On the distribution and scatter of fatigue lives obtained by integration of crack growth curves: does initial crack size distribution matter?

On the distribution and scatter of fatigue lives obtained by integration of crack growth curves: does initial crack size distribution matter?

• January 2018
• Engineering Fracture Mechanics

• DOI
• 10.1016/j.engfracmech.2018.01.019

• Michele Ciavarella
• Antonio Papangelo

通过整合simple deterministic Paris’ law from a distribution of initial defects, in the form of a

Frechet extreme value distribution, it was known that a distribution of Weibull distribution of fatigue

lives follows exactly. However, it had escaped previous researchers that the shape parameter of this

distribution tends to very high values (meaning the scatter is extremely reduced) when Paris’ exponent

m approaches 2, leading to the exponential growth of crackswith number of cycles. In viewof the fact

that values close to m=2 are of great importance in materials for example used for primary aircraft

structures as recognized by some certification requirements (and the so-called “lead crack” methodology),

we believe this conclusion may have some immediate relevance for damage tolerance procedures,

or certification methods where accurate description of scatter is required. Indeed, we extend

the result also to the case when Paris’ constant C is distributed, and give also an estimate of the level of

scatter expected in propagation life in the most general case when C, m are both random variate

alongwith the defect size distribution, based on first transforming them to uncorrelated form C0, m, and

validate this with the famous Virkler set of data. We finally discuss that from known typical values of

fatigue life scatter of aeronautical alloys, it is very likely that an important contribution comes from

short crack growth.