In this teaching and learning package, we have seen how the phenomenon of plastic deformation proceeds by slip. This involves dislocation motion in specific directions on specific planes, which in combination are known as slip systems.
The observed yield stress of a single crystal is related to the geometry of the crystal structure via Schmid's Law:
|τC = σy cos φ cos λ
where τC is the critical resolved shear stress which is related to the stress required to move dislocations across the slip plane.
The macroscopic behaviour of cadmium crystals was examined as an example of slip in a hexagonal close-packed metal. It was demonstrated that the orientation of the crystal with respect to the tensile axis is crucial in determining the behaviour of a single crystal undergoing deformation. Microscopic slip steps were observed on the crystals, which confirm the geometry of slipand show that certain geometrical relationships are obeyed as slip proceeds.
The crystal structure of the material can affect the nature of slip. We have seen how cubic close-packed metals undergo work hardening due to the simultaneous operation of several slip systems - this mechanism cannot occur in hexagonal close-packed crystals unless unusual slip systems operate.
In polycrystalline materials, the distribution of grain orientations and the constraint to deformation offered by neighbouring grains gives rise to a simplified overall stress-strain curve in comparison to the curve from a single crystal sample. Crystal structure is also important in polycrystalline samples - the von Mises criterion states that a minimum of five independent slip systems must exist for general yielding.