{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T15:51:44Z","timestamp":1762444304827,"version":"3.41.2"},"reference-count":32,"publisher":"Emerald","issue":"2","license":[{"start":{"date-parts":[[2012,5,25]],"date-time":"2012-05-25T00:00:00Z","timestamp":1337904000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012,5,25]]},"abstract":"<jats:sec><jats:title content-type=\"abstract-heading\">Purpose<\/jats:title><jats:p>Recently, a new class of fatigue crack growth models based on elastoplastic stress\u2010strain histories at the crack tip region and strain\u2010life fatigue damage models have been proposed. The fatigue crack propagation is understood as a process of continuous crack initializations, over elementary material blocks, which may be governed by strain\u2010life data of the plain material. The residual stresses developed at the crack tip play a central role in these models, since they are used to assess the actual crack driving force, taking into account mean stresses and loading sequential effects. The UniGrow model fits this particular class of fatigue crack propagation models. The purpose of this paper is to propose an extension of the UniGrow model to derive probabilistic fatigue crack propagation data, in particular the derivation of the <jats:italic>P\u2013da\/dN\u2013\u0394K\u2013R<\/jats:italic> fields.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Design\/methodology\/approach<\/jats:title><jats:p>An existing deterministic fatigue crack propagation model, based on local strain\u2010life data is first assessed. In particular, an alternative methodology for residual stress computation is proposed, based on elastoplastic finite element analysis, in order to overcome inconsistencies found in the analytical approximate approaches often used in literature. Then, using probabilistic strain\u2010life fields, a probabilistic output for the fatigue crack propagation growth rates is generated. A new probabilistic fatigue field is also proposed to take mean stress effects into account, using the Smith\u2010Watson\u2010Topper (<jats:italic>SWT<\/jats:italic>) damage parameter. The proposed models are assessed using experimental data available for two materials representative from old Portuguese bridges.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Findings<\/jats:title><jats:p>A new method to generate probabilistic fatigue crack propagation rates (<jats:italic>P\u2013da\/dN\u2013\u0394K\u2013R<\/jats:italic> fields) is proposed and verified using puddle iron from old Portuguese bridges, usually characterized by significant scatter in fatigue properties. Also, a new probabilistic fatigue field for plain material is proposed to deal with mean stress effects.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Originality\/value<\/jats:title><jats:p>A relation between the <jats:italic>P<\/jats:italic>\u2013\u03b5\u2013<jats:italic>N<\/jats:italic> and the <jats:italic>P\u2013da\/dN\u2013\u0394K\u2013R<\/jats:italic> fields is firstly proposed in this research. Furthermore, a new <jats:italic>P<\/jats:italic>\u2013<jats:italic>SWT<\/jats:italic>\u2013<jats:italic>N<\/jats:italic> field is proposed to deal with mean stress effects.<\/jats:p><\/jats:sec>","DOI":"10.1108\/17579861211235183","type":"journal-article","created":{"date-parts":[[2012,5,26]],"date-time":"2012-05-26T07:09:05Z","timestamp":1338016145000},"page":"158-183","source":"Crossref","is-referenced-by-count":35,"title":["A procedure to derive probabilistic fatigue crack propagation data"],"prefix":"10.1108","volume":"3","author":[{"given":"Jos\u00e9 A.F.O.","family":"Correia","sequence":"first","affiliation":[]},{"given":"Abilio M.P.","family":"de Jesus","sequence":"additional","affiliation":[]},{"given":"Alfonso","family":"Fern\u00e1ndez\u2010Canteli","sequence":"additional","affiliation":[]}],"member":"140","reference":[{"key":"key2022030720302191500_b1","unstructured":"ASTM (1998), \u201cASTM E606: standard practice for strain\u2010controlled fatigue testing\u201d, Annual Book of ASTM Standards, Vol. 03.01, American Society for Testing and Materials, West Conshohocken, PA."},{"key":"key2022030720302191500_b2","unstructured":"ASTM (2000), \u201cASTM E647: standard test method for measurement of fatigue crack growth rates\u201d, Annual Book of ASTM Standards, Vol. 03.01, American Society for Testing and Materials, West Conshohocken, PA."},{"key":"key2022030720302191500_b3","unstructured":"Basquin, O.H. (1910), \u201cThe exponential law of endurance tests\u201d, Proceedings of the Annual Meeting of American Society for Testing Materials, Vol. 10, pp. 625\u201030."},{"key":"key2022030720302191500_b4","unstructured":"Beden, S.M., Abdullah, S. and Ariffin, A.K. (2009), \u201cReview of fatigue crack propagation models for metallic components\u201d, European Journal of Scientific Research, Vol. 28, pp. 364\u201097."},{"key":"key2022030720302191500_b5","unstructured":"Castillo, E. and Fern\u00e1ndez\u2010Canteli, A. (2009), A Unified Statistical Methodology for Modeling Fatigue Damage, Springer, Dordrecht."},{"key":"key2022030720302191500_b7","doi-asserted-by":"crossref","unstructured":"Castillo, E. and Galambos, J. (1987), \u201cLifetime regression models based on a functional equation of physical nature\u201d, Journal of Applied Probability, Vol. 24, pp. 160\u20109.","DOI":"10.2307\/3214067"},{"key":"key2022030720302191500_b6","doi-asserted-by":"crossref","unstructured":"Castillo, E., Fern\u00e1ndez\u2010Canteli, A., Hadi, A.S. and L\u00f3pez\u2010Anelle, M. (2006), \u201cA fatigue model with local sensitivity analysis\u201d, Fatigue and Fracture of Engineering Material and Structure, Vol. 30, pp. 149\u201068.","DOI":"10.1111\/j.1460-2695.2006.01099.x"},{"key":"key2022030720302191500_b8","unstructured":"Coffin, L.F. (1954), \u201cA study of the effects of the cyclic thermal stresses on a ductile metal\u201d, Transactions of the American Society of Mechanical Engineers, Vol. 76, pp. 931\u201050."},{"key":"key2022030720302191500_b9","doi-asserted-by":"crossref","unstructured":"Creager, M. and Paris, P.C. 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