PSI - Issue 41

Jesús Toribio et al. / Procedia Structural Integrity 41 (2022) 728–735 Jesús Toribio / Procedia Structural Integrity 00 (2022) 000–000

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The last requirement of the model is the value x s , depth of the maximum hydrostatic stress point . This cannot be obtained by LEFM, because it predicts a value of 0 (maximum just at the crack tip). Therefore, x S was estimated by two elastic-plastic approaches. The first one consists of using an approximate stress distribution in the vicinity of the crack tip in elastic-plastic regime (Doig and Jones, 1977), based on the slip-line field theory, as follows:

x s  ) ] =

(1+  ) K I 2  x S

1 2 + ln (1+

2 3

 Y [

(8)

where  Y is the yield strength of the material and  the curvature radius at the crack tip. The depth x S of the maximum hydrostatic stress point changes with the loading process (strongly in the beginning and slightly when the plastic zone is fully developed). However, an approximate value can be adopted by using the fracture toughness K IC as the critical stress intensity value, which corresponds to the final situation of the air-test. The curvature radius may be calculated as half of the critical crack tip opening displacement CTOD c (assuming a circular crack tip shape), and this value may be related to the critical J-integral (J IC ) and the fracture toughness:  c = COD c 2 = 1 2 J IC  Y = 1 2 K IC 2 E  Y (9) Introducing the material characteristics in (10), a value  c =10 –5 m was obtained, and equation (8) gives an approximate value x S =10 –4 m. The second approach is based on the asymptotic depth (for quasi-static tests) of the hydrogen-affected area. For notched specimens of a similar pearlitic steel (Toribio, 2012) it has been demonstrated that —apart from the earliest steps of loading— the depth of the maximum hydrostatic stress does not depend on the loading process, and it can be considered a characteristic of the geometry. For quasi-static tests, the depth of the TTS region (hydrogen affected area) reaches that of the maximum hydrostatic stress point, i.e., for t c  ∞  x TTS  x S , where t c is he time to failure or critical time. For cracked samples, the point of maximum hydrostatic stress does change with the loading process. However, as a first approach, the asymptotic depth of the TTS region ( quasi-static tests ) can be used to estimate the depth x S . From Table 1, this value is about 5x10 –4 m. Both approaches give similar values of x S . Adopting the average (x S =3x10 -4 m), and computing the variables  (6) and  (7) for all tests, the plot of Fig. 4 is obtained, which offers the experimental results in dimensionless form, expressed in terms of the CTSR, averaged over the test period and the hydrogen affected area. Results expressed in this manner have an objective character, as demonstrated by Toribio and Elices (1992).

Fig. 4. Results of the SSRT under HAC conditions expressed in dimensionless form: fracture stress vs . CTSR.