A crystal begins to slip when the shear stress resolved onto an available slip system reaches a material-dependent threshold.

For a single crystal under uniaxial tensile stress $\sigma$, Schmid's law gives the resolved shear stress

$$\tau_R=\sigma\cos\phi\cos\lambda,$$

where $\phi$ is the angle between the loading axis and the slip-plane normal, and $\lambda$ is the angle between the loading axis and the slip direction.

The product

$$m=\cos\phi\cos\lambda$$

is the Schmid factor, so $\tau_R=m\sigma$. For uniaxial loading its maximum possible magnitude is $0.5$.

Slip begins when

$$|\tau_R|\ge \tau_{CRSS},$$

where $\tau_{CRSS}$ is the critical resolved shear stress for that slip system.

Example

If $\sigma=120,\mathrm{MPa}$, $\phi=45^\circ$ and $\lambda=45^\circ$,

$$\tau_R=120(\cos45^\circ)^2=60,\mathrm{MPa}.$$

If the CRSS is $50,\mathrm{MPa}$, that slip system can activate.

Schmid's law explains why crystallographically identical grains with different orientations can yield at different applied stresses. In a polycrystal, neighboring grains constrain one another, so macroscopic yielding is more complex than applying this single-crystal criterion independently to every grain.