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

Abstract

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.

A model for the thermodynamics of and strengthening due to co-clusters in Al–Mg–Si-based alloys

“…Two strengthening mechanisms related to obstacle shearing need to be considered: a) Order strengthening (including stacking fault strengthening), or configurational strengthening [27], and b) Modulus hardening [28].…”

“…Modulus hardening Nembach [28] analysed modulus hardening by a calculation of the interaction forces of screw and edge dislocations as they pass through the area (precipitate) with differing modulus. This approach is based on Friedel's approximation:…”

“…Nembach's analysis [28] shows that the critical shear stress due to modulus hardening can be represented as:…”

“…As different dislocation core models predict somewhat different interaction forces between dislocations and precipitates [28], some uncertainty in  m results. Averaged values are obtained for  1 = 0.096 and  2 = 0.76, respectively.…”

Microstrucure and strengthening of Al–Li–Cu–Mg alloys and MMCs: II. Modelling of yield strength

“…Refs. [3,31]), but some theoretical justification may be found in the rather weak size dependency obtained in the modulus hardening model due to Nembach [31]. The accuracy of these simplified expressions for prediction of strengthening due to GPB zones will be further discussed in section 4.1, where they will be compared with experimental data for ternary Al-Cu-Mg alloys.…”