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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Based on the mathematical expressions for Q -1 max and E a , the H-CW peaks may be further analyzed. The same expression is found for the peak intensity as in the case of the Schoeck relaxation, i.e equation 2. However, in this case Λ only involves the <111>{112} screw or { 110} non-screw dislocations. The main difference between Schoeck ’s model and the kink-pair formation model is situated in the expression for τ . For inverted torsion pendulum experiments on metals, an expression for τ can be derived as presented in equation 4. ~ 02 ( ) 3/2 exp ( ) / (4) Here, E k represents the kink formation energy, l 0 again the mean free length of the dislocations, and D k the kink diffusivity. Consequently, the corresponding E a will depend on E k as well as on D k and can be written as: = 2 − ( 1 ⁄ ) − 2 (5a) Usually, the kink migration energy (E k m ) is very small compared to E k and hence the second term may be neglected. However, the interaction of interstitials with dislocations may affect D k . The pinning effect of the interstitials was found to be influenced by the interstitials concentration at the dislocations as well their diffusivity. Again, a distinction can be made for saturated and unsaturated cores, leading to two possible expressions for the activation energy. = 2 + + − 2 (5b) = 2 + + + − 2 (5c) According to previous discussion, PH1 might be related to the kink-pair formation on <111>{112} screw dislocations being facilitated by the presence of H. This facilitation results from H binding to the kink leading to a decreased kink formation energy (Hirth (1980), Kirchheim (2007)). Consequently, the effective kink formation energy can be regarded as E k,eff = E k,screw – E B . Generally, E B values around 20 kJ/mol up to 30 kJ/mol have been found for the screw dislocations. Using an E B of 20 kJ/mol, a critical temperature of around -185°C can be found. Therefore, the screw dislocations might not be fully saturated and hence equation 5c may be used to describe PH1 (with the modification for the kink pair formation energy). Using typical values for E k,screw (35 kJ/mol), E m k (4.8 kJ/mol), E m H (5 kJ/mol) and E B (20 kJ/mol) from literature, an E a of 57 kJ/mol is found, which is considerably higher than the observed E a . Considering that the kink-pair formation is the rate determining step in the relaxation process, a more appropriate expression may be the expression for kink-pair formation relaxation with a different E k . Hence an alternative expression for E a can be found in equation 6. Entering the same values as before in this expression, an E a of around 33 kJ/mol is obtained which is fairly close to the observed E a of 37 kJ/mol, indicating that PH1 might indeed be related to the kink pair formation on screw dislocations, being facilitated by the H presence. = 2 , + − 2 (6) PH2, on the other hand, is supposed to correspond to kink-pair formation on {110} edge and mixed dislocations with H exerting a dragging force on the migrating kinks. Calculated binding energies at the core of these dislocations types resulted in an average E B of 40 kJ/mol, corresponding to a critical temperature of around -102°C. Consequently, the dislocations can be considered as saturated and equation 5c should be used. Using E k =5 kJ/mol, E m k = 4.8 kJ/mol, and E m H = 5 kJ/mol, leads to an E a of 11.5 kJ/mol, which is substantially lower than the E a found for PH2. This might be related to the assumption of the H lattice migration energy as the representative migration energy. Instead, the migration energy of H at the dislocation core might be needed. A simple approximation for diffusion in the dislocation field is given by the sum of E m H and E B . In this way, a better agreement is obtained, namely E a =50 kJ/mol, although this results in an overestimation. Consequently, the effective migration energy might be an intermediate value. 5. Conclusions The H-CW peak was studied to obtain more insights in the H-defect interactions in steel. Cold rolling introduced a clear H-CW peak, consisting out of two separate peaks, PH1 and PH2. Based on the complete annihilation after recovery annealing at 350°C, both H-CW peaks were related to metastable H-dislocation interactions. Moreover, the higher E a peak, PH2, decreased faster than the lower E a peak, PH1. This was related to either preferential segregation