PSI - Issue 13

Tomasz Tomaszewski / Procedia Structural Integrity 13 (2018) 1756–1761 Author name / Structural Integrity Procedia 00 (2018) 000–000

1760

5

characteristics. Fig. 3 shows the experimental points, linear regression line, confidence intervals and calculation results. Evaluation of the matching of the estimated characteristics based on the model to the experimental data was performed by calculating the standard error of the estimate and the coefficient of residual variation (Table 3).

700

300

F

F

M

M

280

600

220 Stress amplitude [MPa] σ a 240 260

400 Stress amplitude [MPa] σ a 500

Minispecimen - experiment Standard specimen - experiment Standard specimen - confidence interval Standard specimen - analytical

Minispecimen - experiment Standard specimen - experiment Standard specimen - confidence interval Standard specimen - analytical

300

200

300

300

10 3

10 4

10 5

10 6

10 7

10 3

10 4

10 5

10 6

10 7

Number of cycles, [cycle] N

Number of cycles, [cycle] N

Fig. 3. Fatigue characteristic σ a -N for stainless steel 1.4301 and various load.

Table 3. Average error of the estimate against the empirical values.

Standard error of the estimate

Coefficient of residual variation 100%   a exp e e V S 

Linear regression line log σ a = a log N + b

n

1   i

2

(

)







Data

, a exp i

, a cal i

S



e

2

n



S e [MPa]

V e [%]

a

b

Axial load

-0.0451 -0.0743

2.608 3.001

5.1

2.1

Bending load

52.0

11.4

The estimated values of fatigue strength for the standard specimen are smaller than the experimental values for the minispecimen. The differences of fatigue strength are higher for the bending load, which is consistent with theoretical assumptions. The applied statistical size effect model with a critical volume correctly takes into account the angle change of the fatigue characteristics σ a -N for a larger cross-sectional area of the object. The values of the slope coefficient a are smaller. This causes a lower slope of the straight line and better adjustment of the estimated line to the experimental line. 5. Summary Application of a statistical size effect model with a critical volume allows to estimate the σ a -N characteristic for sections other than determined experimentally. The model uses two areas of the size effect analysis. The statistical approach uses the probability distribution parameters, which requires use of a large number of experimental points at the same load amplitude σ a . The second area allows for a load gradient by determining the critical volume V P depending on the model parameters. The calculated σ a -N characteristics have different directional coefficient of the regression lines than the reference characteristics. The lines are not parallel. Since the scatter of the fatigue life results at higher stress amplitudes σ a is lower than at lower levels, the angle of an estimated line can be changed due to the use of a shape distribution coefficient m in the analysed model. The characteristic estimation errors for the reference specimen are due to a small amount of experimental data.