Stress-free edge effects on the transverse response of a unidirectional metal matrix composite

Abstract

In using a representative volume element of a unidirectional composite, two out-of-plane boundary conditions represent edge and internal regions of a transversely loaded SCS-6/Timetal® 21S composite. A plane stress condition is proposed to represent a stress-free edge region of the composite, while a generalized plane (uniform longitudinal) strain condition is considered for internal regions. Numerical simulations with elastic-plastic matrix behavior and several different fiber-matrix interface strengths reveal a complex interaction of residual stress, fiber-matrix separation and matrix inelastic behavior which are all dependent on the out-of-plane boundary condition. Several permutations of plane stress and generalized plane strain solutions with several fiber-matrix interface strengths fail to accurately capture the non-linear behavior measured from experiments. The bounding of the experimentally determined transverse response between the plane stress and generalized plane strain solutions suggests that the transverse response may be a combination of both solutions. Strain measurements from the transversely loaded composite support speculation that the plane stress solution better represents edge regions of the composite than a generalized plane strain solution. Likewise, the generalized plane strain solution represents the internal strain state of the composite better than the plane stress case at low loads. Photomicrographs before and after transverse loading show fibers which have protruded from the edge of the specimen; thus, the strain state within the composite is transitioning to a less constrained condition.