PSI - Issue 39

Giovanni Pio Pucillo et al. / Procedia Structural Integrity 39 (2022) 700–710 Author name / Structural Integrity Procedia 00 (2019) 000–000

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conditions adopted for the experiments. A mean value of 1. 29∙10 -14 and 5.73 were found for C and m , respectively, having R = 0.05 and assuming K c = 100 MPa √ m from literature. ⁄ = ∙ ∆ [(1 − ) ∙ − ∆ ] ⁄ (2) Once C and m were evaluated for the not expanded specimens, it was decided to proceed as follows to predict the propagation curves of the expanded specimens: • the actual Stress Intensity Factor range, Δ K act , was calculated by superposition of the effects of the stress field due to applied loads and the residual one generated by cold expansion, setting the minimum value of the stress intensity factor K act min equal to zero if it was negative. The Stress Intensity Factors due to residual stresses induced by cold expansion have been evaluated by mean of the weight functions given by Wu & Carlsson (Wu and Carlsson 1991) and Shen & Glinka (Shen and Glinka 1991) for crack lengths smaller or greater than 6 mm, respectively; • since the SIF due to applied load was calculated analytically, whereas the weight functions require the knowledge of the stress field in the uncracked body, a finite element model was realized (see Appendix A) to predict the residual stresses induced by cold expansion; • using the parameters of the Forman’s law, the crack growth rate concerning the expanded specimens was predicted as a function of the crack length, using Δ K values obtained by the superposition of the ones due to external load and those due to cold expansion. The results are shown, as an example for the load level of 290 MPa, in Fig. 7, for both 2% and 4% of cold expansion. As you can see, the predictive model overestimates the cycles to rupture by a factor of 2, or 8 in the worst case. This result is in line with what can be found in the literature, and yet refers only to the final part of the entire fatigue life, specifically at about 10%. The higher predicted crack growth rates suggest the inadequacy of models based on the Linear Elastic Fracture Mechanics, as well as that FE model capable to take into account diffuse plasticity would be able to better grasp the real behaviour of the material.

a vs. N - 290 MPa - Exp 2%

a vs. N - 290 MPa - Exp 4%

0 1 2 3 4 5 6 7

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15

B08

C01

Prediction (2 cracks)

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C15

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a [mm]

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Prediction (2 cracks)

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100000 200000 300000

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N

a vs. N - 290 MPa - Exp 2%

a vs. N - 290 MPa - Exp 4%

0 1 2 3 4 5 6 7 0 100000 200000 300000 400000 a N

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B15

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C16

B11

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C14

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Prediction (1 crack)

Prediction (1 crack)

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Fig. 7. Typical measured (symbols) and predicted (continuous line) crack growth curves for CE degree equal to 2% (left) and 4% (right). Two cracks (top) and single crack (bottom) configuration.