Question

If a ferritic stainless steel has a yield strength of 350 MPa with a grain size of 0.1 mm and 450 MPa with a grain size of 0.03 mm, which grain size would give a yield strength of 500 MPa?

Answer 1

To determine the grain size that would give a yield strength of 500 MPa in a ferritic stainless steel, we can use the Hall-Petch equation.

Step-by-step explanation:

To determine the grain size that would give a yield strength of 500 MPa, we can use the Hall-Petch equation:

Ys = Y0 + K/d^(0.5)

Where Ys is the yield strength, Y0 is the initial yield strength, K is a constant, and d is the grain size. Rearranging the equation, we get:

d = (Ys - Y0) / K^(0.5)

Given that Y0 = 350 MPa and d = 0.1 mm at one point, and Y0 = 450 MPa and d = 0.03 mm at another point:

d = (500 - 350) / K^(0.5)

Let's solve for d:

d = 150 / K^(0.5)

Now, we can use the second set of data (Y0 = 450 MPa and d = 0.03 mm) to find the value of K:

K = (Ys - Y0)^2 / (d - Ys)^2

Substituting the values we have, we get:

K = (450 - 350)^2 / (0.03 - 450)^2

Now that we know the value of K, we can substitute it back into the first equation to find the value of d:

d = 150 / K^(0.5)

Solving this equation will give us the grain size that would give a yield strength of 500 MPa.