PSI - Issue 47

Robert Eriksson et al. / Procedia Structural Integrity 47 (2023) 227–237

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R. Eriksson, A. Azeez / Structural Integrity Procedia 00 (2023) 000–000

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Fig. 6. Comparison between experimental WPS results and predictions: a) and b) shows results from the LCF cycle as function of load and temperature respectively; c) and d) shows results from the LUCF cycle as function of load and temperature respectively.

Fig. 6 a) shows K f from the LCF cycle as function of load tested at 300 ◦ C. The prediction of the WPS e ff ect is quite good and comparable to the Wallin model. Fig. 6 a) shows K f from the LCF cycle as function of temperature tested at 50 kN maximum load. Again, the prediction is quite reasonable albeit a bit on the conservative side. In addition, the temperature dependence is captured reasonable well whereas the Wallin model does not include any temperature dependence; even so, the Wallin model works satisfactory. Fig. 6 c) shows K f from the LUCF cycle as function of load tested at 300 ◦ C. For LUCF, the prediction is somewhat worse, but still better than the Wallin model. Fig. 6 d) shows K f from the LUCF cycle as function of temperature tested at 50 kN maximum load. The prediction is rather acceptable; however, there seems to be some scatter in the experimental data, so further testing might be needed in order to assess the predictive capability for the LUCF cycle. Compared to LCF, the prediction is less accurate for the LUCF cycle. Overall, the prediction is somewhat lower than the experimental data. This is rather expected since the model assumes the specimen to fracture as the plastic zone at T 2 reaches exactly the same size as the plastic zone at T 1 . It seems reasonable that the material, even in the brittle state, would be able to endure at least some minor amount of plasticity and hence fracture at a plastic zone size slightly larger than that at T 1 . It should be noted, that the fracture mechanics based model has not been calibrated to any of the WPS tests. Considering this, the prediction is surprisingly accurate. The plastic zone size seem to work reasonably well as a fracture criteria (i.e. failure below the DBTT occurs at a similar plastic zone size as of that introduced above the DBTT). This supports the both the idea that the WPS plastic zone does not plasticize significantly Chell (1986) and that active plasticity is necessary for cleavage fracture Jacquemoud et al. (2013). Most importantly, the fact that the suggested (physically based) model at least comes close to the experimental values indicates that the assumed mechanisms are reasonable and that the plastic zone size does play a crucial role in the WPS phenomenon. The introduction of a “residual stress intensity” to account for residual stresses may not be entirely intuitive, but is somewhat in line with early modeling e ff orts of WPS loading; see e.g. Chell (1986). It should also be noted that the strain hardening of the material in the plastic zone (where plastic deformation is extensive) may play a more crucial role than previously acknowledged; this has been overlooked by several researchers which mostly attributes the WPS e ff ect to residual stresses Reed and Knott (1996); Blumenauer and Krempe (2001); Chen et al. (2002) based on the fact that relief heat treatments reduce the e ff ect of WPS. However, it should be noted that a heat treatment not only relieve residual stresses, it also anneals the material and restores its original yield limit.