Polycrystals are composed of many grains with different relative crystallographic orientation. If the material is untextured, the grains are randomly oriented. When the bulk material is deformed, each individual grain undergoes slip. The stress at which slip begins in each grain depends on its orientation with respect to the tensile axis, following Schmid’s Law. The shape change in a plastically deforming grain may be constrained by neighbouring grains that have not yet reached their yield point. The result of these two factors is that there are no distinct stages in the stress-strain curve for the sample.

When a c.c.p. metal exhibits stage I, II and III regions in the single crystal stress-strain curve, these stages will not be seen in a stress-strain curve from a polycrystalline sample of the same material: each individual grain goes through these stages at the same resolved shear stress and hence at different applied stress. The only well-defined feature in the stress-strain curve is the yield point, at which plastic deformation begins across the whole sample.

Each grain has a different Schmid factor (cos f cos l). The average value of the Schmid factor over the whole sample can be calculated, assuming that the grains are randomly oriented. The result is known as the Taylor factor, approximately equal to [one-third]. This gives s_y approximately equal to 3t_c.

Plot of normal stress against normal strain for a polycrystalline sample.

For example, consider a region in which all grains are slipping on their primary slip systems. If one grain only begins to slip on two slip systems the stress required to produce a given deformation in that one grain would increase due to work hardening. However, the surrounding grains deform more to accommodate this hardened grain, moderating the effect of work hardening. The observed stress required for a given extension of the whole sample therefore rises smoothly, as grains begin to work harden one-by-one.

The crystal structure of the material plays an important role in determining the behaviour of polycrystalline samples. We have seen that h.c.p. crystal structures have only three distinct slip systems (two of which are independent), whereas c.c.p. crystals have twelve distinct slip systems (five of which are independent). It can be shown that for general plastic strain of a polycrystalline sample, five independent slip systems must be available for the strain to be accommodated purely by glide. This is known as the von Mises condition. This is the reason that polycrystalline samples of h.c.p. metals like zinc and magnesium are less ductile at room temperature than their c.c.p. and b.c.c. counterparts.

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