Solving Hall-Petch Equation Homework

  • Thread starter Thread starter TyErd
  • Start date Start date
Click For Summary

Homework Help Overview

The discussion revolves around the Hall-Petch equation, which relates the yield strength of materials to their grain size. Participants are analyzing specific calculations involving the equation and questioning the accuracy of their results.

Discussion Character

  • Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants present calculations for the Hall-Petch equation, questioning the correctness of their derived values for σo and k. There is also a discussion on the units used in the calculations, with some participants suggesting a potential error in the order of magnitude for the yield strength results.

Discussion Status

There is ongoing exploration of the calculations, with some participants providing feedback on the results. Questions about the accuracy of the values and units are being raised, indicating a productive dialogue around the problem.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information available for their calculations. There is a focus on ensuring the correct interpretation of the Hall-Petch equation and its parameters.

TyErd
Messages
297
Reaction score
0

Homework Statement


I've attached the question.


Homework Equations


σy = σo + k(d^-(1/2))


The Attempt at a Solution



450 x 10^6 =σo + k / sqrt(17 x 10^-6)-------------1
565 x 10^6 =σo + k / sqrt (0.8 x 10^-6)------------2

σo = 4.18142 x 10^8 Pa and k = 131354

is that right for the first part?

the second part: σy =4.18142 x 10^8 + 131354 / sqrt(0.2 x 10^-6)

σy = 7.11858 x 10^-6 Pa

is that correct?
 

Attachments

  • ffffffff.png
    ffffffff.png
    9.2 KB · Views: 760
Physics news on Phys.org
TyErd said:

Homework Statement


I've attached the question.


Homework Equations


σy = σo + k(d^-(1/2))


The Attempt at a Solution



450 x 10^6 =σo + k / sqrt(17 x 10^-6)-------------1
565 x 10^6 =σo + k / sqrt (0.8 x 10^-6)------------2

σo = 4.18142 x 10^8 Pa and k = 131354

is that right for the first part?

the second part: σy =4.18142 x 10^8 + 131354 / sqrt(0.2 x 10^-6)

σy = 7.11858 x 10^-6 Pa

is that correct?

I got the same numbers for the first part and for the second part I think you are off by a factor of one hundred?
 
I think the strength of titanium is on the order of MPa, not μPa.
 
lewando said:
I think the strength of titanium is on the order of MPa, not μPa.

Did not notice the minus sign, the second answer I got was about σy = 7.1 x 10^8 Pa
 

Similar threads

  • · Replies 17 ·
Replies
17
Views
2K
  • · Replies 1 ·
Replies
1
Views
6K
Replies
9
Views
2K
Replies
31
Views
2K
Replies
17
Views
3K
  • · Replies 7 ·
Replies
7
Views
2K
Replies
7
Views
1K
Replies
3
Views
1K
  • · Replies 6 ·
Replies
6
Views
1K