PSI - Issue 13

Danilo D’ Angela et al. / Procedia Structural Integrity 13 (2018) 939–946 Danilo D’Angela and Marianna Ercolino / Structural Integrity Procedia 00 ( 2018) 000 – 000

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The numerical plane stress curve is always below the plane strain one: the failure is reached at a smaller crack length as well as at a higher fatigue life. There is no significant difference in terms of accuracy between the different FE curves; however, the plane strain Φ -based and plane stress ASTM-based model gives slightly better fitting results with the experimental values for room and cryogenic temperature, respectively. It is noted that the experimental curve was evaluated by Kim et al (2015) using the ASTM correlation (ASTM International, 2015) shown in Eq. 9, and not directly measuring the actual crack length. Therefore, the slightly better good matching between the numerical ASTM based crack length and the experimental one is more than reasonable. The analytical curves presented a quick crack propagation and an early fracture failure. In (London et al., 2015), the reduced integration plane stress and strain curves (i.e., CPS4R/CPE4R ) resulted quite similar between them, and both underestimated the analytical solution (in terms of a(N) values); this also happens with reference to this study.

Fig. 4. Numerical, analytical and experimental (Kim et al., 2015) crack growth curves: crack length ( a ) vs. number of cycles for (a) room temperature and (b) cryogenic temperature.

Numerical and analytical fatigue life are compared to the experimental results and reported in Table 2. Plane stress and plane strain models estimate very similar fatigue life, matching with good agreement the experimental result; the accuracy is better for the room temperature case. The analytical fatigue life is underestimated with respect to the experimental one.

Table 2. Numerical, analytical and experimental fatigue life.

Fatigue life [cycles]

Room temperature

Cryogenic temperature

plane stress plane strain

39311 38834 35871 40019

308069 304828 282718 349541

Numerical

Analytical

/ /

Experimental

ABAQUS does not provide the stress intensity factor range (or the energy release rate) along with the cycles. Therefore, the numerical fracture toughness, i.e., the stress intensity factor range value at the failure, is computed by applying Eq. 10 (ASTM International, 2015) to the conventional failure condition; Table 3 shows the results. Both Φ based and ASTM-based crack curves were used. All the models underestimate the fracture toughness (i.e., the numerical critical crack length is smaller than the experimental one). ASTM-based curves resulted more accurate than the Φ -based ; nevertheless, the difference is not significant.