Calculating Critical Surface Edge Crack for Fatigue Life of Material

In summary, the problem involves finding the critical surface edge crack for a given fatigue life, maximum tensile stress, initial crack edge, and coefficient values. The equation used is from the book "Foundations of Material Science and Engineering" and can be found in Chapter 7. However, there seems to be an issue with the calculation, specifically with the term (-m/2+1) in the denominator. This may be the reason for getting a negative crack length in the solution attempt.
  • #1
chiraganand
113
1

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
 

Attachments

  • equation.docx
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  • #2
can someone please help me out in this.. i am using the correct equation substituting correctly both still not able to get the answer..
 
  • #3
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.
 
  • #4
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?
 
  • #5
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
    12.7 KB · Views: 430
  • #6
Desperately need a solution to the problem! please somebody help me.. i am substituting the values but still get a negative value!
 
  • #7
I can't read your calculation snapshot.
 
  • #8
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..
 
  • #9
I have attached my solution attempt.. I have substituted and attempted the solutuion
 

Attachments

  • 1366891891221.jpg
    1366891891221.jpg
    6.3 KB · Views: 414
  • #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.
 

1. What is fatigue of materials?

Fatigue of materials is the weakening or failure of a material under repeated or cyclic loading. It occurs when a material is subjected to alternating stresses, causing microscopic cracks to form and grow, eventually leading to failure.

2. What are the main factors that contribute to fatigue of materials?

The main factors that contribute to fatigue of materials include the magnitude and frequency of loading, the type and direction of loading, the material's properties, and the presence of stress concentrations or defects in the material.

3. How is fatigue of materials tested and measured?

Fatigue testing involves subjecting a material to repeated loading cycles while monitoring the stress and strain on the material. The number of cycles required to cause failure is recorded and used to determine the material's fatigue strength or endurance limit.

4. How can fatigue of materials be prevented or mitigated?

Fatigue of materials can be prevented or mitigated by using materials with high fatigue strength, avoiding stress concentrations or defects in the material, and designing structures with appropriate load factors and safety margins. Additionally, regular inspections and maintenance can help identify and repair any potential fatigue-related issues.

5. What industries are most affected by fatigue of materials?

Fatigue of materials is a common problem in industries that involve repetitive loading, such as transportation, aerospace, and construction. It can also occur in everyday objects, such as household appliances and electronics.

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