Shemy's Puzzle: Calculating Yield Stress for a Metal

[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.

 

[Mapes]

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

 

[Mapes]

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 let's 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 that's right, it can't be far off...It's between 560 and 720

Cheers,

Shemy