{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T12:49:51Z","timestamp":1753879791854,"version":"3.41.2"},"reference-count":26,"publisher":"ASME International","issue":"2","content-domain":{"domain":["asmedigitalcollection.asme.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2012,4,1]]},"abstract":"<jats:p>Probabilistic fatigue models are required to account conveniently for the several sources of uncertainty arising in the prediction procedures, such as the scatter in material behavior. In this paper, a recently proposed stress-based probabilistic model is assessed using fatigue data available for the P355NL1 steel (a pressure vessel steel). The referred probabilistic model is a log-Gumbel regression model, able to predict the probabilistic W\u00f6hler field (P\u2013S\u2013N field), taking into account the mean stress (or stress R-ratio) effects. The parameters of the probabilistic model are identified using stress-life data derived for the P355NL1 steel, from smooth specimens, for three distinct stress R-ratios, namely R\u2009=\u2009\u22121, R\u2009=\u2009\u22120.5, and R\u2009=\u20090. The model requires a minimum of two test series with distinct stress R-ratios. Since data from three test series is available, extrapolations are performed to test the adequacy of the model to make extrapolations for stress R-ratios other than those used in the model parameters assessment. Finally, the probabilistic model is used to model the fatigue behavior of a notched plate made of P355NL1 steel. In particular, the P\u2013S\u2013N field of the plate is modeled and compared with available experimental data. Cyclic elastoplastic analysis of the plate is performed since plasticity at the notch root is developed. The probabilistic model correlated appropriately the stress-life data available for the P355NL1 steel and was able to perform extrapolations for stress ratios other than those used in the model identification. The P\u2013S\u2013N field identified using data from smooth specimens led to consistent predictions of the P\u2013S\u2013N field for a notched plate, demonstrating the adequacy of the probabilistic model also to predict the probabilistic W\u00f6hler field for notched components.<\/jats:p>","DOI":"10.1115\/1.4005392","type":"journal-article","created":{"date-parts":[[2012,1,14]],"date-time":"2012-01-14T08:35:31Z","timestamp":1326530131000},"update-policy":"https:\/\/doi.org\/10.1115\/crossmarkpolicy-asme","source":"Crossref","is-referenced-by-count":4,"title":["Probabilistic Fatigue Assessment of a Notched Detail Taking Into Account Mean Stress Effects"],"prefix":"10.1115","volume":"134","author":[{"given":"Ab\u00edlio M. P.","family":"De Jesus","sequence":"first","affiliation":[{"name":"Engineering Department, School of Sciences and Technology, University of Tr\u00e1s-os-Montes and Alto Douro, Quinta de Prados, 5001-801 Vila Real, Portugal"}]},{"given":"M.","family":"Luisa Ruiz Ripoll","sequence":"additional","affiliation":[{"name":"Lifetime Concepts, Thermomechanics, Business Unit Component Safety, Fraunhofer Institut\u2014IWM, Woehlerstr. 11, 79108 Freiburg, Germany"}]},{"given":"Alfonso","family":"Fern\u00e1ndez-Canteli","sequence":"additional","affiliation":[{"name":"Department of Construction and Manufacturing Engineering, University of Oviedo, Campus Viesques, 33203 Gij\u00f3n, Spain"}]},{"given":"Enrique","family":"Castillo","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Computational Sciences, University of Cantabria, 39005 Santander, Spain"}]},{"given":"H\u00e9lder F. S. G.","family":"Pereira","sequence":"additional","affiliation":[{"name":"UCVE, IDMEC\u2014P\u00f3lo FEUP, Campus FEUP, Rua Dr. Roberto Frias, 404, 4200-465 Porto, Portugal"}]}],"member":"33","published-online":{"date-parts":[[2012,1,13]]},"reference":[{"key":"2019100520154217100_c1","first-page":"89","article-title":"Some Considerations in the Statistical Determination of the Shape of S-N Curves","volume-title":"Statistical Analysis of Fatigue Data","author":"Spindel"},{"key":"2019100520154217100_c2","doi-asserted-by":"publisher","first-page":"277","DOI":"10.2307\/1271342","article-title":"Estimating Fatigue Curves With the Random Fatigue-Limit Model","volume":"41","author":"Pascual","journal-title":"Technometrics"},{"key":"2019100520154217100_c3","doi-asserted-by":"publisher","first-page":"813","DOI":"10.1016\/S0142-1123(99)00044-4","article-title":"A New Function Describing Fatigue Crack Growth Curves","volume":"21","author":"Kohout","journal-title":"Int. J. Fatigue"},{"key":"2019100520154217100_c4","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1016\/S0142-1123(00)00082-7","article-title":"A New Function for Fatigue Curves Characterization and Its Multiple Merits","volume":"23","author":"Kohout","journal-title":"Int. J. Fatigue"},{"volume-title":"A Unified Statistical Methodology for Modeling Fatigue Damage","author":"Castillo","key":"2019100520154217100_c5"},{"key":"2019100520154217100_c6","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1520\/STP43764S","article-title":"Cyclic Plastic Strain Energy and Fatigue of Metals","volume":"378","author":"Morrow","journal-title":"International Friction, Damping, and Cyclic Plasticity"},{"issue":"4","key":"2019100520154217100_c7","first-page":"767","article-title":"A Stress-Strain Function for the Fatigue of Metals","volume":"5","author":"Smith","journal-title":"J. Mater."},{"key":"2019100520154217100_c8","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1023\/A:1007624803955","article-title":"A General Regression Model for Lifetime Evaluation and prediction","volume":"107","author":"Castillo","journal-title":"Int. J. Fract."},{"key":"2019100520154217100_c9","doi-asserted-by":"publisher","first-page":"1047","DOI":"10.1016\/j.ijfatigue.2005.11.006","article-title":"Specimen Length Effect on Parameter Estimation in Modelling Fatigue Strength by Weibull Distribution","volume":"28","author":"Castillo","journal-title":"Int. J. Fatigue"},{"key":"2019100520154217100_c10","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1016\/j.ijfatigue.2007.02.011","article-title":"A General Model for Fatigue Damage Due to Any Stress History","volume":"30","author":"Castillo","journal-title":"Int. J. Fatigue"},{"volume-title":"Mechanics of Fatigue","author":"Bolotin","key":"2019100520154217100_c11","doi-asserted-by":"crossref","DOI":"10.1201\/9780138747848"},{"key":"2019100520154217100_c12","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1111\/j.1460-2695.2006.01099.x","article-title":"A Fatigue Model With Local Sensitivity Analysis","volume":"30","author":"Castillo","journal-title":"Fatigue Fract. Eng. Mater. Struct."},{"key":"2019100520154217100_c13","doi-asserted-by":"publisher","first-page":"1031","DOI":"10.1111\/j.1460-2695.2006.01068.x","article-title":"A Parametric Lifetime Model for the Prediction of High Cycle Fatigue Based on Stress Level and Amplitude","volume":"29","author":"Castillo","journal-title":"Fatigue Fract. Eng. Mater. Struct."},{"key":"2019100520154217100_c14","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1016\/j.probengmech.2008.06.003","article-title":"A Statistical Fatigue Model Covering the Tension and Compression W\u00f6hler Fields","volume":"24","author":"Castillo","journal-title":"Probab. Eng. Mech."},{"key":"2019100520154217100_c15","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1016\/j.ijfatigue.2008.09.003","article-title":"Experimental Validation of a Statistical Model for the W\u00f6hler Field Corresponding to Any Stress Level and Amplitude","volume":"31","author":"Koller","journal-title":"Int. J. Fatigue"},{"key":"2019100520154217100_c16","doi-asserted-by":"publisher","first-page":"1041","DOI":"10.2307\/2291341","article-title":"Modelling Lifetime Data With Application to Fatigue Models","volume":"90","author":"Castillo","journal-title":"J. Am. Stat. Assoc."},{"key":"2019100520154217100_c17","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1115\/1.1858927","article-title":"Finite Element Modeling of Fatigue Damage Using a Continuum Damage Mechanics Approach","volume":"127","author":"De Jesus","journal-title":"J. Pressure Vessel Technol."},{"key":"2019100520154217100_c18","doi-asserted-by":"publisher","first-page":"021407","DOI":"10.1115\/1.3066774","article-title":"Fatigue Damage Behavior of a Structural Component Made of P355NL1 Steel Under Block Loading","volume":"131","author":"Pereira","journal-title":"J. Pressure Vessel Technol."},{"key":"2019100520154217100_c19","doi-asserted-by":"publisher","first-page":"051402","DOI":"10.1115\/1.3147986","article-title":"Analysis of Variable Amplitude Fatigue Data of the P355NL1 Steel Using the Effective Strain Damage Model","volume":"131","author":"Pereira","journal-title":"J. Pressure Vessel Technol."},{"issue":"4","key":"2019100520154217100_c20","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1520\/JTE11613J","article-title":"Generalised Application of Neuber\u2019s Rule","volume":"8","author":"Seeger","journal-title":"J. Test. Eval."},{"key":"2019100520154217100_c21","doi-asserted-by":"publisher","first-page":"544","DOI":"10.1115\/1.3641780","article-title":"Theory of Stress Concentration for Shear-Strained Prismatic Bodies With Arbitrary Nonlinear Stress-Strain Law","volume":"28","author":"Neuber","journal-title":"Trans. ASME J. Appl. Mech."},{"key":"2019100520154217100_c22","unstructured":"Ramberg, W., and Osgood, W. R., 1943, \u201cDescription of Stress-Strain Curves by Three Parameters,\u201d NACA Technical Note No. 902."},{"key":"2019100520154217100_c23","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1111\/j.1475-1305.2007.00389.x","article-title":"Analysis of Fatigue Damage under Block Loading in a Low Carbon Steel","volume":"44","author":"Pereira","journal-title":"Strain"},{"key":"2019100520154217100_c24","doi-asserted-by":"publisher","first-page":"021210","DOI":"10.1115\/1.3062965","article-title":"Cyclic and Fatigue Behavior of the P355NL1 Steel Under Block Loading","volume":"131","author":"Pereira","journal-title":"J. Pressure Vessel Technol"},{"article-title":"Validation of Procedures for Fatigue Assessment of Pressure Vessels","volume-title":"Ph.D. thesis","author":"de Jesus","key":"2019100520154217100_c25"},{"key":"2019100520154217100_c26","first-page":"293","article-title":"Notch Sensitivity","volume-title":"Metal Fatigue","author":"Peterson"}],"container-title":["Journal of Pressure Vessel Technology"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/asmedigitalcollection.asme.org\/pressurevesseltech\/article-pdf\/doi\/10.1115\/1.4005392\/5551439\/021203_1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/asmedigitalcollection.asme.org\/pressurevesseltech\/article-pdf\/doi\/10.1115\/1.4005392\/5551439\/021203_1.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,12,26]],"date-time":"2021-12-26T00:39:28Z","timestamp":1640479168000},"score":1,"resource":{"primary":{"URL":"https:\/\/asmedigitalcollection.asme.org\/pressurevesseltech\/article\/doi\/10.1115\/1.4005392\/455754\/Probabilistic-Fatigue-Assessment-of-a-Notched"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,1,13]]},"references-count":26,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2012,4,1]]}},"URL":"https:\/\/doi.org\/10.1115\/1.4005392","relation":{},"ISSN":["0094-9930","1528-8978"],"issn-type":[{"type":"print","value":"0094-9930"},{"type":"electronic","value":"1528-8978"}],"subject":[],"published":{"date-parts":[[2012,1,13]]},"article-number":"021203"}}