Evaluation of gigacycle fatigue limit and life of high-strength steel with interior inclusion-induced failureby W. Li, P. Wang, L.-T. Lu, T. Sakai

International Journal of Damage Mechanics



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Evaluation of gigacycle fatigue limit and life of high-strength steel with interior inclusion-induced failure

Wei Li1, Ping Wang2, Lian-Tao Lu3 and Tatsuo Sakai4


The gigacycle fatigue properties with the interior inclusion-induced failure for three kinds of high-strength steels are investigated in this study. Fatigue strength of these steels in the gigacycle regime is highly related to the sizes of inclusions that are present in the effective damage zone under loading condition.

The induced stress concentration at the inclusion–matrix interface plays a key role in the small crack growth process within fine granular area, but has little effect on the macroscopic crack growth outside the fine granular area. Considering the effect of stress gradient around the inclusion, new models were developed to evaluate the values of stress intensity factor at the front of the fine granular area and the fish-eye. A nearly constant stress intensity factor value of 4.5MPa ffiffiffiffi m p for the fine granular area can be regarded as the threshold value controlling interior macroscopic crack growth. A method from the viewpoint of small crack growth was proposed to evaluate the fatigue limit/life of high-strength steel with the interior inclusion-induced failure in the gigacycle regime, which reveals the influences of loading condition, inclusion size, and specimen size. In life prediction, this method is mainly based on the relationship between the fine granular area size and the fatigue life. Because of the maximum inclusion sizes used, the partially predicted results may be somewhat conservative, but they are more satisfied with the requirement of safety design.


High-strength steel, gigacycle fatigue, interior crack growth, fatigue limit, life prediction

International Journal of Damage

Mechanics 2014, Vol. 23(7) 931–948 ! The Author(s) 2014

Reprints and permissions: sagepub.co.uk/journalsPermissions.nav

DOI: 10.1177/1056789513520175 ijd.sagepub.com 1School of Mechanical Engineering, Beijing Institute of Technology, Beijing, China 2Institute of Oceanographic Instrumentation, Shandong Academy of Sciences, Qingdao, China 3State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu, China 4Research Center of Advanced Materials Technology, Ritsumeikan University, Kusatsu, Japan

Corresponding author:

Wei Li, Beijing Institute of Technology, 5 South Zhongguancun Street, Haidian District, Beijing 100081, China.

Email: lw_cy@sina.com at LAKEHEAD UNIV on March 13, 2015ijd.sagepub.comDownloaded from


The gigacycle fatigue of metallic materials in the life regime beyond 107 cycles has been a subject of growing interest in recent years, which is mainly due to the unexpected fatigue failures of some metallic materials that were presumed to be operating at the stresses below the traditional fatigue limit (Bathias, 1999). The traditional fatigue design concepts are no longer satisfied with the demands of safety and reliability design for the mechanical structures or components serving in the gigacycle regime. New methods or models for evaluating the fatigue strength and the fatigue life in the gigacycle regime are urgently needed to be developed. As an essential prerequisite, furthermore, it is very important to understand the fundamental failure mechanisms of metallic materials in the gigacycle regime.

The interior crack-induced failure at low stress region is a typical failure mode of high-strength steels with tensile strength above 1200MPa in the gigacycle regime (Li et al., 2010; Sakai et al., 2000;

Shiozawa et al., 2001; Wang et al., 1999). Compared with surface crack, the interior crack is extremely difficult to be directly observed and measured during the experiment. As a result, the analysis on fracture morphology after the experiment has become a commonly used means of investigating interior failure mechanism. Generally speaking, the interior crack of high-strength steel mainly initiates from some small non-metallic inclusions that are produced during the melting process of steel and is shaped like a fish-eye. Sometimes, a peculiar rough area, named as fine granular area (FGA) (Sakai et al., 2000), can occur around the inclusion, and its formation is considered to dominate the gigacycle fatigue properties of steels (Li et al., 2010; Shiozawa et al., 2001; Wang et al., 1999). Based on the idea that the crack initiation is predominant in the fatigue damage process with long fatigue life, some models based on the dislocation theory (Li et al., 2010) were developed to evaluate the crack initiation life within the FGA, but it is still a difficult task because the crack initiation mechanism within the FGA is not yet well understood (Sakai, 2007).

Conversely, the ultrasonic fatigue tests about crack growth behavior (Stanzl-Tschegg, 1999;

Stanzl-Tschegg and Scho¨nbauer, 2010) show that fatigue crack still can propagate even if the stress intensity factor (SIF) at the crack tip is less than the traditional threshold value controlling macroscopic crack growth, and that in vacuum the effective crack growth rate of high-strength steel can be reduced to 5 1013m/cycle (Stanzl-Tschegg and Scho¨nbauer, 2010). In addition, the crack morphology similar to the FGA is observed on the fracture surface of specimen for the crack growth rate testing in vacuum (Nakamura et al., 2010). In view of the fact that the interior crack-induced failure takes place in vacuum and the propagating crack can be formed in very few cycles (Kuroshima et al., 1998; Murakami and Miller, 2010), some researchers pointed out (Akiniwa et al., 2006; Tanaka and Akiniwa, 2002) that fatigue life consumed in the formation process of the FGA, i.e. assumed as total fatigue life, could be evaluated from the viewpoint of crack growth.

Based on the assumption that small material discontinuities such as inclusions can be considered to be small existed cracks, the ffiffiffiffiffiffiffiffiffi area p parameter model has been used to evaluate the SIF value of the inclusion (Murakami and Endo, 1994). Furthermore, based on the ffiffiffiffiffiffiffiffiffi area p model, the interior inclusion-induced crack growth behavior can be approximately characterized by the Paris law in combination with S–N data (Tanaka and Akiniwa, 2002), and the evaluated crack growth rate within the FGA is in the range of 1012 to 1016m/cycle (Akiniwa et al., 2006; Li et al., 2010;