Critical resolved shear stress

In materials science, critical resolved shear stress (CRSS) is the component of shear stress, resolved in the direction of slip, necessary to initiate slip in a grain. Resolved shear stress (RSS) is the shear component of an applied tensile or compressive stress resolved along a slip plane that is other than perpendicular or parallel to the stress axis. The RSS is related to the applied stress by a geometrical factor, m, typically the Schmid factor: where σapp is the magnitude of the applied tensile stress, Φ is the angle between the normal of the slip plane and the direction of the applied force, and λ is the angle between the slip direction and the direction of the applied force. The Schmid factor is most applicable to FCC single-crystal metals, but for polycrystal metals the Taylor factor has been shown to be more accurate. The CRSS is the value of resolved shear stress at which yielding of the grain occurs, marking the onset of plastic deformation. CRSS, therefore, is a material property and is not dependent on the applied load or grain orientation. The CRSS is related to the observed yield strength of the material by the maximum value of the Schmid factor: CRSS is a constant for crystal families. Hexagonal close-packed crystals, for example, have three main families - basal, prismatic, and pyramidal - with different values for the critical resolved shear stress. In crystalline metals, slip occurs in specific directions on crystallographic planes, and each combination of slip direction and slip plane will have its own Schmid factor. As an example, for a face-centered cubic (FCC) system the primary slip plane is {111} and primary slip directions exist within the permutation families. The Schmid Factor for an axial applied stress in the direction, along the primary slip plane of , with the critical applied shear stress acting in the direction can be calculated by quickly determining if any of the dot product between the axial applied stress and slip plane, or dot product of axial applied stress and shear stress direction equal to zero.