Technology of metallic materials - Microplasticity in polycrystalline materials

Microplasticity in polycrystalline materials

So far, we have talked about plastic deformation in a single crystal or in individual grains. But in practice, most materials we employ in industry and applications are polycrystalline. Our question is: how does the previous theory apply or may change when dealing with polycrystalline materials? Fortunately, the discussion of plastic deformation does not change significantly when going to polycrystalline materials. We shall not change a lot the content of what we learned; we just need to justify some important steps.

Slide 2

When we spoke about plastic deformation, we assumed that dislocations were moving on the slip plane and along the slip direction. This is always true, and the stress that makes dislocations move must be parallel to the slip plane (shear stress). But you must understand that plastic deformation into materials is also visible in a tensile test. How can we visualize plasticity in a tensile test by relying on the previous theory? How can the normal stress (usually applied in a tensile test) be converted into a shear stress which effectively makes dislocations move? We want a relationship between these two stresses.

We have to consider the tensile sample and identify in this sample the general slip plane (cuts the sample to make the cross-section elliptical). On this slip plane, dislocations can move in the slip direction (shown by the arrow). In general geometry, we may identify the plane and the direction of this type with two angles with respect to the symmetric axis of the sample (where the force is applied). These two angles must refer to the angle of the plane and the angle of the slip direction.

From LAG, I know that the normal direction identifies the plane. Theta is the angle between the normal vector and the axis. The angle between the slip direction and the axis will be phi. Now we apply a force and let’s see what happens. In principle, when we apply a force, the dislocations will move in the plane along that direction.

When we apply a normal force, a shear stress will activate the motion of the dislocations. If we divide the force by the cross-section area, we have sigma, while on the slip system we have tao. This is a resolved shear stress. It means that it is the projection of the normal stress over the slip plane. When the resolved shear stress exceeds a critical value (the value at which the dislocations start to move).

What is the normal stress that provides movement of dislocations in a tensile test? When sigma will reach yield stress (plastic deformation). When sigma reaches on the cross section the yield stress, the shear stress acting in the system will be the starting point for making dislocations move. When we reach the yield stress, the resolved shear stress will reach a critical resolved shear stress. This spatial shear stress is named critical resolved shear stress.