Plastic Deformation

· The shear stress due to dislocation pile up at a ductile precipitate particle may cause the particle to shear and increase its surface area. The area increases as the dislocation enters and leaves the particle, a distance of 2b.

From: Courtney, "Mechanical Behavior of Materials,"
McGraw Hill (1990)

· The particle surface area increases by 2πrb, where r is the particle radius. This increase in surface area changes the particle energy by dU_S= 2πrbγ, where γ= surface energy.
· The force, F, required to cause the shear is dU_S/dx , where dx = 2b, so that F =πrγ , and must come from the external force causing deformation.