In situ strengths of matrix in a composite
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A major obstacle to achieving reasonable strength prediction of a composite only from its constituent information is in the determination of in situ strengths of the matrix. One can measure only the original strengths of the pure matrix, on the basis of which the predicted transverse strengths of a unidirectional (UD) composite are far from reality. It is impossible to reliably measure matrix in situ strengths. This paper focuses on the correlation between in situ and original strengths. Stress concentrations in a matrix owing to the introduction of fibers are attributed to the strength variation. Once stress concentration factors (SCFs) are obtained, the matrix in situ strengths are assigned as the original counterparts divided by them. Such an SCF cannot be defined following a classical approach. All of the relevant issues associated with determining it are systematically addressed in this paper. Analytical expressions for SCFs under transverse tension, transverse compression, and transverse shear are derived. Closed-form and compact formulas for all of the uniaxial strengths of a UD composite are first presented in this paper. Their application to strength predictions of a number of typical UD composites demonstrates the correctness of these formulas.
KeywordsComposites Strength formulas Micromechanics Stress concentration factor Matrix in situ strength
The project was supported by the National Natural Science Foundation of China (Grants 11272238, 11472192) and the Doctoral Fund of the Ministry of Education of China (Grant 20120072110036). The authors greatly appreciate discussions of this work with our colleague Prof. Y.-D. Xue at Tongji University.
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