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Computer simulations of particle strengthening: lattice mismatch strengthening
Precipitation hardening is investigated by simulating the dislocation glide through obstacle fields and determining the critical resolved shear stress. In these simulations, the elastic interaction of the dislocations with themselves and with other dislocations is fully allowed for, similarly as has been done by Brown  and Bacon . The obstacles considered are coherent spherical particles with a lattice mismatch (e.g. Cu-rich Full-size image (<1 K)Co-alloys). The respective obstacle stress is derived from Eshelby's elastic stress tensor of spherical inclusions. The distribution of the particle radii and their three dimensional spatial arrangement are the same ones as in an Ostwald ripened crystal. The mean particle radius r̄ is varied over a wide range, covering both the underaged and the overaged region. Small precipitates are cut and large ones are circumvented by the Orowan process. The volume fraction f of the particles and the constrained lattice mismatch parameter ε are varied as well. Thus, the critical resolved shear stress is obtained as a function of all three parameters r̄, f and ε.