Computer experiment on superposition of strengthening effects of differentparticles

Particle-hardening materials, particularly high strength aluminum alloys, u sually contain two or more types of second-phase particles. While the stren gthening effect of mono-dispersed particles has been studied extensively an d hence well formulated, a rational and consolidated evaluation of superpos ed hardening effects of different particle mixtures is still an open proble m both experimentally and theoretically. A computer simulation technique is utilized to examine the details of the problem. The technique developed is based on the circle-rolling approach of Morris el al. The strengthening st ress tau(p) due to the mixture of different particles is determined by exam ination of a dislocation-slip process through the particles on one slip pla ne and along one slip direction under the action of an applied shear stress tau. Two kinds of particle mixtures are investigated. One consists of hard or unshearable point-like particles and soft or shearable point-like ones. The other is a mixture of two types of unshearable plate-like particles. T he simulation results indicate that the superposition law can be well descr ibed by an equation tau(alpha) = n(A)(alpha/2)tau(A)(alpha) + n(B)(alpha/2) tau(B)(alpha) where n(A) and n(B) are the density fractions of A- and B-par ticles, tau(A) and tau(B) the strengthening stresses due to pure A- and B-p articles, and the exponent alpha varies between 1.0 and 2.0. Application to the spherical precipitates predicts that a bi-modal particle size distribu tion can give rise to about an 8% increment in strengthening stress with re gard to a single size distribution that is normally produced by conventiona l aging. For a mixture of {theta' (or theta ") + T-1} in Al-Cu-Li alloys th e simulation predicts that the larger T-1-plates may either reduce or incre ase the strengthening effect depending on the particular circumstances. A s tructure comparison factor kappa(AB) is introduced to describe the various effects. Calculated values using the simulation method compare favorably wi th those determined experimentally. (C) 1999 Acta Metallurgica Inc. Publish ed by Elsevier Science Ltd. All rights reserved.