The graph on the right shows the yield strength of an AI5Mg

The graph on the right shows the yield strength of an AI-5%Mg alloy (weight percent) as a function of aging time at 150 degree C. The aging was initiated after a one hour solution heat treatment at 500 degree C which was followed by a water quench. At 150 degree C, the solute (Mg) is slowly transformed to beta phase which is a non-strengthening precipitate. However, some (2% by weight) magnesium is retained in solid solution in equilibrium at 150 degree C after 100 hours of aging. Also shown is a plot of a/a_0 (normalized lattice parameter) as a function of Mg content in atom%: where a = the alloy lattice parameter and a_0 = the lattice parameter of pure aluminum. From the data presented, determine the values of relevant parameters (Delta sigma/Delta c, epsilon, and K) in the following equation (note that epsilon is the normalized change in lattice parameter per unit change in solute content): Delta sigma/Delta c=KG epsilon^4/3 Assume G=27 GPa.

Solution

From the curve on the left slope of tthe curve is 1.002 = epsilon

The right hand curve shows D(YS) = 230 approx.

DC= .03 (initial 5 %- 2% retained), so delta sigma/delta c is known

Hence all numbes in the eqn re known except K

Solve for K==>

230/.03 = 27*K* (1.002)^4/3

K = 28.32 * 10 ^-9 ( G in GPa)