behavior of continuous fiber reinforced MMCs. Finally, related future research topics are discussed briefly.

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