# NUMERICAL TOOLS AND MATHEMATICAL CONCEPTS OF FATIGUE AND FRACTURE MECHANICS APPLIED TO THE STRUCTURAL INTEGRITY EVAL-UATION OF MECHANICAL COMPONENTS

### Teixeira, G. M.; Lima, L. G. B. S.; Diesel, F. N.; Boniatti, D. L.; Cesário, A. A.;

There are a lot of numerical approaches related to fatigue (HCF or LCF) and frac-ture mechanics which are followed by the different industries. The aerospace industry is espe-cially concerned with the “damage tolerant approaches”. The automotive industry prefers SN based methodologies. The offshore industry uses a mix of both SN and EN approaches. De-spite the preferences, an issue comes first when FE analysis is employed: which stress(es) and/or strain(s) value(s) should be regarded in the calculations? Which amount is physical and which one is mathematical singularity? Many standards try to answer that question or, at least, overcome the side effects of the numerical tools, by linearization and related proce-dures. There is, however, a better way to address this problem, which has becoming increas-ingly important nowadays: “The Critical Distance Methods”. In some circumstances, it’s not necessary to completely avoid cracks. If we can determine correctly if such crack will grow or not, we can step forward and work with higher stress(es) values until we get that point where the crack will safely just not propagate. This can get us savings in material costs and weight. And all we need to do is to recall the concepts of transition length, from fracture mechanics, and turn it into the critical distance one, which stands for the position, away from the notch, where our measurements were supposed to be performed. At this distance, the stress(es) val-ues can be taken and combined as needed. So, the present paper intends to show the state-of-the-art of the procedures employed to deal with the finite element results and apply it to the structural integrity evaluation of mechanical components.

Palavras-chave: Theory of Critical Distance, Stress Gradients, Fatigue assessment, Fracture Me-chanics.,

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DOI: 10.5151/meceng-wccm2012-16658

##### Referências bibliográficas
• [1] The Theory of Critical Distance (Elsevier, 2007), 1st ED, by David Taylor.
• [2] Multiaxial Notch Fatigue (CRC press, 2009), 1st ED, by Luca Susmel.
• [3] NORMAN E. DOWLING (2007). Mechanical Behavior of Materials, Prentice Hall, 3rd ED.
• [4] Peterson’s Stress Concentration Factors (John Wiley Andamp; Sons, 1997), 2nd ED, Walter D. Pilkey.
• [5] E. Siebel and M. Stieler. Ungleichförmige Spannungsverteilung bei schwingender Beanspruchung.VDI–Zeitschrift, 97(5):121–126, 195 ISSN 0042-1766.
• [6] Recommended Practice DNV-RP-C203 – Fatigue Design of Offshore Steel Structures.
• [7] Fatigue Analysis by local stress concept based on finite element results (Computers and Structures 80 (2002), 2109-2113), Eichlseder, W.
##### Como citar:

Teixeira, G. M.; Lima, L. G. B. S.; Diesel, F. N.; Boniatti, D. L.; Cesário, A. A.; "NUMERICAL TOOLS AND MATHEMATICAL CONCEPTS OF FATIGUE AND FRACTURE MECHANICS APPLIED TO THE STRUCTURAL INTEGRITY EVAL-UATION OF MECHANICAL COMPONENTS", p. 129-140 . In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1]. São Paulo: Blucher, 2014.
ISSN 2358-0828, DOI 10.5151/meceng-wccm2012-16658

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