text: 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  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. For the example cited above, the dot product of axial applied stress in the  direction and shear stress resulting from the former in the  direction yields a zero. For such a case, it is suitable to find a permutation of the family of the  permutation direction for the shear stress slip direction has been chosen:
  In a single crystal sample, the macroscopic yield stress will be determined by the Schmid factor of the single grain. Thus, in general, different yield strengths will be observed for applied stresses along different crystallographic directions. In polycrystalline specimens, the yield strength of each grain is different depending on its maximum Schmid factor, which indicates the operational slip system(s). The macroscopically observed yield stress will be related to the material's CRSS by an average Schmid factor, which is roughly 1/3.06 for FCC and 1/2.75 for body-centered cubic (BCC) structures.
  The onset of plasticity in polycrystals is influenced by the number of available slip systems to accommodate incompatibilities at the grain boundaries. In the case of two adjacent, randomly oriented grains, one grain will have a larger Schmid factor and thus a smaller yield stress. Under load, this "weaker" grain will yield prior to the "stronger" grain, and as it deforms a stress concentration will build up in the stronger grain near the boundary between them. This stress concentration will activate dislocation motion in the available glide planes. These dislocations are geometrically necessary to ensure that the strain in each grain is equivalent at the grain boundary, so that the compatibility criteria are satisfied. G. I. Taylor showed that a minimum of five active slip systems are required to accommodate an arbitrary deformation. In crystal structures with fewer than 5 active slip systems, such as hexagonal close-packed (HCP) metals, the specimen will exhibit brittle failure instead of plastic deformation.