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:^[1]

${\displaystyle \tau _{\text{RSS}}=\sigma _{\text{app}}m=\sigma _{\text{app}}(\cos \phi \cos \lambda )}$^[2]

where σ_app 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,^[3] but for polycrystal metals the Taylor factor has been shown to be more accurate.^[4] 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:

${\displaystyle \sigma _{y}={\frac {\tau _{\text{CRSS}}}{m_{\text{max}}}}}$

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.