This simulation illustrates the process of particle by-passing by the so-called Orowan bowing mechanism.

The Orowan stress required to force a dislocation past an obstacle is inversely proportional to the particle separtation, λ, as given by:

τ_Orowan = αμb / λ

Try changing the particle spacing using the slider bar, and record the Orowan Stress for each spacing.

Plot τ_Orowan as a function of λ.

Note, The Orowan bowing mechanisms results in the production of dislocation loops around the particles. As subsequent dislocations pass, dense tangles of dislocations form, leading to a high rate of work hardening.