Critical resolved shear stress
Encyclopedia
Critical resolved shear stress is the component of shear stress
Shear stress
A shear stress, denoted \tau\, , is defined as the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section...

, resolved in the direction of slip, necessary to initiate slip in a grain. It is a constant for a given crystal
Crystal
A crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is known as crystallography...

.

Tests have been conducted on single crystals of metals to measure the shear stress required to initiate plastic deformation, or cause atomic planes to slip. Since this is a threshold value, it is referred to as critical; and since it is a component of the applied force or stress, it is said to be resolved; that is, the critical resolved shear stress.

Resolved shear stress is given by
τ = σ cos Φ cos λ
where
σ 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 plane direction and the direction of the applied force.
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