Revised Orowan Strengthening: Effective Interparticle Spacing and Strain Field Considerations

The increase in yield strength resulting from a dispersed unshearable secondary phase is important in precipitation-hardenable alloys and is considered one of the primary strengthening mechanisms of metal matrix nanocomposites. The Orowan strengthening equation, which is used to predict increases in yield stress, consists of two parameters: the interparticle mean free path for dislocation motion and the matrix distortion parameter. Upon comparison with experimental and simulated data over a large range of particles sizes, it is shown that descriptions of the interparticle mean free path used by various researchers all differ and fail to accurately predict the experimental data. An alternative description is proposed that describes interparticle spacing for a random particle distribution rather than applying the regular particle arrangements of the current formulations. Second, an alternate description of the matrix distortion parameter, which is less arbitrary than the current descriptions, is also proposed. Taken together, a revised Orowan strengthening equation results and more accurately describes the increase in yield strength for real materials that possess random particle arrangements.