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.