FATIGUE LIFE PREDICTION OF SMALL NOTCHED TI-6AL-4V BASED ON THE THEORY OF CRITICAL DISTANCE

This study investigated the estimating method for small notched fatigue strength of Ti-6Al-4V alloy using the theory of critical distance that employ the stress distribution in the vicinity of the notch. Circumferential notched round bar axial-loading fatigue tests were conducted to investigate the effect of notch radius and notch depth on fatigue strength. The fatigue tests show that the larger notch radius gives the increase of fatigue strength and the larger notch depth gives the decrease of fatigue strength. The theory of critical distance assumes that fatigue damage can be correctly estimated only if the entire stress field damaging the fatigue fracture process zone is taken into account. Critical distance stress is defined as the average stress within the fatigue fracture process zone where satisfies the area in the critical distance, a0, from the notch root. It has been found that there exists the good correlation between critical distance stress and crack initiation life of small notched specimen if the critical distance, a0, is determined with 10 cycle plain fatigue limit stress range, 0 σ ∆ , and threshold stress intensity factor range, th K ∆ using the stress intensity factor equation of semi-circle surface crack. INTRODUCTION The high cycle fatigue (HCF) of titanium alloy turbine engine components remains a principal cause of failures in aircraft engines. HCF can result from vibration, M. Bos (ed.), ICAF 2009, Bridging the Gap between Theory and Operational Practice, 685–706. © Springer Science+Business Media B.V. 2009 Y. Yamashita, M. Shinozaki, H. Kuroki, Y. Ueda 686 forced response, unsteady aerodynamic loads, or other fluctuating loads. Gas turbine engine rotor blades and stator vanes are subject to all types of loads and are particularly vulnerable to HCF failures. Rotating blades in gas turbine engine are often subjected to impact from debris ingested into the engine during takeoff and landing which is called foreign object damage (FOD). Such debris may result in small notches at the leading or trailing edges of airfoils which in turn, reduces the fatigue strength of the material. Therefore, FOD-induced HCF is one of the significant themes in fatigue problems of aero-engine component [1-3]. Figure 1 shows the photographs leading edge notches by FOD and it is much concerned whether these defects may cause HCF or not. In these view points, notched fatigue problem is important to investigate the effects of FOD on fatigue strength of Ti6Al-4V alloy. (a) fan blade (b) small FOD damage Fig. 1 Schematics of FOD damage at leading edge of airfoil. This study investigated the estimating method for notched fatigue strength of aeroengine fan blade and compressor blade of forged Ti-6Al-4V alloy. Fatigue predictions for notched specimens based on the maximum peak stress at the notch root are often inaccurate. It has been recognized that the simple use of the maximum peak stress at the notch root is often inadequate for characterizing the fatigue life of notched components. The stress state and stress distribution in the vicinity of the notch root are contributing factors to the fatigue process. The stress gradient at the surface of the notch root has been used in several early investigations, resulting in the fatigue predictions of Neuber [4], Peterson[5] that are utilized in current engineering design. Several more recent investigations have produced models that predict fatigue failure by employing the stress distributions in the region of the notch root [6-13]. The physical reasoning behind these investigations is that a critical volume of material must be subjected to a critical stress level for fatigue failure to occur at a given failure life. If one considers this volume to remain constant for notches of any size or shape within the same material, the observation that sharp notches have higher fatigue strengths than mild Fatigue life prediction of small notched Ti-6Al-4V 687 notches for the same magnitude stress concentration factor is partial evidence for such a theory [4,5]. In this study, the method for fatigue life prediction of small notched Ti-6Al-4V specimens using the theory of the critical distance (TCD) [6,7] has been investigated. The TCD applied to fatigue problems assumes that fatigue damage depends on the stress field distribution in the vicinity of the stress concentrator. In other words, the TCD assumes that fatigue damage can correctly be estimated only if the entire stress field damaging the fatigue process zone is taken into account. Conventionally, critical distance stress is defined as the average stress in the material characteristic length as the distance from the notch-tip. And material characteristic length, a0, may be calculated with the threshold value of the stress intensity factor range, th K ∆ , and the smooth specimen’s fatigue limit, 0 σ ∆ . Taylor [6] and Susmel [7] were reviewed the most interesting findings in the use of the theory of critical distances to predict fatigue strength of notched mechanical components. They investigated the physical meaning of the theory and tried to verify its accuracy in predicting notch fatigue strength under different loading conditions and concluded that the theory is a powerful engineering tool suitable for assessing real mechanical components in situations of practical interests. And they reviewed that the theory of critical distance formalizations based on the use of linear-elastic stresses. They suggest that such theory can successfully be used to post-process simple linear-elastic finite element (FE) models reducing time and costs of the design process. Wang [8] used a critical distance calculated from the fatigue limit stress and crack growth threshold, th K ∆ . The maximum principal stress at this distance from the notch root of a stress concentration was then compared to another notch geometry and loading condition and used to predict fatigue failure. Lanning [9] studied the critical distance at which the notched specimen stresses correspond to the stresses in a smooth bar that produces the same fatigue limit stress have resulted in modest success using Ti-6Al-4V alloy. The results of their investigation seem to indicate that a single parameter involving a critical distance may be a viable approach for predicting fatigue limit stresses in notched Ti-6Al-4V components. But they concluded that a size effect may exist with very small notches, in which case a single parameter may not be applicable. A lot of studies in the theory of critical distances have been conducted as mentioned above. But the unified recognition in determining the critical distance is not constructed so far in the practical engineering use especially for very small notches. In this study, the practical and appropriate approach in determining the critical distance and the critical distance stress has been investigated using simple Y. Yamashita, M. Shinozaki, H. Kuroki, Y. Ueda 688 linear-elastic finite element (FE) results. The critical distance stress is defined as the average stress in the critical distance region. In the experimental study, small notched round bar axial-loading fatigue tests have been conducted with forged Ti-6Al-4V alloy to investigate the effect of notch radius and notch depth on fatigue strength of the material. Notch radius is varied from 0.05 to 0.2mm and notch depth is varied as 0.1, 0.3 and 0.5mm. And in the analytical study, the investigation into the appropriate determination method of the critical distance and the critical distance stress to predict crack initiation life of notched round bar specimen has been conducted using forged Ti6Al-4V alloy. This study shows that the appropriate method to evaluate fatigue life of Ti-6Al-4V material with various notch radius and notch depth can be constructed from the relationships between the critical distance stress and fatigue crack initiation life.