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.