Answer:
A) - Yield strength before operation = 32 kpsi
- Ultimate Strength before operation = 49.5 kpsi
- Yield strength after operation = 61.854 kpsi
- Ultimate Strength after operation = 61.875 kpsi
- Percentage increase of yield strength = 93.29%
- Percentage increase of ultimate strength = 25%
B) ratio before operation = 1.55
Ratio after operation = 1
Explanation:
From online values of the properties of this material, we have;
Yield strength; S_y = 32 kpsi
Ultimate Strength; S_u = 49.5 kpsi
Modulus; m = 0.25
Percentage of cold work; W_c = 0.2
S_o = 90 kpsi
A) Let's calculate the strain(ε) from the formula;
A_o/A = 1/(1 - W_c)
A_o/A = 1/(1 - 0.2)
A_o/A = 1.25
Thus, strain is;
ε = In(A_o/A)
ε = In(1.25)
ε = 0.2231
Yield strength after the cold work operation is;
S'_y = S_o(ε)^(m)
Plugging in the relevant values;
S'_y = 90(0.2231)^(0.25)
S'_y = 61.854 kpsi
Percentage increase of yield strength = S'_y/(S'_y - S_u) × 100% = (61.854 - 32)/32 × 100% = 93.29%
Ultimate strength after the cold work operation is;
S'_u = S_u/(1 - W_c)
S'_u = 49.5/(1 - 0.2)
S'u = 61.875 kpsi
Percentage increase of ultimate strength = S'_u/(S'_u - S_u) × 100% = (61.875 - 49.5)/49.5 × 100% = 25%
B) Ratio of ultimate strength and yield strength before cold work operations is;
S_u/S_y = 49.5/32
S_u/S_y = 1.547
Ratio of ultimate strength and yield strength after cold work operations is;
S'_u/S'_y = 61.875/61.854 = 1
The ratio after the operation is less than before the operation, thus the ductility reduced.
