For a bronze alloy, the stress at which plastic deformation begins is \(275 \mathrm{MPa}\) (40,000 psi), and the modulus of elasticity is \(115 \mathrm{GPa}\) \(\left(16.7 \times 10^{6} \mathrm{psi}\right) .\) (a) What is the maximum load that may be applied to a specimen with a cross- sectional area of \(325 \mathrm{~mm}^{2}\left(0.5 \mathrm{in} .^{2}\right)\) without plastic deformation? (b) If the original specimen length is \(115 \mathrm{~mm}\) (4.5 in.), what is the maximum length to which it may be stretched without causing plastic deformation?

To calculate the maximum load that can be applied to the specimen without causing plastic deformation, we can use the formula for stress: Stress = Force / Area From the given values, the stress at which plastic deformation begins is 275 MPa and the cross-sectional area of the specimen is 325 mm². Rearrange the formula to get: Force = Stress × Area Substitute the given values: Force = 275 MPa × 325 mm² Now we can convert MPa to N/mm², so 1 MPa = 1 N/mm²: Force = 275 N/mm² × 325 mm² Calculate the Force: Force = 89375 N So, the maximum load that may be applied to the specimen without causing plastic deformation is 89,375 N.

To find the maximum length the specimen can be stretched without causing plastic deformation, we need to first calculate the strain. The strain can be found using the following formula: Strain = Stress / Modulus of Elasticity Substitute the given values: Strain = (275 MPa) / 115 GPa Convert the units so that both stress and modulus of elasticity have the same units (in this case, GPa). 1 MPa = 0.001 GPa: Strain = (0.275 GPa) / 115 GPa Calculate the Strain: Strain ≈ 0.002391 Now, we can calculate the change in length by multiplying the Strain by the original length: Change in length = Strain × Original_length Substitute the given value for original length (115 mm): Change in length = 0.002391 × 115 mm Calculate the change in length: Change in length ≈ 0.275 mm So, the change in length without causing plastic deformation is approximately 0.275 mm. Now, we will add this change in length to the original length to find the maximum length the specimen can be stretched without causing plastic deformation: Maximum_length = Original_length + Change_Length Maximum_length = 115 mm + 0.275 mm ≈ 115.275 mm Therefore, the maximum length to which the specimen may be stretched without causing plastic deformation is approximately 115.275 mm (4.534 inches).