Rule of mixtures were an essential feature of the modeling of plastic deformation in complex materials in which more than one strain-hardening mechanism was involved. Use was made here of dislocation dynamics simulations in order to characterize the individual and the superposed contributions of two major mechanisms of crystal plasticity, i.e. Orowan strengthening and forest hardening. Based on a formal description of each hardening mechanism, evidence was presented to show that a quadratic rule of mixtures has the ability to predict quantitatively the flow stress of complex materials such as reactor pressure vessel steel.

Orowan Strengthening and Forest Hardening Superposition Examined by Dislocation Dynamics Simulations. S.Queyreau, G.Monnet, B.Devincre: Acta Materialia, 2010, 58[17], 5586-95