Issue 58

S. Çal ı ş kan et al.ii, Frattura ed Integrità Strutturale, 25 (2021) 344-364; DOI: 10.3221/IGF-ESIS.58.25

To estimate 95% confidence interval for the population, SN curves are plotted for each specimen using same fitting parameters and ensuring passing over the observed test data for each specimen. Eventually, standard deviation is calculated on 10 7 cycles (chosen as run-out criterion) with known stress points coming from each curve.

Figure 14: Constructing SN curve by AGARD-AG-292 method.

Accordingly, mean value with 50% probability of failure is 593.4 MPa and standard deviation is 33.3. Fatigue limit was estimated as 574.3 MPa by applying t α -variable for 95% confidence interval. Fatigue Reliability Analysis It is important to present accurate data without any bias providing theoretical data after analysis that meets the requirement of desired lifetime of a component. Reliability is basically to intends to the probability of data without failure in real life conditions. Fatigue life evaluation through statical analysis is carried out to prevent fatigue failure under operation with accurate estimation. Negative relationship exists between fatigue life and reliability such that decreasing reliability results in increased fatigue life meaning that probability decreases and fatigue failure change increases. SN curve can be generalized such that there is a linear relationship between life and applied stress in logarithmic base. By applying linear regression, model minimizes error by optimizing prediction. After estimation of observation, outliers shall be defined for reliable data by calculating residuals which is the difference between test data and prediction. For the sake of simplicity, standardized residuals are identified for each data point as corresponding error ( i e ) divided by an estimate of standard deviation.

e

i



r

(39)

i





 1 MSE h

ii

   2 1 1 n i i

MSE e n

(40)





2

 x x

1 n

i

 (41) where r i is the standardized residuals, e i is the standard error, h ii is leverage, i x is fatigue life of corresponding specimen, ̅ is mean life of specimens and MSE is the mean square error. Outliers can be detected by looking at residuals and influential point is accepted an outlier if standardized residuals are greater than three in absolute value. Presence of potential outlier in data set influences regression model and results in biased predictor coefficients; therefore, studentized residuals are introduced by removing i-th observation from regression model. Then the formula becomes:      x x  2 1 ii n i i h

357