Calculating Critical Surface Edge Crack for Fatigue Life of Material

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The discussion focuses on calculating the critical surface edge crack for a material with a fatigue life of 8,000,000 cycles and a maximum tensile stress of 21,000 psi. The user is struggling with the correct substitutions in the provided equation, particularly with converting units from ksi to psi and handling the parameters correctly. They consistently obtain a negative value for the crack length, indicating a potential error in their calculations, especially concerning the term involving 'm' in the denominator. Assistance is requested from those familiar with the relevant material science principles and the specific equation from "Foundations of Material Science and Engineering." The user emphasizes the need for clarification on the correct application of the equation and accurate unit conversions.
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Homework Statement


Compute the crtitical surface edge crack if the fatigue life = 8000000 cycles and maximum tensile stress is 21000 psi. m=3.5 and A= 0.00000000004 in ksi and in. units. Initial crack edge is 0.120 in. Y= 1.15

Homework Equations



The equation is given in the attached file and a0 is the initial crack length and af is final crack length


The Attempt at a Solution


I have tried substitutuing the values in the equation but on substitution and solving i am not getting the correct answer.
I think i am going wrong in the conversion of ksi to psi

Please help me out in this
 

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can someone please help me out in this.. i am using the correct equation substituting correctly both still not able to get the answer..
 
The conversion from ksi to psi is simple: 1 ksi = 1000 psi.

Instead of showing only the raw formula, show your calculations. It may be some simple arithmetic mistake.
 
I have been doing it over and over but get the same answer... I want to know conceptually it is just substitution in the equation right?
 
I am attaching my substitutions in the formula. When I solve I end up getting a negative value for the crack length
 

Attachments

  • 1366825387115.jpg
    1366825387115.jpg
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Desperately need a solution to the problem! please somebody help me.. i am substituting the values but still get a negative value!
 
I can't read your calculation snapshot.
 
Oh ok sorry for the poor resolution... basically what I have done is just substituted the values in the equation..
I have converted 21000 psi into 21 ksi as in the question it says that A = 4.1x10^-11 in ksi and in..
 
I have attached my solution attempt.. I have substituted and attempted the solutuion
 

Attachments

  • 1366891891221.jpg
    1366891891221.jpg
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  • #10
I'm not familiar with this equation, but I would check m, especially the term (-m/2+1) in the denominator. That is one reason you are getting a negative crack length. Can you provide a source for this equation?
 
  • #11
The equation is from foundations of material science and engineering 5th edition. by William F Smith and Javad Hashemi... chapter 7
 
  • #12
Somebody... anybody please help me out in this
 
  • #13
If anyone could please help me out in this. If anyone is familar with the Willaim smith book and knows how to solve the problem please let me know.
 

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