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[Yuhei Ogawa](https://orcid.org/0000-0003-2713-9822), Takeshi Fujita

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[Solid solution-hardening by hydrogen in Fe–Cr–Ni-based austenitic steel studied by strain rate sensitivity measurement: Contributions of effective stress and solute drag](https://mdr.nims.go.jp/datasets/8cc1bce4-9984-4872-9e96-d322be4568c8)

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Submitted to Materials Science and Engineering A 8th July 2024  1  Solid solution-hardening by hydrogen in Fe-Cr-Ni-based austenitic steel 1 studied by strain rate sensitivity measurement: 2 contributions of effective stress and solute drag 3  4 Yuhei Ogawa a,b, Takeshi Fujita c 5  6 a Research Center for Structural Materials, National Institute for Materials Science 7 (NIMS), 1-2-1 Sengen, Tsukuba, 305-0047, Japan 8 b Department of Mechanical Engineering, Kyushu University, 744 Motooka, Nishi-ku, 9 Fukuoka 819-0395, Japan 10 c Graduate School of Engineering, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 11 819-0395, Japan 12  13 Corresponding author: Yuhei Ogawa, Email: OGAWA.Yuhei@nims.go.jp 14  15 Abstract 16 Dissolution of atomic hydrogen (H) into Fe-Cr-Ni austenitic steels causes a significant 17 increase in flow stress (i.e., solid solution-hardening, SSH) during their plastic 18 deformation. In this study, the characteristics and kinetics of H-induced SSH in AISI Type 19 310S steel with 7600 at. ppm H were studied through the measurements of strain rate 20 sensitivity, S, by stress relaxation and strain rate jump experiments at 296 K. Two factors 21 were found to contribute to the SSH: (i) the role of H as thermally activatable obstacles 22 that increase the effective stress; (ii) the resistance acting on moving dislocations due to 23 their dragging of H atmosphere (solute drag). These factors operated cooperatively or 24 competitively in determining the S value and its dependencies on stress, strain, and strain 25 rate. The peak SSH can be achieved where the sum of dislocation glide resistances from 26 (i) and (ii) is maximized. The anticipated strain rate range for establishing such a situation 27 coincided accurately with the author's previous experiments. 28  29 Keywords:  30 Austenitic steel; Hydrogen; Solid solution-hardening; Plasticity; Thermal activation 31  32 1. Introduction 33 The dissolution of hydrogen (H) atoms into Fe-Cr-Ni-based austenitic stainless steels 34 and other face-centered cubic (FCC) metals/alloys triggers a significant strengthening 35 effect via solid solution-hardening (SSH) [1–10]. The phenomenon manifests most 36 straightforwardly as increases in tensile flow stress and indentation hardness, to an extent 37 equivalent to other conventional interstitial atoms, including carbon and nitrogen [2,3]. 38 Considering the general understanding that one of the root causes of SSH is lattice strain 39 around solute atoms [11–16], the remarkable hardenability of H is somewhat abnormal 40 Submitted to Materials Science and Engineering A 8th July 2024  2  since the lattice dilatation around an H atom (≈ 2×10−30 m3 [17,18]) is much smaller than 1 those around carbon and nitrogen (≈ 8.6×10−30 m3 [19]). This apparent deviation from the 2 standard theory urges us to rationalize the H-induced SSH by envisaging specific 3 interactions between H and dislocations [2,3]. 4    An elaboration of the H-induced SSH in Fe-24Cr-19Ni-based steel (AISI Type310S) 5 was recently performed by the authors through a series of tensile tests in the temperature 6 range of 173-423 K [3]. In analogy with the general behavior of SSH, solute H increased 7 the effective (i.e., thermal) stress component of the total flow stress [5,20], which can be 8 relaxed with the aid of temperature and time. However, even though such a standard 9 temperature dependence was identified above room temperature, the SSH was maximized 10 around 300 K in terms of yield stress, decaying as the temperature decreased to 173 K [3]. 11 At ≈ 300 K, H atoms are highly diffusible and energetically favorable to segregate around 12 moving dislocations [21–23]. Thus, in addition to H atoms dispersed in the FCC lattice, 13 some dynamic interactions between H and dislocations might be the rationales behind 14 such a maximized SSH. Some potential mechanisms that explain the phenomenology of 15 H-induced SSH have been discussed by the authors' group [3,20]. 16    The effective stress component of SSH stems from short-range (i.e., the extent of a 17 few interatomic distances) interactions between dislocation and solute atoms, where 18 thermal vibration aids its progress [24]. Under a given temperature, a conventionally used 19 physical parameter for measuring the significance of those short-range interactions and 20 resultant effective stress is strain rate sensitivity, S [25–27]: increase or decrease in the 21 flow stress after a tenfold increase in strain rate. The parameter S normally exhibits 22 positive values and increases as the predominant rate-controlling obstacles for 23 deformation are weaker and more thermally activatable, a typical example of which are 24 solute atoms [28,29]. Indeed, strain rate sensitivity (or the amount of stress relaxation, 25 which has the same physical sense with an increasing S, cf. eq. (2)) in Type310S steel 26 becomes higher after the introduction of H [4,20,30], substantiating our statement on the 27 role of solute H in increasing the effective stress. On the other hand, there may be another 28 contribution to S and SSH from a longer-range remote interaction when solute atoms are 29 diffusible enough and able to follow the movement of dislocations. That is the force 30 exerted by dragging the solute atmosphere, called solute drag [23,31–33]. Although H-31 induced drag resistance has been invoked in H-charged FCC metals and alloys both 32 theoretically and experimentally [1,3,7,23,34], its effectiveness and impact on the strain 33 rate- and temperature-dependent plastic flow remain elusive. Since the resistance to 34 dislocation motion by atmosphere dragging is also sensitive to the dislocation velocity 35 and strain rate, the S value (i.e., change in flow stress in response to the strain rate 36 variation) is anticipated to work as an effective probe of the significance of solute drag. 37 Submitted to Materials Science and Engineering A 8th July 2024  3     The effective stress stemming from short-range interactions exhibits its logarithmic 1 dependence on the dislocation velocity and strain rate [35]. For solute atoms, the effective 2 stress can be approximated as background friction and almost invariable during a tensile 3 test under a constant strain rate when the solutes are sufficiently dense compared with the 4 interspacing between dislocations [29,36,37]. Meanwhile, the linear dependence of drag 5 force on dislocation velocity [16,33,38] potentially makes it more rate-sensitive than 6 short-range interactions. This possibly renders the flow stress a function of mobile 7 dislocation density (i.e., strain) even when the macroscopic strain rate is constant. As such, 8 investigating the simultaneous dependencies of S on strain rate and strain should provide 9 some key insights into the relative contributions of effective stress and solute drag on the 10 total flow stress under a given condition. In this study, S values in Type310S steel with 11 7600 at. ppm H were measured by stress relaxation and strain rate jump tests throughout 12 the tensile deformation at room temperature with various base strain rates (BSR) in order 13 to figure out the components (i.e., effective stress and solute drag) responsible for the H-14 induced SSH. Comparison of the experimental results with theoretical formulae 15 demonstrated the competitive or cooperative contributions of H-induced effective stress 16 and solute drag to the S value in plausible strain rate ranges and mobile dislocation density. 17  18 2. Methodology 19 2.1 Material, specimen, and test equipment 20 A commercial rod of Type310S steel with a diameter of 20 mm and a chemical 21 composition of Fe-0.02C-0.37Si-1.10Mn-0.023P-0.001S-19.18Ni-24.18Cr (mass %) was 22 prepared. The rod was supplied after solution annealing at 1353 K and subsequent water-23 quenching. Fig. 1 (a) shows the initial microstructure on the plane perpendicular to the 24 rod axis, captured by electron backscattered diffraction (EBSD) in a scanning electron 25 microscope (SEM). The heat treatment resulted in an average grain size with an 26 equivalent diameter of 40 μm, excluding annealing twins. Because of its high Cr and Ni 27 contents, the Type310S steel is immune to martensitic transformation, and the austenite 28 phase remains totally stable during the deformation around room temperature [39]. 29 Cylindrical tensile specimens with a diameter of 6 mm and a gage length of 30 mm (Fig. 30 1 (b)) were machined from the rod center, and the surfaces of their gage parts were mirror-31 polished via buffing by a cloth with 1 μm diamond suspension. 32 All the mechanical tests were performed by a screw-driven electromechanical test 33 frame (Shimadzu AGX-plus) with a 100 kN load capacity. The temperature during the 34 tests was kept at 296±1 K. For the measurement of tensile strain, a strain-gage 35 extensometer was clipped on the specimen's gage part. Prior to the experiments, H-36 charging was done by exposing the specimens to a gaseous hydrogen environment at 100 37 Submitted to Materials Science and Engineering A 8th July 2024  4  MPa and 543 K (the maximum pressure and temperature feasible in our equipment) for 1 200 h. This condition can realize a uniform H concentration in the specimen's gage part 2 [4]. The H concentrations in the gage part were measured after mechanical tests by 3 thermal desorption analysis (TDA) equipped with a thermal conductivity detector (STF-4 20A Series, J-Science Lab, Japan). In the H-charged specimen, the H concentration was 5 140 mass ppm (7600 at. ppm), while it was 5 mass ppm (300 at. ppm) in the non-charged 6 one, as shown in the H desorption profiles in Fig. 1 (c). 7  8  9 Fig. 1 (a) Microstructure of the Type310S steel on the plane normal to the rod axis, 10 captured by EBSD. (b) Configuration and dimensions (mm) of the tensile specimen. (c) 11 H desorption curves from the deformed gage parts of the specimens measured by TDA. 12  13 2.2 Transient mechanical tests 14 Two types of mechanical transient, i.e., stress relaxation and strain rate jump, were 15 employed in the course of deformation under the base crosshead speeds of 0.0003, 0.003, 16 and 0.03 mm/s. These correspond to the initial tensile strain rates (base strain rates, BSR), 17 𝜀̇, of 10−5, 10−4, and 10−3/s, respectively. Note that the base crosshead speed and BSR here 18 mean the standard tensile (not shear) deformation rate before and after the stress 19 relaxation or strain rate jump was implemented. As references, monotonic tensile tests 20 with these three BSRs were also carried out. 21  22 2.3 Theoretical background and the details of experiments 23 2.3.1 Stress relaxation test 24 The repeated stress relaxation procedure invented by Spätig et al. [40] was 25 implemented at multiple stress/strain levels during the tensile deformation (Fig. 2 (a)). 26 This methodology was established for a precise measurement of activation parameters 27 controlling the plastic flow by taking the changes in the internal material state during the 28 relaxation into account. Indeed, exhaustion of mobile dislocations and work-hardening 29 during stress relaxation possibly affect experimental results obtained by a single 30 Submitted to Materials Science and Engineering A 8th July 2024  5  relaxation [41–43]. Although another rigorous way was recently proposed by Prasad et al. 1 [44], we stayed with a more conventional method for the purpose of comparatively 2 studying the differences between non-charged and H-charged samples. For each 3 relaxation, crosshead holding for 30 s and subsequent stress reversion were repeated 5 4 times. A shorter holding time is recommended in [40] to minimize the internal state 5 changes in the material with the progress of relaxation. Thus, we selected 30 s as the 6 possibly shortest time, wherein the magnitude of stress drop was sufficient enough as 7 compared with the fluctuation of load cell signal. 8 During the relaxation period, the elastic strain in the specimen's gage part is gradually 9 relaxed through sluggish plasticity with a plastic strain rate of 𝜀𝑝̇ = −𝜎̇/𝑀, where 𝜎̇ is 10 the rate of stress decay and M is the elastic modulus of the specimen-machine assembly. 11 The test enables us to measure the activation volume, V, which is the area swept by a 12 dislocation segment during overcoming an obstacle, multiplied by the Burgers vector, b 13 (later explained in Section 4.1.2 and Fig. 9). V is recognized as a physical parameter for 14 thermally activated deformation that characterizes the distribution and strength of the 15 rate-controlling obstacles [45,46]. Given that the kinetics of plastic deformation obeys 16 the Arrhenius type rate equation (later described in Section 4.1.2), V is inversely 17 correlated with the strain rate sensitivity, S, as follows [24,47]: 18 𝑆 =𝜕𝜏𝜕ln𝛾̇=1𝑀T𝜕𝜎𝜕ln𝜀̇=  𝑘𝑇𝑉                     (1) 19 where τ and 𝛾̇ are applied shear stress and shear strain rate, respectively. k is Boltzmann's 20 constant, and T is temperature. τ and 𝛾̇ were calculated from the tensile stress, σ, and 21 tensile strain rate, 𝜀̇, assuming an average Taylor factor, MT, of 3.06 in FCC polycrystals 22 (i.e., σ = MTτ and 𝛾̇ = MT𝜀̇). Note that the present definition of strain rate sensitivity is 23 slightly different from the generally defined one, in which a logarithm of stress is used 24 instead in the numerator [44]. Given that the stress reversion process (Fig. 2 (a)) is nearly 25 elastic, S can also be measured as a parameter purely reflecting the stress-dependence of 26 dislocation velocity with a minimized effect of mobile dislocation exhaustion [24,40]: 27 𝑆 =1𝑀T∆𝜎1ln(𝜀2𝑏̇ /𝜀1𝑒̇ )=∆𝜏1ln(𝛾2𝑏̇ /𝛾1𝑒̇ )                   (2) 28 where Δσ1 (= MTΔτ1) is the magnitude of the stress drop in the first relaxation. 𝜀1𝑒̇  (= 29 𝛾̇1e/MT) and 𝜀2𝑏̇  (= 𝛾̇2b/MT) are the strain rates at the end of the first relaxation and the 30 beginning of the second relaxation, respectively (Fig. 2 (a)). Repeating this procedure 31 over all five relaxations can derive an average and reliable value for S. For more details 32 on the test method and the derivation of V and S, the readers should refer to [40]. It should 33 be noted that some strain aging mechanisms related to carbon diffusion or carbon-vacancy 34 interactions can affect the amount of stress transients as well [48,49]. Nonetheless, 35 Submitted to Materials Science and Engineering A 8th July 2024  6  Hannula et al. evaluated room temperature aging in Type316L steel containing 0.07% 1 carbon, reporting that the aging-induced stress change is merely around 1 MPa under the 2 aging time of an order of 10 s [49]. Considering the much lower carbon content in our 3 present material (0.02%), the influence of strain aging should not be significant compared 4 with the amount of total stress relaxation. 5  6 2.3.2 Strain rate jump test 7 The S can also be evaluated by a strain rate jump test (Fig. 2 (b)), where the flow 8 stress increase, Δσ (= MTΔτ), after a rapid escalation of strain rate from 𝜀1̇ (= 𝛾̇1/MT) to 9 𝜀2̇ (= 𝛾̇2/MT) is measured [24,47]. Eq. (2) is slightly modified for this test type: 10 𝑆 =1𝑀T∆𝜎ln(𝜀2̇/𝜀1̇)=∆𝜏ln(𝛾2̇/𝛾1̇)                      (3) 11 In this study, a tenfold increase from each BSR was implemented at various stress and 12 strain levels. The determination of S is straightforward when the stress-strain curve after 13 the strain rate jump is smooth. However, a small yield point (Fig. 2 (b)) was sometimes 14 observed, making the definition of S not explicit. In such a case, a tangent line having the 15 same slope as the stress-strain curve was drawn through the yield point (Fig. 2 (b)). Since 16 the temporal stress drop after the yield point is often attributed to dislocation 17 multiplication [24,50], this latter definition of S may be more appropriate to measure the 18 change in dislocations glide resistance by excluding the multiplication effect. 19    One has to be aware that the present S is all calculated based on the shear stress-strain, 20 which was converted from the measured tensile stress-strain through MT. Since the 21 numerator of S (eq. (1)-(3)) is defined linearly rather than logarithmically, the obtained 22 results should be different by a factor of MT if tensile stress-strain is used as has been 23 done in some previous works [28,29]. 24  25  26 Fig. 2 Schematic drawings of (a) repeated stress relaxation and (b) strain rate jump tests. 27 Refer to Sections 2.2.1 and 2.2.2 for the corresponding descriptions of methodologies. 28   29 Submitted to Materials Science and Engineering A 8th July 2024  7  3. Results 1 3.1 Rate-dependence of stress-strain behavior 2 The stress-strain curves in the monotonic tensile tests at different strain rates (10−5, 3 10−4, and 10−3/s) are shown in Fig. 3. In what follows, true stress and strain are used for 4 all descriptions rather than nominal values (i.e., the calculation of shear stress through MT 5 (Section 2.3.1) is also based on σt). In non-charged specimens, flow stress was 6 monotonically increased with the tenfold increase in the strain rate. The flow stress in H-7 charged specimens consistently exhibited higher values than that in non-charged 8 specimens under all the strain rates due to the H-induced SSH effect [2–4]. A positive 9 correlation between flow stress and strain rate was also observed even in H-charged 10 specimens, although the flow stress gap between 10−4/s and 10−3/s was somewhat smaller 11 than that between 10−5/s and 10−4/s. In the inset of Fig. 3, the yield (0.2% proof) stresses, 12 which were measured by an average of 3 specimens for each, are plotted as a function of 13 strain rate. The gap of yield stress between non-charged and H-charged specimens at 14 10−5/s and 10−4/s was somewhat greater than that at 10−3/s by an extent of almost 10 MPa. 15  16  17 Fig. 3 True stress-true strain curves of non-charged (blue) and H-charged (red) specimens 18 in the monotonic tensile tests at room temperature with three different strain rates. The 19 inset magnifies around the yield point. 20  21 Fig. 4 compares the stress-strain behaviors during stress relaxation and strain rate 22 jump tests under three different BSRs with those in monotonic tensile tests. In stress 23 relaxation tests, a gradual drop of flow stress after crosshead holding was observed in all 24 the experimental conditions (Fig. 4 (a)~(c)). With an increase in BSR, the magnitude of 25 the stress drop was amplified monotonically in both non-charged and H-charged 26 Submitted to Materials Science and Engineering A 8th July 2024  8  specimens. Meanwhile, a prompt increase in the flow stress was evident after the rapid 1 strain rate jump (Fig. 4 (d)~(f)). 2 Disregarding some exceptions (see Section 3.2.2), the extent of these stress transients 3 in H-charged specimens was more remarkable than those in non-charged specimens when 4 the comparison was done under the same BSR (cf. magnifications in the insets of Fig. 4). 5 This result indicates an increase in S due to solute H, reproducing the previous results 6 reported by the authors and other researchers [20,30]. Note that stress-strain curves in 7 stress relaxation and strain rate jump tests coincided well with the monotonic deformation 8 curves, except for the relaxation and strain rate jump phases. Thus, it can be deduced that 9 the overall flow behavior is not affected by the mediation of these procedures. For the 10 information about stress and strain values at which stress relaxation and strain rate jump 11 were implemented, as well as the magnitude of stress relaxation in all the examined 12 stress/strain levels, the readers shall refer to Table A1 and Fig. A1 in Supplementary 13 Material. 14  15  16 Fig. 4 True stress-true strain curves in monotonic tensile (dashed lines) and transient 17 mechanical (solid lines) tests with different base strain rates (BSR). The results of stress 18 relaxation tests are shown in (a)~(c), while those of strain rate jump tests are displayed in 19 (d)~(f). Magnifications of the rectangle A~F are shown in the insets. 20   21 Submitted to Materials Science and Engineering A 8th July 2024  9  3.2 Stress-, strain-, and strain rate-dependences of S 1 3.2.1 Stress relaxation test 2 The S values measured by stress relaxation tests under three different BSRs are 3 summarized in Fig. 5 as the functions of shear flow stress, τ-τy (τy was approximated as 4 σ0.2/MT, where σ0.2 is 0.2% proof stress), and tensile strain, wherein the distinctions 5 between non-charged and H-charged specimens are evident. Note that each curve in Fig. 6 5 was constructed from the results of two individual specimens to check the 7 reproducibility. 8 In non-charged specimens, the S values increased gradually and linearly with the 9 increases in applied stress and strain. The magnitude of S was barely dependent on the 10 BSR, converging all three curves on each other. On the other hand, the S was increased 11 approximately twofold by solute H. Almost horizontal (i.e., stress- and strain-insensitive) 12 plots were obtained in H-charged specimens, although they accompanied slight concave 13 downs in the small stress/strain domain at BSR = 10−3/s and 10−4/s. Moreover, they 14 exhibited slight and non-monotonic dependence on BSR. While the S once increased with 15 an increase in BSR from 10−5/s to 10−4/s, it decreased again when BSR was further raised 16 to 10−3/s: the result at BSR = 10−3/s lay in-between those at 10−5 and 10−4/s.  17  18  19 Fig. 5 Strain rate sensitivity, S, in non-charged (blue) and H-charged (red) specimens 20 measured by stress relaxation tests with different base strain rates (BSR). The results are 21 plotted as a function of (a) flow stress and (b) true tensile strain. 22  23 3.2.2 Strain rate jump test 24 The shapes and BSR-dependencies of the S-stress/strain plots drastically changed 25 when measured by strain rate jump tests. As shown in Fig. 6, the S in non-charged 26 specimens also became slightly BSR-dependent (i.e., it monotonically increased with an 27 increase in BSR), although the plots maintained their linearity. The S values closest to 28 Submitted to Materials Science and Engineering A 8th July 2024  10  those in stress relaxation tests (Fig. 5) were obtained in the strain rate jump test at BSR = 1 10−5/s. 2 The S in the H-charged specimen exhibited a behavior almost identical to stress 3 relaxation tests at BSR = 10−5/s. However, unique S-stress/strain plots manifested when 4 BSR was increased to 10−4 and 10−3/s. That is, the initial concave part at low stress/strain 5 was more pronounced as the BSR increased, decreasing the S to the level equivalent to 6 that of the non-charged case. Notably, the initial S at low stress/strain was even smaller 7 than those in non-charged specimens at BSR = 10−3/s, the exceptional case described in 8 Section 3.1. The S in H-charged specimens then gradually escalated with increases in 9 stress and strain. Eventually, it far exceeded the S in non-charged specimens, and its 10 magnitude finally followed the rank order of BSR at high stress (τ-τy > 100 MPa) and 11 large strain (εt > 0.15). One has to append that, at BSR = 10−4 and 10−3/s, the S at this 12 large stress/strain regime (3.5~4.0) was greater than the values measured in stress 13 relaxation tests (2.5~3.0): compare Fig. 6 with Fig. 5. 14  15  16 Fig. 6 Strain rate sensitivity, S, in non-charged (blue) and H-charged (red) specimens 17 measured by strain rate jump tests with different base strain rates (BSR). The results are 18 plotted as a function of (a) flow stress and (b) true tensile strain. 19  20 3.3 Transient behavior after strain rate jump 21 Another impact of solute H and BSR was discovered on the stress transient behavior 22 after the strain rate jump. In Fig. 7, magnifications of the stress-strain curves around the 23 points of strain rate jump at εt ≈ 0.03 and 0.11 are depicted for BSR = 10−5 and 10−3/s. At 24 a small strain regime (≈ 0.03) with a lower BSR (10−5/s), the stress-strain curves after the 25 strain rate jump were relatively smooth in both non-charged and H-charged specimens, 26 having the slopes almost the same as those before the jump (Fig. 7 (a)). Meanwhile, a 27 slight yield-drop appeared after the strain rate jump in the H-charged specimen at BSR = 28 Submitted to Materials Science and Engineering A 8th July 2024  11  10−3/s (cf. red arrow in Fig. 7 (b)). Interestingly, such a yield-drop was indistinct in the 1 non-charged specimen (Fig. 7 (a) and (b)), as well as for the H-charged specimen at BSR 2 = 10−5/s (Fig. 7 (a)), under this small strain domain. With an increase in εt above 0.1, the 3 yield-drop after the strain rate jump began to manifest in all the testing conditions (Fig. 7 4 (c) and (d)), possibly ascribable to some multiplication event of dislocations [24,50]. 5 Although the results are omitted from Fig. 7, the tendency of stress-strain behavior under 6 BSR = 10−4/s was almost similar to the case of BSR = 10−5/s. The appearance of yield-7 drop after the mechanical transient has often been attributed to some strain aging 8 phenomena [48,49]. However, its presence under the faster BSR and its absence under 9 slower BSR contradict any basic theories of strain aging. Note that a similar yield-drop 10 phenomenon was identified at the reloading process after stress relaxation as the applied 11 strain became relatively large (Fig. 4 (a)-(c)). This may also be due to the dislocation 12 multiplication event, trying to continue the deformation by compensating for the density 13 of mobile dislocations that were exhausted during the relaxation process [51]. 14  15  16 Fig. 7 True stress-true strain curves during the strain rate jump tests with the BSR of (a)(c) 17 10−5/s and (b)(d) 10−3/s. (a) and (b) correspond to the small strain regime below 0.05, 18 while (c) and (d) show a larger strain beyond 0.1. The arrows denote the minute yield-19 drop manifesting after the strain rate jump. 20   21 Submitted to Materials Science and Engineering A 8th July 2024  12  4. Discussion 1 4.1 Strain rate sensitivity in non-charged specimens 2 4.1.1 Linearity of the SRS vs. flow stress plot: Cottrell-Stokes law 3 When plotted versus flow stress, the S values in non-charged specimens exhibited 4 almost linear behavior accompanying a gradual increase in S with a positive slope. Such 5 linearity between S and flow stress has been reported in a variety of FCC metals and 6 alloys, a feature of the so-called Cottrell-Stokes law [52–54]: effective stress is 7 proportional to the total flow stress. 8  9  10 Fig. 8 Schematic drawing of the strain rate sensitivity (S) vs. flow stress (τ-τy) plot on the 11 basis of eq. (4). The linearity of the plot appears when it obeys Cottrell-Stokes law. 12  13 The S value in engineering alloys is determined as a sum of the contributions from 14 multiple thermal obstacles [26,29,36,37]. The primary obstacles in the present material 15 are substitutional solutes (i.e., Cr and Ni) and forest dislocations introduced by plastic 16 deformation. Given that their contributions are additive, an accepted case for a 17 combination of solutes and forest dislocations [36,37,46], eq. (1) can be decomposed into 18 two separate terms. 19 𝑆 =𝜕𝜏𝜕ln𝛾̇=𝜕𝜏𝑦𝜕ln𝛾̇+𝜕𝜏𝑑𝜕ln𝛾̇=𝜕𝜏𝑦𝜕ln𝛾̇+𝜕ln𝜏𝑑𝜕ln𝛾̇(𝜏 − 𝜏𝑦)              (4) 20 where τd is the amount of strain-hardening, equals to τ-τy. A major part of S at the yield 21 point, τy, stems from the contribution of solutes. Thus, the first term in eq. (4) (i.e., the 22 intercept of S−(τ-τy) plot) reflects the S component of solutes only, while the second term 23 expresses the forest dislocation component. The linearity of S−(τ-τy) plot indicates a 24 constant coefficient of the second term, a parameter reflecting the strength of the 25 intersection between mobile and forest dislocations [29,36]. In Fig. 8, the general 26 Submitted to Materials Science and Engineering A 8th July 2024  13  behavior of S−(τ-τy) plot is schematically drawn, together with how it is affected by the 1 involvement of a new type of thermally activatable obstacles (discussed in Section 4.2.1). 2 One can also recognize how this general behavior breaks down in the case of H-charged 3 specimens from the comparison of Fig. 8 with Fig. 5 and Fig. 6. This is due to the 4 contribution of solute drag as will be discussed later in Section 4.2.2. 5    The activation parameters measured by mechanical transient tests can reflect not only 6 the mobility of individual dislocations but also their annihilation process: dynamic 7 recovery. Nonetheless, the typical consequence when dynamic recovery is interposed is 8 the deviation of S−(τ-τy) plot from linearity and its shape change into a concave upward 9 [29,54]. Such behavior was not observed in non-charged specimens (Fig. 5 and Fig. 6), 10 indicating that the influence of dynamic recovery was minor in the presently examined 11 stress/strain range. Also, we have preliminarily confirmed in Fe-Cr-Ni alloy system that 12 the impact of solute H on the propensity for dynamic recovery is insignificant [55]. 13  14 4.1.2 BSR vs. S in strain rate jump test 15 Although S−(τ-τy) plots in non-charged specimens satisfied linearity in both stress 16 relaxation and strain rate jump tests, a difference was identified as their BSR-dependence. 17 BSR barely affected S in the former tests, whereas an increase in BSR caused an upward 18 shift of S−(τ-τy) plot in the latter tests. Since the shift occurred parallelly with an almost 19 constant slope (i.e., a constant second term in eq. (4)), it is due to changes in the 20 interaction of mobile dislocations with solutes rather than their interactions with forests. 21    The dislocation configuration and its force-distance profile during a thermal 22 activation event for overcoming a short-range obstacle is usually drawn in the form of 23 Fig. 9 [46]. Several shapes of obstacle profiles have been established, amongst which 24 parabolic, triangular, or Cottrell-Bilby potentials with finite slopes are most widely 25 employed for the case of solute-dislocation interactions [13,24,56]. In Fig. 9 (c) and (d), 26 ΔG (shaded with black) expresses the free energy change during the thermally activated 27 overcome, i.e., energy supplied by thermal fluctuation. This enters into the numerator of 28 the exponent in the Arrhenius type rate equation for plasticity [24,50]. 29 𝛾̇ = 𝛾̇0exp (−∆𝐺𝑘𝑇)                         (5) 30 where 𝛾̇0  is a pre-exponential factor involving the density and velocity of mobile 31 dislocations. The area below ΔG (shaded with gray) in Fig. 9 (c) and (d) is the externally 32 applied mechanical work, which is the product of applied stress and activation volume, 33 τV. V is a purely geometric parameter multiplying the effective obstacle width, d, their 34 mean interspacing, L, and the Burgers vector, b: V = bdL (Fig. 9 (a) and (b)). It is also 35 defined by the stress derivative of ΔG [24] as 36 Submitted to Materials Science and Engineering A 8th July 2024  14  𝑉 = −𝜕∆𝐺𝜕𝜏|𝑇                           (6) 1 By combining eq. (6) with eq. (5), one can obtain eq. (1). From eq. (5), it can be noticed 2 that ΔG is a linearly decreasing function with a logarithm of strain rate: 3 ∆𝐺 = 𝑘𝑇ln(𝛾̇0𝛾̇⁄ ) = 𝑘𝑇(ln𝛾̇0 − ln𝛾̇)                 (7) 4 ΔG probabilistically decreases as the strain rate increases, making the d value statistically 5 narrower. In other words, a higher stress is required for dislocations to overcome these 6 obstacles due to a lesser aid from thermal fluctuation. Given that the L is constant during 7 the deformation (e.g., for solutes), a decrease in d leads to a decrease in V. This, in turn, 8 causes an increase in S (cf. eq. (1)), a plausible reason for a larger S under a higher BSR 9 in non-charged specimens (Fig. 6). According to eq. (7), an increase in strain rate has the 10 same physical sense as a decrease in deformation temperature. In fact, decreasing V and 11 increasing S with a lowering temperature is a common trend [27,57]. 12  13  14 Fig. 9 Illustration of the movement of a dislocation segment via overcoming short-range 15 obstacles. (a) and (c) are the top view of the slip plane, while (b) and (d) are its side view. 16 (a) and (b) denotes the effect of strain rate on the free energy and activation volume, 17 whereas the influence of obstacle extent on these parameters is shown in (c) and (d). 18  19 4.1.3 BSR vs. S in stress relaxation test 20    To understand the BSR-insensitivity of S in the stress relaxation test, not only BSR 21 but also the strain rate during stress relaxation should be considered. This is because the 22 S in the stress relaxation test is derived from the difference in plastic strain rates between 23 the end of one relaxation and the beginning of the next relaxation (Section 2.2.1). In Fig. 24 Submitted to Materials Science and Engineering A 8th July 2024  15  10 (a), the plastic strain rates, 𝜀𝑝̇, in non-charged specimens during 1st~5th relaxations 1 at εt ≈ 0.1 are shown for three different BSRs. Although the experimentally obtained 2 stress-time data seemed smooth in Fig. 4 (a)-(c), they necessarily involve some noises 3 due to tiny fluctuation of the load cell signal. Thus, its time derivative also involves some 4 scatters especially when 𝜀𝑝̇ was below 10−5/s. 5 Due to a necessity for deformation continuity, 𝜀𝑝̇  at the beginning of all the 1st 6 relaxations coincided well with their corresponding BSR. Then, 𝜀𝑝̇ gradually decayed 7 as the relaxation progressed, which is typical behavior of the logarithmic deformation 8 transient [24], eventually settling at 4×10−5~7×10−5/s. After the reversion of stress to the 9 original level, the 2nd relaxation started with 𝜀𝑝̇  slightly smaller than that at the 10 beginning of 1st relaxation. These 𝜀𝑝̇ ranges were scarcely affected by εt. The variation 11 of 𝜀𝑝̇ during the relaxation was greatest at BSR = 10−3/s, while it was smallest at BSR = 12 10−5/s. Because of the limited crosshead-holding time of 30 s, the 𝜀𝑝̇ at the end of each 13 relaxation exhibited slightly higher values at BSR = 10−3/s and 10−4/s than at BSR = 10−5/s. 14 With the prolongment of the holding time, these strain rates would converge with each 15 other and eventually settle into zero upon the effective stress component is fully relaxed. 16  17  18 Fig. 10 Plastic strain rate, 𝜀𝑝̇, during the stress relaxation series in (a) non-charged and 19 (b) H-charged specimens at a true tensile strain, εt, of around 0.10. These plastic strain 20 rate ranges during the relaxations were almost similar for each BSR condition, even when 21 the strain level was larger and smaller. 22  23    An important indication from Fig. 10 is that, in the stress relaxation test, the 24 denominator of eq. (2) or eq. (3) depends on BSR (i.e., it should increase with an increase 25 in BSR), while it does not in strain rate jump test as long as the 𝛾̇2/𝛾̇1 ratio is constant. 26 Therefore, an increase in S with BSR, which is due to the reason explained in Section 27 4.1.2, can be compensated by this increase in the denominator term. In other words, the 28 S value inherently includes the influences of continuously decreasing 𝜀𝑝̇ (i.e., sluggish 29 Submitted to Materials Science and Engineering A 8th July 2024  16  decrease in dislocation velocity during the relaxation), an inevitable consequence owing 1 to the nature of this experimental methodology. From a physical perspective, the strain 2 rate jump test may reflect an instantaneous change in the glide resistance to mobile 3 dislocations more adequately, whereas some transient effects in a finite timeframe are 4 added to the result of stress relaxation tests. A similar viewpoint of the strain rate during 5 relaxation is also vital to interpreting the complex S-BSR correlations in H-charged 6 specimens and their dependences on the test types (Fig. 5 and Fig. 6). 7  8 4.2 Strain rate sensitivity in H-charged specimens 9 4.2.1 Solute H as thermal obstacles 10 In the stress relaxation tests of H-charged specimens, Fig. 5 (a) shows that the back 11 extrapolations of the horizontal parts of S−(τ-τy) plots yield positive intercepts, the values 12 larger than those in non-charged specimens. According to eq. (4) and Fig. 8, a larger 13 intercept implicitly indicates a greater 𝜕𝜏𝑦/𝜕ln𝛾̇ term and an additional contribution of 14 another type of solute atoms to S. In the present case, it is precisely H. They act as 15 additional short-range obstacles, amplifying the effective stress and causing SSH [3,20]. 16 The role of solute H as a short-range obstacle and its interaction form with 17 dislocations have been discussed in the authors' companion papers [3,20], thereby not 18 described here in depth. In short, H atoms segregating into dislocation core, as well as 19 those dispersed in austenite lattice, act as weak and more thermally activatable obstacles 20 than other intrinsic obstacles contained in the material. The bowing-out of short 21 dislocation segments from the row of segregated solute H, accompanying an atomic jump 22 of those H toward the direction of dislocation movement, maybe a particular rate-23 controlling process of deformation. Such a model was deduced from the interrelationship 24 between H concentration, yield stress, and activation volume [20]. Additionally, it has 25 also been inferred from previous work that the effective stress component stemming from 26 this type of H-dislocation interaction is proportional to the total amount of solute H 27 contained in the material [20]. 28 Considering its more thermally activatable nature, H potentially has a narrower force-29 distance profile in Fig. 9 (d), whereas the height of its profile is not exactly known. Since 30 a weaker and more localized obstacle generally yields a smaller V and, in turn, a larger S 31 [29], it has a positive contribution to 𝜕𝜏𝑦/𝜕ln𝛾̇ term in eq. (4) (Fig. 5 (a) and Fig. 8). At 32 the same time, it may be time for dislocations to overcome these newly involved obstacles 33 that control the deformation kinetics [26,28,46] in a relaxation timeframe of 30 s. A high 34 density of these additional rate-controlling obstacles potentially weakens the 35 effectiveness of 𝜕𝜏d/𝜕ln𝛾̇ term in eq. (4) and decreases the slope of the S−(τ-τy) plot. 36 Indeed, our stress relaxation tests in [20] demonstrated a gradual slope decrease with an 37 Submitted to Materials Science and Engineering A 8th July 2024  17  increase in H concentration, an extreme case of which is the horizontal plot in Fig. 5 (a). 1    Given that H acts as a short-range obstacle, one would attempt to understand the BSR-2 dependences of S in H-charged specimens in a context similar to Section 4.1. Nonetheless, 3 the concave curvature of S−(τ-τy) plots (Fig. 5 (a)), as well as their non-linearity in strain 4 rate jump tests (Fig. 6 (a)), are beyond the spectrum that can be covered by the description 5 employed in Section 4.1. Thus, another hypothesis, solute drag, should be involved to 6 establish a more comprehensive interpretation. 7  8 4.2.2 Contribution of solute drag 9 A resistance to dislocation motion by dragging solute atmosphere is envisaged in a 10 situation where the diffusivity of solute is comparable to an average velocity of 11 dislocations [16,31–33]. This can apply to the present experiments because of the high 12 mobility of H in austenite lattice even at room temperature [3,58,59]. Cottrell first 13 attempted to roughly estimate the critical strain rate for solute drag under a given solute 14 diffusivity and mobile dislocation density [16]. Later on, the theory was numerically 15 refined, quantifying the drag stress and its variation concerning the dislocation velocity 16 [31–33]. Here, the latest formulation by Sills and co-workers [23,38] is employed to 17 assess the contribution of solute drag in Fig. 5 and Fig. 6. These formulae were successful 18 in explaining some anomalies in the flow behavior of H-charged austenitic steel in our 19 previous publication [3]. 20  21  22 Fig. 11 (a) strain rate range, where drag of H atmosphere is feasible to exert a resistance 23 force (drag force) against steady-state (i.e., constant velocity) dislocation motion, as a 24 function of mobile dislocation density. (b) and (c) indicate the situations in (b) stress 25 relaxation and (c) strain rate jump tests under different base strain rates, which were 26 estimated from (a). The calculations were performed based on eq. (8) ~ eq. (10). 27  28 Submitted to Materials Science and Engineering A 8th July 2024  18  Based on Orowan's formula, the critical strain rate for the dynamic interaction between 1 mobile dislocation and diffusible solutes, 𝜀𝑐̇, is given by 2 𝜀𝑐̇ =4𝑄𝐷𝑘𝑇𝑀T𝛽𝜌m𝑏                         (8) 3 where D is the bulk diffusion coefficient of solute, and ρm is the density of mobile 4 dislocations [23]. The parameter Q characterizes the velocity of mobile dislocations, 5 which is non-dimensionalized as: 6 𝑄 =𝑣d𝛽4𝐷𝑘𝑇                            (9) 7 Here, β is an elastic interaction parameter for an edge dislocation that is defined via shear 8 modulus, μ, Poisson's ratio, ν, and the volume expansion per solute atom, ΔV (≈ 2×10−30 9 m3 for H in Fe-Cr-Ni austenitic steels [2,18]):  10   𝛽 = ∆𝑉𝜇𝑏3𝜋(1+𝜈1−𝜈)                        (10) 11 The dislocation is pulled away from the atmosphere when Q > 100: breakaway limit. 12 Meanwhile, under Q < 0.01, the atmosphere can follow the dislocation by maintaining its 13 near-equilibrium distribution: equilibrium limit. At 0.01 < Q < 100, the atmosphere lags 14 behind the dislocation, and a resultant non-equilibrium distribution exerts a drag 15 resistance with its maximum at Q ≈ 1: maximum drag force (Fig. 11 (b) and (c)) [23,38].  16 The H diffusivity, D, in Type310S steel was measured by Perng and Altstetter [60]. 17 Extrapolation of their data yields D = 3.2×10−16 m2/s at 296 K. In Fig. 11 (a), these 18 breakaway limit (Q = 100), maximum drag (Q = 1), and equilibrium limit (Q = 0.01) are 19 drawn for arbitral values of 𝜀𝑝̇ and ρm. Note that a band with finite width decorates each 20 limit line to take the possible errors of ΔV and D into account. Our theoretical calculation 21 estimated that a dense H atmosphere around a stationary edge dislocation is formed in a 22 Type310S steel with 7600 at. ppm H at room temperature [3]. The whole or a part of the 23 atmosphere is feasible to migrate with dislocation when 𝜀𝑝̇ and ρm lay in-between the 24 range of 0.01 < Q < 100 (area shaded with red in Fig. 11 (a)). Note that these Q-based 25 criteria can also be applied even to the dislocations extended into two Shockley partials, 26 although the magnitude of drag resistance is somewhat affected by dislocation's character 27 (i.e., fractions of edge and screw components) [38]. For slightly extended dislocations 28 like in Type310S steel with medium stacking fault energy [61], the impact of solute drag 29 on the overall flow stress appears as a statistical average of such character-dependent 30 variation.  31  32   33 Submitted to Materials Science and Engineering A 8th July 2024  19  4.2.3 Effect of BSR in stress relaxation tests 1    A critical but experimentally unmeasurable parameter that enters into eq. (8) is ρm. 2 Nonetheless, a theoretical fitting of the stress-strain curve was implemented by Alden 3 [62], giving ρm = 1011~1012/m2 around the yield point and its sudden increase over 1013/m2 4 at a later deformation stage for austenitic steel (cf. horizontal bars in Fig. 11 (a)). In Fig. 5 10 (b), the 𝜀𝑝̇  during the stress relaxation in H-charged specimens at εt ≈ 0.1 are 6 presented. These ranges of 𝜀𝑝̇  roughly yields the situations during the relaxation and 7 their BSR-dependence as the black, blue, and gray arrows in Fig. 11 (b). 8 At BSR = 10−5/s, the drag force spontaneously decreases with the slowing down of 9 𝜀𝑝̇ at a small strain around the yield point (gray arrow in Fig. 11 (b-1)). Therefore, the 10 dislocation velocity is primarily dominated by their short-range (thermal) interactions 11 with obstacle H (Section 4.2.1) rather than the interaction with an atmosphere. Moreover, 12 due to the narrow range of 𝜀𝑝̇ (Fig. 10 (b)), the variation of drag force during relaxation 13 should also be small. The drag force becomes further absent at a later deformation stage 14 (gray arrow in Fig. 11 (b-2)). These limited contributions of drag force led to a totally 15 horizontal S−(τ-τy) plot at BSR = 10−5/s (Fig. 5 (a)). 16 The situation around the yield point is somewhat different for BSR = 10−4 and 10−3/s 17 (blue and black arrows in Fig. 11 (b-1)). The drag force gradually increases with the decay 18 of 𝜀𝑝̇. Thus, the dislocations, which would be mobile if there was no drag resistance, 19 could eventually lose their mobility as the relaxation progressed. This should have a 20 negative contribution to S by limiting the relaxation stress drop, Δτ1, in eq. (2), as well as 21 by increasing 𝛾̇2𝑏  term due to the release of dislocations from drag resistance upon 22 reloading. Such a negative contribution can be ascribed to the initial concave down of 23 S−(τ-τy) plots at small stress/strain under these two BSRs (Fig. 5). Explicitly, as expected 24 from Fig. 11 (a) and (b-1), the initial concave down was more substantial for BSR = 10−3 25 than for 10−4/s. As εt becomes larger, the situation same as BSR = 10−5/s (i.e., the limited 26 contribution of drag force) can be reached even for BSR = 10−4 and 10−3/s (Fig. 11 (b-2)). 27 Namely, S−(τ-τy) plots become horizontal after a certain extent of deformation (Fig. 5). 28 Even though the initial concave down of S−(τ-τy) plot at low stress/strain can be 29 interpreted by solute drag, the BSR-dependence of S in the horizontal part of S−(τ-τy) 30 plots (e.g., τ-τy > 40 MPa in Fig. 5 (a)) is not straightforward. Possibly, in the case of H-31 charged specimens, the same explanation with Section 4.1.2 can be applied even for stress 32 relaxation tests due to the greater magnitude of Δτ1 (Fig. 4 (a)~(c)) that cannot be 33 compensated by an increase in 𝛾̇2𝑏/𝛾̇1𝑒   in eq. (2). This can be the reason for the 34 constantly larger S at BSR = 10−4/s than at 10−5/s (Fig. 5). On the other hand, the density 35 of segregated H atoms in dislocation core, which work as thermal obstacles [20], could 36 be reduced at a higher BSR, rendering the S at BSR = 10−3/s smaller than that at 10−4/s. 37 Submitted to Materials Science and Engineering A 8th July 2024  20  Measurement conditions (e.g., relaxation time) must be optimized to clarify these points, 1 some dedicated experiments for which are ongoing by the authors. 2  3 4.2.4 Effect of BSR in strain rate jump tests 4 The shapes of S−(τ-τy) plots were more complex in strain rate jump tests, an 5 interpretation for which is now attempted based on Fig. 11 (c). Around the yield point at 6 BSR = 10−4/s and 10−3/s (Fig. 11 (c-1)), the drag force sharply decreases upon the strain 7 rate jump. This should have a significant negative contribution to S, while this effect could 8 be limited at BSR = 10−5/s. One thus envisages that the initial concave down, discussed 9 in Section 4.2.3, appears more explicitly at BSR = 10−4/s and 10−3/s. Notably, the S−(τ-10 τy) plots in Fig. 6 indeed exhibited such a tendency. 11 Fig. 11 (c-1) expects that (I) 𝜀𝑝̇ reached the breakaway limit (Q = 100), and the drag 12 force disappeared upon the strain rate jump from 10−3 to 10−2/s, while the drag force might 13 more or less exist after the jump from 10−4 to 10−3/s. Furthermore, (II) the decreasing rate 14 of drag force potentially becomes steeper as log-𝜀𝑝̇ gets away from Q = 1 (cf. blue and 15 black arrows in Fig. 11 (c-1)) [38]. Both these (I) and (II) amplify the negative 16 contribution of drag force to S at a higher BSR condition, one of the reasons for 17 consistently smaller S at BSR = 10−3/s than at 10−4/s in the low stress/strain domain in 18 Fig. 6. Additionally, since a major part of H atmosphere is left behind the moving 19 dislocation under such a circumstance, (III) the concentration of H along the dislocation 20 core (thermal obstacles to dislocation motion) could also be reduced: increase in the 21 intercept of S−(τ-τy) plots by H (Fig. 8) could be minor. A combination of (I)~(III) works 22 to reduce the S in H-charged specimens, making it equivalent to or even smaller than the 23 values in non-charged specimens at the same stress/strain level (cf. τy = ~40 MPa and εt 24 = ~0.05 in Fig. 6). Note also that the relief of dislocations from their drag resistance 25 seemingly appeared on the characteristics of stress-strain behavior after the strain rate 26 jump. Namely, the density of dislocations with higher mobility suddenly increases, 27 causing the yield-drop phenomenon captured in Fig. 7 (b). 28 According to Fig. 11 (a), the above factors (I)~(III) are gradually weakened with an 29 increase in ρm: 𝜀𝑝̇-range of 10−4~10−2/s gets away from Q = 100 and lays close to or 30 below Q = 1. The S thus eventually recovers to the same level with stress relaxation tests, 31 wherein a larger strain (ρm) is required for the recovery at BSR = 10−3/s than at 10−4/s (Fig. 32 6). Afterwards, the situation turns into Fig. 11 (c-2) when ρm exceeds 1013/m2. In this 33 regime, the strain rate jump oppositely increases the drag force and can positively 34 contribute to S, the impact of which is most significant at BSR = 10−4/s (cf. blue arrow in 35 Fig. 11 (c-2)). This is a rationale behind the larger S at BSR = 10−4/s as compared with at 36 10−5/s (Fig. 6). Ultimately, the additive contribution by drag force could escalate S in 37 Submitted to Materials Science and Engineering A 8th July 2024  21  strain rate jump tests to a greater level than those in stress relaxation tests as the 1 deformation goes into a later stage with τy > 80 MPa and εt > 0.1 (Fig. 6). 2 Meanwhile, the S value at BSR = 10−3/s exceeded that at 10−4/s in a further large 3 stress/strain domain with τy > 100 MPa and εt > 0.15, although the reason for it is yet to 4 be known. Probably, multiple factors (e.g., inherent dependence of S on BSR (Section 5 4.1.2), role of H as thermal obstacles (Section 4.2.1), and solute drag) might be complexly 6 mixed here, and individual contribution of these influencing factors cannot be 7 distinguished unfortunately in the present test program. Note also that the present analysis 8 and interpretations are all based on the assumption that the density and arrangement of 9 dislocations are not affected significantly by the presence of H. Fortunately, it was 10 confirmed by our past evaluations of the deformation microstructures and strain-11 hardening properties in the same material [3,4,20,55]. 12  13 5. Summary: roles of effective stress and solute drag on SRS and SSH 14 The experimental assessment of the strain rate sensitivity, S, and its match-up with 15 theoretical formulae substantiated the competitive or cooperative contributions of the H-16 induced effective stress and atmosphere drag resistance to the flow stress in Type310S 17 austenitic steel. Even though the confirmation was carried out indirectly and some 18 uncertain issues were left, it can reinforce our previous statement [3,20] estimating the 19 presence of solute drag, particularly around the yield point. Those experiments were 20 performed only under the condition of 7600 at. ppm H, leaving the H concentration-21 dependence of the magnitude of drag stress being unraveled. Nonetheless, considering 22 the linear concentration-dependence in the conventional theories of solute drag [16,33], 23 the H-induced drag resistance should also be proportional to H concentration in a similar 24 manner to the effective stress component caused by H [20]. 25 Fig. 12 schematically summarizes the relationship between effective stress and glide 26 resistance by solute drag as a function of a logarithm of the mobile dislocation velocity. 27 The effective stress should increase linearly in terms of the Arrhenius type rate equation 28 (eq. (5)), whereas the decreasing density of H atoms along the dislocation core in the 29 regime above Q = 1 could make it deviate from the linearity toward the lower side. When 30 the velocity is in the regime below Q =1, the effective stress and drag force additively 31 contribute to enhancing both the flow stress and S. A typical example of such a situation 32 was the strain rate jump test with BSR = 10−4/s at a later stage of deformation (Fig. 11 (c-33 2)) where the S value was significantly large (Fig. 6). On the other hand, although these 34 two factors are additive under a constant velocity of dislocations, their prompt 35 acceleration diminishes the drag resistance and negatively contribute to S when the 36 velocity is greater than Q = 1. A representative case was the strain rate jump test with 37 Submitted to Materials Science and Engineering A 8th July 2024  22  BSR = 10−3/s around the yield point (Fig. 11 (c-1)), where S in the H-charged specimen 1 sank below that in the non-charged one. The last fact indicates that the net H-related S 2 value can notably be negative due to a sudden loss of solute drag. Nonetheless, a sufficient 3 positive contribution from other intrinsic thermal obstacles (e.g., solute atoms and forest 4 dislocations) compensates for such a negative impact of H (Fig. 8). This maintains the 5 total S value still positive, preventing the emergence of plastic flow instability [24,63]. 6 Fig. 12 anticipates that, in terms of the yield stress, the SSH by solute H at room 7 temperature should be maximized around Q = 1 where effective stress and solute drag 8 most effectively cooperate. The corresponding strain rate is 10−5~10−4/s if one refers to 9 the small ρm regime in Fig. 11 again. Indeed, our measurement for the same Type310S 10 steel demonstrated such a trend when the yield stress in the H-charged specimen was 11 evaluated in the strain rate range of 5×10−7~5×10−3/s [3,4]. Also in the present study, the 12 gap of yield stress between non-charged and H-charged specimens was greater at the 13 strain rates of 10−5 and 10−4/s than that at 10−3/s (Fig. 3).  14 In the present study, we only dealt with the condition of 7600 at. ppm H, leaving the 15 influence of H concentration on the mechanical transient and S parameter both unraveled.  16  17  18 Fig. 12 Schematic illustration of the cooperative or competitive contribution of effective 19 stress and solute drag force by H to the strain rate sensitivity at room temperature. 20  21   22 Submitted to Materials Science and Engineering A 8th July 2024  23  6. Conclusions 1 The H-induced SSH at 296 K was studied in Type310S austenitic steel containing 2 7600 at. ppm H. Two types of transient mechanical tests: stress relaxation; and strain rate 3 jump, were performed under various BSRs, determining the SRS as a measure of stress 4 components responsible for SSH under a given deformation condition.  5 The SRS clarified two possible roles of H that contribute to the flow stress 6 components: (i) H atoms as short-range, thermally activatable obstacles; and (ii) a 7 resistance to dislocation motion by dragging the diffusible H atmosphere (i.e., solute drag). 8 The significance of both these components was strain rate dependent. Factor (i) 9 consistently exerts a positive contribution to SRS, a typical characteristic when an 10 obstacle type that is more thermally activatable than others is newly involved. Meanwhile, 11 factor (ii) either increases or decreases SRS depending on whether the dislocation velocity 12 range of interest, which is a function of mobile dislocation density and strain rate, lays 13 below or above the limit of maximum drag force. The most effective H-induced SSH can 14 be derived when the sum of the contributions from (i) and (ii) is optimally maximized. In 15 terms of yield stress, for instance, such a situation is achieved in the strain rate range of 16 10−5~10−4/s. 17  18 Acknowledgments 19 This work was supported by research funding from JSPS KAKENHI (Grant Numbers: 20 21K14045 and 24K17180), JFE 21st Century Foundation, and The Iwatani Naoji 21 Foundation. All the experiments in this study were performed during Y.O.'s tenure at 22 Kyushu University, where he was affiliated until February 2023 (currently affiliated with 23 NIMS). The authors are grateful to the members of the Research Center for Hydrogen 24 Industrial Use and Storage (HYDROGENIUS), Kyushu University, for their provision of 25 research facilities and experimental support. 26  27 Data availability 28 The raw/processed data for reproducing the findings in this study are available from the 29 corresponding author upon request by readers. However, the availability will be 30 determined on a case-by-case basis in consultation with the organizations who funded to 31 this research. 32  33   34 Submitted to Materials Science and Engineering A 8th July 2024  24  References 1 [1] T. Boniszewski, G.C. Smith, The influence of hydrogen on the plastic deformation ductility, 2 and fracture of nickel in tension, Acta Metallurgica 11 (1963) 165–178. 3 https://doi.org/10.1016/0001-6160(63)90209-8. 4 [2] D.P. Abraham, C.J. Altstetter, The effect of hydrogen on the yield and flow stress of an 5 austenitic stainless steel, Metallurgical and Materials Transactions A 26 (1995) 2849–2858. 6 https://doi.org/10.1007/BF02669643. 7 [3] Y. Ogawa, O. Takakuwa, K. Tsuzaki, Solid-solution hardening by hydrogen in Fe–Cr–Ni-8 based austenitic steel: Temperature and strain rate effects, Materials Science and 9 Engineering: A (2023) 145281. https://doi.org/10.1016/j.msea.2023.145281. 10 [4] Y. Ogawa, H. Hosoi, K. Tsuzaki, T. Redarce, O. Takakuwa, H. 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