PSI - Issue 59

Jesús Toribio et al. / Procedia Structural Integrity 59 (2024) 90–97 Jesús Toribio / Procedia Structural Integrit y 00 (2024) 000 – 000

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Table 4. Coefficients M ijk of eqs. (9,10), given by Shin and Cai (2004) i j k = 0 k = 1

k = 2

0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2

0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7

0.22000 28.513 -354.78 2178.6 -7140.2 12957 -12228 4721.9 -0.32600 -3.7800 79.489 -571.09 1976.3 -3583.4 3256.8 -1163.2 0.26600 -9.1180 85.381 -465.01 1475.9 -2794.5 2878.9 -1261.3

0.12300 0.51100 -2.0340 -19.569 144.43 -359.28 393.52 -159.21 0.065000 -6.8780 47.747 -119.95 14.769 423.17 -661.61 306.18 0.11800 -3.5150 75.016 -587.59 2197.4 -4264.8 4138.3 -1588.1

-0.40900 -9.7640 128.82 -727.08 2201.1 -3732.8 3343.5 -1240.2 1.0110 -3.9460 41.099 -316.68 1284.9 -2563.3 2455.2 -880.30 -1.5840 45.562 -552.89 3322.5 -10812

19328 -17830 6638.7

front ( a H /b H =0). In order to include intermediate cases, diverse semi-elliptical shapes defined by an aspect ratio 0< a H /b H <1 were considered to define the TTS regions. The SIF was claculated at the point A (Fig. 2) where maximum depth of TTS zone, a H , is reached and therefore this location could be considered as the weakest poin t. So the value of Shin-Cai parameter x/h (eqs. 9-10) is null in all cases studied in this paper. Fig. 4 shows the evolution of critical SIF in harsh environment ( K H ) against applied fatigue pre-cracking load ( K max ) for cracked wires with different aspect ratio of the emi-elliptic TTS region ( a H /b H ). The values of K H grow linearly with the maximum fatigue pre-cracking load ( K max ) for all semi-elliptic TTS regions considered (with independence of the TTS shape). In addition, for a given K max , the critical SIF K H is a decreasing function of the TTS zone aspect ratio ( a H /b H ). In order to obtain a better understanding of the aforesaid trend, Fig. 5 plots the evolution against the aspect ratio a H /b H of the slope (defined by a parameter m ) of the linear relationship K H vs. K max slope obtained by a simple linear fit where a correlation coefficient higher than 0.997 was obtained in all geometries. It is seen that the value of m decreases as the TTS zone approaches the semicircular shape ( a H /b H =1). A big difference was found between the two limit cases: straight TTS front a H /b H =0 and semicircular front a H /b H =1. The variation of the parameter m allows one to establish that the influence of geometric TTS factor a H /b H on K H decreases when K max becomes smaller and, therefore, the maximum influence of the aspect ratio a H /b H on K H is reached at high K max (cf. Fig. 4).