Calculating Critical Surface Edge Crack for Fatigue Life of Material

[chiraganand]

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

 

[chiraganand]

can someone please help me out in this.. i am using the correct equation substituting correctly both still not able to get the answer..

 

[SteamKing]

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.

 

[chiraganand]

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?

 

[chiraganand]

I am attaching my substitutions in the formula. When I solve I end up getting a negative value for the crack length

 

[chiraganand]

Desperately need a solution to the problem! please somebody help me.. i am substituting the values but still get a negative value!

 

[SteamKing]

I can't read your calculation snapshot.

 

[chiraganand]

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..

 

[chiraganand]

I have attached my solution attempt.. I have substituted and attempted the solutuion

 

[SteamKing]

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?

 

[chiraganand]

The equation is from foundations of material science and engineering 5th edition. by William F Smith and Javad Hashemi... chapter 7

 

[chiraganand]

Somebody... anybody please help me out in this

 

[chiraganand]

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.