PSI - Issue 19

Ho Sung Kim / Procedia Structural Integrity 19 (2019) 472–481 Author name / Structural Integrity Procedia 00 (2019) 000–000

480

9

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For some applications, theoretical data for α and β may be obtained as functions of stress ratio ( R ) for curve fitting of the following polynomial equations with an adequate polynomial order n (Microsoft Excel is sufficiently capable for this process).

0 10 20 30 40 50 60 0 10 20 30 40 50 60 70 σ a (MPa) σ m (MPa) 1.0E01cycles 1.0E02 cycles 1.0E03 cycles 1.0E04 cycles 1.0E05 cycles Prediction R =0 R =0.5 R =0.9 R =0.05

0 10 20 30 40 50 60 70

s max (MPa)

R=0.05 (Experiment) R=0.5 (Experiment) R=0.9 (Experiment) R=0.05 (Fitted) R=0.5 (Fitted) R=0.5 (Predicted) R=0.9 (Fitted)

-1

1

3

5

7

Log N f

(a)

(b)

Fig. 3. T-T loading: (a) experimental data for fibre reinforced composites with σ uT =52 MPa (Miyano and Nakada, 1995) and prediction for R =0.5; and (b) CFL diagram for experimental data and prediction. 3. Discussion For T-T loading (or for 0≤ R < R r0 < R ≤ R r1T ≤ R <1 in Fig.2a), unidirectional carbon fibre reinforced composites with σ uT =52 MPa obtained for 50°C by Miyano and Nakada (1995) at R = R r0 =0.05 and R r1T =0.9 were employed as TRED and another experimental data set obtained at R =0.5 was used for comparison with theoretical prediction. The fitting/damage parameters in Equation (3) for R r0 =0.05 were found to be log α = − 38.61 and β =21.54; for R =0.5, log α =77.14 and β =43.96; and for R r1T =0.9, log α =136.79 and β =78.95.The predicted S-N curve for R =0.5 is shown in Fig. 3a in comparison with a fitted S-N curve for experiment data. Also, Fig. 3b shows a CFL diagram, in which data points were taken from the fitted S-N curves of experiment data, and the linear fatigue CFL lines represented by the dashed lines for prediction. It is seen that the fatigue CFL lines tend to deviate a little from the data points at high values of N f . This minor discrepancy, however, may be expected because of: (a) the sensitivity of N f to the applied peak stress ( σ max ) at high stress ratios ( R >0.5); and (b) the 3-point bending testing method for the obtained experimental data generating a relatively high scatter compared to the uniaxial testing. A linear relationship between log α and β was found to be log with a correlation coefficient (cc) of 1.000. To find α and β as functions of R , a range of values at various stress ratios were theoretically calculated using the one-point method. For the data, the following polynomial equations with a correlation coefficient (cc) of 1.000 for both were obtained: log α = −503.67R 5 + 872.74R 4 − 635.84R 3 + 166.66R 2 − 52.333R - 36.33 and β = 294.52R 5 − 510.33R 4 + 371.8R 3 − 97.452R 2 + 30.601R + 20.203. For other fatigue loadings of T-C, C-T, and C-C, theoretical predictions were also found to be in agreement with the experimental results obtained by Kawai and Itoh (2014). 4. Conclusion The characteristics of the constant fatigue life (CFL) diagram have been clarified for theoretical capability and limitations, and dependence of experimental fatigue behaviour. The Kim and Zhang S-N curve model was dovetailed with the linear CFL lines of the four segments for predicting S-N curves for the whole range of stress ratios. With the benefits of analytical relationship of fatigue damage parameters with the Kim and Zhang S-N curve model, analytical