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VDI-Fortschrittsberichte 18/90, VDI-Verlag, Düsseldod, 1990. Micromechanics for Macroscopic Material 47 16. Plast. 7, 781-802, 1991. 17. : Treatment of Micromechanical Phenomena by Finite Elements; in "Discretization M ethods in Structural M echanics" (Eds. 393-404, Springer-Verlag, Berlin, 1990. 18. Mech. 25, 197228, 1986. 19. mater. 38, 185-194, 1990. 20. mater. 43, 1833-1844,1993. 21. : Analytical Descriptions of the Material Behavior of Composites (A Summary of Formulas). CDLJLMW-Report 27-1991, TU Wien, Vienna, 1991.
Doing this and assuming the interface shear stress to be constant with r = ry along the load transfer length, which is a very rough approximation (justified by plastification of the matrix), eqn. (37) leads to (39), as lang as the maximum fiber stress accepted by the fiber embedded in the matrix is not reached. , corresponds to strain coupling between fiber and matrix in analogy to continuousfiber composites from that point on where e;U) = e;(m) is reached. Hence, (40). ) Umt~z l tr = r -- (41).
Ol(l/d) 2 (52). 35. 3 Strength Predictions for Short-Fiber Composites For aligned short-fiber composites uniaxially loaded by tension in fiber direction the rule of mixtures Ieads to (53), with the average fiber stress ii(f) given by eqns. (44) or (45), respectively. ). 33 For many practical applications (cr(Tn)) CJl is replaced by the matrix tensile strength cr~Tn) and e,. eqn. (55) reads (56). In analogy to eqns. (30) and (31) the minimum and the critical fiber volume fractions, respectively, are given by (57), (58).