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4) a. The yield stress (oy) of copper has been measured for different grain sizes (D) giving the following results: D(um) 20 50 200 500 Oy (MPa) 150 100 70 50 Plot a graph (use a spread sheet; e.g. Excel) of o, against D-1/2 and use a linear regression fit to obtain the base metal strength and Hall Petch slope. Use this fit to predict the yield strength if the grain size could be reduced to 1 um. (8 marks) b. Plot (using Excel or similar) the effect of particle spacing, 2, on the strength of a dispersion of non-shearable particles in a copper alloy for 2 in the range of 0.1 -5 um, if the constant, a, in this case ~1. Comment on the significance of your answer for particle strengthening. (7 marks) For Cu, b = 0.26 nm, G = 48 GPa y = 00 + k. D-0.5 Gb Δτ = 2α λ