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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Fig. 3. Effect of torsional deformation. (a) full IF spectrum of H-charged recovered sample after torsional deformation (b) effect of ageing at 77°C for various times on the H-CW peak (c) evolution of the H-CW peaks (PH1 and PH2) intensity and their ratio upon annealing.

4.1. Schoeck: viscous dragging of vibrating string model According to the Schoeck model (Schoeck (1963), (1982), (1988)), the relaxation arises due to the stress-induced bowing of dislocation segments, dragging the interstitial impurities along, as visualized in Fig. 4.a. The dragging of impurities then acts as a viscous damping term in the vibrating string model. The resulting equations describing the relaxation time , τ, and Q -1 max are given below in equation 1 and 2. = 1 9 6 √3 2 02 5 , (1) −1 = 02 Λ (2) With k B the Boltzmann constant, T the temperature, A constant depending on the dislocation segment length distribution and geometrical factors, C d the H concentration at the dislocation, G the shear modulus, b the burgers vector, and D H,disl the diffusion coefficient for H at the dislocation, l 0 the mean free dislocation length, and Λ the total dislocation length of the dislocations participating in the relaxation. Schoeck stated that all dislocations surrounded by a H atmosphere will participate in the H-CW relaxation, on the condition that l 0 is sufficiently large. Since C atoms can act as strong pinning points at the relevant temperatures, dislocations surrounded by dense C atmospheres, are not able to participate in the process. From equation 2 it is clear that the peak intensity will strongly depend on the mean free dislocation length and total dislocation density. Hence, the decrease in intensities upon annealing can be related either to a decrease of l 0 , for instance by pinning due to C atoms segregating at the dislocations, or to annihilation of dislocation segments resulting in a decrease of Λ . This might explain the absence of the H-CW peak in the tensile strained specimens. Namely, the high amount of immobile dislocations in the recovered specimen and only small amount of newly introduced dislocations by tensile deformation, may result in a too small l 0 to introduce an observable H-CW peak. From equation 1, it can be seen that the E a of the relaxation process will depend on the temperature dependency of D H,disl and C d . It has been recognized that C d will be saturated and hence independent of the temperature below a critical temperature, T c , and only becomes dependent of the temperature above T c according to equilibrium partitioning between dislocation and lattice sites. The resulting expressions for both cases are given in equation 3a and b. = + , for > (dilute core) (3a) = , for < (saturated core) (3b) As a first step one may assume the cores are saturated and E a is given by equation 3b. Additionally, it can be assumed that the migration energy in the dislocation field (E H m,disl ) equals the sum of the binding energy and the lattice