Particle Technology and Engineering

8.2. Interaction of Elastic-Plastic Particles

8.2.1. Yield

In many industrial processes, particles are subject to high forces or impact at high speeds, as a consequence of which plastic deformation can take place. To define the onset of plastic deformation, the theory of plasticity introduces two yield criteria:

1. The von Mises yield criterion, in which plastic deformation is initiated when the distortion energy exceeds the distortion energy for yield in simple tension, i.e., when the second invariant J₂ of the stress deviator tensor (s_ij) reaches a critical value:

J2=12sijsij=16[(σ1−σ2)2+(σ2−σ3)2+(σ3−σ1)2]=k2=Y23

(8.76)

where σ₁, σ₂, and σ₃ are the ...