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[Yuhei Ogawa](https://orcid.org/0000-0003-2713-9822), Osamu Takakuwa, [Kaneaki Tsuzaki](https://orcid.org/0000-0003-2400-7605)

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[Solid-solution hardening by hydrogen in Fe–Cr–Ni-based austenitic steel: Temperature and strain rate effects](https://mdr.nims.go.jp/datasets/b934af4b-6e1d-4c60-8f33-82376c31dbbb)

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Submitted to Materials Science and Engineering A 1  Solid-solution hardening by hydrogen in Fe-Cr-Ni-based austenitic steel: 1 temperature and strain rate effects 2  3 Yuhei Ogawaa, Osamu Takakuwab, Kaneaki Tsuzakia,c 4  5 a Research Center for Structural Materials, National Institute for Materials Science 6 (NIMS), 1-2-1 Sengen, Tsukuba, 305-0047, Japan 7 b Department of Mechanical Engineering, Kyushu University, 744 Motooka, Nishi-8 ku, Fukuoka 819-0395, Japan 9 c Professor Emeritus, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, 10 Japan 11  12 Corresponding Author: Yuhei Ogawa 13 E-mail: OGAWA.yuhei@nims.go.jp 14  15 Abstract 16 Solid-solution hardening caused by dissolved hydrogen (H) atoms in face-centered 17 cubic metals is a favorable phenomenon that counteracts the H-induced degradation of 18 mechanical performance in structural alloys, i.e., hydrogen embrittlement. In the present 19 study, the changes of yield and flow stresses by solute H with the concentrations of 20 2000~7600 at ppm were systematically investigated in a Fe-24Cr-19Ni-based austenitic 21 stainless steel under the temperature range of 173~423 K and two different strain rates: 22 5×10−5 and 5×10−3/s. Stress relaxation tests were subsidiarily employed in order to 23 elaborate the underlying mechanisms predominating the H-related hardening at low and 24 ambient temperatures. Four essential ingredients of the H-induced hardening were 25 identified: (i) H atoms in the matrix lattice as dispersed obstacles; (ii) pinning of 26 stationary dislocations by H atmosphere; (iii) dynamic pinning of dislocations resting at 27 obstacles; (iv) drag force to moving dislocations by migratable H clouds. The hardening 28 around 173 K was attributed to (i) and (ii), where the primary importance of interstitial-29 substitutional interaction between Cr and H was explicitly invoked. Meanwhile, the 30 magnitude of hardening was maximized at around 298 K under the slow strain rate 31 condition owing to the increasing contributions from (iii) and (iv). 32  33 Keywords: Austenitic stainless steel; Hydrogen; Solid-solution hardening; Dislocations 34   35  Submitted to Materials Science and Engineering A 2  1. Introduction 36  In face-centered-cubic (FCC) metals and alloys, interstitial hydrogen (H) atoms are 37 known to cause an intense augmentation of yield strength, flow stress, and indentation 38 hardness [1–10]. The phenomenon was first elaborated in an old paper by Boniszewski 39 and Smith in electrochemically charged pure Ni [1], later identified in Ni-based alloys 40 [3,8,11,12], austenitic stainless steels (ASSs) [4–7,9], and FCC high-entropy alloys 41 (HEAs) [13–15]. Despite its notable hardening effect, a significant drawback of the H 42 occlusion has long been recognized: the ductility is degraded simultaneously, i.e., 43 hydrogen embrittlement, owing to the premature failure accompanying intergranular or 44 cleavage-like fracture features [1,5,6,11–13,16]. Such a negative aspect still impregnates 45 the well-accepted understanding of H as a detrimental element rather than a proactive 46 agent for structural metals [17–19]. However, the present authors recently uncovered a 47 concurrent improvement of the strength and ductility in ASSs with specific chemical 48 compositions after uniformly charging an extensive amount of solute H (~7000 at. ppm) 49 [20,21]. This epoch-making finding now gives rise to a prospect for utilizing H to 50 strengthen the ASSs in the same manner as other interstitials like carbon (C) and nitrogen 51 (N) [22–26]. 52    The hardening by interstitial atoms is generally attributed to the statistical interactions 53 between dislocations and short-range lattice strain or different modulus zone around the 54 interstitials: solid-solution hardening [27–31]. Nevertheless, because of its small atomic 55 diameter and extensive diffusivity, several forms of dynamic interactions of diffusible H 56 and mobile dislocations have been of great importance in understanding the rationales 57 behind the H-induced strengthening effect [1,3,4,8,32–36]. Such dynamic interactions 58 were evidenced by serrated yielding in H-charged Ni and Ni-alloys within the temperature 59 and strain rate ranges in which the diffusion of H and the velocity of dislocations become 60 mutually competitive [1–3,37,38]. Segregation of H into dislocation core region and 61 potential nucleation of local hydride phase [2,4,39–41] pin the mobile dislocations, 62 leading to the intermittent stress drop (i.e., Portevin-Le Chatelier effect) in association 63 with the dislocations depinning or activation of other dislocation sources. The latter event 64 results from the exhaustion of mobile dislocations due to the dynamic pinning, which 65 amplifies dislocation density and substructure evolution, thereby enhancing the work-66 hardening as a secondary impact [37]. H-induced dislocations pinning was further 67  Submitted to Materials Science and Engineering A 3  supported in Ni-Cr alloys by identifying the yield point discontinuity after static strain-68 aging experiments [42]. Moreover, the hardening outcome has also been ascribed to the 69 changes in dislocation gliding character when the dislocation velocity is slow enough to 70 allow the coordinative motion of its segregated H atmosphere [8,16,34,43]: planar 71 dislocation structures or smaller cell sizes are favored owing to a suppressed cross-slip 72 [9,44,45] and shielding of the elastic stress field around dislocations, i.e., H-enhanced 73 localized plasticity (HELP) theory [32,46]. 74 On the other hand, in Fe-Cr-Ni-based ASSs and HEAs, critical information is lacking 75 for getting to the bottoms of H-induced strengthening phenomena [4,6,7,9,15,20,35]. 76 Despite their coordinative capability for the hardening with Ni and Ni-alloys [1,3,8,11], 77 it is still not explicit whether the responsible H-dislocation interactions are dynamic, static, 78 or both. A careful examination of the tensile flow behavior was conducted by Altstetter 79 and co-workers on the thin foils of AISI Type304 and 310S steels after cathodically 80 charging ~10 at% H [4–6]. They found that the escalation of yield stress by solute H in 81 austenite was comparable to those caused by C and N, which was later reproduced in the 82 bulk samples of ASSs thermally charged in a pressurized H2 gas environment [21]. Upon 83 the H concentration exceeding 5 at%, a distinct yield drop appeared on the stress-strain 84 curve, attributed to the locking of pre-existing dislocations and dislocation sources by 85 forming the H-Cottrell atmosphere [4–6]. However, the re-appearance of such yield drop 86 or its amplification by H was not confirmed when the materials were pre-strained, aged, 87 and re-strained at room temperature [5,20]. This implies that the pinning effect of 88 dislocations by H at ambient conditions is, if any, not so significant or might be weaker 89 than that in Ni alloys. A strain localization due to HELP (i.e., reduction in the effective 90 gauge length) was also pointed out as a trigger of the apparent hardening effect [9,32,36]. 91 Although, the strengthening that emerged at cryogenic temperature or high strain rate 92 [12,15,20,47], where coordinative H-dislocation motion is infeasible, contradicts the 93 presumptions in the HELP hypothesis [32,46]. 94 In terms of the static solute-dislocation interactions, the presence of H-H or 95 substitutional-H pairs, which may function as short-range and thermally-activatable 96 obstacles via lattice swelling or tetragonal distortion, was implicated in the internal 97 friction measurements [48–50]. Indeed, Koyama et al. recently identified that an H-98 charged HEA contained an enhanced thermal component in its yield stress [15]. Moreover, 99  Submitted to Materials Science and Engineering A 4  through a continuum mechanics study of the dynamic interactions between diffusible 100 interstitials and perfect/extended dislocations, a significant contribution of the H-101 atmosphere dragging to obstructing dislocation movement was simulated by Sills and co-102 workers [35,51]. In the course of practical tensile deformation, either or several of these 103 factors and possibly some different ones may selectively or synergistically be activated, 104 predominating the H-induced strengthening as a final consequence. Ultimately, a more 105 systematic experimental framework is now required to isolate the leading mechanisms 106 under given deformation conditions. 107    The most elemental approach to probe the solute-dislocation interactions is to 108 examine temperature- and strain rate-dependences as well as thermal activation behaviors 109 of plastic flow [15,23,52–58]. In the present study, a Fe-24Cr-19Ni-based (AISI 110 Type310S) ASS was uniformly charged with 2000~7600 at ppm solute H. Yield/flow 111 stresses, work-hardening characteristics, stress-relaxation properties, and strain rate-112 sensitivity were evaluated under a wide range of temperature. The rationales of the 113 solution hardening were classified into several essential ingredients incorporating both 114 the static and dynamic effects. Finally, individual contributions from these controlling 115 factors were weighted as a function of the employed experimental variables. 116  117 2. Material and experimental methods 118 The materials used in this study was a commercially available Type310S ASS with a 119 chemical composition shown in Table 1. A hot-rolled bar with a diameter of 20 mm was 120 solution-annealed at 1353 K, followed by water-quenching, resulting in a grain size of 121 40~70 μm (see Fig. 1 (a)). The cylindrical tensile specimen having a 6 mm diameter and 122 30 mm-interval flanges on its gauge part (Fig. 1 (b)) was machined, the surface of which 123 was finished by polishing with #1000 silicone-carbide paper.  124 Tensile tests were performed with a screw-driven electromechanical test frame 125 attached to a thermostat chamber. The tests were conducted at temperatures of 173~423 126 K with crosshead displacement speeds (CHS) of 0.0015 and 0.15 mm/s, corresponding to 127 the initial strain rates of ≈ 5×10−5 and 5×10−3/s, respectively. The elongation of the gauge 128 part between the two flanges was monitored by using a linear variable differential 129 transformer (LVDT). Additionally, stress-relaxation tests were carried out at 173 and 298 130 K with the same testing equipment. The crosshead position was fixed after applying the 131  Submitted to Materials Science and Engineering A 5  true strain of 0.06 with CHS = 0.0015 mm/s, and the stress decay was recorded as a 132 function of time for 500 s with a data acquisition interval of 0.2 s. 133 Some of the tensile specimens were H-charged by exposing them to a pressurized 134 gaseous H2 environment at 543 K for 200 hours in an autoclave. Considering the H 135 diffusion coefficient in Type310S ASS, the charging temperature and duration are enough 136 to realize a uniform distribution of solute H inside the gauge part of the tensile specimen 137 with a 6 mm diameter (see authors’ previous publications [20,21] for detail). For varying 138 the H concentration, the H2 gas pressures for charging were set as 10, 40, 70, and 100 139 MPa. We also checked that the heating at elevated temperature itself and possible 140 microstructural changes do not affect the mechanical behavior by preparing a specimen 141 that was heat treated in a vacuum at 543 K and 200 hours. 142 After the tensile tests, cylindrical samples with a height of 5 mm were cut from the 143 uniformly deformed parts of the specimens, the residual H concentrations of which were 144 measured by gas chromatography thermal desorption analysis (TDA). The temperature 145 range and heating rate for the TDA were 298~1073 K and 100 K/h, respectively. 146  147 Table 1 Chemical composition (mass %) of Type 310S stainless steel used in this study. 148 C Si Mn P S Ni Cr Fe 0.02 0.37 1.10 0.023 0.001 19.18 24.18 Bal.  149  150 Fig. 1 (a) Initial microstructure on the plane perpendicular to the bar-axis, analyzed by 151 electron backscattering diffraction. (b) dimensions (mm) of the tensile specimen. 152   153  Submitted to Materials Science and Engineering A 6  3. Results 154 3.1 Hydrogen absorption property 155 The dissolution behavior of H atoms into the crystal lattice of metals from a gaseous 156 phase follows Sievert’s law [59], wherein the saturated solute H concentration, C0, is 157 correlated with the solubility, KS, as follows. 158 𝐶0 = 𝐾S√𝑓                             (1) 159 Here, f is the fugacity of H2 gas, which is defined by the Abel-Noble equation of state, 160 𝑓 = 𝑃exp (𝑃𝑏0𝑅𝑇)                          (2) 161 where P is H2 gas pressure, b0 = 15.84 cm3/mol [59], R is the universal gas constant, and 162 T is the absolute temperature.  163  164  165 Fig. 2 Solute H concentration as a function of the square root of H2 gas fugacity for 166 charging. The linear relationship indicates the satisfaction of Sievert’s law. 167  168 In Fig. 2, the H concentrations in the specimens in this study are plotted versus the 169 square root of H2 fugacity corresponding to the charging temperature and pressure 170 conditions in line with eq. (1). A linear relation was obtained between the two parameters 171 with KS = 0.62 at ppm/MPa1/2, indicating that the solute H atoms primarily dissolved into 172 interstitial lattice sites (i.e., octahedral sites in FCC crystal) rather than defects, such as 173 grain boundaries and pre-existing dislocations. The maximum H concentration of 7570 at 174 ppm (138 mass ppm) was achieved after charging at 100 MPa, consistent with the authors’ 175  Submitted to Materials Science and Engineering A 7  previous research using a same-grade material [20,21]. The measurement error of the H 176 concentration under each charging condition was within ±5% and even reduced to ±2% 177 as the charging pressure increased from 10 to 100 MPa. Note that in the fractured 178 specimens tested at 373~423 K, a ~10% decrease of the residual H concentration was 179 recognized due to an enhanced H diffusion. Nevertheless, the influence of H-loss on the 180 mechanical properties could be trivial because the H desorption should be limited at the 181 near-surface parts as well as because the focus of this paper was a small strain domain 182 after yielding where the test duration was much shorter than that until the fracture. 183  184 3.2 Tensile flow behavior 185 3.2.1 Effect of deformation temperature 186 Fig. 3 depicts the true stress-true strain curves of the small strain domain covering the 187 yield point of non-charged and H-charged specimens with C0 = 7570 at ppm at five 188 different deformation temperatures (i.e., 173, 223, 298, 373, and 423 K). In what follows, 189 the standard CHS for acquiring the presented results is 0.0015 mm/s (i.e., initial strain 190 rate of 5×10−5/s) unless otherwise noted. Comparing the solid and open symbols at each 191 temperature, one can notice that evident escalations of the yield and flow stresses emerged 192 owing to the H-charging at temperatures below 373 K, while the effect was gradually 193 diminished as the temperature increased.  194  195  196 Fig. 3 True stress-true strain curves of non-charged and H-charged (C0 = 7570 at ppm) 197 specimens for the strain range of ~0.10 at five different deformation temperatures. 198  199  Submitted to Materials Science and Engineering A 8  The yield stresses (0.2% proof stresses, σ0.2, defined on the true stress-true strain 200 curves) were extracted from Fig. 3, and their absolute values, as well as the gaps between 201 non-charged and H-charged specimens (i.e., the magnitude of solid-solution hardening at 202 yielding), are plotted as a function of deformation temperature in Fig. 4 (a) and (b). 203 Monotonic increases of the yield stress with the decrease in temperature were apparent 204 both in non-charged and H-charged specimens, whereas the magnitude of H-induced 205 strengthening was maximized at 298 K. At the lower temperatures, the strengthening was 206 still substantial, yet the extent was smaller with respect to that at 298 K. 207  208  209 Fig. 4 (a) yield stress (0.2% proof stress) in non-charged and H-charged (C0 = 7570 at 210 ppm) specimens and (b) their gaps at five different deformation temperatures under 211 several strain rate conditions. The authors’ previous data on Type310S steel with similar 212 hydrogen concentration [20] are plotted as three gray marks in (b) for comparison. 213  214 Fig. 5 (a)~(e) show the work-hardening rate curves of the non-charged and H-charged 215 (C0 = 7570 at ppm) specimens at five testing temperatures plotted against true stress. The 216 stress of each specimen was presented after subtracting the yield stress from the total flow 217 stress for canceling the contribution of solid-solution hardening on the horizontal axis. 218 Also, both axes were normalized by shear modulus, G, at each temperature [60] in order 219 to eliminate the modulus-dependent component of the work-hardening rate and flow 220 stress [61]. Interestingly, the work-hardening rate in the H-charged specimen at 298 K 221 exhibited a temporal decay after yielding, recovering gradually and then merging into the 222 curve of the non-charged specimen with the increase of stress and strain (Fig. 5 (c)). The 223 same phenomenon was discovered in our previous publication [21], yet the underlying 224 reason was ambiguous. However, such a transient work-hardening behavior in the H-225  Submitted to Materials Science and Engineering A 9  charged specimen notably disappeared when the temperature was both increased and 226 decreased from 298 K: the curves of non-charged and H-charged specimens became 227 coincident with each other.  228 In Fig. 5 (f), the gaps in flow stress between non-charged and H-charged specimens 229 at each temperature are indicated as a function of true strain, wherein the underlying 230 reason for the temporal decay of work-hardening at 298 K (Fig. 5 (c)) is now uncovered. 231 That is, even though the flow stress gap at 298 K was the greatest among the five 232 temperatures at the beginning of deformation, it suddenly decreased by almost 30 MPa 233 as the strain evolved to 0.05, then settled with the value falling below those at 223 and 234 173 K. A similar but a weaker strain-dependent tendency of the flow stress gap was 235 observed at 373 K. Meanwhile, at other three temperatures, the gap of flow stress 236 remained almost constant irrespective of strain within a range of fluctuation, except for a 237 sudden decrease immediately after the onset of yielding at 173 K.  238  239  240 Fig. 5 (a)~(e) work-hardening rate versus flow stress curves of non-charged and H-241 charged (C0 = 7570 at ppm) specimens at 173~423 K and a strain rate of 5×10−5/s, wherein 242 the vertical and horizontal axes were normalized by shear modulus at each temperature. 243 (f) depicts the gap of flow stress between non-charged and H-charged specimens at 244 173~423 K and at two different strain rates as a function of true strain.  245  Submitted to Materials Science and Engineering A 10  3.2.2 Effect of strain rate 246 The influence of strain rate was examined at two representative temperatures of 298 247 and 173 K. Two orders of magnitude faster CHS than the standard one (i.e., initial strain 248 rate of 5×10−3/s) was applied for non-charged and H-charged (C0 = 7570 at ppm) 249 specimens. The yield stress, as well as its magnitude of enhancement by H, are inserted 250 in Fig. 4. In the non-charged specimens, the faster strain rate resulted in slightly higher 251 yield stress at both testing temperatures, as supposed from the basic thermal activation 252 theory of dislocation dynamics [62]. The yield stress of the H-charged specimen was also 253 augmented at 173 K (Fig. 4 (a)), although the magnitude of yield stress enhancement by 254 solute H was rather independent of strain rate (Fig. 4 (b)). Notwithstanding, the most 255 notable discovery here was that no recognizable impact of strain rate manifested on the 256 yield stress of the H-charged specimen at 298 K (Fig. 4 (a)). According to the strain rate-257 dependent increase of yield stress in the non-charged specimen at 298 K, this led to a 258 weakened solid-solution hardening by H, as is visible in Fig. 4 (b).  259 In order to check the reproducibility of the experimental results, Fig. 4 (b) also 260 includes the yield stress enhancement under three different strain rates (5×10−3, 5×10−5, 261 and 5×10−7/s) at 298 K measured in our previous paper on the same grade material with 262 identical solute H concentration [20]. An agreement between the previous and present 263 results was confirmed at the strain rates of 5×10−3 and 5×10−5/s. Furthermore, the yield 264 stress enhancement by H at 5×10−7/s was smaller than those at 5×10−3 and 5×10−5/s: the 265 strain rate dependence of the solid-solution hardening at the yield point in the H-charged 266 samples was not monotonous. 267 The flow stress gaps between non-charged and H-charged specimens under a faster 268 strain rate of 5×10−3/s are overlaid in Fig. 5 (f). It is noteworthy that the overall flow stress 269 augmentation by H was more remarkable, and no stress drop was seen under the faster 270 strain rate at 298 K, while the yield stress increase was inferior to that at the slower strain 271 rate (Fig. 4 (b)). In contrast, the magnitude and propensity of the increase in flow stress 272 were almost independent of the strain rate at 173 K. 273  274 3.2.3 Effect of H concentration 275 At 298 and 173 K, where H-induced strengthening was substantial, the H 276 concentration dependence of the flow behavior was also studied. The true stress-true 277  Submitted to Materials Science and Engineering A 11  strain curves around the yield point and small strain domain are shown in Fig. 6 (a). The 278 yield stresses were augmented as a monotonic function of C0 at both temperatures, 279 although temporal decreases of the flow stress below those of non-charged specimens 280 were observable after yielding, particularly at low H concentrations, as clearly seen in 281 Fig. 6 (b) and (c). 282  283  284 Fig. 6 (a) true stress-true strain curves of the non-charged specimen as well as the H-285 charged specimen with various H concentrations at 298 and 173 K with the strain rate of 286 5×10−5/s. (b) and (c) show the gap of flow stress between the non-charged and H-charged 287 conditions, which were derived from (a). 288  289 Fig. 7 (a) and (b) present the H concentration-dependence of the magnitude of yield 290 stress enhancement at 298 and 173 K. The increase in yield stress was linearly correlated 291 with the solute H concentration with the slope of ≈ G/86 at 298 K, a result that coincides 292 with the tendency acquired in the authors’ previous study on some ASSs with various Cr 293 and Ni contents [21] as overlayed in Fig. 7 (a). On the other hand, a non-linear 294 interrelation between the H concentration and the yield stress increase was recognized at 295 173 K (Fig. 7 (b)). Rather, the yield stress was amplified in a slightly exponential tendency 296 with augmenting the H concentration. 297 The gaps between the flow stress in the non-charged specimen, as well as H-charged 298 specimens with different H concentrations, are depicted in Fig. 6 (b) and (c), like Fig. 5 299 (f). At 298 K, the shape of the four curves was not significantly changed by the H 300 concentration, and the overall curve shifted downward with the decrease of C0. However, 301 the propensity at 173 K was somewhat different from the case of 298 K. Namely, the 302 gradual decay of the flow stress gap toward 0.05 true strain, which was milder but 303 reminiscent of the behavior at 298 K, emerged at lower H concentrations of 2030 and 304  Submitted to Materials Science and Engineering A 12  4180 at ppm, although such temporal decay was not distinct at 7570 at ppm H. 305 Additionally, a sudden drop of the stress gap between the yield point and 0.01 true strain 306 was a common distinction under all the examined hydrogen concentrations. 307  308  309 Fig. 7 Increases of the yield stress (0.2% proof stress) by H-charging, which were 310 measured at 298 and 173 K with a strain rate of 5×10−5/s, as a function of linear H 311 concentration. The results of some ASSs with different Cr and Ni contents measured in 312 the authors’ previous study [21] are plotted together with open symbols in (a). 313  314 3.3 Stress relaxation behavior 315 Fig. 8 (a) shows the stress-relaxation curves of non-charged and H-charged specimens 316 (C0 = 7570 at ppm) at 298 and 173 K, where the stress at the beginning of relaxation for 317 each specimen is defined as zero. Note that the fluctuation on the curves in 173 K is not 318 a specific material behavior but merely a noise associated with the data recording at a 319 cryogenic temperature. For both temperatures, large relaxation occurred during the first 320 100 s, followed by gradual settling down of the stress decay in the remaining time frame. 321 The amount of relaxation was larger in the H-charged specimens, yet the temperature 322 dependence was distinct depending on the presence and absence of H. In the non-charged 323 specimens, more rapid relaxation ensued in a shorter time at 173 K, eventually ceasing 324 upon the passage of 500 s. On the other hand, the relaxation rate at 173 K was slower than 325 that at 298 K in the H-charged specimens, a totally different tendency from the non-326 charged case. The distinct stress relaxation behavior between non-charged and H-charged 327 specimens was also apparent when focusing on the short time period, as depicted in the 328  Submitted to Materials Science and Engineering A 13  inset of Fig. 8 (a). Namely, during the first 20 s, H-charging resulted in an obviously 329 accelerated relaxation rate at 298 K, while the relaxation curves of non-charged and H-330 charged specimens were close to each other at 173 K. As the relaxation time exceeded 331 102 s, the two curves at 173 K eventually diverged. 332 In Fig. 8 (b), the stress-relaxation results are reproduced in the form of the absolute 333 stress values versus the logarithm of the relaxation time. Under all the experimental 334 conditions, the curves were almost straight after 10 s relaxation, indicating a typical 335 logarithmic transient observed in most metallic materials [58]. The slope of the 336 logarithmic relaxation curve of the H-charged specimen was steeper than that in the non-337 charged one at 298 K, merging into each other as the curves were extrapolated to the 338 relaxation time of 107 s order. Meanwhile, the curves of H-charged and non-charged 339 specimens were mutually more parallel at 173 K, which implies that a much longer time 340 would be required for the two curves to be finally merged.  341  342  343 Fig. 8 Stress relaxation curves of non-charged and H-charged (C0 = 7570 at ppm) 344 specimens at 298 and 173 K after applying a true strain of 0.06 with a strain rate of 345 5×10−5/s. The relaxation time in the horizontal axis is linear in (a), while it is logarithmic 346 and extrapolated into longer time scales in (b). The inset in (a) magnifies the relaxation 347 curves at the beginning short time period. 348   349  Submitted to Materials Science and Engineering A 14  4. Discussion 350 4.1 Preface 351 The hardening of FCC metals and alloys via H occlusion has often been discussed 352 from the perspective of the H-induced plasticity localization (i.e., HELP) model 353 [5,6,9,32,36,63]. Suppression of dislocations cross-slip may decrease the number of 354 active slip planes, rendering the distribution of slip bands coarser and more heterogeneous 355 [5,6,9]. As a result, the effective gauge length bearing the applied strain is reduced, as 356 well as the density of mobile dislocations in individual slip bands is augmented [32,36]. 357 These scenarios bring about an escalated flow stress under a given macroscopic strain. 358 An alteration in the deformation mode caused by H also affects the evolution of 359 dislocation substructures and resultant work-hardening [8,16,34,43]. In conform to the 360 HELP model, H atoms segregating around a moving dislocation shield its elastic stress 361 field in addition to inhibiting cross-slip [32,44,46,64]. Such modifications potentially 362 shrink the dislocation cell size or promote the formation of more planar dislocation 363 substructures [16,34,43], playing a role in amplifying the flow stress as a secondary 364 influence. 365 In ASSs, the modification of dislocation behavior, particularly slip localization, has 366 been evidenced by the increases in slip line spacing and height on the material surface 367 [5,6,65]. Nonetheless, Aubert et al. statistically analyzed the slip line distribution of a 368 Type316L steel with grain sizes of 140 and 300 μm charged with ~135 mass ppm H [63]. 369 They identified that the H-impact on the strain localization was minor for the material 370 with a smaller grain size, especially under a small strain regime with a few percent. Kamei 371 et al. reported the results of dislocation density measurement via X-ray on a 316L steel, 372 wherein the difference between non-charged and H-charged samples was not significant 373 until the strain reached ~20% [66]. Even in the authors’ experiments, no H-effect was 374 recognized in the work-hardening rate, except for the peculiar domain immediately after 375 yielding at ambient temperature (Fig. 5) and a large strain regime where deformation 376 twinning commenced [20,21,67]. Kocks and Mecking, who elaborated on the work-377 hardening in FCC metals, pointed out that the dislocation structures (i.e., density and 378 arrangement) exhibit a mutually similar distinction when a given material undergoes an 379 identical work-hardening rate [61]. Taking these perceptions, the grain size (i.e., 30~70 380 μm), and the targeted strain level in the present study into account, the H-induced 381  Submitted to Materials Science and Engineering A 15  hardening in ASSs is not merely an indirect consequence of the strain localization and the 382 modification of dislocation glide/accumulation characteristics. Rather, a major part of the 383 hardening should rely on the intrinsic effects of H, which act as obstacles to the movement 384 of individual dislocations. The manifestation of stress enhancement at 173 K (Fig. 3), 385 where the formation of an H-dislocation atmosphere during deformation would be 386 infeasible, also supports such a presumption. Note that when discussing H-material 387 interactions, H segregation and diffusion along grain boundaries are sometimes of great 388 importance [12,18,68]. Even concerning the yield strength, the segregation of interstitial 389 atoms (e.g., C and N) along grain boundaries possibly affects the mechanical behavior by 390 altering the extent of the Hall-Petch strengthening [69]. However, it has been clarified in 391 Type310S ASS that the trapping is negligible due to almost equivalent solution energy of 392 H between grain boundaries and interstitial lattice sites [70]. Thus, we assume that the 393 grain boundary effect on the yield stress change after H-charging is trivial, and the 394 interactions of H with dislocations are much more critical. 395 The glide resistances arising from solutes are classified into lattice friction by dispersed 396 atoms [27,31], pinning by Cottrell atmosphere around a stationary dislocation [29,71], a 397 force pulling back the dislocation via solute drag [35,72], and dynamic pinning (i.e., 398 dynamic strain-aging, DSA) [56,73,74]. In the following sub-sections, contributions from 399 these multiple factors at each temperature are discussed based on the findings provided 400 in Section 3. Note, on the other hand, that enhanced mobility of dislocations by H has, 401 contrary, been envisaged through an accelerated velocity of dislocations in in-situ 402 transmission electron microscopy (TEM) studies [32,46,64,75]. Nevertheless, recent 403 molecular dynamics simulations revealed that solute H indeed obstructs the dislocation 404 movement except for some specific cases [33,76,77], arguing that what was observed in 405 TEM was a unique phenomenon that occurs only in thin foils [78]. 406  407 4.2 Mobility of H atoms during deformation 408 In an attempt to evaluate the significance of the above-listed roles of solutes that resist 409 dislocation movement, an estimation of H mobility during deformation is a principal 410 piece. Several researchers experimentally measured the H diffusivity in 310S steel by 411 means of gas desorption or permeation techniques [79–82], in which the temperature 412 dependence of the diffusion coefficient, D, followed the Arrhenius equation: 413  Submitted to Materials Science and Engineering A 16  𝐷 = 𝐷0exp (−𝐸D𝑅𝑇)                         (3) 414 where D0 is the pre-exponential factor, and ED is the activation energy for lattice diffusion. 415 Fig. 9 (a) shows the D vs. temperature curves obtained by plugging the D0 and ED values 416 in the references [79–82] into eq. (3). The solid lines indicate the temperature ranges 417 where diffusion data were experimentally acquired in [79–82]. Since the measurement of 418 diffusivity in ASSs at lower temperatures is infeasible, we were compelled to extrapolate 419 these data owing to eq. (3), as described by dashed lines in Fig. 9 (a). Once the plastic 420 deformation commences, the bulk hydrogen diffusivity is more or less affected by the 421 defect-trapping effects, particularly when the temperature is low [18,79,83]. Nevertheless, 422 extrapolation of eq. (3) can be a good approximation in the present case because it is the 423 lattice diffusivity that predominates the interactions between diffusible solutes and mobile 424 dislocations [51,56,72]. 425    Considering a random jump of an H atom from an octahedral (O-) site to the 426 neighboring twelve O-sites, the diffusivity data also gives an estimation of the jump 427 frequency of H, f, through the lattice parameter, a (approximated as 3.6 nm), as f = 12D/a2. 428 The f vs. temperature curves derived from Fig. 9 (a) are reproduced in Fig. 9 (b). At 173 429 K, the f lies at 10−5~10−2/s. The time for acquiring the data in Fig. 3 and Fig. 6 was the 430 order of 103 s, denoting that H barely migrated through the lattice at such a low 431 temperature. Meanwhile, H becomes substantially active at 298 K, with the f beyond 104/s. 432 Therefore, some forms of dynamic interactions with mobile dislocations are anticipated 433 at and above 298 K.  434  435  436  Submitted to Materials Science and Engineering A 17   437 Fig. 9 Diffusion coefficient (a) and jump frequency (b) of H atoms in Type310S steel, 438 which were previously measured by several researchers [79–82]. The solid lines denote 439 the experimentally acquired data, while the dashed lines are the extrapolation of the 440 experimental data via eq. (3). 441  442   443  Submitted to Materials Science and Engineering A 18  4.3 Estimating H segregation around a dislocation 444 The strength of the interaction between H and a stationary dislocation [4,40–42,77] is 445 another essential factor for scrutinizing the H-induced hardening. In this sub-section, the 446 segregation of H around a perfect edge dislocation was examined by simply assuming the 447 size effect driven from the stress field around the dislocation line (i.e., Cottrell atmosphere 448 [29,71]). Even though the presumption fails to assess the segregation to the core where 449 linear elasticity breaks down [29,71] and neglects any electronic effects [39,40,84], it still 450 provides qualitative information regarding the magnitude of H-dislocation interactions at 451 each temperature. Additionally, since the dislocations in FCC metals with low to medium 452 stacking fault energy (e.g., ≈ 40 mJ/m2 in 310S steel [85]) are extended into two Shockley 453 partials, the H segregation into screw dislocations through the size effect is also plausible 454 [29,51]. 455 In a solid-solution with an average solute concentration of C0, the local concentration 456 around a segregation (trapping) site, CT, obeys the Fermi-Dirac formula. 457 𝐶T1−𝐶T=𝐶01−𝐶0exp (𝐸B𝑅𝑇)                        (4) 458 Here, EB is the binding energy of the trap site with a solute atom. Assuming a positive 459 edge dislocation lying along the z-axis in a Cartesian coordinate, the distribution of EB 460 due to the dislocation’s dilatational stress field on the x-y plane is given as [29]: 461 𝐸𝐵 = 𝛽𝑦𝑥2+𝑦2                             (5) 462 𝛽 = ∆𝑉𝐺𝑏3𝜋(1+𝜈1−𝜈)                          (6) 463 where b is the Burgers vector (≈ 2.5×10−10 m), ν is Poisson’s ratio, and ΔV is the swelling 464 volume per solute atom for which ≈ 2×10−30 m3 were experimentally and analytically 465 reported in the case of H [86,87]. β is called an elastic interaction parameter.  466    Fig. 10 (a)~(c) show the CT distribution at the solute-condensed region below the slip 467 plane, wherein C0 = 7570 at ppm and three different temperature conditions were adopted. 468 In ASSs, EB ≈ 13 kJ/mol was reported as the binding energy of H with dislocations 469 [79,87–90], which is quite identical to the values in pure FCC metals such as Ni and Al 470 [40,41,91]. The black dashed lines in Fig. 10 (a)~(c) delineate the border that corresponds 471 to EB ≈ 13 kJ/mol according to eq. (5). Although linear elasticity leaves some uncertainties 472 in the proximity of the dislocation line, the results demonstrate that the EB reported in the 473  Submitted to Materials Science and Engineering A 19  previous investigations [79,87–90] potentially reflects the H trapping at the dislocation 474 core. The H segregation via the size effect spreads well outside the core, an extension of 475 which enlarges with a decrease in temperature. 476  477  478 Fig. 10 Segregation behavior of hydrogen atoms around a perfect edge dislocation via 479 size effect: (a)(b)(c) distribution of the Cottrell atmosphere at 173, 298, and 423 K under 480 an average hydrogen concentration of 7570 at ppm; (d) temperature dependence of the 481 local hydrogen concentration at dislocation core with EB = 13 kJ/mol; (e) extension of the 482 Cottrell atmosphere below the slip plane at 173 and 298 K under various average 483 concentration of hydrogen. Note that the curves of Co of 3.7, 5.3, and 7.2 at % will be 484 described and discussed in Section 4.7 later.   485  486    Fig. 10 (d) shows the temperature dependence of CT, which was calculated according 487 to eq. (4), at the region corresponding to EB = 13 kJ/mol under various conditions of C0. 488 Above 200 K, CT continuously increases with a decrease in temperature and depends 489 significantly on C0. Meanwhile, although the values close to 100% are physically 490 unrealistic for interstitial solutes, it is apparent that the CT at the dislocation core tends to 491 saturate irrespective of C0 at temperatures below 200 K. Note, however, that the situation 492 is different outside the saturated core, as the CT distribution along the negative side of the 493  Submitted to Materials Science and Engineering A 20  y-axis is shown in Fig. 10 (e). In the regime away from the dislocation center, the H 494 segregation depends on C0 even at 173 K, in which the extent of the atmosphere becomes 495 greater as C0 increases. The same tendency can be seen at 298 K, while the overall H 496 concentration in the atmosphere is low compared with 173 K. 497    At 173 K where H diffusion is slow, a completely equilibrated atmosphere (Fig. 10) 498 was unlikely to be achieved. Even so, it took one hour to decrease the temperature to 173 499 K, and 10 minutes of preservation was interpolated before the start of the test: H atoms 500 were allowed to migrate slowly through the lattice. According to an old treatment by 501 Harper, the fractional interstitial segregation rate at a site with EB is approximated as [92]: 502 𝑞 = 1 − exp {−2𝜌 (𝜋2)1/3(𝐸B𝐷𝑡/𝑅𝑇)2/3}                  (7) 503 where ρ is dislocation density, and t is aging time. Taking EB ≈ 4 kJ/mol as a binding 504 energy at the outer periphery of the Cottrell atmosphere (eq. (5)) and ρ = 1012 m2/m3, q 505 exceeds 90% after the passage of 4000 s at 173 K. Thus, the atmosphere should become 506 wider and denser as the temperature is lowered, and it could take a quasi-equilibrated 507 state close to the distribution shown in Fig. 10. 508  509 4.4 Contribution of solute drag 510 From the jump frequency estimation in Section 4.2, an emergence of dynamic H-511 dislocation interactions during deformation has been envisaged at and above 298 K. In 512 fact, the magnitude of yield stress enhancement by H exhibited its peak at 298 K (Fig. 4). 513 Such a maximization of yield/flow stresses under a certain temperature range, which 514 cannot be interpreted in the thermal activation theory of solid-solution hardening, is an 515 outcome when dynamic interactions of solutes with moving dislocations operate [52,58].  516 Sills and co-workers numerically calculated the interference between a diffusible solute 517 atmosphere and a dislocation moving at a constant velocity [35,51]. Based on Orowan’s 518 formula [62], they derived the equation describing the critical strain rates, 𝜀𝑐̇, for the 519 occurrence of dynamic interactions under a given temperature. 520 𝜀𝑐̇ =4𝑄𝐷𝑘𝑇𝑀𝛽𝜌m𝑏                           (8) 521 where M is the Taylor factor (3.06 for polycrystalline FCC metals), k is the Boltzmann 522 constant, β is defined by eq. (6), and ρm is the mobile dislocation density. The parameter 523 Q signifies the velocity of mobile dislocations, vd, which is non-dimensionalized using β, 524  Submitted to Materials Science and Engineering A 21  D, k, and T as: 525 𝑄 =𝑣d𝛽4𝐷𝑘𝑇                              (9) 526 According to their calculations on a steady-state condition, the dislocation is completely 527 pulled away from the solute atmosphere when Q is greater than ≈ 102. Meanwhile, when 528 Q is smaller than ≈ 10−2, the atmosphere can follow the dislocation movement with 529 maintaining its near-equilibrium distribution [35]. These two opposite extremes will be 530 referred to as breakaway and equilibrium limits, respectively. At a dislocation velocity 531 between breakaway and equilibrium limits, the atmosphere partially lags behind the 532 dislocation. A resultant non-equilibrium distribution of the atmosphere exerts a drag force 533 on the moving dislocation, representing its maximum around Q ≈ 100, which is consistent 534 with the theoretical derivation by Cottrell [71].  535 𝜀𝑐̇ =4𝐷𝜌m𝑏𝑀𝐼                            (10) 536 where I is the atmosphere radius that can be taken as ≈ 4b (see Fig. 10). Here, we 537 parametrically simulated the feasibility of the solute drag by H atmosphere under ρm = 538 1010~1013 m/m3 using eq. (8)~(10), as well as the diffusivity data by Perng and Altstetter 539 [79] shown in Fig. 9 (a). Although an accurate determination of ρm is difficult, it has been 540 invoked by correlating the experimental stress-strain curve to theoretical equations that 541 ρm promptly augments from 1010 to 1013 m/m3 orders in ASS and FCC metals around the 542 yield point [93,94]. It has been clarified that the Q-based criterion is applicable to 543 extended dislocations, albeit the magnitude of drag force is slightly changed [51]. 544    Fig. 11 shows the breakaway (Q = 102) and equilibrium (Q = 10−2) limits at ρm = 1010, 545 1011, 1012, and 1013 m/m3 calculated by eq. (9) as a function of temperature, in addition 546 to the 𝜀𝑐̇ at the maximum steady-state drag force via eq. (10). The black horizontal lines 547 at the middle height denote our base strain rate of 5×10−5/s. In metallic materials, 548 dislocation motion is more or less jerky [95], while eq. (10) only describes an average 549 velocity, including the waiting time at internal obstacles such as forest dislocations. 550 Therefore, when considering the true velocity in their motion between the obstacles, the 551 three curves corresponding to Q = 102, 100, and 10−2 in Fig. 11 may lay at a somewhat 552 lower strain rate in practice. 553  Submitted to Materials Science and Engineering A 22   554 Fig. 11 Critical strain rates characterizing the diffusible hydrogen-mobile dislocation 555 interactions, which are defined by Q = 102 and 10−2 in eq. (8)(9) as well as by eq. (10), as 556 a function of temperature. The mobile dislocation density, ρm, is set as (a) 1010, (b) 1011, 557 (c) 1012, and (d) 1013 m/m3. The black horizontal lines at the middle height in each 558 diagram correspond to the base strain rate used in this study: 5×10−5/s. 559  560 A numerical simulation performed by Yoshinaga and Morozumi has shown that the 561 drag force exerted by solutes abruptly increases upon the dislocation velocity falling 562 below the breakaway limit (Q = 102-100, red-shaded area in Fig. 11), then gradually 563 decreases and asymptotically reaches zero after undergoing its peak (Q = 100-10−2, blue-564 shaded area in Fig. 11) [72,96]. In view of this, the most remarkable situation in Fig. 11 565 is 298 K, where deformation starts near Q = 102 and proceeds to Q = 10−2 via Q = 100. 566 This means that the drag force suddenly augments at the beginning of deformation, 567 followed by a gradual decrease in association with the multiplication and slowing down 568 of mobile dislocations. Assuming that the drag force significantly contributes to the 569  Submitted to Materials Science and Engineering A 23  hardening caused by solute H, it is important to note that the reduction in the flow stress 570 gap at 298 K with the increase of strain (Fig. 5 (f)) now seems a plausible consequence. 571 Furthermore, the linearity of the yield stress enhancement at 298 K (Fig. 7 (a)) can 572 somehow be attributed to the results [29,72,97,98] reporting that the drag force is 573 proportional to the average solute concentration, albeit the hardening is aided by other 574 factors discussed below. Conversely, no coordinative motion between diffusible H and 575 mobile dislocations is feasible near the yield point at 173~223 K or under a faster strain 576 rate of 5×10−3/s at 298 K. Besides, dislocation velocity soon falls around and below the 577 equilibrium limit at 423 K as well as at 298 K with the strain rate of 5×10−7/s. These are 578 potential rationales of the strain-independent flow stress gaps at those conditions (Fig. 5 579 (f)) and weaker yield stress enhancement at 298 K under strain rates of 5×10−7and 580 5×10−3/s (Fig. 4 (b)). From Fig. 11, the emergence of drag force around the yield point is 581 somewhat anticipated at 373 K. This appears in a slight decay of the flow stress gap with 582 the progress of deformation at 373 K (Fig. 5 (f)). 583    The decreasing magnitude of H-induced hardening after yielding at 298 K (Fig. 5 (f)) 584 and temporal decrease in work-hardening rate (Fig. 5 (c)) can also be attributed to the 585 yield point theory proposed by Johnston and Gilman (J-G) [99]. Since the dislocation 586 velocity obeys a power low of the applied shear stress, τ, (i.e., vd = (τ/τ0)m where τ0 and m 587 are material parameters [62]), a sudden increase in ρm leads to a deceleration of vd (cf. eq. 588 (8)(9)) and a resultant decrease in the flow stress under a constant strain rate. In materials 589 with relatively high dislocation mobility, the plastic strain rate is controlled by the 590 multiplication rate of dislocations instead of their individual velocity [100]. A typical 591 example is FCC metals, in which dislocations activity is predominated by extrinsic 592 obstacles (e.g., forest dislocations) rather than intrinsic lattice frictions (e.g., Peierls-593 Nabbaro potential) that render dislocations glide more viscous. Under such a 594 circumstance, the J-G type yielding is unlikely to appear because the microscopic strain 595 rate induced by each mobile dislocation promptly exceeds the macroscopic strain rate 596 once the multiplication of dislocations commences [100,101]. The activation volume of 597 dislocation motion up to hundreds of b3 has been measured for the 310S steel at ambient 598 temperature [5,20]. Even though these values are smaller than pure FCC metals (i.e., 599 thousands of b3) and imply the involvement of intrinsic resistances by the presence of 600 alloying elements, they are still larger compared with the conditions where the Peierls-601  Submitted to Materials Science and Engineering A 24  Nabbaro mechanism works significantly (i.e., less than 100b3) [58,102,103]. However, 602 things may change as the dislocation movement becomes slower and more viscous under 603 the influence of solute drag: when the multiplication rate is also controlled by the mobility 604 of individual dislocations. Indeed, a smooth yield point discontinuity owing to the solute 605 drag was confirmed in the high-temperature deformation of Al-Mg alloys [104,105], a 606 phenomenon possibly applicable to our present case of an H-alloyed ASS. In reference 607 [104,105], an evident yield drop was identified, while the H-charged ASS in this study 608 retained a positive work-hardening rate (Fig. 5 (c)). This present result stems from a large 609 work-hardening that overwhelms the stress drop due to the slowing down of dislocations: 610 a different situation from [104,105], where work-hardening is negligible owing to the 611 high homologous temperature. Note that the J-G type yielding at 298 K can seemingly be 612 ascribed to the pinning of dislocation by the H-Cottrell atmosphere (Fig. 10 (b)) [4,5]. 613 Nevertheless, the pinning effect cannot explain the lowing of yield stress by the strain 614 rate augmentation (Fig. 4 (b)). 615  616 4.5 Implication of dynamic pinning 617    It is worth noting that higher yield and flow stresses were measured at 223 K than at 618 173 K (Fig.4 (b); Fig. 5 (f)), even though solute drag around the yield point is not 619 anticipated (Fig. 11). Therefore, a different form of dynamic interaction should now be 620 considered. One potential mechanism is the re-segregation of H atoms at the resting 621 mobile dislocations at obstacles, pinning the dislocation when it attempts to move again 622 (i.e., DSA [56,73,74]). Although a coordinative motion between H and dislocation is 623 infeasible at 223 K, a decent jump frequency up to 102/s (Fig. 9 (b)) might make it possible 624 to segregate around a stationary dislocation and form an atmosphere in a relatively short 625 time frame. In fact, a calculation by eq. (7) estimates the time for re-segregation to the 626 dislocation core as only a few seconds, rationalizing the dynamic pinning under a slow 627 strain rate situation. Another possibility is the formation of H-vacancy complexes through 628 the deformation [106], which has analytically and experimentally been reported to pin the 629 mobile dislocations [107,108] as with the case of DSA by C/N-vacancy complexes in 630 ASSs [109]. Albeit, since the obstruction strength via these specific interactions might be 631 marginal, it could easily be surmounted by thermal activation. The pinning by H-632 atmosphere supposedly contributed to the thermal component of flow stress at 223 K, 633  Submitted to Materials Science and Engineering A 25  whereas it became not influential as the lowering of strain rate and increasing temperature. 634  635 4.6 Lattice friction by dispersed hydrogen atoms 636    Except for the yielding domain at 298 K and a special case at 223 K, the H-induced 637 flow stress enhancement was monotonically augmented with the decrease in temperature 638 (Fig. 5 (f)). Moreover, after a true strain of 0.05, the flow stress enhancement was 639 positively correlated with an increase in strain rate at 298 K (Fig. 5 (f)). These findings 640 intimate that the H atoms dispersed into the matrix worked as short-range obstacles to 641 amplify the thermal component of flow stress, which particularly played an important 642 role when dynamic interactions (Sections 4.4 and 4.5) were not effective and thermal 643 vibration of the lattice was marginal. Such a thermal behavior caused by dispersed H has 644 recently been pointed out by Koyama et al. for HEAs [15]. The strengthening of ASSs by 645 dispersed interstitials is typified by C and N, wherein short-range lattice dilation around 646 them is a root cause of the dislocation obstructing effect [22,25,110,111]. A volume 647 expansion by C was determined as 8.6×10−30 m3 [22], an almost fourfold greater value 648 than the lattice swelling by H dissolved in an O-site [86,87]. The dilation by N is even 649 larger than C [22], giving rise to a query about how tiny atoms like H provoke a substantial 650 hardening over tens of MPa. 651 The internal friction studies by Gavriljuk et al. and other researchers uncovered the 652 Snoek-type relaxation peaks in cathodically or thermally H-charged ASSs (e.g., Fe–653 25Cr–20Ni and Fe–18Cr–15Ni) [48–50,90,112,113]. Some of them ascribed the peak to 654 a tetragonal lattice distortion stemming from H–H pairs in adjacent O-sites or 655 substitutional-H pairs comprising Cr-H or Ni-H. Assuming Cr–H pairs as the primary 656 cause of the Snoek peak, recent analytical claims inferring a strong affinity of Cr with H 657 [87,114] can be reinforced. This idea also supports the previous results exhibiting the 658 augmentation of H solubility and H-induced hardening capability with increasing the Cr 659 content in the Fe-Cr-Ni alloy system [11,21,50]. In general, lattice strain by interstitial 660 atoms in an O-site of FCC lattice is isotropic, interacting only with edge dislocation 661 components that possess hydrostatic stress in their environs. On the contrary, the shear 662 stress due to the anisotropic strain field around Cr–H pairs may interact with both edge 663 and screw, thereby could work as a predominant piece for the hardening effect related to 664 H atoms statistically dispersed in the lattice. Even for C and N, there is an argument that 665  Submitted to Materials Science and Engineering A 26  lattice dilation is not sufficient to explain the large strengthening by these elements; 666 thereby, the contribution of interstitial-substitutional complexes should be considered 667 [24,115]. Assuming that the Cr-H pairs are randomly dispersed at temperatures around 668 298 K, the average interspacing between each H atom in our experiments is estimated to 669 be b/(C0)1/3 = 1~2 nm, letting a dislocation line to simultaneously interact with plural 670 obstacles due to their extremely dense distribution. Under such a circumstance, the linear 671 dependence of flow stress on the average solute concentration is envisaged [29], which 672 further rationalizes the tendency in Fig. 7 (a).  673 Our stress relaxation tests at 298 K identified the presence of a thermal component of 674 the flow stress, which might be related to dispersed H atoms or partially to the pinning of 675 resting mobile dislocations by re-segregated H (Section 4.5). The rate of relaxation from 676 a fixed strain of 0.06 became higher by the presence of H, while the stresses in non-677 charged and H-charged specimens asymptotically approached each other when the 678 relaxation curves were extrapolated (Fig. 8). This means that the activity of dislocations 679 lagged in the continuous straining due to the introduction of weak and more thermally 680 activatable obstacles, i.e., H, catching up later during the crosshead holding with the aid 681 of time. The same physical meaning can be acquired from an increased strain rate 682 sensitivity and a reduction in activation volume in H-charged ASSs [5,20]. 683 The increase in stress relaxation rate (or creep rate) and reduced activation volume 684 after H introduction has been attributed to the H-induced enhancement of thermally 685 activated dislocation motion [5,20,57,116]. However, it seems a superficial interpretation 686 disregarding that the relaxation was started at a fixed strain where the absolute stress level 687 at the beginning was higher in the H-charged sample. Indeed, the creep tests from fixed 688 stress carried out by Tien and Altstetter demonstrated a decreased creep rate at the initial 689 short transient and, conversely, a longer creep duration in an H-doped 310S ASS [116]. 690 These are clear evidence for the role of solute H that impedes the dislocation movement 691 and renders the deformation more sluggish under a given driving force (i.e., applied 692 stress). Care is also required for understanding the magnitude of activation volume 693 because the parameter is determined by the combination of multiple obstacles with 694 various strengths, including alloying elements, dislocation intersections, precipitates, and, 695 obviously, solute H [54,55,117,118]. Curtin theoretically stated that when more than two 696 obstruction mechanisms cooperate, the activation area and enthalpy are primarily 697  Submitted to Materials Science and Engineering A 27  dominated by either of the obstacles that are more easily thermally activated than others 698 [118]. In this regard, the smaller activation volume in the H-charged ASSs and FCC 699 metals [5,20,57] might mainly stem from H itself (the weakest obstacle), whereas it is 700 rooted in substitutional solutes as well as forest dislocations in the non-charged specimen. 701  702 4.7 Pinning by hydrogen atmosphere and low-temperature hardening 703 The significance of dislocation pinning by H atmosphere was denied at 298 K since the 704 yield stress exhibited an inverse strain rate sensitivity when the strain rate was increased 705 from 5×10−5 to 5×10−3/s (Fig. 4 (b)). Because the radius of the atmosphere is a mere ~4b 706 (Fig. 10 (e)), the core is unsaturated by H (Fig. 10 (d)), and the H atoms are mobile, it is 707 envisaged that dislocations might be able to readily overcome the pinning even if it 708 existed. Nevertheless, such insignificance of the atmosphere pinning shall not be applied 709 when the solute H concentration is extremely high over a few at %. 710 Altstetter and co-workers identified the appearance of a distinct yield point in a room 711 temperature tensile test with the strain rate of 5.5×10−5/s when a 310S steel was 712 cathodically charged with more than 4 at % H [4–6]. The H concentrations in their 713 experiments (C0 = 3.7, 5.3, and 7.2 at %) were adopted into eq. (4), a result of which is 714 included in Fig. 10 (d) and (e). As the C0 exceeds 5.3 at %, the core is saturated, and the 715 atmosphere radius extends over 10b. Under these extreme conditions, the pinning by the 716 atmosphere turns into a substantial magnitude [119], which impacts the H-induced 717 enhancement of yield stress at 298 K. Such strong pinning inherently causes the decrease 718 of initially mobile dislocation density. Thus, the dislocations, which once broke away 719 from the pinning at the yield point, must rapidly move and multiply so that the specimen’s 720 gauge length conforms to the externally applied strain rate. Ultimately, the scenario forces 721 depinning and subsequent fast movement for dislocations rather than their viscous motion 722 accompanying solute drag. This might be the rationale for the abrupt yield drop observed 723 at high C0 in [4–6] instead of the smooth reduction of the flow stress enhancement in the 724 present study (Fig. 5 (f)). 725 Hypothesizing the pinning by H atmosphere, the core saturation, and large atmosphere 726 radius (i.e., more than 6b) at 173 K under the C0 up to 7570 at ppm is worthy of attention 727 (Fig. 10 (d) and (e)). Since the aid of thermal activation for breaking away from the 728 atmosphere fades exponentially at low temperatures, it is quite likely that the expected 729  Submitted to Materials Science and Engineering A 28  strong pinning of dislocations acted as a primary factor for determining the yield stress at 730 173 K. Moreover, as the partial dislocations separation increases at low temperatures and 731 solute H is known to decrease stacking fault energy in ASSs [120,121], the chemical 732 locking by segregated hydrogen, i.e., Suzuki locking [29,122], is an anticipated outcome 733 as well. Actually, the static strain-aging experiments performed by Girardin and Delafosse 734 elegantly demonstrated the H-induced dislocations pinning at 173 K and its amplification 735 by aging time in pure Ni and a Ni-Cr alloy with ~1900 at ppm H [42]. The H-induced 736 dislocations pinning by their atmosphere or Suzuki locking were also inferred by room 737 temperature internal friction measurements on Fe-18Cr-Ni alloys at a high vibrational 738 frequency [89,112]. Fig. 4 (b) and Fig. 5 (f) notably revealed no influence of strain rate 739 on the yield stress at 173 K when C0 = 7570 at ppm. This means that most parts of the 740 work required for surmounting the atmosphere pinning were supplied by an external force 741 [58,62]. In this context, the prompt reduction in the flow stress enhancement immediately 742 after the yielding at 173 K (Fig. 6 (c)) can now be considered a sign of dislocations 743 depinning from their H atmosphere. The concentrated atmosphere is left behind the 744 dislocation and cannot readily diffuse at low temperatures; the matrix H concentration 745 was supposedly not enough under a small C0 such as 2030 at ppm. Accordingly, the drop 746 of the flow stress enhancement continued during a certain range of strain (Fig. 6 (c)). On 747 the contrary, the matrix might also contain a significant amount of dispersed H atoms at 748 a high C0, e.g., 7570 at ppm, obstructing the dislocations even after the depinning so as 749 no further flow stress drop to persist in the course of straining (Fig. 6 (c)). 750    Other two striking distinctions at 173 K should be treated finally: H-induced yield 751 stress enhancement increased as an apparently exponential function of C0 (Fig. 7 (b)); the 752 flow stress enhancement after yielding possessed an athermal character and did not 753 depend on strain rate (Fig. 5 (e)). Although these features still have room for argument, 754 the atmosphere distributions shown in Fig. 10 give a clue to the former if one assumes 755 that the yield stress at 173 K was predominated by the dislocation depinning mechanism. 756 Barnett et al. theoretically treated the pinning force by the Fermi-Dirac atmosphere with 757 consideration of thermally activated breakaway and emphasized that the probability of 758 breakaway is determined by the atmosphere radius besides the local solute concentration 759 in the core [119]. In this regard, the aid of thermal activation might be somewhat helpful 760 to facilitate the depinning at a lower C0 (2030~5630 at ppm) where the extension of the 761  Submitted to Materials Science and Engineering A 29  atmosphere is smaller (Fig. 10 (e)), while it was not so influential at C0 = 7570 at ppm. In 762 a conventional dislocation theory considering the size effect, the maximum stress for the 763 breakaway from the Cottrell atmosphere without any thermal activation, a large part of 764 which comes from the solute segregation in or adjacent to the core, is proportional to the 765 bulk solute concentration, C0 [29]. Moreover, it seems in Fig. 10 (e) that the atmosphere 766 also extends almost proportionally to C0. Simply assuming these two are multipliable to 767 determine the zero-temperature activation energy in a dislocation force-distance profile, 768 the required stress for surmounting the obstacle should increase exponentially to C0 when 769 the energy supplied by thermal fluctuation is fixed, i.e., at the same temperature. 770    An athermal hardening at low temperatures in which solutes are unlikely to diffuse 771 has typically been observed in N-strengthened ASSs [23]. The phenomenon was ascribed 772 to the presence of short-range order (SRO) comprising Cr-N aggregates [24,123,124], 773 escalating the work for shear deformation corresponding to the formation energy of anti-774 phase boundaries [29,125]. The authors recently performed Ab-initio calculations to 775 investigate the H absorption energies in an O-site of FCC iron by partially substituting 776 the surrounding atoms with Ni and Cr [126]. Great reductions of the absorption energies 777 manifested when one or two Cr atoms were located adjacent to the O-site, a consequence 778 that stemmed from electronic interactions between H and Cr. On the basis of this affinity 779 of H with Cr, one can expect the presence of Cr-H SRO in the Fe-Cr-Ni alloy system in a 780 similar manner to Cr-N SRO [123,124] at the region where a high concentration of Cr is 781 statistically clustered. During the cooling process to 173 K, H atoms might be 782 preferentially coordinated at the O-sites adjacent to Cr, then frozen in due to the low 783 diffusion coefficient. The athermal nature of H-induced hardening at 173 K appeared in 784 the short transient stress relaxation (the inset in Fig. 8 (a)) as well, where relaxation curves 785 in non-charged and H-charged specimens were close to each other, a case distinct from 786 that at 298 K. Nonetheless, such athermal obstacles could not completely be stable owing 787 to the still non-negligible jump frequency of H up to 10−2/s (Fig. 9 (b)), inferring the 788 collapse and reconstruction of the SRO zones during the time scale greater than 102 s. 789 This led to the greater stress relaxation rate in the H-charged specimen at 173 K after the 790 passage of 102 s (Fig. 8 (a)). 791  792   793  Submitted to Materials Science and Engineering A 30  5. Summary and conclusion 794 The solid-solution hardening by H was studied at 173~423 K and two different strain 795 rates: 5×10−5 and 5×10−3 /s in Fe-24Cr-19Ni-based ASS charged with 2000~7600 at ppm 796 H, resulting in the main experimental findings as follows.  797 1. The hardening was maximized at 298 K under the slow strain rate condition of 798 5×10−5 /s, where the magnitude of yield stress enhancement was a linear function of 799 the H concentration. Nonetheless, the extent of strengthening decayed as the strain 800 increased. 801 2. The hardening was still significant at the lower temperatures, such as 173 K and 223 802 K, yet its concentration dependence was not linear but rather relatively exponential 803 at 173 K. 804 3. Above 373 K, the hardening was minimized and became negligible at 423 K. 805 Ultimately, the rationales for the strengthening were discussed in terms of four essential 806 ingredients: (i) H atoms in the lattice as dispersed obstacles; (ii) pinning of stationary 807 dislocations by H atmosphere; (iii) dynamic pinning of dislocations resting at obstacles; 808 (iv) drag force to moving dislocations by migratable H clouds. In Table 2 and Fig. 12, the 809 feasibilities of these (i)~(iv) under the test conditions in this study are summarized, in 810 addition to the schematic strengthening mechanism map as functions of strain rate and 811 temperature. (i), (iii), and (iv) predominated the yield and flow stress around ambient 812 temperature, albeit their individual significance was changed depending on the strain rate. 813 Meanwhile, as the temperature decreased below 200 K, (i) and (ii) became more essential 814 contributors due to the low diffusivity of H and weak thermal fluctuation. With the aid of 815 enhanced thermal activation and fast diffusion of H, all the (i)~(iv) were diminished, 816 resulting in the absence of strengthening at high-temperatures above 400 K. 817  818   819  Submitted to Materials Science and Engineering A 31  Table 2 Summary of the strengthening factors under each testing condition. 820 Temp. Strain rate (1/s) (i)  Dispersed Obstacles (ii)  Static  Pinning (iii)  Dynamic  Pinning (iv)  Atmosphere Drag Force Low (< 200 K) 5×10−5 Significant for flow stress (Athermal) Significant for yield stress (Themal/Athermal) Absent (H is not diffusible) 5×10−3 Medium (≈ 300 K) 5×10−5 Moderate (Thermally activated) Trivial (Thermally activated) Moderate (Thermally activated) Significant for yield stress 5×10−3 Significant Absent (Breakaway or equilibration of atmosphere) High (> 400 K) 5×10−5 Trivial (Thermally activated) 5×10−3  821  822 Fig. 12 Schematic illustration of the predominant H-induced strengthening mechanisms 823 in austenitic steel with the H concentration up to 7600 at ppm under the given strain rate 824 and temperature conditions. 825  826 Acknowledgments 827 This work was supported by JSPS KAKENHI (Grant Numbers: 21K14045 and 828 21K04702). YO would also like to acknowledge financial support from JFE 21st Century 829 Foundation and The Iwatani Naoji Foundation. 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