PSI - Issue 24

Chiara Colombo et al. / Procedia Structural Integrity 24 (2019) 658–666 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

664

7

Table 3: Summary of stepwise results for: a. R=-1; b. R=0.1. m and q coefficients are the slope and intercept of the linear regression of the E-mode amplitude, as defined in Fig.5.a,d; R is the related coefficient of determination. , is the fatigue limit estimated by E-mode; , is the fatigue limit estimated by D-mode; , is the fatigue limit estimated by the slope method; , is the average of the fatigue limits estimated with the three methods. a. MI-03 MI-04 m 1 (°C/MPa) 0.0018 0.0019 q 1 (°C) 0.0379 0.0138 R 21 0.9949 0.9984 m 2 (°C/MPa) 0.0207 0.0199 q 2 (°C) -5.8070 -5.4825 R 22 0.9735 0.9589 σ lim,E (MPa) 309 305 σ lim,D (MPa) 305 290 σ lim,slope (MPa) 320 320 σ lim,avg,R=−1 (MPa) 311±8 305±15 b. MI-05 MI-06 m 1 (°C/MPa) 0.0018 0.0018 q 1 (°C) 0.0310 0.0340 R 21 0.9897 0.9877 m 2 (°C/MPa) 0.0043 0.0043 q 2 (°C) -0.5350 -0.5535 R 22 0.9667 0.9294 σ lim,E (MPa) 228 235 σ lim,D (MPa) 212 225 σ lim,slope (MPa) 218 232 σ lim,avg,R=0.1 (MPa) 219±8 231±5 4.3. Comparison and discussion Based on the results of Par.4.1 and 4.2, it is evident that the two stress ratios have a deep effect not only on the fatigue life of the specimens, but also on their thermal response. Comparing the E-mode trends of Fig.5.a,d. and Table 3, we can see that the initial slope ( m 1 coefficient) is almost equal for all the tested samples, thus independent on the stress ratio R. This is correlated with the thermoelastic law and constant, i.e. the measured temperature is directly proportional to the applied stress. After the breakup points, the secondary slopes ( m 2 coefficients) of the specimens tested at R=-1 are approximately 5 times higher than the ones of specimens tested at R=0.1. Also, the transition region at the breakup point between the two interpolation lines is quite different: R=-1 specimens have a net change of thermal behavior, and all the available points of Fig.5.a can be used for the regression of the first or the secondary lines. On the other hand, R=0.1 specimens show a smooth transition between the two lines, and some of the points of Fig.5.d in the range 220< σ a <250MPa have to be excluded from both the regressions. This smooth transition is typical of tests performed at R=0.1; indeed, in some works of our group performed in the past on composite materials, usually tested in tensile-tensile R=0.1 loading, we found very similar trends, Vergani et al. (2014). Comparing the D-mode trend of Fig.5.b,e., we can identify clearly the initial region as fully flat, i.e. D-mode=0. Again, points corresponding to stresses beyond the fatigue limit have a different behavior. R=-1 specimens show a progressive increase of the D-mode, almost linear (Fig.5.b); R=0.1 specimens experience a much smoother increase, reaching only at the last block values of D-mode similar to R=-1 samples (Fig.5.e). Finally, the comparison of the slope trends shows that the R=-1 specimens have a net gap before and after the fatigue limit, and the ΔT/ΔN values remain quite constant beyond this applied stress (Fig.5.c). Also for R=0.1 samples of Fig.5.e there is a gap in the slope at the fatigue limit, but after this point the slope is constantly increasing. Another interesting comment can be added to differentiate the thermal behavior of R=-1 and R=0.1 specimens. During the tests, R=-1 specimens warmed up to 230°C, while R=0.1 samples failed in correspondence of 65°C. As a final comment, we can compare also the results of the fatigue limits estimated by the thermal analysis. The fatigue limit of the specimens tested at R=-1, σ lim,R=-1 =308MPa, averaged value between MI-03 and MI-04, can be analytically correlated to the average fatigue limit of the specimens tested at R=0.1, σ lim,R=0.1 , through Goodman’s law and Haigh diagram (Fig.6):       1 lim, 1 lim, 0.1 lim,        R R R k UTS UTS    (1)

where k is the slope of the line corresponding to R=0.1 in Fig.6, defined as: