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.

[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:

Hexagonal close-packed crystals, for example, have three main families - basal, prismatic, and pyramidal - with different values for the critical resolved shear stress.

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).

[5] 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.

[6] The onset of plasticity in polycrystals is influenced by the number of available slip systems to accommodate incompatibilities at the grain boundaries.

This stress concentration will activate dislocation motion in the available glide planes.

G. I. Taylor showed[4] 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.

At lower temperatures, more energy (i.e. - larger applied stress) is required to activate some slip systems.

In general BCC metals have higher critical resolved shear stress values compared to FCC.

However, the relationship between the CRSS and temperature and strain rate is worth examining further.

however is attributed to short range internal stress fields that arise from defect atoms or precipitates within the lattice that are obstacles for dislocation glide.

With increasing temperature, the dislocations within the material have sufficient energy to overcome these short-range stresses.

In the third region, diffusive processes begin to play a significant role in plastic deformation of the material and so the critically resolved shear stress decreases once again with temperature.

In general, the CRSS increases as the homologous temperature decreases because it becomes energetically more costly to activate the slip systems, although this effect is much less pronounced in FCC.

Solid solution strengthening also increases the CRSS compared to a pure single component material because the solute atoms distort the lattice, preventing the dislocation motion necessary for plasticity.

With dislocation motion inhibited, it becomes harder to activate the necessary 5 independent slip systems, so the material becomes stronger and more brittle.

Slip systems activated near grain boundary to ensure compatibility.
Geometrically necessary dislocations for bending of a bar of material.
The relationship between CRSS and temperature and strain rate. In region I, the athermal and thermally dependent components of CRSS are active. At the boundary between I and II, becomes 0. Finally, at very high temperatures, the CRSS decreases as diffusion processes start to play a significant role in plastic deformation. Increasing strain rate shifts the trend to the right and therefore does not increase CRSS in the intermediate temperatures of region II.