4 | Fatigue life prediction based on micro scratches
4.1| Condition fatigue strength model
The well-known condition fatigue strength model proposed by Murakami has
been widely verified and applied to describe the effect of surface
defect on fatigue strength:
\(\sigma_{w}=\frac{1.43(HV+120)}{{\sqrt{\text{area}}}^{1/6}}\),
(2)
where HV is Vickers hardness, and C =1.43 for the surface
defect. For a certain material, the projected area is the critical
factor that control fatigue strength.
4.2 | Three-parameter model
Classic fatigue analysis theory depends on the S -N curve.
On the basis of being widely recognized by scholars, mathematical
expression of S -N curve can be classified into four types
as follows: Basquin model 31, Langer
model32, Weibull three-parameter model33 and Manson-Coffin model. 34 The
effect of fatigue strength on S -N curve can be reflected
by the three-parameter model. The introduction of three parameter make
it much more flexible and accurate in describing S -N curve
under a given R :
\(N_{P}=C{(\sigma_{a}-\sigma_{w})}^{-m}\), (3)
Where \(N_{P}\) is the predicted
life, \(\sigma_{a}\) is stress amplitude; \(\sigma_{w}\) is fatigue
strength, m and care constant which related to material, R and loading mode.
4.3 | Fatigue life prediction
It should be pointed out that it is the smooth specimen without surface
defect that is used in the experiment to obtain fatigue strength\(\sigma_{w}\).\(\ \sigma_{w}\) is constant for a certain material under
required experimental conditions. In the aeronautical practice, the
parts would inevitably have surface defects, especially micro scratches.
Fatigue strength will be reduced due to the serious stress
concentration, and different geometric size of micro scratches can lead
to different fatigue strength. Thus, the traditional fatigue strength
would be not applicable in the three-parameter model for parts
containing micro scratches.
In order to introduce the effect of micro scratch into fatigue strength,
combined with the proposed \(\sqrt{\text{area}}\), the modified
condition surface conditional fatigue strength with the consideration of
micro scratches is obtained as:
\(\sigma_{w,}=\frac{1.43(HV+120)}{{\sqrt{\text{area}}}^{1/6}}\),
(4)
In this paper, condition fatigue strength is introduced to in the
three-parameter model to describe the effect of micro scratches on HCF
life of TC17:
\(N_{P}=C{(\sigma_{a}-\sigma_{w,})}^{-m}\), (5)
Equation 5 derives from the combination of Murakami theory and the
three-parameter model, which establishes the link between surface
fatigue damage caused by micro scratches and HCF life of TC17 in HCF
regime. But two parameters for micro scratches, m and Ccontinue to be undetermined. There is no reference to the unknown
parameters in the current literature, especially relating to micro
scratches. The two parameters can reflect the effect of micro scratches
on HCF life of TC17, so it can be obtained from the designed fatigue
experiment data. The fitting algorithm uses continuous curves or
analytical expressions to represent discrete data and the functional
relationship between the variables. By using of the experiment data, the
results of the parameter are estimated as \(m=1.8,\ C=9.33E+8\).
Then substitute the obtained parameters m and C into
Equation 5, the HCF life model of TC17 with the consideration of micro
scratch can be obtained:
\(N_{P}=9.33E+8{(\sigma_{a}-680.68/{\sqrt{\text{area}}}^{1/6})}^{-1.8}\),
(6)
Fig. 5 present the result of fatigue life prediction. The predicted life
values mainly fall into the scatter band of factor 2. In general and
despite of some dispersion, a fair correlation between the experimental
and predicted value is achieved, indicating that the\(\sqrt{\text{area}}\) is also
applicable to classic fatigue theory.