Bursting pressure of autofrettaged cylinders with inclined external cracks Rahman Seifi * , Majid Babalhavaeji Mechanical Engineering Department, Faculty of Engineering, Bu-Ali Sina University, Hamedan, Iran article info Article history: Received 19 February 2011 Received in revised form 27 September 2011 Accepted 11 October 2011 Keywords: Bursting pressure Autofrettage External crack Inclined crack Modified J-Integral abstract Autofrettaging a pressure vessel improves its pressure capacity. This is reliable if there isn’t any crack or other type of flaws. In this paper, the effects of external surface cracks on bursting pressure of auto- frettaged cylinders are studied. It is observed that bursting pressure decreases considerably (up to 30%) due to external cracks in the cylinders without autofrettage. This reduction increases for high levels of the applied autofrettage. External axial cracks have more effects than inclined cracks. Comparing experimental and numerical results show that the numerical methods can acceptably predict the bursting pressure of the autofrettaged cracked cylinders. These predictions are valid when the fracture parameter (J-Integral) is calculated from the modified equation that takes into account the effects of residual stresses. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction Increasing the pressure carrying capacity of cylinders with autofrettage process is one of the major methods for improving of the materials usage. In the autofrettage process the internal pressure is increased until some portions of cylinder’s wall deform plastically. Then internal pressure is removed and compressive residual stresses are created in the inner portions of the pressure vessel. In this method, tension residual stresses are remained in the outer portions of the wall. If defects or cuttings such as dents or gouges exist on outer surface, these stresses reduce the pres- sure capacity of the vessels due to stress concentrations. This reduction is increased if there is a surface crack. Defects or cracks may be created in any direction thus study on their behaviors can be useful. The distributions of the residual stresses in thick-walled cylin- ders due to the autofrettage process were studied comprehensively in literature. Blazinski [1] studied the effects of elastic-perfectly plastic behavior of materials on the residual stress distributions. Xiaoying and Gangling [2] investigated two different methods for determination of the residual stresses due to the autofrettage in the elasticeplastic materials. In other studies, the deformations and residual stresses in thick-walled cylinders were analyzed [3,4]. Recent years, numerous studies were done on this topic from different views. The applied autofrettage introduces advantageous compressive residual stresses into the inner parts of the cross section of the pressure vessels but the Bauschinger effect (BE) (reduction of reversed yielding stress and change of stress-strain curve in compression after tension) can decreases the compres- sive residual hoop stresses near the bore. The Bauschinger effect changes the distribution of residual stress within about one quarter of wall thickness. Out of this portion the influence of the BE vanishes. For thin cylinders with the ratio of outer to inner radius smaller than 1.2, the BE can be neglected [5]. Livieri and Lazzarin [6] used the proper analytical methods to evaluation of the residual stress distributions. Only near the inner surface, the BE and hard- ening behavior of materials can influence these distributions [7,8]. Majzoobi et al. [9] studied the increasing of strength and bursting pressure of the autofrettaged thick cylinders. They investigated the effects of autofrettage pressure and number of autofrettage stages with different levels. In the base of this study, optimized auto- frettage pressure for largest bursting pressure is achieved when cross section becomes fully plastic (100% autofrettage) but the number of autofrettage stages have no effects on the pressure capacity. Effect of re-autofrettage procedure was investigated by numerical methods. It was shown that the cylinder will sustain a higher pressure after re-yielding than in its original state after initial autofrettage. After triple autofrettage the loss of residual hoop stress due to the BE was reduced significantly and the influ- ence of the BE can be ignored [10]. The experimental data of the slit tests of a disk cut from a thick-walled cylinder with different level of the autofrettage ratio were compared to the numerical results. This comparing shows that the experimental data correlate with non-Bauschinger or ideal isotropic hardening assumptions [8]. * Corresponding author. Tel.: þ98 8118292630; fax: þ98 8118292631. E-mail address: rseifi@basu.ac.ir (R. Seifi). Contents lists available at SciVerse ScienceDirect International Journal of Pressure Vessels and Piping journal homepage: www.elsevier.com/locate/ijpvp 0308-0161/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijpvp.2011.10.018 International Journal of Pressure Vessels and Piping 89 (2012) 112e119