Solving Hall-Petch Equation Homework

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

The forum discussion centers on solving the Hall-Petch equation, specifically the calculations involving the yield strength (σy) of titanium. The participants confirmed that the initial calculations yielded σo = 4.18142 x 10^8 Pa and k = 131354. However, a correction was made regarding the second part of the solution, where the yield strength was initially miscalculated as σy = 7.11858 x 10^-6 Pa, which was later corrected to σy = 7.1 x 10^8 Pa. This highlights the importance of unit consistency in material strength calculations.

PREREQUISITES
  • Understanding of the Hall-Petch equation and its application in materials science.
  • Familiarity with yield strength calculations and material properties.
  • Knowledge of unit conversions, particularly between pascals (Pa) and megapascals (MPa).
  • Basic algebra skills to manipulate equations and solve for unknowns.
NEXT STEPS
  • Study the Hall-Petch equation in detail, focusing on its implications in materials engineering.
  • Learn about the mechanical properties of titanium and other materials relevant to the Hall-Petch relationship.
  • Explore unit conversion techniques, especially between different scales of pressure and strength.
  • Practice solving similar equations with varying parameters to reinforce understanding of the concepts.
USEFUL FOR

Students in materials science, engineers working with titanium and other metals, and anyone involved in mechanical property calculations will benefit from this discussion.

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: 750
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
1K
  • · 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