Positive and Negative Failure-Shears in Orthotropic Materials

Failure predictions of off-axis loaded fiber composite laminae are given according to the elliptic paraboloid failure criterion for anisotropic solids [1]. The failure condition assumes that for any anisotropic solid a safe triaxial loading path exists, along the hydrostatic compression, and thus the failure surface must be open-ended. By appropriately formulating the failure criterion, it is shown that the geometric interpretation of the failure surface in the principal stress space is an elliptic paraboloid (EPFS) whose axis of symmetry is parallel to the hydrostatic axis in the principal stress space. Because of the shape and position of the EPFS, the intersections by principal stress planes corresponding to loadings of off-axis laminae of a fiber composite are represented by ellipses whose origins are displaced from the origin of the stress reference frame. This fact creates unequal shear yield stresses in the positive and negative sense clearly manifested in a pure shear failure loading. The predictions of the above criterion for plane stress failure loadings of laminae, and especially for pure shear induced failures, are compared with existing experimental data for various fiber composites and are shown to be in satisfactory agreement.