Question

Compute the strain-hardening exponent n in equation 6.19 for an alloy in which a true stress of 415 mpa (60,000 psi) produces a true strain of 0.10; assume a value of 1035 mpa (150,000 psi) for k.

Answer 1

To compute the strain-hardening exponent n, we can use the equation: σ = kε^n, where σ is the true stress, ε is the true strain, and k is a constant. Given the values provided, we can calculate n as approximately -0.473.

Step-by-step explanation:

To compute the strain-hardening exponent n in equation 6.19, we can use the equation: σ = kε^n, where σ is the true stress, ε is the true strain, and k is a constant. Given that a true stress of 415 MPa produces a true strain of 0.10, and k is 1035 MPa, we can rearrange the equation to solve for n:

415 = 1035 * 0.10^n

Now we can take the logarithm of both sides to solve for n:

ln(415) = ln(1035) + n * ln(0.10)

n = (ln(415) - ln(1035)) / ln(0.10)

Using a calculator, we find that n ≈ -0.473.