Nuclear Engineering and Design 188 (1999) 129 – 137 Simplified J estimation methods for cracked cylinders under combined thermal and mechanical loading S. Ignaccolo a, *, B. Drubay b , M.H. Papin b , B. Michel c , P. Gilles d a EDF 12 – 14 Aenue Dutrieoz, 69628 Villeurbanne, France b CEA/DMT/SEMT/RDMS, 91191 Gif sur Yette, France c CEA/DER/SERA/LDCS, 13108 St Paul lez Durance, France d FRAMATOME/Tour FRA, 92084 Paris la De ´fense, France Received 9 June 1997; received in revised form 4 June 1998; accepted 10 July 1998 Abstract In the field of non-linear fracture mechanics, a lot of work has been done on structures submitted to mechanical loadings. However, for thermal loadings and particularly for thermal shocks, only few results are available. The aim of this paper is to present the main results of a complete set of finite element (FE) computations, conducted by CEA, EDF and FRAMATOME, on cracked cylinders submitted to combined mechanical and thermal loads. The interaction between these two types of loads is analysed in the cases of austenitic and ferritic structures. Moreover, these results are compared to the predictions obtained by simplified engineering methods (R6 procedure and two French approaches) in order to improve them. Their domain of validity is also discussed. © 1999 Elsevier Science S.A. All rights reserved. 1. Introduction Nuclear pressure vessels, or piping, can be sub- jected throughout their life to severe mechanical and thermal loadings. In this type of structure, precise and simple engineering methods are neces- sary to assess the flaws. Therefore, the basic prob- lem of a cylinder, with an inner circumferential surface crack, under combined pressure, tension and thermal load, has been studied. The case of the linear thermal gradient through the thickness (Ignaccolo et al., 1996) has been completed now with a thermal shock. The scope is to improve simplified rules in non-linear fracture mechanics, through the understanding of the behaviour of these cylinders. Following the presentation of the non-linear computational program and the sim- plified methods tested, the results are discussed and some recommendations on their application are provided. 2. Validation program A set of configurations representative of the nuclear industry components have been achieved, and constitute the reference data base to assess * Corresponding author. Tel.: +33-47-282-7777; fax: +33- 47-282-7000. 0029-5493/99/$ - see front matter © 1999 Elsevier Science S.A. All rights reserved. PII:S0029-5493(99)00010-2