PSI - Issue 45

Yipu Guo et al. / Procedia Structural Integrity 45 (2023) 66–73

71

6

Yipu Guo et al. / Structural Integrity Procedia 00 (2019) 000 – 000

experimental data in the current study. Three statistic indicators, the average absolute error ( AAE ), the mean square error ( MSE ), and the standard deviation ( SD ), which are defined by Eqs. (6) – (8), are employed to assess the degree of associated scatters: = ∑ − =1 (6) = ∑ ( − ) 2 =1 (7) = √ ∑ [ −( ) ] 2 =1 −1 (8) where denotes number of data; and represent th theoretical value and experimental value, respectively; ( ) denotes average ratio of the ratios between the theoretical value and the corresponding experimental value. Although the assessment of NAC has fewer data scatters, all three statistic indicators are larger for NAC than RACI. Nevertheless, the predictive results are generally within ±10% as shown in Fig. 5, supporting the good performance of obtained compression meridians for NAC and RACI. The above analysis indicates that the acquired failure criterion of Multi-RAC based on Willam-Warnke failure criterion should have a satisfactory predictive accuracy The correlations for the coefficients 0 , 1 and 2 have the following relationships with the number of recycling cycles ( ) based on mathematical regression analysis: 0 = 0.0683 + 0.116 − 0.117 2 + 0.0259 3 ( 2 =0.998) (9) 1 = 0.928 − 0.401 + 0.411 2 − 0.0913 3 ( 2 =0.981) (10) 2 = −0.184 − 0.315 − 0.282 2 + 0.0592 3 ( 2 =0.997) (11)

1.50

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 NAC Fitting curve NAC RACI Fitting curve RACI RACII Fitting curve RACII RACIII Fitting curve RACIII t oct,c /¦ co s oct /¦ co

Eq (2) of NAC NAC - This study NAC - Yang et al.

Eq (3) of RAC1 RACI - This study RACI - Yang et al.

NAC - Folino & Xargay NAC - Chen et al.

RACI - Folino & Xargay RACI - Chen et al.

1.25

1.00

t oct,c /¦ co

0.75

0.50

0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 0.25

s oct /¦ co

(a) William-Warnke failure criterion (b) Comparison with other studies Fig. 4. William-Warnke failure criterion and comparison [Data collected from (Chen et al., 2015; Folino & Xargay, 2014; Yang et al., 2011)].