Abstract：The internal stresses in a composite obtained by a micromechanics theory are homogenized quantities. They must be converted into true values before a failure assessment and strength prediction can be made. While the theories for obtaining all of the other directional true stresses have already been established, only the true stress of the matrix in the short fiber reinforced composite (SFRC) under a longitudinal compression is not known. The matrix true stress is obtained by multiplying its homogenized counterpart with the stress concentration factor (SCF). The stress field in the matrix of the SFRC subjected to a longitudinal compression is determined elastically, and is used to derive the longitudinal SCF of the matrix in the composite. Different from definition of the other directional SCFs, a longitudinal SCF of the SFRC must be obtained by subdividing its RVE (representative volume element) into three segments, i.e., two end plus a central ones, so that we can obtain a SCF applicable to any fiber aspect ratio. The homogenized stresses of the fiber and matrix are calculated by Bridging Model. And the compressive strength of a SFRC with any aspect ratio can be predicted easily. Only the geometrical and mechanical properties of the constituent materials are required. The predicted results are in good agreement with the experimental values, the efficiency of the theory established in this paper is finally verified.
2022, Vol. 43 
