Paris' law
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In materials science and fracture mechanics, Paris' Law is used to relate the stress intensity factor to subcritical crack growth under a fatigue stress regime.
Where a is crack length, C and m are material constants, and ΔK is the stress intensity factor range.
[edit] History and Use
This formula was generated from P.C. Paris' 1961 realization that on a log-log plot of crack growth rate vs stress intensity factor showed a linear relationship linear plot. Using this law, one can quantitative predictions about the residual life of a specimen given a particular crack size. Finding the beginning of the initiation of fast crack initiation:
One can then find the remaining lifetime using the following simple mathematical manipulations:
From here we can integrate over the size of the crack:
[edit] References
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