Interpreting load ratio dependence of near-threshold fatigue crack growth by a new crack closure model Ming-Liang Zhu, Fu-Zhen Xuan * , Shan-Tung Tu Key Laboratory of Pressure System and Safety, MOE, School of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai 200237, China Keywords: Fatigue crack growth Crack closure Near-threshold fatigue Load ratio Crack driving force abstract It was still short of generalized fatigue crack growth (FCG) models in the near-threshold regime due to its complex influencing factors. The near-threshold FCG behaviour of a rotor steel 25Cr2Ni2MoV at different load ratios was investigated experimentally, and the FCG driving mechanism was theoretically analysed based on equivalent driving force model. It was found that the crack growth process was determined by combined effects of equivalent driving force at constant amplitude loading and crack closure. A new crack closure model was proposed by considering the influences of load ratio and FCG rate, which could successfully interpret the effect of load ratio on FCG. The correlation of the crack closure model with the transition of driving forces in crack advance was beneficial to unify crack closure theory and crack growth driving parameters in the near-threshold regime. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction Understanding the fatigue performance of materials and thus developing a service-life prediction method is a hot issue of structural integrity assessment. In practice, some components have complex loading conditions. For example, in rotating components, the rotors or blades undergo mechanical, thermal, residual and randomly vibrating stresses [1]. On one hand, both constant and variable amplitude fatigue need to be investigated. On the other hand, the load patterns in the components are featured by various stress ratios (the ratio of minimum to maximum loads, P min /P max ), making the integrity assessment complicated. Therefore, it is crit- ical to understand the fatigue mechanisms of materials at different load ratios. During the past several years, the load ratio dependence of fa- tigue behaviour has been widely investigated. Walker [2] devel- oped an equation including the load ratio parameter, and it was always used in the Paris regime. Elber [3] proposed the crack closure concept in 1970s, since then the influence of the load ratio on long crack growth has been explained by an effective stress intensity range DK eff (DK eff ¼ K max  K c ) approach based on the plasticity-induced crack closure mechanism. Subsequently the popular NASGRO [4] formula has been developed and incorporated into damage tolerant design process. In addition, models for correlating fatigue threshold with load ratio have been established in many materials and documented by Kwofie [5] and Bulloch [6]. Until now, it has been generally accepted that load ratio can affect fatigue threshold, but whether crack closure dominates near- threshold fatigue crack growth (FCG) is still an open issue [7,8]. In fact, the key point in the crack closure concept is the deter- mination of crack opening load. Newman Jr. [9] and Schijve [10] deduced equations to correlate crack closure level with stress ra- tio, load level and specimen constraint under constant amplitude loading procedure. However, it would be improper to transfer these kinds of crack closure equations into describing FCG in the load- shedding procedure in near-threshold regime. This has been veri- fied by Yamada et al. [11e 13] who found that the crack opening load was tended to increase with the decreasing of load level. Unfortu- nately, little has been reported in crack closure models for FCG in near-threshold regime. Another approach to load ratio dependence of FCG is from the perspective of crack growth driving force. Sadananda and Vasu- devan [14e16] argued that both DK and K max parameters controlled FCG. While Kwofie [5,17] thought it was DK and K m that drive crack growth under cyclic loadings, and attempted to generalize da/dNe DK curve at different load ratios. However, whether crack closure plays a role in the transition of crack growth driving parameter is not clear yet. Therefore, in the present work, near-threshold FCG behaviour of a rotor steel 25Cr2Ni2MoV was investigated at various stress ratios. * Corresponding author. E-mail address: fzxuan@ecust.edu.cn (F.-Z. Xuan). 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 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijpvp.2013.04.015 International Journal of Pressure Vessels and Piping 110 (2013) 9e13