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Precipitation hardening is investigated by simulating the dislocation glide through obstacle fields and determining the critical resolved shear stress. Lattice mismatch strengthened materials are considered (e.g. Cu-rich Cu–Co alloys). The precipitates are spherical; the distribution of their radii and their three-dimensional spatial arrangement are close to those of an actual Ostwald-ripened crystal. The basic simulation approach is the same one as in [V. Mohles, in press]. Unlike in [V. Mohles, in press], the dislocation dissociation into Shockley partials is taken into account; two dislocations with Burgers vectors of the type (a/6) 〈112〉 are simulated, where a is the lattice constant. The elastic interaction of each of them with itself and with the other one is fully allowed for. This interaction concept is basically identical with that introduced by Brown [L.M. Brown, Phil. Mag. 10 (1964) 441] and Bacon [D.J. Bacon, Phys. Stat. Sol. 23 (1967) 527]. The mean particle radius Full-size image (<1 K) is varied within the range 0.5≤Full-size image (<1 K)≤16 nm. Both cases Full-size image (<1 K)d are covered by this range where d is the eqilibrium distance between the Shockley partials of a dissociated dislocation in a Cu-matrix.