# Determine the Yield stress for a metal with an average grain diameter, can't get my h

shemy
Right this is the question,

Determine the yield stress for a metal with an average grain diameter of 0.045mm, if the yield stress for a metal changed from 650Nmm^-2 to 720Nmm^-2 when the average grain diameter decreases from 0.054mm to 0.037mm.

I cannot figure this out, I've been trying for hours and I'm stuck!

Cheers,

Shemy.

## Answers and Replies

Homework Helper
Gold Member

Hi shemy, welcome to PF. What equation are you using? Do you know of any equations that relate grain size to yield stress?

shemy

Yeh I'm using

SigmaY = Sigma0 + Ky(D)-1/2

I guess you have to substitute in, but I'm not sure.

Regards,

Shemy

Homework Helper
Gold Member

Right. You're giving two pairs of values. Try to get two equations in two unknowns, then solve for these and use the equation one more time with a grain size of 0.045 mm.

shemy

Right lets see!

(1) 560 = Sigma0 + Ky(0.054)^-1/2
(2) 720 = Sigma0 + Ky(0.037)^-1/2

(3)160 = Ky(0.895)

Ky=160/03895 = 178.77

560-(178.68)0.037^-1/2 = -368.91
-368.91+178.68*0.045^-1/2 = 473.95

720-(178.680.037^-1/2 = -208.91
-208.91+(178.68)0.037^-1/2 = 1137.82

1137.82-473.95 = 664.43Nmm^-2

Dunno if thats right, it can't be far off.....It's between 560 and 720

Cheers,

Shemy