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Precipitation hardening of metals and alloys is investigated by means of computer simulations of dislocations gliding through a matrix with spherical coherent precipitates. The critical resolved shear stress is derived. Most realistic models are applied in these simulations: the radius distribution and the three-dimensional spatial arrangement of the particles are close to those of an actual Ostwald ripened crystal. Unlike the surrounding matrix, the precipitates are long-range ordered. A dislocation cutting through them generates an antiphase boundary and hence senses an obstacle stress inside the precipitates, which impedes dislocation glide. Such a strengthening mechanism is effective for instance in the nickel-based superalloy Nimonic PE16. The simulations are based on the local stress equilibrium along the dislocation line. The linear elastic interaction of the dislocations with themselves and with other dislocations is fully allowed for, similar to the approaches of Brown and of Bacon. Overaged crystals are considered in which dislocation glide is governed by the Orowan process. The average particle radius r and the particle volume fraction ƒ are varied. The strengthening contribution of these particles is derived as a function of the parameters r and f. This function is compared with a recent theoretical function suggested by Nembach; after adding a minor correction term to the latter function, it represents the present simulation results well.