# Local and Non-Local Approaches to Fatigue Crack Initiation and Propagation

• S.E. Mikhailov
• I.V. Namestnikova
Conference paper
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 113)

## Abstract

A functional form of local strength conditions under fatigue loading is introduced and employed to formulation and analysis of fatigue crack initiation and propagation. For the strength conditions associated with the Palmgren-Miner linear damage accumulation rule and the power-type S-N diagram, the problem is reduced to a non-linear integral Volterra equation, which can be transformed to a linear one for the case of a single crack. An analytical solution of some simple problems are presented for the latter case and shortcomings of the local approach are pointed out. A non-local approach free from the shortcomings is presented along with an example of its implementation.

## Keywords

Non-local strength conditions Durability Cyclic loading Crack initiation Crack propagation Volterra equations

## References

1. [1]
Mikhailov S.E., (1995-I,II). A functional approach to non-local strength conditions and fracture criteria — I. Body and point fracture. II. Discrete fracture. Engng Fracture Mech. 52, p. 731–754.
2. [2]
Mikhailov, S.E., (2003) Theoretical Backgrounds of Durability Analysis by Normalized Equivalent Stress Functionals, Mathematics and Mechanics of Solids, 8, p. 105–142.
3. [3]
Mikhailov, S.E., Namestnikova I.V., (2001) Normalised Equivalent Stress Functionals for Cyclic Fatigue, Preprint PP/MAT/SEM/0102-005, Glasgow Caledonian University, 53 p.Google Scholar
4. [4]
Rabotnov Yu.N., (1980) Elements of hereditary solid mechanics, Moscow, Mir Publishers, 387 p.Google Scholar
5. [5]
Savin G.N., (1961) Stress concentration around holes, Oxford, Pergamon Press.Google Scholar
6. [6]
Seweryn A. and Mróoz Z., (1996) A non-local stress failure and fatigue damage accumulation condition, In Multiaxial Fatigue and Design, ESIS 21 (Edited by A. Pineau, G. Cailletaud, and T.C. Lindley), Mechanical Engineering Publications, London, p. 261–282.Google Scholar
7. [7]
Shang D.G., Wang D.K., Li M., Yao W.X., (2001) Local stress-strain field intensity approach to fatigue life prediction under random cyclic loading, International Journal of Fatigue, 23, p. 903–910.
8. [8]
Sheppard S.D., (1989) Field e ects in fatigue crack initiation long life atigue strength, In Failure Prevention and Reliability — 89, ASME, New York, p. 119–127.Google Scholar
9. [9]
Taylor D., (2001) A mechanistic approach to critical-distance methods in notch fatigue, Fatigue and Fracture of Engineering Materials and Structures, 24(4), p. 215–224.