Yielding of Fiber Reinforced Tresca Material

A plane stress theory of plastic failure of a composite material is formulated by considering how the plastic failure surface of the matrix is altered by the addition of an array of parallel fibers. The matrix is assumed to obey the classical Tresca maximum shear stress yield criterion. The fibers are assumed to be infinitesimally thin and perfectly rigid. The fiber-matrix bond is such that a principal effect of the fibers is to restrict the plastic flow of the matrix in such a way that no extentional plastic strain increments in the direction of the fibers may occur. The limit stresses of a unidirectionally reinforced sheet are discussed and compared to results if the composite has a matrix which obeys the von Mises yield criterion. The limit stresses of laminates depend upon the bond between the laminae. Upper and lower bounds are obtained for two-ply laminate yield stresses.