Shemy's Puzzle: Calculating Yield Stress for a Metal

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Discussion Overview

The discussion revolves around calculating the yield stress for a metal based on its grain diameter, specifically addressing a scenario where the yield stress changes with varying grain sizes. The focus is on applying a specific equation that relates grain size to yield stress.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • Shemy presents a problem involving the determination of yield stress for a metal with a specific grain diameter and provides initial yield stress values for different grain sizes.
  • Some participants inquire about the equations being used to relate grain size to yield stress, suggesting a need for clarity on the methodology.
  • Shemy shares the equation SigmaY = Sigma0 + Ky(D)^-1/2 and attempts to substitute values to find unknowns.
  • Another participant suggests forming two equations based on the provided pairs of values to solve for the unknowns.
  • Shemy attempts to calculate Ky and subsequently the yield stress for the specified grain diameter, presenting intermediate calculations and results.
  • Shemy expresses uncertainty regarding the correctness of the final yield stress value calculated, noting it falls within the expected range of previous values.

Areas of Agreement / Disagreement

The discussion remains unresolved, with participants exploring different approaches and calculations without reaching a consensus on the correctness of the results or methodology.

Contextual Notes

Participants have not fully clarified assumptions regarding the constants in the equation or the accuracy of the calculations presented. There are also unresolved steps in the mathematical process.

shemy
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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.
 
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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
 

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