Probabilistic high cycle fatigue behaviour prediction based on global approach criteria q R. Ben Sghaier a , Ch. Bouraoui a , R. Fathallah b, * , T. Hassine a , A. Dogui a a Laboratoire de Ge ´nie Me ´canique, Ecole Nationale d’Inge ´nieurs de Monastir, Avenue Ibn El Jazzar, 5019 Monastir, Tunisia b Laboratoire de Ge ´nie Me ´canique, Ecole Nationale d’Inge ´nieurs de Sousse, Cite ´ Taffala, 4003 Sousse, Tunisia Received 15 July 2005; received in revised form 27 March 2006; accepted 28 March 2006 Available online 6 June 2006 Abstract This paper presents an approach to predict the reliability of high cycle fatigue (HCF) behaviour of metallic parts using the multi-axial HCF criterion of Crossland, for the case of normally distributed in-phase fully reversed torsion and bending loading and HCF material characteristic parameters. The dispersions of: (i) the HCF criterion material characteristic parameters and (ii) the applied loading have been taken into account. The reliability of the HCF resistance was determined by using the ‘‘Strength Load’’ with first order reliability method (FORM). This approach gives iso-probabilistic Crossland diagrams (PCD) corresponding to different coefficient of variation (COV) of loading and material HCF characteristic parameters. An application has been carried out on a hard steel metal submitted to a fully reversed torsion and bending loading. Two types of various dispersed loadings, having different COV, are studied: (i) only random torsion amplitude loading and (ii) both random torsion and bending amplitude loading. The proposed method allows evaluation of the influences of different dispersions on the reliability of the HCF behaviour. It has been observed that, the proposed method is qual- itatively consistent with the physical observations and leads to a more reliable HCF prediction compared to the deterministic approach, which takes into account separately two fatigue limits corresponding to a given reliability value, in the HCF criterion of Crossland. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Probabilistic fatigue; High cycle fatigue; Fatigue reliability; FORM; Global approach fatigue criteria; Fatigue scattering parameters 1. Introduction Practical computation of HCF reliability of mechanical components, used in automotive, aerospace, naval struc- tures, nuclear plants etc. is much needed [1–4] for a better secure design of mechanical parts. The HCF reliability is usually affected by many uncertainties and characterised by several random variables. Various causes of uncertainty having influence on the HCF behaviour are summarised by Sevensson [5], as follows: (i) material properties, (ii) struc- tural properties of components, (iii) load variation, (iv) parameter estimation; and (v) model error. The prediction of the HCF behaviour of a representative volume element of a mechanical component is carried out, in the majority of cases, by deterministic multi-axial HCF criteria, such as Sines [6], Crossland [7], Dang Van [8] and Papadopoulos [9,10]. Their applications are carried out in a deterministic way, and generally use experimental fatigue limits corresponding to failure probability of 50%. They do not include the stochastic effects, particularly the loading and the material dispersions effects, on the HCF prediction. As a consequence, the calculations may predict, but not correctly, the total reliability of the HCF behaviour of mechanical parts. Several works were carried out to take into account the probabilistic effects on the fatigue behaviour. The majority of them have been used in the one-dimensional loading 0142-1123/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijfatigue.2006.03.015 q This work is a part of the Phd thesis of Mr. R. Ben Sghaier supervised by C. Bouraoui and R. Fathallah. * Corresponding author. Tel.: +216 73 332 657; fax: +216 73 332 65. E-mail addresses: raouf.fathallah@gmail.com, raouf.fathallah@ issatso.rnu.tn (R. Fathallah). www.elsevier.com/locate/ijfatigue International Journal of Fatigue 29 (2007) 209–221 International Journalof Fatigue