NOMENCLATURE

\(\sigma_{t}\) ultimate tensile strength
\(\sigma_{s}\) yield stress
E Young’s modulus
HV Vickers hardness
m , c material parameter
\(\overset{\overline{}}{W_{i}}\) width of scratch i
\(\overset{\overline{}}{D_{i}}\) depth of scratch i
R fatigue loading stress ratio
\(\sqrt{\text{area}}\) fatigue damage parameter for micro scratch
\(\sigma_{w}\) fatigue strength
\(\sigma_{w,}\) conditional fatigue strength for micro scratch
\(a_{0}\) initial defect size
\(\frac{\text{da}}{\text{dN}}\) fatigue crack growth rate
\(N_{f}\) experimental fatigue life
\(N_{P}\) predicted fatigue life
Keywords: TC17 titanium alloy, micro scratch, high cycle fatigue life, three-parameter model.
1 | Introduction
In the aerospace industry, titanium alloy compressor blades are the critical parts of an aero engine. The rotor blades are subjected to severe mechanical loads such as centrifugal force, moment load during the operation. Moreover, high-frequency vibration generated by the surge, resonance, and flutter make it prone to fatigue failure.1,2 Titanium alloy has sensitivities for surface integrity, which make it easy to produce various damages, especially micro scratch. Operation at extreme conditions, micro scratches are sufficient to induce early initiation and propagation of fatigue cracks, leading to premature fatigue fracture of blades. 3,4Thus, it will exert potential risk of fatigue failure to the aircraft if have the scratched blade continue to serve.
Fatigue behavior affected by scratches has been a subject of great interest to demand for the development of safe fatigue design, damage assessment and fatigue life prediction. Wiryolukito 3investigated the cause of failure on compressor blade of X-gas turbine in service prior the schedule for overhaul at 40,000 hour. The evidences indicate the scratch has an important role to initiate fatigue crack on blade root chamfer. Gourdin5 found that the fatigue crack growth of natural cracks initiating from scratches without residual stresses is identical and similar to the long crack growth behavior of a nickel based superalloy. Inchekel and Talia6 revealed that the fatigue life decreased sharply as the scratch depth increased and an edge scratch is more detrimental than a center scratch. Mayer 7 investigated fatigue life of bainitic bearing steel under fully reversed tension-compression loading at cycling frequency 20 kHz. They found that surface cracks are initiated at surface defects produced during machining and deep scratches (approximately 8 μm) can be considered as pre-cracks. Poulain8 also pointed out that the location and the growth of fatigue cracks in the early stages are controlled by the presence and the geometry of grinding scratches. It can be concluded that once scratched blades continue to serve, there will be huge potential safety hazards to the aircraft.
The fatigue life of scratched structures can be predicted using dynamic analysis of scratch generation combined with the continuum damage mechanics based fatigue damage model9. A new method to calculate the fatigue life and defect tolerance for a30CrMnSiA steel specimen with artificial scratches was proposed.10Xu11 estimated the fatigue limit curve for highspeed railway axles with surface scratch using Murakami theory. The sensitivity of the HCF and VHCF strength to small scratches under torsional and rotating bending fatigue tests can be evaluated by parameter model. 12
Traditionally, surface roughness parameter such as Ra , Rzcan be a common method to evaluation on surface condition. Stylus method is commonly employed to collect surface morphology data. But stylus method cannot aim at the specific scratches directly, and actual depth and width maybe not reflected by surface roughness. Researches have pointed out that surface roughness cannot be applied directly to express the relationship between fatigue failure performance and the surface defects.13-15 There are also few parameters on expressing fatigue damage quantitatively caused by actual micro scratch.
In previous work, we proposed a parameter \(\sqrt{\text{area}}\) to describe fatigue damage caused by micro scratch.\(\sqrt{\text{area}}\) is inspired by Murakami theory and developed for actual micro scratch. The ability of \(\sqrt{\text{area}}\) in conditional fatigue strength prediction was verified by high strength steel FV520B-I and Ti-6Al-4V.16 Prediction error is below 10% for the two material. Using actual scratch depth and width of micro scratch of EA4T steel from Xu 17, prediction error is also lower than 10%.18 For the scratch with a depth from 10-45μm, the error can be lower than 5%.
Using roughness profiles from stylus method can be an alternative method to determine scratch depth and width in current study.19,20 Considering the practical situation that scratch direction and length own the characteristic of randomness, this method may obtain inaccurate actual scratch geometry parameters. Facing with this problem, we modified the surface location parameter in Murakami fatigue strength model to 1.06C for stylus method.16 Prediction error of modified fatigue strength model is below 6%.
Fatigue life prediction are crucial for the design and maintenance process of components. Two major types of methodologies are available for fatigue life prediction. One approach is the classic fatigue theory based on the material fatigue-life curves (e.g., S–N curves or ε–N curves) and a damage accumulation rule, which is the focus of the current study. The other approach is based on the fracture mechanics and crack growth analysis. \(\sqrt{\text{area}}\) can be used as fatigue damage parameter, also as equivalent initial defect size for micro scratch. Its rationality and validity of \(\sqrt{\text{area}}\) in fatigue life prediction was checked by fracture mechanics.18 A fine prediction result was obtained under the combination of Paris law and \(\sqrt{\text{area}}\).
The present study attempts to prove the validity of\(\sqrt{\text{area}}\) in the field of the classic fatigue method, e.g., material fatigue-life curves. The ultrasonic fatigue tensile experiment was performed to obtain fatigue data, and fracture properties are observed by SEM (Scanning Electron Microscope). Combined with the condition fatigue strength model modified by \(\sqrt{\text{area}}\)and the three-parameter model, an HCF life model for TC17 is established. The model was verified being effective to the fatigue life prediction of TC17. What is more, the application of\(\sqrt{\text{area}}\) combined with current fatigue theories in fatigue strength and fatigue life analysis was also discussed.
2 | Brief introduction of \(\sqrt{\text{area}}\)
Murakami and Endo proposed the parameter \(\sqrt{\text{area}}\) as fatigue damage size for the prediction of the fatigue limit of specimens with surface defects. 21,22 \(\sqrt{\text{area}}\) is defined as the square root of the area obtained by projecting a small defect or crack onto a plane perpendicular to the maximum principal stress. It is an useful and simple method to express fatigue damage caused by scratch11,23, micro notch24, hole, micropore25 and non-metallic inclusions26.
Micro scratch has tens of microns along the surface, and a depth of a few micrometers with a length of potentially several millimeters. Compared with the size of artificial defect in Murakami experiment27, the studied scratch size has microscopic geometric characteristics, as can be seen in Fig. 2 below. What is more, its direction and length own the characteristic of randomness. This is because that the impact angle and time of foreign objects on the component surface are random and uncontrollable.
Thus, it seems that Murakami theory cannot applied to micro scratch directly in estimating the projected area. Unreasonable result may be produced in condition fatigue strength prediction if both scratch direction and length considered at the same time. Nevertheless, we found that if only take section area of micro scratch into consideration, better predicting results will obtained. Thus, we proposed the two principles that there may be no obvious influence of scratch direction and length on fatigue life.
Inspired by Murakami theory, also for considering the particularity of geometrical size of micro scratch, we proposed the fatigue damage parameter \(\sqrt{\text{area}}\) for micro scratch, which is defined as the square root of triangle area of scratch section:
\(\sqrt{\text{area}_{i}}=\sqrt{\frac{\overset{\overline{}}{W_{i}}\ \overset{\overline{}}{D_{i}}}{2}}\), (1)
where\(\overset{\overline{}}{W_{i}}\) and \(\overset{\overline{}}{D_{i}}\)are defined as the width and depth of scratch i . If there are multiple scratches on the detected surface, \(\sqrt{\text{area}}\) is determined by the maximum value of Equation 1 due to larger scratch has more severe stress concentration. Detailed discussion about\(\sqrt{\text{area}}\) can be found in Ref. [18].\(\ \sqrt{\text{area}}\) only take depth and width of micro scratch as fatigue damage control factors.
3 | Material and experiment

3.1 | Material and experiment

With a requirement of aero-engine with high thrust-weight ratio, the design and manufacture of blisk has been regarded as the key technology by many countries. TC17 Titanium alloy has attracted more and more attention in blisk manufacturing due to its outstanding mechanical performance, such as high-strength, excellent corrosion resistance and excellent toughness.
TC17 Titanium had the following mechanical properties: ultimate tensile strength\(\sigma_{t}\)=1108 MPa, yield stress \(\sigma_{s}\)=1060 MPa, and Young’s modulus E =111.5 GMPa, Vickers hardnessHV= 356\(\ \text{Kgf}/\text{mm}^{2}\).
The specimen used in the experiment is the hourglass type as shown in Fig. 1.