A Discrete Element Method for the Calculation of the Thermal Expansion Coefficients of Unidirectional Fiber Composites

Abstract

The thermal expansion behavior of unidirectional fiber composites may be predicted by the use of a discrete element method of analysis. A representative “cell” is selected and subdivided into triangular elements. Matrix equations relating the forces and displacements at each vertix with allowance for thermal expansion, together with equilibrium, compatibility and boundary conditions provide the longitudinal and transverse thermal expansion coefficients. The anisotropy in the thermal expansion and elastic behavior of the fibers is taken into account. The method is applied to boron‐aluminum composites of hexagonal and square array of fibers, and served to check the accuracy of computations. It is found that a cell of 58 nodes and 90 elements is adequate. Applied to hexagonal array graphite‐epoxy composites, the method was used to examine the effects of the fiber volume fraction and fiber elastic constants on the expansion behavior. It is found that both longitudinal and transverse coefficients deviate greatly from the rule of mixture's values. Poisson's ratios of the fiber and its transverse Young's modulus are found to have very little effect on the thermal expansion behavior of the composite.