
Interpretation:
The integration of
Concept introduction:
Crack growth rate is defined as the rate at which propagation of crack is considered before failure with respect to stress intensity factor
The variation of crack growth rate with stress intensity factor is shown in the graph below:
The relationship for power law model is given by,
Where,
C and n are empirical constants depending upon the material.

Explanation of Solution
The given equation for basis is:
The value of stress intensity factor has a dependency on the size of the material.
The value of growth rate increases in unstable manner till fracture occurred,
Defining the relation based on geometrical factor and stress, the value of maximum and minimum stress intensity factor is,
Putting the values in the formula of stress intensity factor,
The difference between the maximum and minimum stress,
Replacing minimum and maximum stress with
Considering the value of stress intensity factor in terms of constant variable n,
On rearranging equation (1),
Putting the value of
Integrating the above equation with respect to initial and final flaw size. By Applying limits,
Thus, the required value of equation is
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Chapter 7 Solutions
Essentials Of Materials Science And Engineering, Si Edition
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