Grain-Boundary Strengthening in Copper-Base Solid Solutions

Abstract

The relationship between grain size and flow stress at 1% strain has been examined between 77 and 450 K in copper and in an extensive range of binary copper-base solid solutions. The strengthening effect of the grain boundaries can be described by the empirical relationship <disp-formula> <mml:math> <mml:mrow> <mml:mi>σ</mml:mi> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>σ</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>+</mml:mo> <mml:msup> <mml:mrow> <mml:mi>k</mml:mi> <mml:mi>d</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> </disp-formula> where σ₀ and k depend on the type and concentration of solute. The stress at infinite grain size, σ₀, increases significantly with increasing strain but the slope, k, tends to decrease; k varies only slightly with temperature. The strengthening effects of grain boundaries are qualitatively consistent with a model based on a greater dislocation density in deformed fine-grained, as compared to coarse-grained, material due to dislocations originating from grain-boundary defects.