Random models versus periodic models for fibre reinforced composites

Quantitative description and numerical simulation of random microstructures of composites and their effective elastic moduli

The effective elastic moduli of composite materials are investigated in the presence of imperfect interfaces between the inclusions and the matrix. The primary focus is on the spherical particle reinforced composites. By admitting the displacement jumps at the particle–matrix interface, the modified Eshelby inclusion problem is studied anew. To derive the modified Eshelby tensor, three approximate methods are presented and compared by emphasizing the existence of a unique solution and computational efficiency. Subsequently, the effective elastic stiffness tensor of the composite is formulated based on the proposed micromechanical framework and homogenization. Specifically, by incorporating imperfect interface, the modified versions of the Mori–Tanaka method, the self-consistent method, and the differential scheme are presented. By comparing these three methods, the effects of interfacial sliding and separation on the degradation (damage) of the effective elastic moduli of composites are analyzed and asses...

Effective Elastic Moduli of Spherical Particle Reinforced Composites Containing Imperfect Interfaces

In this study, the effects of fiber waviness on the effective elastic responses of CNT–polymer composites are investigated based on the framework of micromechanics and homogenization. By taking advantage of an ad hoc Eshelby tensor, the load-transfer capability of wavy carbon nanotube (CNT) embedded in the polymer matrix is accounted for. Further, the effective elastic responses of composites are simulated by using the multi-phase Mori–Tanaka method to study the influence of randomly oriented wavy CNT. It is demonstrated that the proposed micromechanics-based closed form solution is effective to tackle the underlying problem. The present predictions and the comparisons with the available experimental data indicate that the CNT waviness leads to the degradation of effective responses of composites. Finally, in addition to the effect of CNT waviness, the significance of CNT interface is briefly discussed based on the experimental observations.

Effects of CNT waviness on the effective elastic responses of CNT-reinforced polymer composites

A micromechanical damage mechanics framework is proposed to predict the overall elastoplastic behavior and interfacial damage evolution of fiber- reinforced ductile composites. Progressively debonded fibers are replaced by equivalent voids. The effective elastic moduli of three-phase composites, composed of a ductile matrix, randomly located yet unidirectionally aligned circular fibers, and voids, are derived by using a rigorous micromechanical formulation. In order to characterize the homogenized elastoplastic behavior, an effective yield criterion is derived based on the ensemble area averaging process and the first-order effects of eigenstrains. The resulting effective yield criterion, together with the overall associative plastic flow rule and the hardening law, constitutes the analytical framework for the estimation of effective elastoplastic damage responses of ductile composites containing both perfectly bonded and completely debonded fibers. An evolutionary interfacial fiber debonding process, governed by the internal stresses of fibers and interfacial strength, is incorporated into the proposed framework. The Weibull's function is employed to describe the varying probability of fiber debonding. Further, comparison between predictions and available experimental data are presented to illustrate the potential of the proposed methodology.

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X.D. Zhang

Papers

Micromechanics and effective transverse elastic moduli of composites with randomly located aligned circular fibers

Effective elastoplastic behavior of ductile matrix composites containing randomly located aligned circular fibers