Effect of particle size distribution on strength of precipitation-hardened alloys
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S.P. Deshmukh and R.S. Mishraa) Department of Metallurgical Engineering, University of Missouri–Rolla, Rolla, Missouri 65409 (Received 29 December 2003; accepted 29 June 2004)
Aging of precipitation hardened alloys results in particle coarsening, which in turn affects the strength. In this study, the effect of particle size distribution on the strength of precipitation-hardened alloys was considered. To better represent real alloys, the particle radii were distributed using the Wagner and Lifshitz and Slyozov (WLS) particle size distribution theory. The dislocation motion was simulated for a range of mean radii and the critical resolved shear stress (CRSS) was calculated in each case. Results were also obtained by simulating the dislocation motion through the same system but with the glide plane populated by equal strength particles, which represent mean radii for each of the aging times. The CRSS value with the WLS particle distribution tends to decrease for lower radii than it does for the mean radius approach. The general trend of the simulation results compares well with the analytical values obtained using the equation for particle shearing and the Orowan equation.
I. INTRODUCTION
Precipitation hardening is a widely used method for increasing the critical resolved shear stress (CRSS) of a material. The CRSS is defined as the resolved shear stress necessary to make dislocations glide over macroscopic distances.1 In a real material, the motion of a dislocation is affected by precipitates (precipitation hardening) and by atoms dissolved in the matrix (solution hardening). Therefore, in precipitation-hardened materials, the CRSS is defined as the external stress required to overcome the interaction between dislocations and particles. Particles act as obstacles to the glide of the dislocations and thus reduce their mobility. Dislocations can overcome these obstacles either by shearing these particles or bypassing them. The path a dislocation takes is predominantly dictated by the nature of particles (shearable or unshearable), particle size distribution and the inter-particle spacing. Aging of precipitation hardened alloys leads to particle coarsening. Coarsening of particles from a very small size at a constant volume fraction helps in increasing the stress required to shear them. However, at a certain radius, it becomes easier for the dislocation to bow around a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2004.0364 J. Mater. Res., Vol. 19, No. 9, Sep 2004
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the particles rather than shear them. Beyond this radius, the growth of the particles actually leads to a decrease in the stress required to overcome them, an effect of increased inter-particle spacing. Existing models for aging response of alloys and the aforementioned two mechanisms predict the CRSS of the material to a modest approximation. These models have been modified and refined according to experimental results obtained for a wide range of materials. But
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