Precipitation hardening caused by a difference in shear modulus between particle and matrix

The interaction force between a spherical precipitate, whose shear modulus differs from the one of the matrix, and a dislocation is calculated numerically. From the maximum and the range of this interaction force, the critical resolved shear stress τc is derived. If the total precipitated volume fraction stays constant and the particle radius rp is varied between 8 and 50 times the Burgers vector, τc increases monotonously with rp. This is in contrast to the findings published by other authors. Modulus hardening is weak compared with other mechanisms of precipitation strengthening.