モンテカルロ・シミュレーションを用いた一方向ＦＲＭの引張強度の評価

Abstract

A Monte-Carlo simulation technique, using a shear-lag model, is proposed to elucidate the tensile fracture process and the tensile strength of unidirectional fiber reinforced metal matrix composite materials, on the condition that the fiber behaves elastically and the matrix metal is approximated as an elastic linear hardening plastic material in accordance with the kinematic hardening model. In the simulation procedure, a conventional technique is modified by γmin method based on the minimum value of the incremental ratios which can be calculated from the element strengths and the stresses working on each fiber element and each matrix element. The simulated results show that the average value and the coefficient of variation of tensile strength are improved by an increase in the Weibull's shape parameter of the fiber, although the average value does not reach the value estimated from a rule of mixture. Then, in order to investigate the validity of the present technique, the simulated strength data are compared with the theoretical cumulative distribution curve given by a recursion analysis technique. Additionally, it is shown that the structural uncertainty, e.g. random fiber spacing, lowers the composite average strength and increases its scatter.