A micromechanical approach is developed to determine the micro stress within a unidirectional composite under various mechanical and thermal loading conditions. Based on linear stress—strain relations, the concept of a stress amplification factor is introduced, and the correlations between macro stress and micro stress are explicitly expressed in mathematical equations. Three unit cell models, square, hexagonal, and diamond fiber arrays, are analyzed and compared using three-dimensional finite element methods. Subsequently, effective material properties, the distribution of micro stress in the fiber/matrix, as well as traction distribution at the fiber—matrix interface, and the effect of different interfacial stiffness, are obtained.
A three-dimensional micromechanics of failure model was developed and applied in order to predict triaxial failure envelopes and stress-strain curves for 12 test cases in the Second World-Wide Failure Exercise (WWFE-II), which involves five continuous fiber-matrix laminates and multi-axial loadings, including those in through-thickness direction. The micromechanics of failure is based on micromechanical unit cell models, which characterize the microstructure of composites, and consists of independent constituent failure criteria and a progressive damage model for the matrix. Nonlinear ply behavior in the matrix-dominant directions was successfully simulated. Thermal stresses were also considered. Results of prediction were presented together with an explanation of the phenomena.
Finite element representative unit cell models are established for the study of progressive failure of woven fabrics: plain weave, twill weave, and satin weave. A multi-scale approach ranging from the meso-scale to micro-scale regime is used, providing the failure observation inside the constituents. The constituent stresses of the fiber and matrix in the warp and fill tows of the woven fabric unit cell are calculated using micromechanics. Correlations between meso-scale tow stresses and micro-scale constituent stresses are established by using stress amplification factors. After calculating micro-scale stresses, the micromechanics of failure damage model is employed to determine the progressive damage statuses in each constituent of woven fabric composites. For the matrix of tows, a volume-averaging homogenization method is utilized to eliminate damage localization by smearing local damages over the whole matrix region of the unit cell. Subsequently, the ultimate strength is predicted for woven composites with different tow architectures. The prediction results are compared with the experimental values, and good agreement is observed.
The research presented in this article is a continuation of the authors' work in Part A of the second world-wide failure exercise (WWFE-II). In Part A, a constituent damage model based on micromechanics of failure was employed in order to predict the failure envelopes and stress-strain curves for unidirectional and laminated composites under multi-axial loadings. In this study, original predictions were compared with experimental data, supplied in Part B of the second world-wide failure exercise. Three modifications were made to the previous model: (a) a quadratic fiber failure criterion was proposed to replace the maximum longitudinal stress failure criterion used for fibers in the original model; (b) a three-dimensional kinking model was introduced so as to take into account the influence of the formation of kinking bands on micro stresses in the matrix, when a ply is under longitudinal compression; and (c) in-plane shear terms in stress amplification factors were averaged to avoid overestimation of local stress concentration for regions within the matrix and in the vicinity of the fiber-matrix interface. Questions regarding the discrepancies between the idealized and actual tests were also raised and are discussed in this study.
Micromechanical approaches are employed to investigate the influence of different fiber arrangement on the mechanical behavior of unidirectional composites (UD) under various loading conditions. A micromechanical model with a random fiber array is generated and used in a finite element analysis together with two frequently used representative volume elements (RVE), or unit cell models of square and hexagonal arrays. The algorithm for generating the random fiber array is verified by comparing the comprehensive performance of a unit cell based on our random array and that of a unit cell based on a real fiber distribution in the UD cross-section. Performance of the random and regular fiber arrays is also evaluated through frequency distributions of stress invariants in matrix and tractions at the fiber—matrix interface due to various loading types. The effects of different loading angles on the overall response of regular arrays to various loading conditions are investigated thoroughly. Finally, the Weibull distribution of the maximum normal interfacial traction in random array is compared with the cumulative probability distribution of transverse strength data acquired from experiment, and good agreement is achieved.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.