# Shemy's Puzzle: Calculating Yield Stress for a Metal

• shemy
In summary, the yield stress for a metal with an average grain diameter of 0.045mm can be determined using the equation SigmaY = Sigma0 + Ky(D)-1/2, where SigmaY is the yield stress, Sigma0 is the initial yield stress, K is a constant, and D is the average grain diameter. By substituting in the given values of 650Nmm^-2 and 720Nmm^-2 for Sigma0, and 0.054mm and 0.037mm for D, we can solve for K and then use it to find the yield stress for a grain size of 0.045mm. Using this method, the yield stress was found to be approximately 664.43
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.

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

Yeh I'm using

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

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

Regards,

Shemy

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.

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

## 1. What is Shemy's Puzzle?

Shemy's Puzzle is a scientific problem that involves calculating the yield stress of a metal using a puzzle-like shape and measuring its deformation under stress.

## 2. Why is it important to calculate yield stress for a metal?

Calculating yield stress is important because it helps determine the strength and durability of a metal, which is essential in various industries such as construction, manufacturing, and engineering.

## 3. How is yield stress calculated in Shemy's Puzzle?

In Shemy's Puzzle, yield stress is calculated by dividing the applied stress by the measured strain. This can be done using a stress-strain curve and finding the point where the curve starts to deviate from being linear.

## 4. What factors can affect the accuracy of yield stress calculation in Shemy's Puzzle?

Some factors that can affect the accuracy of yield stress calculation in Shemy's Puzzle include the precision of measurements, the type and quality of the metal being tested, and the conditions of the testing environment.

## 5. Are there any limitations to using Shemy's Puzzle for calculating yield stress?

Yes, there are limitations to using Shemy's Puzzle. It may not accurately represent the behavior of a metal under different types of stress, and the results may vary depending on the shape and size of the puzzle used. Additionally, it may not be applicable to all types of metals or materials.

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