Question: The figure demonstrates the yield strength dependence on a grain size

Question

Question: The figure demonstrates the yield strength dependence on a grain size for a 70Cu-30Zn brass alloy.  Determine the values for the constants (sigma)_0 and k_y in the Hall-Petch equation.

I attemtped to find two equations by simply looking at points on the line according to their position, however, I feel I am doing something incorrect.  Hall-Petch eqn is (sigma)_y=(sigma)_0 + k_y/d^1/2

The figure demonstrates the yield strength dependence on a grain size for a 70Cu-30Zn brass alloy. Determine the values for the constants (sigma)_0 and k_y in the Hall-Petch equation. I attemtped to find two equations by simply looking at points on the line according to their position, however, I feel I am doing something incorrect. Hall-Petch eqn is (sigma)_y=(sigma)_0 + k_y/d^1/2

Explanation / Answer

denoting sigma_y by Y and sigma_0 by c and k_y by m

the plot is between Y and d^-0.5 which I denote by X

So, equation stands as Y=mX+c

This is a straight line equation , so the y-intercept is c,

So, from graph c= 25 MPa approximately

The line also approximately passes through ( (5*10^(-3))^(-1/2), 200 MPa).....5*10^-3 is the grain size d, So to substitute X which is d^-1/2, I have taken a power of -1/2....

Substitute this in the equation to obtain m....and hence you obtain the parameters in Mpa and mm^-1/2....

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.