OK, I couldn\'t rotate the picture for some reason. Answer both 3-17 and 3-18 fo

Question

OK, I couldn't rotate the picture for some reason.

Answer both 3-17 and 3-18 for max credits on points

Please show your work for credit.

A tension test was performed on a magnesium alloy specimen having a diameter 0.5 in. and gauge length 2 in. The resulting stress-strain diagram is shown in the figure. Determine the approximate modulus of elasticity and the yield strength of the alloy using the 0.2% strain offset method. A tension test was performed on a magnesium alloy specimen having a diameter 0.5 in. and gauge length of 2 in. The resulting stress-strain diagram is shown in the figure. If the specimen is stressed to 30 ksi and unloaded, determine the permanent elongation of the specimen.

Explanation / Answer

3-17

Mod. of Elasticity = Slope of linear portion = 12.5/0.002 = 6250 ksi

0.2% strain = 0.002 on x-axis.

Eqn of line passing through (0.002, 0) and having slope = 6250 is

y - 0 = 6250*(x - 0.002)

or y = 6250x - 12.5

This line crosses the curve at 26 ksi.

Hence, yield stress = 26 ksi.

3-18

At y = 30 ksi, from the curve we get x = 0.0078

Eqn of line passing through (0.0078, 30) and having slope = 6250 is

y - 30 = 6250*(x - 0.0078)

This line will cross x-axis when y = 0.

Putting y = 0 in above eqn we get

0 - 30 = 6250*(x - 0.0078)

x = 0.003

Permanent elongation = 0.003*2 = 0.006 in

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