PSI - Issue 42

Liese Vandewalle et al. / Procedia Structural Integrity 42 (2022) 1428–1435 Vandewalle et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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migration energy. Using an E m

H of 5 kJ/mol (Hayward and Fu (2013), Lu et al. (2016)), this would result in an E B of

32 kJ/mol and 41 kJ/mol for PH1 and PH2, respectively. Using these E B values, one may calculate the corresponding critical temperature according to Hirth (1980), which results in T c values of -130°C and -85°C for PH1 and PH2 respectively, confirming the validity of the assumption of saturated cores. Therefore, two major types of binding sites associated to dislocations may be present. Considering literature data of theoretical calculations together with the observed peak behavior, these binding sites might be identified. For all dislocation types various sites with a large range of E B are found in literature (Itakura et al. (2013), Lu et al. (2018), Ramasubramaniam et al. (2009), Taketomi et al. (2008)). However, screw dislocations generally provide less strong traps than edge dislocations. Hence, PH1 might be related to screw dislocations while PH2 is related to edge dislocations. Clearly, the stronger binding sites, related to PH2, are removed first upon annealing. Considering the expression for the peak maximum, this is either related to the decrease of l 0 or a decrease of Λ . Preferential segregation of C to the edge dislocation sites during annealing might cause a more rapid decrease of l 0 . Indeed, C is found to be stronger attracted to edge than to screw dislocations and thus would preferentially bind to the edge dislocations, resulting in a more rapid decrease of l 0 for PH2. However, the annihilation of edge dislocations is also found to be promoted over the annihilation of screw dislocations (Tomita et al. (2017)). Additionally, the difference between the (relative) peak heights depending on deformation mode must also be explained. It would appear that torsional deformation results in a higher fraction of edge dislocations than after cold rolling. Literature data regarding the influence of the deformation mode on the dislocation types introduced seems to be rather limited. According to Kumagai et al. (2014) the ratio of edge over screw induced by cold rolling was close to one while Wauthier-Monnin et al. (2015) claimed that mainly screw type dislocations remained after cold rolling. However, considering the easier glide and annihilation of edge dislocations, it seems likely that the lower deformation temperature during torsion compared to cold rolling might cause an increased relative amount of edge dislocations. Another interpretation could be related to room temperature ageing of the cold rolled material before testing, resulting again in preferential segregation of C atoms to the edge dislocations. However, it must be noted that the assumption of E H m,disl =E m H +E B can be discussed. For example, Kimizuka and Ogata (2011) used DFT calculations to study the migration of H along a screw dislocation and found different migration energies associated with different diffusion paths. The maximum diffusion barrier perpendicular to the dislocation line was found to be 35 kJ/mol which is close to the E a -value of PH1. Additionally, they found that diffusion along the <111> axis may be associated with a higher E H m,disl of 41.5 kJ/mol which is relatively close to the E a of PH2. Hence, another possible interpretation for the different peaks may involve different H migration paths along the dislocation cores. However, this does not explain the different annealing behavior of the peak intensities. 4.2. Seeger and Hirth: kink-pair formation model The models proposed by Seeger ((1979), (1982)) and Hirth (1980) assume thermally activated kink-pair formation and kink migration in a H atmosphere to be responsible for the relaxation, as visualized in Fig. 4.b. Consequently, only dislocations being close to the closest packed <111> direction are involved in the relaxation. Seeger considers the non-screw type dislocations on {110} planes, i.e. 90°-edge and mixed 71° and 39° dislocations, to be involved in the H-CW peak, with H exerting a dragging force on the kink migration action. Hirth, on the other hand, considers the <111>{112} screw dislocations to be responsible, with H facilitating kink-pair formation. Combining both models, as proposed by Gibala et al. (2018), PH1 and PH2 might correspond to either the {110} non-screw dislocations or the <111>{112} screw dislocations. Again the annealing behavior may help in the identification of the different peaks. Considering the easier glide of the non-screw dislocations, their annihilation may be expected to occur faster and hence PH2 can be related to these dislocations while PH1 may involve the <111>{112} screw dislocations.

Fig. 4. schematic visualization of the relaxation mechanism involved in the H-CW peak according to (a) Schoeck ’s model and (b) the kink-pair formation model, with l the distance between strong pinning points (represented by x) and H atoms represented by blue dots. The area swept by the dislocation is a measure for the relaxation strength and is colored in grey.