Micromechanics of finite length fibers in composite materials

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1991-12-14

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Virginia Tech

Abstract

A theoretical model is derived to study the point-wise stress variations which occur in the constituents of a hybrid 3-D short fiber composite subjected to arbitrary homogeneous loading conditions. The model includes the capability to analyze composites containing different types of fibers, different aspect ratios of fibers (as well as continuous fibers), and different fiber orientations. The composite’s stiffness tensor is developed by volume averaging the point-wise stress field in each constituent present in the material system. Validation of the model is accomplished by comparing predicted stiffness properties to experimental data and other accepted models presently available in the literature for PMC’s, MMC’s, and BMC’s.

A derivation of a theoretical model describing the resulting point-wise stress redistribution which occurs in the matrix and the fibrous regions caused by fiber-fiber interaction at the ends of finite length fibers or fractured fibers is also presented. This theoretical development includes the significant dependence of stress redistribution on fiber volume fraction, constituent properties, and crack size. Therefore, its use is not limited to polymeric composites but is also applicable to metal matrix and ceramic matrix systems. The model is extended to include one of the first quantitative analyses of variable fiber spacing which occurs in virtually every composite manufactured. A novel fiber discount method is proposed to study multiple fiber fractures which are of extreme importance when attempting to predict tensile strength of fiber dominated composite laminates.

A test methodology employing a macro-model composite with embedded strain gauges is presented which can be used to validate (or invalidate) micro-mechanical models currently being developed and used by the scientific community. Results obtained with the embedded resistance gauges and the embedded fiber optic strain sensors (FP-FOSS) are validated with classical test and analytical techniques. These techniques include model composites subjected to thermal effects and mechanical loading sequences. The ability to vary specific physical parameters in the experimental model, such as fiber aspect ratio, fiber volume fraction, interphase/interface, and constituent properties (i.e. model PMC’s and MMC’s), in a systematic fashion enables this technique to study various physical aspects present in actual composite systems. The capability to initiate a fiber fracture at a specific location and load level is demonstrated. It is revealed that significantly different strain concentration exists in PMC composites which contain different fiber volume fractions and crack sizes. By varying fiber spacing between neighbors, a study is initiated on composites containing eccentrically located fibers. These results demonstrate that an asymmetric stress state exists in composites containing variable fiber spacing and fiber fractures. The fact that multiple fiber fracture is achieved in a methodical fashion demonstrates the versatility of the model. These studies show that this experimental technique can model various physical phenomena which occur in actual composite systems.

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