FLOW IN POLYCRYSTALLINE ICE

Part 2 - Background information

By Chris Wilson and Brett Marmo

2.10 Critical resolved shear stress

Crystalline slip results from the action of a shear stress on the slip plane. Within the range of stresses in natural situations, the component of stress normal to the slip plane does not influence slip. Thus the slip process must be considered in terms of the shear stress resolved on the slip plane in the slip direction. Consider a single crystal of cross-sectional area A under a tensile force F (Fig. 2.10.1). Let be the angle between the slip plane normal and the compression axis, and the angle between the slip direction and the tensile axis. The component of the applied force, acting in the slip direction is , and the area of the slip plane is . The shear stress resolved in the slip direction is then

where is the applied tensile stress F/A.

Figure 2.10.1:Two separated portions of a crystal showing a model for calculating the resolved shear stress in a single-crystal specimen. F is the applied force, A is the cross-sectional area of the specimen, is the angle between the normal-to-the-slip plane and the compression axis, and is the angle between the slip direction and the compression axis.

The stress required to initiate slip in a pure and perfect single crystal, the critical resolved shear stress (CRSS) is a constant for a material at a given temperature. This rule, known as Schmid's Law, has been experimentally proven for a large number of single crystals. The critical stress required to cause yielding is a function of or the Schmid factor. The slip plane with the greatest resolved shear stress acting upon it will predominate in the slip process.