Fatigue life predictions including the Bauschinger effect M. Buciumeanu a, * , L. Palaghian a , A.S. Miranda b , F.S. Silva b a Faculty of Mechanical Engineering, ‘‘Dunarea de Jos” University, Galati, Romania b Department of Mechanical Engineering, University of Minho, Azurém, 4800-058 Guimarães, Portugal article info Article history: Received 20 November 2009 Received in revised form 23 July 2010 Accepted 28 July 2010 Available online 1 August 2010 Keywords: Bauschinger effect (BE) Fatigue Smith–Watson–Topper (SWT) Morrow abstract This paper proposes a modification on both the Smith–Watson–Topper and the Morrow models in order to take into account the Bauschinger effect. Two materials with substantially different Bauschinger effects, an Al7175 alloy with approximately no Bauschinger and Ck45 steel with a substantial Bauschin- ger effect will be assessed with the previous models. The paper discusses possible consequences of the Bauschinger effect on fatigue life of the two materials. The main objective of this paper is to demonstrate that the Bauschinger effect may play a significant role on fatigue life of materials and should then be con- sidered in fatigue life prediction models. Ó 2010 Elsevier Ltd. All rights reserved. 1. Introduction The Bauschinger effect (BE), which reflects a material deviation from the ideal plastic behavior, is schematically described in Fig. 1. It can be seen from Fig. 1 that when the materials are loaded uniax- ially in one direction (e.g. in tension) into the plastic regime, un- loaded to zero stress level, then reloaded in reverse direction (e.g. compression), they yield during the reloading at a stress level lower (r y,rev < r y ) than if the reloading were carried out in the ori- ginal direction. In the last years it was demonstrated [1,2] that BE is more com- plex than only a lowering of reverse yield stress, the whole shape of the second loading work-hardening curve is modified. For exam- ple, the BE induces a material anisotropy leading to a shift of the center of the stress–strain hysteresis loop. The BE has been shown to occur in a variety of materials, and it was observed that the ef- fect is more pronounced in face centered cubic (fcc) materials com- pared to the body-centered cubic (bcc) materials. In view of these complexities it is not surprising that many dif- ferent features [1–5] have been used to understand/describe the BE. The physical origins are generally attributed to: (i) internal stresses; (ii) dislocation theories; (iii) composite model (Masing’s model or Asaro’s model). Many studies [6–18] showed that the understanding of BE has several important practical applications. There are studies that show that BE is important in the case of autofrettaged thick cylinders. Autofrettage is used to introduce beneficial residual stresses into pressure vessels and to improve their later fatigue life. Several authors [12–18] concluded that the BE serves to reduce the yield strength in compression as a result of prior tensile plastic overload. Chawla and co-authors [19] highlighted the importance of BE on the residual stress relief operations (by stretching). It has been shown that in stretching operations it may produce a material with a lower flow stress if loading is in direction opposite to the stretching direction. There are also studies that show that the BE is important for forming processes of materials and for other mechanical properties of formed components [1,3,20,21]. However its possible effects on fatigue initiation life were not sufficiently discussed. According to the authors of this work, two possible effects may arise from the change in the hysteresis loop (BE) (Fig. 1):  The first one is based on energy principles. The first interpreta- tion is based on the fact that the dissipated energy in each cycle may be reduced due to the BE (Fig. 1). Consequently the reduc- tion on the hysteresis loop internal area causes an increase in fatigue life.  The second possible effect was provided by Pommier [8]. Pom- mier stated that, in crack propagation, due to the reduced reverse yield stress, the BE changes the plastic deformed areas both ahead and behind the crack tip affecting the residual stress field ahead of the crack tip but also the closure level behind the crack tip. The consequence of the previous effects would be a decrease in propagation life. According to Pommier the increased damaged area ahead of the crack tip, responsible for propagation life reduction, may eventually also apply for fatigue initiation whenever plastic deformation occur. 0142-1123/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijfatigue.2010.07.012 * Corresponding author. Tel.: +40 747636387; fax: +40 236 46 13 53. E-mail addresses: mihaela.buciumeanu@ugal.ro (M. Buciumeanu), liviu. palaghian@ugal.ro (L. Palaghian), asm@dem.uminho.pt (A.S. Miranda), fsamuel@ dem.uminho.pt (F.S. Silva). International Journal of Fatigue 33 (2011) 145–152 Contents lists available at ScienceDirect International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue