# Fileset

[67_MT-M2025161.pdf](https://mdr.nims.go.jp/filesets/6f0604a8-ac65-46b1-bee3-8b4cf6a04ad6/download)

## Creator

[Yuhei Ogawa](https://orcid.org/0000-0003-2713-9822), Osamu Takakuwa, Junichiro Moriyama, Haruki Nishida, Kaneaki Tsuzaki, [Akinobu Shibata](https://orcid.org/0000-0001-8577-6411)

## Rights

[Creative Commons BY-NC-ND Attribution-NonCommercial-NoDerivs 4.0 International](https://creativecommons.org/licenses/by-nc-nd/4.0/)

## Other metadata

[Phenomenology and Mechanisms of Hydrogen–Induced Solid Solution–Hardening in Fe–Cr–Ni Austenitic Steels](https://mdr.nims.go.jp/datasets/20cf744f-10d7-4230-a6cd-96d118982ffb)

## Fulltext

Phenomenology and Mechanisms of Hydrogen–Induced Solid Solution–Hardening in Fe–Cr–Ni Austenitic SteelsPhenomenology and Mechanisms of Hydrogen–Induced Solid Solution–Hardening inFe–Cr–Ni Austenitic Steels+1Yuhei Ogawa1,+2, Osamu Takakuwa2, Junichiro Moriyama3, Haruki Nishida1,4,+3, Kaneaki Tsuzaki1,2 andAkinobu Shibata1,41Research Center for Structural Materials, National Institute for Materials Science (NIMS), Tsukuba 305-0047, Japan2Department of Mechanical Engineering, Kyushu University, Fukuoka 819-0395, Japan3Department of Mechanical Systems Engineering, Shinshu University, Nagano 380-8553, Japan4NIMS Joint Subprogram in Materials Science and Engineering, Degree Programs in Pure and Applied Sciences, Graduate School ofScience and Technology, University of Tsukuba, Tsukuba 305-8577, JapanAs for the alloying additions of carbon (C) and nitrogen (N), the involvement of solute hydrogen (H) in face–centered–cubic (FCC) Fe–Cr–Ni–based austenitic steels causes considerable magnitude of solid solution–hardening. Notably, the strengthening ability of these threeinterstitial elements is almost comparable to each other, although H is significantly smaller than C and N in its atomic size. The present paperoverviews the phenomenology of such H–induced solid solution–hardening and its underlying rationales in commercial 300–series Fe–Cr–Niaustenitic steels after uniform H–charging in pressurized gaseous H2 environment at elevated temperatures. The effects of H concentration,deformation temperature, strain rate, and chemical composition of the alloy, as well as the thermal activation process of deformation, areextensively reviewed based mainly on the authors’ recent works. Potential roles of three key factors: 1) solute drag of H atmosphere around adislocation; 2) H–diffusion–controlled glide of dislocation core; and 3) the presence of H–substitutional complex, are discussed in light of theconventionally established theories of dislocation dynamics and plasticity. The H–induced solid solution–hardening is maximized when thefactors 1) and 2) (i.e., dynamic interactions between diffusible H and mobile dislocation) exert primary contributions to the flow stress. This factis attributed to the exclusively high mobility of H atoms in austenite lattice even at around an ambient temperature, which is not the case for Cand N that remain immobile during the deformation. [doi:10.2320/matertrans.MT-M2025161](Received December 1, 2025; Accepted January 6, 2026; Published January 23, 2026)Keywords: austenitic steels, strengthening, interstitial atoms, hydrogen1. IntroductionHydrogen, a potential energy carrier for achieving carbonneutrality, has attracted increasing attention from globalsociety—especially since the 2000s—as a solution toworsening environmental issues and the depletion of fossilfuels. However, for structural metallic materials that areused for long durations under severe hydrogenatingconditions in hydrogen–utilizing equipment, concerns onhydrogen embrittlement (i.e., degradation of strength,ductility, and other mechanical properties due to the ingressof hydrogen atoms) [1, 2] remain an unresolved technicalissue. In hydrogen refueling stations for fuel cell vehicles—representative hydrogen–utilizing facilities—componentssuch as pipes, joints, valves, and dispenser nozzles, whichcome into contact with high–pressure hydrogen (H2) gas,are made of 300–series austenitic stainless steels primarilycomposed of Fe–Cr–Ni. Austenitic steels with a face–centered–cubic (FCC) crystal structure may also sufferembrittlement through stress– or strain–induced phasetransformation to body–centered–cubic (BCC) or hexago-nal–close–packed (HCP) structures during plasticdeformation. However, when FCC matrix remains stablethroughout deformation, these steels exhibit superiorresistance to hydrogen embrittlement compared to other steeltypes [3–8]. Accordingly, in currently operating hydrogenrefueling stations, materials such as JIS–SUS316 andSUS316L—classified as stable austenitic steels—are mainlyemployed. Suitable materials are selected under strictregulations regarding the total threshold amount of Ni andother FCC–stabilizing elements (i.e., Ni equivalent) [9, 10].Despite their excellent resistance to hydrogen embrittle-ment, the yield strength of stable austenitic steels at roomtemperature is generally limited to 200–300MPa. Theirstrength is significantly lower than the yield strength ofmedium carbon steels or low–alloy steels (400–800MPa),which are widely used in structural applications, therebyleading to a reduction in allowable stress and an increasein material thickness. Solid solution–hardening through theaddition of carbon (C) and nitrogen (N) [11–15], dispersion–hardening via precipitation of γA (Ni3(Al,Ti)) phases orcarbides such as VC [16, 17], and grain refinement [18, 19]have long been studied as effective strengthening methodsfor austenitic steels. Among them, solid solution–hardeningcan be combined additively with all other strengtheningmechanisms [20], making it the most fundamental approach.Hydrogen (H), one of the interstitial elements, typicallyinduces solid solution–hardening in FCC materials similarto other elements, while it is commonly accompanied by atrade–off in degraded ductility [8, 21, 22]. However, thepresent authors recently discovered that when high concen-trations of H are added to specific types of stable austeniticsteels—such as SUS310S (Type310S) and SUS309S(Type309S)—both yield and tensile strength increase propor-tionally with H concentration, without compromising theintrinsic ductility of the material [23–25]. Notably, theincrease in yield strength due to H is comparable to thatachieved by the same atomic concentration of C or N(Fig. 1).+1This Paper was Originally Published in Japanese in J. Japan Inst. Met.Mater. 89 (2025) 287–306.+2Corresponding author, E-mail: OGAWA.Yuhei@nims.go.jp+3Graduate Student, University of TsukubaMaterials Transactions, Vol. 67, No. 4 (2026) pp. 385 to 404©2026 The Japan Institute of Metals and Materials OVERVIEWhttps://doi.org/10.2320/matertrans.MT-M2025161The pronounced solid solution–hardening caused by H(hereinafter referred to as H–induced solid solution–harden-ing), and the associated increase in plastic deformationresistance, offer significant application potential. In compo-nents such as high–pressure gas pipelines—where the appliedstress is maximized at the surface in contact with H2 (the entryside of H)—this effect may serve not only to spontaneouslystrengthen the material and suppress fracture but also toenhance resistance against fatigue failure [26]. Nevertheless,despite similar phenomena having been reported in a widerange of FCC materials—including pure Ni [27–29], Ni–based alloys [21, 30, 31], austenitic steels [32–34], and morerecently, high–entropy alloys [22, 35]—our understanding ofthe characteristics and underlying mechanisms of H–inducedsolid solution–hardening remains insufficient, even after morethan half a century since research in this area began. Inparticular, considering the most fundamental principle thatsolid solution–hardening originates from the mechanicalinteractions between lattice strain fields around interstitialsand dislocations [36, 37], the finding that H—despite having amuch smaller atomic radius than C or N—can achievecomparable strengthening is seemingly anomalous. Elucidat-ing such an anomaly is a critical issue for revisitingestablished theories of interstitial-induced solid solution–hardening in FCC alloys and for further approaching theessential nature of strengthening mechanisms. Since theaforementioned discovery, the present authors have continuedresearch using both macroscopic mechanical testing andatomic–scale simulations. We aimed for comprehensivelyunderstanding the effects of H concentration, temperature,strain rate, and alloy composition on H–induced solidsolution–hardening in Fe–Cr–Ni austenitic steels, and forconstructing a unified model capable of explaining thedependencies on these parameters without contradiction [23,24, 38–41]. The present paper provides, in relation to relevantliterature, an overview of the latest insights we haveaccumulated and describes the concept of the H–inducedsolid solution–hardening model we have developed. Ulti-mately, the remaining research challenges are raised.2. Phenomenological Characters of H–Induced SolidSolution–Hardening2.1 Lattice strain and concentration–dependenceWhen segregation to lattice defects such as dislocations orgrain boundaries is not taken into account, all three interstitialelements—carbon, nitrogen, and hydrogen—occupy octahe-dral interstitial sites (O–sites) in FCC lattice (Fig. 2).According to a simple rigid–sphere model, the radius ofaustenitic O–site in 300 series stainless steels is approx-imately 52–53 pm, whereas the covalent radii of carbon andnitrogen are relatively large, around 70 pm [42]. In practice,the bonding state and interactions between host metallicatoms and interstitial elements affect this approximation,leaving some doubt about its accuracy. However, X–raydiffraction has experimentally shown a lattice expansion ofapproximately ¦V = 8.6 © 10¹3 nm3 per carbon or nitrogenatom in austenite [43]. Ohkubo et al. added variousinterstitial and substitutional elements to an austenitic steelprimarily composed of Fe–17Cr–12Ni–0.8Mn (mass%).They reported a good correlation between the lattice constantchange due to alloying elements and the amount of solidsolution–hardening [13]. A similar trend is also clearlydemonstrated in the book written by Marshall [44]. As willbe discussed later, the influence of other factors, such ascomplexes formed between interstitial and substitutionalatoms, has been pointed out [11, 12, 45, 46]. Nevertheless, itis an undeniable fact that lattice strain around carbon andnitrogen contributes to solid solution–hardening to a certainextent. According to the work by Slater, who estimatedatomic radii based on experimentally determined interatomicdistances in various crystal structures [42], the covalentradius of H is less than 30 pm (Fig. 2). The present authorsperformed neutron diffraction measurements on bulk speci-mens of Type310S (Fe–24Cr–19Ni) steel uniformly chargedFig. 1 Solid solution-hardening in Fe-Cr-Ni austenitic stainless steels by various concentrations of carbon [11, 12, 51], nitrogen [11, 12,51], and hydrogen [24, 33, 34, 38, 50] at ambient temperature.Fig. 2 Configuration of octahedral site (O-site) in FCC austenite latticeaccording to the simple rigid sphere model and covalent radius ofinterstitial solute atoms (C, N, H) [42]. (online color)Y. Ogawa et al.386with 7600 at ppm H and revealed that the lattice expansionper H atom is ¦V = 2.27 © 10¹3 nm3 [47]. This value isapproximately one–quarter of the lattice expansion causedby carbon or nitrogen, almost consistent with bothexperimental [48] and atomistic simulation results [49] byother researchers.Figure 1 summarizes the dependence of yield stress (0.2%proof stress) enhancement on solute H concentration,measured at room temperature in Fe–Cr–Ni austenitic steelsover a wide range of compositions [24, 33, 34, 38, 50]. Theexperimental data for carbon and nitrogen [11, 12, 51] areincluded together. The amount of H–induced solid solution–hardening is linearly proportional to H concentration;although slightly lower than the strengthening by nitrogen,it is comparable to or even greater than that by carbon. Thisprovides clear evidence that H–induced solid solution–hardening originates not only from lattice strain but alsofrom other intrinsic factors. It should be noted that most ofthe data points in Fig. 1 were obtained from specimensuniformly charged with H via long–term exposure to high–temperature and high–pressure H2 environments. Themaximum H content that can be achieved by gaseousexposure is limited to below 10,000 at ppm (1 at%). Incontrast, Abraham and Altstetter added up to 10 at% H tothin films of Type310S steel by cathodic charging andmeasured the yield stress [33]. In their data, the magnitude ofstrengthening tended to saturate when the H contentexceeded 5 at%.2.2 Effects of temperature and strain rateThe process in which a dislocation overcomes solute atomsas short–range (a few atomic spacings) obstacles—includingtheir strain fields—is generally a thermally activated processaided by atomic vibration [52]. Accordingly, in addition tosolute concentration, the parameters that have beeninvestigated as factors influencing solid solution–hardeningare the deformation temperature and strain rate (i.e.,allowable time to cause a certain amount of deformation).Figure 3 shows the stress–strain curves and the temper-ature– and strain rate–dependences of the yield stress inType310S steel (with the H concentration of 7300–7600 atppm), obtained by the authors in the temperature range of173–423K [38]. As can be seen from Fig. 3(b), the yieldstress increases monotonically with decreasing temperature,regardless of the presence or absence of H. This trendindicates that thermally activated processes contributesignificantly to dislocation motion at the yield point in theType310S steel. On the other hand, H–induced solidsolution–hardening (i.e., the gap of yield stress between H–charged and non–charged specimens) becomes significant attemperatures below 400K (Fig. 3(c)). Although the amountof H–induced solid solution–hardening once tends to increasewith decreasing temperature, it shows a peak around 300K.A particularly notable feature is the influence of strain ratenear 300K; when the strain rate is decreased from 5 © 10¹5/sto 5 © 10¹7/s—equivalent to an increase in temperature interms of thermal activation, the H–induced increase in yieldstress is significantly reduced. However, when the strain rateis increased from 5 © 10¹5/s to 5 © 10¹3/s, the amount ofsolid solution–hardening again decreases, resulting in itspeak around 5 © 10¹5/s. Such a phenomenon, in which solidsolution–hardening is maximized near room temperature andat a specific strain rate, is a characteristic unique to H and notobservable for C or N.The non–monotonic dependence of solid solution–harden-ing on temperature and strain rate is often ascribed to solutediffusion [52–54]. Figure 4 presents the experimentallymeasured diffusion coefficients, D, of C [55–57], N [58–60], and H [8, 61, 62] in austenite, as well as their jumpfrequencies, v, calculated from the following equations.D ¼ D0 exp � EDRT� �ð1Þv ¼ 24Da2ð2ÞHere, D0 is the pre–exponential factor, ED is the diffusionactivation energy, R is the gas constant, T is the absolutetemperature, and a is the lattice constant. It should be notedthat the reported diffusion coefficients for C and N are limitedto temperatures above 700K, and for H, to those above400K. Therefore, the data for temperatures below theseranges were extrapolated using D0 and ED measured at highertemperature domains. The diffusion of C and N in austenite ismore than seven orders of magnitude slower than that of H,and their jump frequencies at 300K are only about 10¹4/s orless. In contrast, the jump frequency of H at 300K is as highas 105/s, indicating that H can diffuse through the materialrapidly even at room temperature. The H diffusivity decreases(a) (b) (c)Fig. 3 Effects of temperature and strain rate on the characteristics of solid solution-hardening in Type310S (Fe-24Cr-19Ni) austenitic steelwith (7300–7600 at ppm) and without hydrogen [38]. (a) true stress-strain curves; (b) yield strength as a function of temperature; and(c) hydrogen-induced increase in yield strength at different temperatures and strain rates.Phenomenology and Mechanisms of Hydrogen–Induced Solid Solution–Hardening in Fe–Cr–Ni Austenitic Steels 387to the level of C and N at 300K only when the temperaturedrops below 200K. Notably, µ200K corresponds to thetemperature range in Fig. 3(c) where the amount of H–induced solid solution–hardening begins to decrease from itsmaximum. This implies that dynamic H diffusion duringdeformation plays an important role in the H–induced solidsolution–hardening at room temperature, although its detailedrole will later be discussed. Owing to its practicalsignificance, the following sections will primarily focus onthe H–induced solid solution–hardening at room temperature.2.3 Effects of alloy compositionThe H–induced solid solution–hardening is linearlyproportional to H concentration (Fig. 1). Thus, for effectivelymanifesting the solid solution–hardening by H supplied fromthe gaseous phase, the alloy must possess high H–solubility,capable of dissolving more H under a given temperature andgas pressure condition. In this regard, substitutional alloyingelements in austenite are of key importance.The thermal equilibrium H concentration, CS, in metalsunder H2 gas environment is determined by the basicSieverts’ law [63]:CS ¼ Kf1=2 ð3Þwhere K is a material constant including the H2 gastemperature and the H–absorption energy. f is the H2 gasfugacity, which accounts for the deviation from ideal gasbehavior due to pressurization [63]:f ¼ P expPbRT� �ð4ÞIn eq. (4), P is the H2 pressure, and b is a constant(15.84 cm3/mol [63]). In general, the temperature–depend-ence of K is weak. Therefore, the equilibrium Hconcentration, CS, in H2 at a given temperature and pressurecan be approximated as being proportional to f 1/2.The present authors investigated the H–solubility inaustenitic steels with various Cr and Ni percentages undercontrolled H2 environment, identifying a strong interrelationbetween the equilibrium H concentration and Cr content [24].Figure 5 presents a compilation of H–solubility data obtainedfrom the authors’ own studies [24, 64] and from the literature[34, 50, 64], in which the product of Cr content (mass%) andf 1/2 is used as a parameter predominating H–solubility. TheH–solubility exhibits a nearly proportional relationship withCr · f 1/2, and the data from various alloys notably convergeinto a unified straight line. Although several materials, e.g.,Type330 and XM19, deviate from the linearity, these alloyscontain relatively large amounts of extra elements such as Si,Mn, and Mo in addition to Fe–Cr–Ni. It is thus presumed thatthe H–solubility in these specific alloys might involve somenon–negligible influences of extra elements other than Cr.In order to rationalize the correlation between Cr contentand H–solubility, Moriyama et al. employed first–principlescalculations [41, 65]. They substituted some of the six Featoms surrounding an O–site in FCC iron with Cr/Ni,(a) (b)Fig. 4 (a) Diffusivity and (b) jump frequency of carbon [55–57], nitrogen [58–60], and hydrogen [8, 61, 62] in austenitic steels as afunction of temperature, reproduced from the literature data. (online color)Fig. 5 Thermal equilibrium hydrogen concentration in Fe-Cr-Ni-based alloys as a function of the product between Cr content (mass%)and the fugacity of hydrogen gas [24, 34, 50, 64].Y. Ogawa et al.388investigating the corresponding changes in H–absorptionenergy, Eab, (the energy required to dissolve one H atom inO–site). Figure 6 depicts the variations in Eab due to Cr/Nisubstitutions, as well as the respective changes in the elasticenergy (mechanical strain energy associated with the insertionof H) and chemical energy (energy arising from changes inelectron density) that constitute Eab. As seen in Fig. 6(a), Eabtends to decrease with either Ni or Cr substitution, wherein Crexhibits a markedly greater impact. Furthermore, in Fig. 6(b),chemical energy is significantly reduced, particularly by Cr,while its effect on mechanical energy is marginal. Theseresults clearly indicate a strong electrochemical affinitybetween H and Cr. That is, increasing Cr content shouldenhance H–solubility, rationalizing the experimental trend inFig. 5. Similar tendencies—albeit to varying degrees—havealso been observed for other substitutional elements such asMn and Al [66, 67]. In the context of alloy design aimed ateffective utilization of H–induced solid solution–hardening,these computational information on the interactions betweenH and substitutional elements is expected to becomeincreasingly important. From an experimental standpoint,measurements of internal friction are also of interest. Asanoet al. [68, 69] and Gavriljuk et al. [70] discovered the Snoek–type relaxation peaks in H–charged Fe–Ni, Fe–Cr–Ni, andFe–Cr–Ni–Mn alloys. The latter authors attributed thesepeaks to tetragonal distortion due to interactions between Hand substitutional elements [70].In accordance with the trend in Fig. 1, alloys with higherCr content inevitably exhibit larger solid solution–hardeningwhen H is introduced under specific gas pressure and tempe-rature conditions. It remains unclear whether such strengthen-ing is solely a consequence of increased H concentration itselfor involves some influences of H–Cr interactions. Aiming atthe practical utilization and comprehensive understanding ofH–induced solid solution–hardening, this point awaits furtherelucidation in future studies.3. H–Dislocation Interactions Controlling the SolidSolution–HardeningSection 2 overviewed the previous experimental andanalytical findings and characteristic features concerningthe dependencies of H–induced solid solution–hardeningon H concentration, temperature, strain rate, and alloycomposition. In Section 3, the discussion will shift towardthe mechanisms underlying such H–induced solid solution–hardening. The mechanistic model to be ultimately estab-lished must be capable of explaining, without contradiction,all the aspects of H–induced solid solution–hardeningenumerated in Section 2. In particular, the peak of solidsolution–hardening at room temperature and at a specificstrain rate (Fig. 3) infers the importance of dynamic H–diffusion during deformation.Just as carbon forms Cottrell atmosphere [71] within itsdiffusible temperature range, an extreme diffusivity of H(Fig. 4) allows their short time segregation to dislocationcores or stress fields even around room temperature [2, 72].When strain rate (i.e., dislocation velocity) is sufficiently low,those segregated H can migrate through the material with themoving dislocations. Although such coordinative motion hasnot directly been visualized, it has been substantiated throughvarious indirect experiments (such as in–situ H–permeationtests during deformation [73]) and atomistic simulations [74].3.1 Solute drag of H–atmosphere3.1.1 Theoretical predictionCottrell and Jaswon were the first to point out, based ontheoretical calculations, that a solute atmosphere dragged bya moving dislocation can act as a resistance to dislocationglide—solute drag [75]. Their theory was subsequentlyadvanced by Hirth et al. [37, 76] and Yoshinaga et al. [77,78], leading to specific formulae that relate the solutedistribution within the atmosphere to the dislocation velocity,vd, solute concentration, and the magnitude of dragresistance. More recently, the applicability of these classicaltheories to H in austenite has been explored by Sills et al.[79, 80]. In Section 3.1, we discuss this solute dragphenomenon by solely placing our focus on the elasticstress–strain fields outside the dislocation core, wherecontinuum mechanics approximation holds. The issue ofmore localized interactions between dislocation core and Hwill be addressed in the following Section 3.2.Sills et al. assumed a steady–state dislocation motion andintroduced the following parameter Q as a dimensionlessdislocation velocity that governs the contribution of theatmosphere to solute drag [80]:Fig. 6 Change in (a) H-absorption energy, effective average of H-absorption energy (effective H-absorption energy), (b) elastic energy,and chemical energy when Fe atoms surrounding an O-site are replaced by Cr and Ni. The round and diamond in (a) represent the H-absorption energy and the effective H-absorption energy, respectively. Red and blue arrows in (b) show elastic and chemical energy,respectively [41, 65]. (online color)Phenomenology and Mechanisms of Hydrogen–Induced Solid Solution–Hardening in Fe–Cr–Ni Austenitic Steels 389Q ¼ vd¢4DkTð5Þwhere k is the Boltzmann constant, and ¢ is solute–dislocation interaction parameter, which includes the volumeexpansion ¦V caused by a solute atom. The presence andmagnitude of the drag force for a given solute species andtemperature are determined by the parameter Q. Accordingto their analysis, the drag force emerges within the range ofapproximately 0.01 < Q < 100. It reaches its maximum nearQ = 1, decreasing as Q increases or decreases beyond thiscriterion [80]. Meanwhile, when Q > 100 or Q < 0.01, thedislocation leaves the atmosphere behind (breakaway limit)or the atmosphere follows the dislocation while maintainingits equilibrium distribution (equilibrium limit), providing nodrag force in either case. By substituting eq. (5) into Orowanequation, which relates mobile dislocation density μm andstrain rate _¾ as _¾ ¼ μmbvd=MT (b is the Burgers vector andMT is the Taylor factor), the following eq. (6) is obtained:_¾ ¼ 4QDkTMT¢μmb ð6ÞFigure 7 depicts the transitions of Q = 0.01, 1, and 100criteria for three different mobile dislocation densities (μm =1011, 1012, 1013/m2) on the temperature–strain rate space.These curves were calculated based on eqs. (5) and (6) byusing the H diffusion coefficient in austenitic steels (Fig. 4)and the volume expansion per H atom, ¦V (see Ref. [38] fordetails). One drawback when comparing Fig. 4 with practicalexperimental data is the difficulty in measuring actual μm.Nevertheless, in FCC materials (e.g., Cu [81] and Type304steel [82]), it has been shown—based on Orowan equationand Bailey–Hirsch relationship (· = ¡Gbμ: · is the flowstress, ¡ is a constant dependent on dislocation characterand material, G is shear modulus, and μ is total dislocationdensity)—that μm increases sharply from the order of1011/m2 to 1013/m2 or more around the yield point.Therefore, Fig. 7(a)–(c) likely represents the successivebehavior before and after the onset of yielding. In Fig. 7,the strain rate of 5 © 10¹5/s, at which H–induced solidsolution–hardening reaches its maximum, is located closeto Q = 1 line around 300K. As μm exceeds 1013/m2 afteryielding, the situation shifts toward Q = 0.01 side. This resultindicates that the atmosphere drag force reaches its maximumat yielding and then diminishes as deformation progresses.Although these calculations are quite simplified, solute dragof H atmosphere seems to contribute significantly to theappearance of the yield stress peak in Fig. 3(c). Furthermore,in conventional theoretical formulations, there exists aproportionality between the atmosphere drag force and theaverage solute concentration [37]. Such a proportionality maybe one of the reasons why solid solution–hardening at roomtemperature linearly augments with H concentration (Fig. 1).3.1.2 Experimental evidence for the contribution ofsolute drag(1) Fluctuation of the strengthening around yield stressIn this subsection, we introduce several experimental factssubstantiating the solute drag of H atmosphere that wassuggested by the theoretical predictions. Figure 8 shows theflow stress gap between H–charged and non–chargedspecimens (i.e., the amount of solid solution–hardening),plotted against true strain, for the same Type310S steelpresented in Fig. 3 [38]. Above 373K, H–induced solidsolution–hardening continues to act even after yielding.However, an eye–catching behavior is observed at 298Kunder a strain rate of 5 © 10¹5/s: from the yielding up to atrue strain of approximately 0.05, the amount of solidsolution–hardening gradually decreases from µ60MPa toµ30MPa. This is reasonably understood in light of thediscussion above (Fig. 7)—under these deformation con-ditions, the Q value transitions from 1 to 0.01 after yielding,gradually diminishing the drag force. In other words, thedecrease in solid solution–hardening with the magnitude ofµ30MPa possibly corresponds to the contribution of the dragforce from the H atmosphere. Supporting this interpretation,(a) (b) (c)Fig. 7 Strain rate characterizing dynamic hydrogen-dislocation interactions, which are defined by Q = 100, 1, and 0.01 in eq. (5) and (6),as a function of temperature [38]. Mobile dislocation density, μm, is parametrically set as (a) 1011, (b) 1012, and (c) 1013/m2. The hatchedareas denote the temperature and strain rate ranges where drag force by solute atmosphere is feasible to emerge.Fig. 8 Magnitude of solid solution-hardening in Type310S (Fe-24Cr-19Ni)steel containing 7600 at ppm H at various temperatures and strain rate [38].Y. Ogawa et al.390no continuous and distinct decrease in the solid solution–hardening after yielding is observed when the pre–yield statelies outside or close to the outer boundaries of the hatchedregion in Fig. 7 (Fig. 8).The reduced magnitude of solid solution–hardening afteryielding could be recognized in Fig. 8, where the flow stresswas plotted in a differential form. However, on the actualstress–strain curves, the influence of work–hardening over-whelms, making the total flow stress increase monotonicallywith strain. Nevertheless, although it is not visible on thestress–strain curves, the effect of reduced solid solution–hardening due to the loss of drag force can be observed as atemporary reduction in the post–yield work–hardening rate[38]. Nishida et al. confirmed such characteristic work–hardening behavior not only in Type310S steel but also inseveral other steel grades, including Type309S and Type316L[24]. Based on these facts, solute drag of H atmosphere islikely a universal phenomenon manifesting in Fe–Cr–Ni–based austenitic steels. Recently, McDowell et al. performedcrystal plasticity finite element simulations incorporating theeffects of solute H on Type316L steel. They accuratelyreproduced experimental stress–strain curves by taking thevariation in drag force around the yield point into account[83].The stress drop caused by a rapid increase in mobiledislocation density and a concomitant decrease in dislocationvelocity—observable also in BCC metals and covalentcrystals such as LiF—can be ascribed to the yield pointtheory developed by Johnston and Gilman (J–G) [84]. Thestress dependence of dislocation velocity generally followsa power law relationship, vd = A¸m (where ¸ is the shearstress and A and m are material constants). When A is largeand dislocation mobility is high as for FCC metals, themicroscopic plastic strain rate promptly exceeds theexternally imposed macroscopic strain rate once the stressexceeds a critical level so that dislocation motion andmultiplication commence. As a result, a stress drop in J–Gmechanism does not occur, rendering the yielding behaviorpredominated by the dislocation multiplication process [85].Nevertheless, Horiuchi and Yoshinaga found a distinct yieldpoint in Al–Mg alloys due to a reduction in dislocationmobility at high temperatures where solute drag is operativeand work–hardening is minimal. In particular, they termedthis unusual phenomenon as “high temperature yield point”[86, 87]. Possibly, Fig. 8 suggests that the phenomenonidentified by Yoshinaga et al. manifested at room temper-ature owing to the diffusion of H—the reduction indislocation mobility (i.e., a decrease in the coefficient A)caused by the H atmosphere drag might transform themultiplication–controlled yielding to mobility–controlled.Indeed, in the experiment by Abraham and Altstetter [33],where more than 1 at% H was introduced into Type310S steelvia cathodic charging, a clear yield drop appeared at roomtemperature and a strain rate of 5.5 © 10¹5/s. In their case,the stress drop seen in Fig. 8 might become more pronouncedthanks to the higher H concentration. It should be noted that,as for the yield point in carbon steels, a yield drop can alsoappear by the sudden breakaway of dislocations from thepinning by solute atmospheres. However, in such a circum-stance, the stress drop should occur regardless of strain rate.At room temperature in Fig. 8, the stress drop ratherdisappears at a high strain rate of 5 © 10¹3/s. This indicatesthat the dislocation pinning by the H atmosphere is notsignificant at room temperature.Another noteworthy point when discussing the post–yielding deformation is the possible effect of H on dislocationaccumulation and associated work–hardening. In some FCCmaterials, such as pure Ni and Ni–based alloys, H–inducedchanges in dislocation structures and dislocation cell sizehave been observed [21, 88–90], making their influence onthe flow stress after yielding not negligible. However, in theauthors’ own investigations of austenitic steels—includingtransmission electron microscopy (TEM) [39], dislocationdensity measurements by neutron diffraction [47], andhardness measurements after H–desorption from thedeformed samples [91]—no significant H–effect on dis-location accumulation or structural evolution has beenidentified in the low to medium (at least ³20%) strain.Therefore, in Fe–Cr–Ni alloys targeted in this paper, thechange in flow behavior after yielding can reasonably beapproximated as being solely governed by the H–effect onthe mobility of individual dislocations.(2) Variation in strain rate sensitivityAn additional experiment that provided the evidence forsolute drag is the measurement of the strain rate sensitivity,S. The authors conducted strain rate jump tests at roomtemperature on Type310S steel charged with 7600 at ppm H[40]. Figure 9(a) shows representative stress–strain curvesmeasured at a base strain rate (i.e., the strain rate before it wasincreased tenfold) of 10¹4/s. On these stress–strain curves,sharp stress–rises correspond to the moments when the strainrate was suddenly increased tenfold from the base, whilesudden stress–drops reflect the return from the elevated rateto the base. These stress changes were measured undermultiple base strain rates, and the increase in flow stress @¸upon strain rate jump (converted from normal stress to shearstress using the Taylor factor of FCC polycrystals, MT =3.06) was plotted against true strain in the form of S ¼@¸=@ ln _¾. The results are shown in Fig. 9(b). The H–chargedspecimens generally exhibit larger S compared to non–charged specimens, the reason for which will be discussedlater.In H–charged specimens, one may notice in Fig. 9(b) thatthe strain rate sensitivity, S, strongly depends on both the basestrain rate and true strain. Particularly, under the base strainrates of 10¹3/s and 10¹4/s, S evolves sharply from µ1MPato µ4MPa over the strain range from just after yielding upto µ0.1. To correlate this behavior to solute drag, Fig. 10(a)reorganizes Fig. 7 by focusing on room temperature andconverting the horizontal axis to mobile dislocation density.If the mobile dislocation density at the post–yield small strainis μm ³ 1012/m2, and in the later deformation stage is1013/m2 order, rapid increases in strain rate by a factor of 10from the bases of 10¹3, 10¹4, and 10¹5/s correspond to theupward arrows indicated in Fig. 10(a). When these arrowsare transferred to the drag force versus strain rate curve, oneyields schematic diagrams like Figs. 10(b) and (c). As ofparticular interest here, in low strain domain with the basestrain rates of 10¹3/s and 10¹4/s, the drag force drops sharplyin response to the strain rate jump (Fig. 10(b)). Given that thePhenomenology and Mechanisms of Hydrogen–Induced Solid Solution–Hardening in Fe–Cr–Ni Austenitic Steels 391intrinsic S in the H–charged specimen without solute drageffect is 3 to 4MPa (the origin of this large S will bediscussed later) measured at the later deformation stage, thelow S of approximately 1MPa in the early deformation stagein Fig. 9(b) should reflect the value in which loss of dragforce due to the strain rate jump is subtracted. Indeed, underthe base strain rate of 10¹5/s, where little change in dragforce is anticipated even after a strain rate jump, the S in theearly deformation stage is quite stable (Fig. 9(b)). In contrast,at the later deformation stage depicted in Fig. 10(c), thetenfold increase in strain rate from 10¹3/s or 10¹4/soppositely results in an increase in drag force. This impliesthat the contribution of drag force to S gradually transitionsfrom negative to positive as deformation proceeds, providinga consistent explanation for the evolution of S in Fig. 9(b).At the base strain rate of 10¹3/s, the initial deformation stageis closer to the boundary of Q = 100 (Fig. 10(a)). Thus,compared to the 10¹4/s case, a larger strain is required torender such S–contribution from negative to positive. For thisreason, the curve of the H–charged specimen at 10¹3/sexhibits a rightward–shift from the one at 10¹4/s (Fig. 9(b)),with a rapid increase in S at a higher strain level.3.2 Thermal activation process of dislocation motionThe foregoing discussion substantiated the significance ofH atmosphere solute drag in the yield stress peak observednear room temperature and a strain rate of µ5 © 10¹5/s. Onthe other hand, even in the later deformation stages wheredrag force diminishes, or at a strain rate of 5 © 10¹7/s wheredrag force is already zero at the yielding (Fig. 10(a)), theH–induced solid solution–hardening still remains substantial(Fig. 3(c)). Furthermore, as noted in Fig. 9(b), the S value—the stress increment via strain rate jump—is greater in H–charged specimens than in non–charged ones. This indicatesthat, in addition to the interaction between H atmosphere anddislocations, individual H atoms contribute to solid solution–hardening by playing the role of short–range (thermal)obstacles.3.2.1 Dislocation motion via overcoming short–range(thermal) obstaclesAs illustrated schematically in Fig. 11, when a dislocationmoves across a slip plane dispersed with short–rangeobstacles, it generally overcomes the obstacles with the aidof both externally applied stress and atomic thermal vibration[52]. The energy that must be supplied by thermal vibrationduring this process, ¦G, is expressed as a function of shearstress, ¸+, acting on the dislocation line, as is also evidentfrom Fig. 11(c):�G ¼ �G0 � ¸�V ð7Þwhere ¦G0 is the intrinsic activation energy of the obstacleat ¸+ = 0, and V is the activation volume. The activationvolume—V = bdL—is defined as the product of Burgersvector, b, and the area swept by dislocation during thermalactivation process (activation area, A: the width of anindividual obstacle, d, multiplied by the average obstacleinterspacing, L) (Fig. 11) [92]. The shear stress ¸+ (alsoreferred to as the effective stress) is given by subtracting theinternal stress, ¸μ—stress component independent of temper-ature and strain rate—from the total flow stress applied tothe material, ¸—¸ = ¸+ + ¸μ. From eq. (7), the followingrelationship is self–evident:(b) (c)(a)Fig. 10 (a) Strain rate range, where H atmosphere exerts drag force againstdislocation motion, as a function of mobile dislocation density. (b) and (c)schematically correlate the situations in strain rate jump tests underdifferent base strain rate with the magnitude of drag force [40].(a) (b)Fig. 9 (a) Examples of true stress-strain curves during strain rate jump test of Type310S steel at room temperature and (b) the measuredstrain rate sensitivity as a function of strain [40].Y. Ogawa et al.392V ¼ � @�G@¸�����Tð8ÞOn the other hand, the shear strain rate _£ of the crystal undereffective stress, ¸+, and thermal energy, ¦G, follows theArrhenius–type rate equation [36, 52], where _£0 is a constantincluding the vibrational frequency of the dislocationsegment, the obstacle interspacing, L, and the mobiledislocation density, μm:_£ ¼ _£0 exp ��GkT� �ð9ÞTaking the logarithm of both sides of eq. (9) and rearrangingwith respect to ¦G, then differentiating by ¸+ according toeq. (8), one yields:kTV¼ @¸�@ ln _£¼ @¸@ ln _£ð10ÞHere, the right–hand side of eq. (10) is equivalent to thestrain rate sensitivity, S ¼ @¸=@ ln _¾, defined in Section3.1.2 (2). An essential theoretical relationship is nowreached: V is inversely proportional to S. Note that ineq. (10), ¸+ is replaced by ¸ since the strain rate–derivativeof ¸μ should be zero.3.2.2 Reduction in activation volume due to HTo understand the nature of short–range obstacles,measurement of activation volume, V—information on thesize and distribution of obstacles—is useful. For this purpose,thermal activation analyses utilizing the transient of plasticdeformation (e.g., stress relaxation and creep tests) have beenemployed [52, 93]. Figure 12 shows an example of a stress–strain curve obtained from a stress relaxation test conductedby the authors on Type310S steel containing approximately7600 at ppm H, together with the activation volume, V,determined by fitting the relaxation curve to a theoreticalequation [39] (for the details for calculating V, refer to [94,95]). A characteristic feature in the H–charged specimen isthat the amount of stress relaxation within a given period(here, 30 seconds) is obviously larger than that in the non–charged specimen. Moreover, as a general behavior of FCCmaterials, V tends to decrease with increasing strain.However, in the H–charged specimen, the strain–dependenceof V becomes weaker with increasing H concentration,besides the overall decrease in V throughout the deformationprocess. According to eq. (10), the trend in Fig. 12(b)indicates the increase in strain rate sensitivity, S, caused byH. This tendency is a direct reproduction of the overallincrease in S due to H shown in Fig. 9(b).As for the specific values of V, when the obstacles arelattice friction such as Peierls potential, V is usually less than100b3; for solute atoms, it ranges from several tens tohundreds of b3; and for dislocation–dislocation intersections,it ranges from several hundreds to thousands of b3 [85, 96].Considering that the Peierls potential in FCC crystal isnegligibly small, the measured values of 100–200b3 inFig. 12(b) indicate that solute atoms—including H and otheralloying elements—as well as forest dislocations, act as therate–controlling obstacles.3.2.3 Extracting H–effects as short–range obstaclesIn Section 3.2.1, thermally activated dislocation motionwas discussed for the case where the obstacle species issingle. However, in practice, multiple obstacle types are often(b) (c)(a) (b)Fig. 11 (a) Schematic drawing of the movement of a dislocation line through the field of short-range obstacles on its slip plane.(b) magnifies the process overcoming single obstacle via thermal activation, while (c) denotes the side view of (b) and the physical senseof activation parameters.(a) (b)Fig. 12 (a) True stress-strain curves during the stress-relaxation tests of Type310S steel at room temperature and (b) the measuredactivation volume under various hydrogen concentrations [39].Phenomenology and Mechanisms of Hydrogen–Induced Solid Solution–Hardening in Fe–Cr–Ni Austenitic Steels 393present, besides additional obstacles, e.g., forest dislocations,are newly introduced during deformation (Fig. 13(a)). Toclarify the role of H within such a complex situation, it isnecessary to extract the pure effect of H on deformationbehavior by screening other factors that influence theactivation volume.Kocks [97] and Mulford [98], focusing on the decompos-ing method of effective stress in the work of Haasen [99],proposed a way to separate the contributions from individualobstacles in a system containing multiple obstacle types. Inthe case where there are two types of short–range obstacles,they first assumed that the flow stresses arising from eachobstacle type, ¸1 and ¸2, follow a linear additivity.¸ ¼ ¸1 þ ¸2 ð11ÞThe additivity holds only in a specific situation. Nevertheless,the combination of forest dislocations with high concen-trations of solutes (Fig. 13(a)) represents a typical example ofsuch a case [92, 97, 100]. In what follows, the contributionfrom solutes is denoted as ¸f, and that from forest dislocationsas ¸d. When total flow stress ¸ is a sum of ¸f and ¸d, theadditivity also holds for strain rate sensitivity, S—a derivativeof ¸.S ¼ @¸@ ln _£¼ @¸f@ ln _£þ @¸d@ ln _£¼ @¸f@ ln _£þ @ ln ¸d@ ln _£¸d ð12ÞNote that in the transformation of the second term of eq. (12),@ ln ¸d=@ ln _£ ¼ ð@ ln ¸d=@¸dÞð@¸d=@ ln _£Þ ¼ ð1=¸dÞð@¸d=@ ln _£Þ.Since ¸d corresponds to the increase in flow stress due towork–hardening, the total strain rate sensitivity S can beexpressed as follows by taking the yield stress as ¸y:S ¼ @¸f@ ln _£þ @ ln ¸d@ ln _£ð¸ � ¸yÞ ð13ÞFurthermore, considering eq. (10) that S £ 1/V, eq. (13) canbe transformed as follows by denoting the solutes and forestdislocation components of activation volume as Vf and Vd,respectively:1V¼ 1Vfþ 1¸dVdð¸ � ¸yÞ ð14ÞTherefore, if the reciprocal of V measured during a tensiledeformation—or S, which is proportional to 1/V—is plottedagainst ¸ ¹ ¸y, the intercept on the vertical axis reflects theinfluence of solutes on V, while the slope represents thecontribution of forest dislocations. This method is known asthe Haasen plot (Fig. 13(b)). It has been widely applied tothe decomposition of strengthening mechanisms in variousmaterials, including solid solution–strengthened and precip-itation–hardened alloys [98, 101–105].In FCC pure metals such as Ni and Ag, where yield stressis low and no short–range obstacles other than forestdislocations are present—that is, where the first term ofeqs. (13) and (14) µ 0—the Haasen plot becomes a straightline passing through the origin [98, 106]. This linearity isreferred to as the Cottrell–Stokes law [106, 107]. Thelinearity of the Haasen plot implies that the product ¸dVd ineq. (14) is constant. It is because the increment of flow stressby work–hardening, ¸d, is proportional to μ1/2 according tothe Bailey–Hirsch equation, while the forest dislocationcomponent of the activation volume, Vd, is proportional to theaverage dislocation interspacing, μ¹1/2 (see Fig. 13(a)).Figure 14 shows an example of Haasen plot for Type310Ssteel [39], obtained by converting the V measured in thestress relaxation test (Fig. 12) into S using eq. (10). In thenon–charged case, the Haasen plot becomes a straight linewith a positive intercept on the vertical axis, satisfying theCottrell–Stokes law. This positive intercept—that is, the firstterm of eqs. (13) and (14)—can be attributed to the combinedcontributions of alloying elements originally contained in thealloy, i.e., Cr, Ni, Si, and C. In contrast, for the H–chargedspecimens, although the linearity of Haasen plot holds, twodistinctions appear with increasing H concentration: (i) anincrease in intercept, and (ii) a decrease in slope. Amongthese, (i) the increased intercept reflects the overlappingeffect of H that acts as additional short–range obstacles,superimposed on the material’s intrinsic positive intercept.By taking this intercept change from the non–chargedcondition and its dependence on H concentration asindicators, the intrinsic H–effect can be discussed whilescreening the influences of other alloying elements and forestdislocations.The increase in Haasen plot intercept corresponds to adecrease in Vf, associated with thermally activated movementof individual dislocations (eq. (14)). Physically, it implies thateither or both of the obstacle size, d, and their interspacing, L,(Fig. 11) have decreased. In other words, thermal activationprocess that controls plastic deformation has become a morelocalized event after the introduction of H. Although (ii) thedecrease in slope is not yet fully understood, it might resultfrom a reduced contribution of forest dislocations tothermally activated deformation. That is, the rate–controlling(a) (b)Fig. 13 Schematic drawings of (a) the movement of dislocations through the field of two different types of obstacles (e.g., solute atoms andforest dislocations) and (b) correspondingHaasen plot, where strain rate sensitivity (or inverse activation volume) is plotted against stress.Y. Ogawa et al.394mechanism has shifted to the process in which dislocationsovercome a newly introduced obstacle: H.3.2.4 Stress equivalence of H–induced solid solution–hardening and activation volumeAs shown in Fig. 14(b), the Haasen plot interceptincreases linearly with both yield stress and H concentration.In addition, an interesting phenomenon here is the correlationbetween yield stress and activation volume Vf calculated fromthese S values at the intercepts [39]. Figure 14(c) shows agraph in which the intercepts in Fig. 14(a) are converted intoactivation volumes using eq. (10) and plotted as functions ofH concentration and yield stress. The Vf at yielding follows apower–law relationship with yield stress, converging all datapoints for both H–charged and non–charged specimens ontoa unified curve.Basinski et al. investigated the relationship between yieldstress and activation volume in Cu alloys containing variousspecies and concentrations of substitutional elements. Theyreported that even when solute species and concentrationsdiffer, materials possessing an equivalent activation volumealso exhibit mutually identical yield stresses [108]. Theytermed this phenomenon “stress equivalence” and furtherdemonstrated that, at a constant deformation temperature,the yield stress and activation volume of all alloys follow apower–law relationship like Fig. 14(c). Figure 14(c) can thusbe interpreted as a manifestation of such “stress equivalence”in the yield stress variation induced by H in austenitic steel.The dependence of activation volume solely on the yieldstress and its independence on solute concentrationnecessitates a correction of the conventional thermalactivation model, in which a dislocation surmounts individualobstacles one by one (Fig. 11). In this regard, Basinski et al.emphasized that the experimentally measured activationvolumes are always larger than the values estimated fromthe average interspacing of solutes—that is, multiple soluteatoms may simultaneously be involved in each thermalactivation event [108]. Indeed, in austenitic steels examinedin our own study, the V values—on the order of 100b3—aremuch larger than expected from the mean interspacing of H(µ10b [39]) for the present concentration range (³7600 atppm). The potential thermally activated mechanisms respon-sible for these macroscopic trends, discussed in Sections3.2.1–3.2.4 will be addressed in the following Sections3.2.5–3.2.6.It should be noted that the yield stress on the horizontalaxes in Fig. 14(b) and (c) includes the influence of solutedrag. However, as described in Section 3.1.1, the magnitudeof such a drag force is also proportional to the average Hconcentration. Therefore, even if the contribution of solutedrag were subtracted from the yield stress, the experimentaltendencies in Fig. 14(b) and (c) would remain unchanged.3.2.5 Thermal activation model for H–induced solidsolution–hardening: Application of trough modelTheories of solid solution–hardening originated with thelattice friction model proposed by Mott and Nabarro [109],subsequently developed through the point–like obstaclemodel by Friedel–Fleischer [110, 111] and Labusch’s modelconsidering simultaneous interactions with plural obstacles[112]. Although these theories can adequately describe solidsolution–hardening in certain alloys, depending on the soluteconcentration and solute–dislocation interaction force, theyunfortunately cannot provide a rational explanation for“stress equivalence”. Later, Kocks applied Fisher’s theory[113], which modeled the breakaway of a dislocation linefrom a row of segregated solutes. He attempted a physicalinterpretation of “stress equivalence” by considering aspecific process, in which a dislocation line bonded withdispersed solute atoms bows–out a short segment via thermalactivation (Fig. 15(a)) [54]. In his model, the bonded stableposition of the dislocation line is approximated by atriangular potential, regarding the pre–bowing dislocationas lying at the bottom of the potential trough (Fig. 15(b));thus, he referred to his model as the trough model. In thisframework, the dominant factors determining the troughdepth are the solute–dislocation interaction energy per unitlength and the corresponding reduction in dislocation’s self–energy and line tension. These quantities are governed bythe bonding strength between the individual solute anddislocation (i.e., solute species) and by the solute densityalong the dislocation line (i.e., solute concentration).Conversely, even for different solute species and concen-trations, the bow–out process under a given applied stressbecomes equivalent if the total reduction in self–energy isfixed. This inherently results in the same activation volume.(a)(b) (c)Fig. 14 Haasen plot of non-charged and hydrogen-charged Type310S steel at room temperature. The plotted strain rate sensitivity, S, wereobtained by converting the activation volume in Fig. 12(b) via eq. (10) [39]. (b) indicates the ordinate intercept of Haasen plot in (a).The plot points in (b) were converted into activation volume via eq. (10) and reproduced in (c).Phenomenology and Mechanisms of Hydrogen–Induced Solid Solution–Hardening in Fe–Cr–Ni Austenitic Steels 395For the application of trough model, the movingdislocation line must interact frequently with solute atomsand take stable configurations—namely, solute concentrationmust be high. This requirement is satisfied in austenitic steelscontaining a large amount of substitutional elements.Furthermore, theoretical calculations have reported thatsegregation of H decreases the dislocation’s line tensionand self–energy [114, 115]. The deformation at roomtemperature and low strain rates, under which H can movecoordinatively with dislocations, are therefore favorable forthe application of trough model. The H–related “stressequivalence” discovered by the authors (Fig. 14(c)) suggeststhe applicability of such a trough model to the H–inducedsolid solution–hardening. In other words, the conventionalthermal activation model in Fig. 11 does not hold for thematerials containing a high concentration of alloyingelements and diffusible solute H. Instead, the bow–outprocess of dislocations from troughs, as depicted in Fig. 15,may govern thermal activation parameters.On the other hand, while the trough model is discussedhere as a mechanism independent of solute drag, when wedeal with H, it is still unclear what atomic–scale processactually governs the escape of dislocation from the trough. Atfirst glance, under deformation conditions where the entire Hatmosphere can follow the dislocation by maintaining itsequilibrium distribution, it seems that the trough itself wouldalso freely move together with the dislocation—that is,dislocation glide resistance is zero. However, the actualsituation is not so.3.2.6 Diffusion–controlled glide of dislocation coreThe coordinative motion of solute atmosphere withdislocation is driven by the drift flow of solutes. This driftflow stems from the gradient of solute–dislocation interactionenergy and solute chemical potential within the dislocation’sstress/strain field [37, 52]. In contrast, at the center of thedislocation line, direct interactions between solutes and thedislocation core are of primary importance rather than thebehavior of the whole solute atmosphere [37, 52]. Figure 16illustrates such a situation according to the model drawn byFriedel [116]. Similar to those constituting the surroundingatmosphere, local solutes in the dislocation core also tendto follow the dislocation’s movement. However, in doingso, they must undergo one–atomic diffusion jump in thedirection of dislocation motion. Given the activation energyfor this diffusion jump as W, the dislocation velocity, vd,under an effective stress, ¸+, can be expressed by anArrhenius–type rate equation analogous to eq. (9) [52].vd ¼12vDb2­exp �W � ¸�b2­kT� �� �ð15ÞHere, vD is the Debye frequency, ­ is the average interspacingof solutes aligned along the dislocation core, and W ¹ ¸+b2­term corresponds to the thermally supplied energy, ¦G.According to the textbooks of Anderson, Hirth, and Lothe[37], as well as of Caillard and Martin [52], the conditionunder which this diffusion barrier, W, predominantly resistsdislocation motion is as follows—when vd is smaller thanthe critical velocity for the maximum atmosphere drag force(i.e., Q = 1 in eq. (5)), and when solute–core binding energy,EB, is greater than thermal vibration energy of the crystal,kT (Fig. 16). Considering that EB = 10–15 kJ/mol (0.1–0.16 eV) in austenitic steels [49, 117, 118], the deformationconditions discussed here (room temperature: kT = 0.026 eV)precisely correspond to such a case.Figure 17 shows the authors’ model illustrating thedislocation bow–out from a row of H (i.e., trough) [39].Similar to the situation shown in Fig. 16, a dislocation linedecorated with H advances by generating a bulge,accompanied by diffusion jumps of H atoms to follow thedislocation core. The significance of the diffusion barrier andthe size of the bulge then govern the thermally activatedprocess of dislocation motion and the correspondingactivation volume. The modification from Friedel’s originalmodel lies in the definition of ­ in eq. (15), where each bulgeassumably involve simultaneous diffusion jumps of multipleH. This assumption is based on two considerations: first, themeasured activation volume, V, is much larger than the onepredicted from the mean interspacing of H atoms under the(a) (b) (c)Fig. 15 Schematic drawings of the trough model for solid solution-hardening proposed by Kocks [54]. (a) Dislocation line, stabilized byrow of solute atoms on the slip plane, tries to move via (b) bulging a small segment. The initial stabilized state is assumed as (b) thebottom of energy trough. The parameters characterizing the bulge are shown in (c).(a)(b)Fig. 16 Description of diffusion- and drift-controlled glide mechanismsand their correspondence with dislocation velocity [37, 116]. The twomechanisms switch each other around the Q µ 1 limit.Y. Ogawa et al.396present concentration range (Section 3.2.4); second, whenH segregation into the dislocation core is considered, H–Hspacing along the core becomes even narrower. According toeq. (15), the effective stress, ¸+, acting on the dislocation lineassists H–diffusion jumps through the energy term, W ¹¸+b2­. Let us assume now that the number of H atomsundergoing jumps within a given time period is statisticallyconstant. If so, as the total H concentration increases and theH atoms aligned along the core become denser, the regionfeasible for such collective H jumps will probabilistically beconfined to shorter dislocation segments. This correspondsto a decrease in ­, meaning that the force exerted by thedislocation line on individual H atoms (Fig. 16(a)) becomessmaller. Consequently, in order to maintain W ¹ ¸+b2­constant so that the dislocation can move at a rate consistentwith the applied strain rate, ¸+ must be increased. As a result,solid solution–hardening occurs through the increase ineffective stress. This hypothesis is quite simplified. Never-theless, it qualitatively explains the involvement of thermallyactivated processes in H–induced solid solution–hardening,the reduction of V (increase in S), and their dependence on Hconcentration.To incorporate the H concentration–dependence of solidsolution–hardening and activation volume to the model inFig. 17, one can refer quantitatively to how the local Hconcentration near the dislocation core is correlated with theaverage H concentration throughout the material. Whensegregation sites such as dislocations coexist with interstitiallattice sites (Fig. 2), the equilibrium H concentration, CT, atthe segregation sites under an average H concentration, C0,follows the Fermi–Dirac statistics [119].CT1� CT¼ C01� C0expEBRT� �ð16ÞFigure 18 shows the relationship between C0 and CT as afunction of temperature, calculated using eq. (16). Here, theH–dislocation binding energy in austenitic steel, EB µ 13kJ/mol, obtained by Atrens et al. [117] via internal frictionmeasurements, was employed. The CT increases sharply withdecreasing temperature, then tends to saturate. Notably, inthe regime around room temperature, the influence of C0 onCT is most pronounced. The inset in Fig. 18 extracts the C0–CT relationship at room temperature (300K). Within the Hconcentration of 2000–8000 at ppm (i.e., the range targetedby the authors), CT is approximately proportional to C0, asfitted by the dashed line.According to the model in Fig. 17, if the number of Hatoms within the bulge (i.e., those capable of jumping withina given time) is statistically constant, the bulge length ­becomes inversely proportional to the H concentration CTalong the dislocation core. Therefore, given that the forwarddisplacement of the bulge during thermal activation issufficiently smaller than ­, the activation volume V becomesinversely proportional to both CT and C0. This aligns with theexperimental observation in Fig. 14(b), where S is propor-tional to C0. Similarly, if ­ £ 1/C0 in eq. (15), then under agiven deformation rate where W ¹ ¸+b2­ is constant, theeffective stress ¸+ becomes proportional to C0 (inverselyproportional to V). Although this is a simple approximation,it reasonably explains the characteristics of H–induced solidsolution–hardening—namely, that the magnitude of strength-ening is proportional to the average H concentration(Fig. 1)—when considered together with the H concen-tration–dependence of solute drag force. Note that ineq. (15), the thermal energy W ¹ ¸+b2­ decreases as a linearfunction of stress. Substituting such a relation into eq. (7)(¦G = ¦G0 ¹ ¸+V ) yields a constant V for a given ­,indicating that the energy barrier resisting dislocation motionhas a rectangular potential profile. In practice, however, theobstacle profile usually possesses a finite slope (Fig. 11(c)).Thus, V also becomes a stress–dependent parameter. Thestress–dependence of thermal energy in real obstacle profilescan be generalized using two constants, 0 < p < 1 and 1 <q < 2, together with the effective stress at 0K, ^̧ (the peakstress in Fig. 11(c)), as follows [52, 92].�G ¼ �G0 1� ¸�^̧� �p� �qð17ÞFig. 17 Schematic drawings of dislocation motion via short bulge nucleation by collective thermally activated diffusion jump of multiplehydrogen atoms segregated along the dislocation core: Low hydrogen concentration (left); and high hydrogen concentration (right) [39].(online color)Fig. 18 Temperature-dependence of the local hydrogen concentrationalong dislocation lines, CT, in austenitic steel estimated from eq. (16).The inset shows the relationship between average hydrogen concentrationin the material, C0, and CT at room temperature.Phenomenology and Mechanisms of Hydrogen–Induced Solid Solution–Hardening in Fe–Cr–Ni Austenitic Steels 397Deriving the specific values of p and q in eq. (17), as well asmeasuring the stress–dependence of activation volume, areamong the tasks that the authors should initiatively dealwith. Such efforts will enable us to further elaborate on thediffusion–jump process of H within the dislocation core.Although the commercial alloy used by the authorscontained dilute H (³300 at ppm) even in the non–chargedcondition, this concentration is far lower than the regime thatfits the linear approximation in the inset of Fig. 18. In thiscase, the H along the dislocation line no longer serves as thepredominant factor for ­. Consequently, denser elementssuch as Cr and Ni may govern the “stress equivalence” ofactivation volume (Fig. 14(c)). In contrast, as can also beinferred from Fig. 18, when C0 exceeds 10000 at ppm, andH becomes highly concentrated throughout the material, CTtends to saturate even at room temperature. Figure 18 thussuggests that, in the high H concentration regime, theproportionality between H–induced solid solution–hardeningand H concentration no longer holds. Indeed, in theexperiments by Abraham and Altstetter (Section 2.1) [33],such a tendency of saturation has been observed.3.3 Roles of randomly dispersed H and H–Cr complexesUnder deformation conditions where H can followdislocation movement, the local H concentration arounddislocations is overwhelmingly higher than the average Hconcentration (Fig. 18). Therefore, the contribution of Hatoms randomly dispersed in the matrix is of limitedimportance to the dislocation’s glide resistance. However,under relatively high strain rate or at low temperatures whereH diffusion becomes infeasible, dispersed H may also playa significant role. Referring to Figs. 3 and 8 again, aconsiderable solid solution–hardening indeed appears evenunder temperatures and strain rates corresponding to Q > 100in Fig. 7. This indicates that dislocations experience someresistance when passing near H atoms occupying interstitiallattice sites. We stated in Section 2.1 that lattice strain causedby H alone cannot account for the observed solid solution–hardening. As an alternative factor, we have focused on theelectrochemical affinity between H and Cr atoms, as shown inFig. 6. The same reasoning applies to carbon and nitrogen:there exists an attractive interaction between Cr and thesethree types of interstitial elements. For carbon, a bindingenergy of approximately 0.1 eV has been reported; fornitrogen, it is about 0.2 eV [120]. If the decrease in H–absorption energy resulting from Cr substitution—comparedto an O–site surrounded solely by Fe atoms—in Fig. 6 isequal to the H–Cr binding energy (e.g., 0.05–0.10 eV for oneor two Cr atoms), its magnitude is comparable to that ofcarbon or nitrogen.When interstitial and substitutional solutes form com-plexes (i–s complexes) on the slip plane, extra energy isrequired for dislocation movement, as the motion passingthrough these i–s complexes necessitates their collapse. Thedislocations consequently experience some glide resistance.Shibata et al. conducted strain–controlled low–cycle fatiguetests of Fe–20Cr–15Ni– and Fe–15Cr–15Ni–based austeniticsteels, to which µ0.3mass% carbon was added, measuringthe flow stress fluctuation during cyclic loading [45]. Theydemonstrated that carbon promotes cyclic softening, chang-ing dislocation structures from cellular to planarconfiguration. Their findings were ascribed to the dissolutionof i–s complexes via the shuttling motion of dislocations andthe consequent glide plane softening. Similar results havealso been reported for nitrogen–added steel [46]. Theseprovide strong experimental evidence supporting thecontribution of i–s complexes to solid solution–hardening.Although H–diffusion becomes slower at low temper-atures, H atoms are still capable of jumping on a relativelyshort time scale of µ100 s even at temperatures as low as200K (Fig. 4(b)). This is markedly different from thebehavior of carbon and nitrogen. To say, even if an i–scomplex comprising H is dissolved by dislocation motion, itcan be readily repaired through subsequent diffusion jumpsof H. The repetition of such processes, which are notanticipated for carbon and nitrogen, may play a significantrole in strengthening, particularly in the later stages ofdeformation. As insistently mentioned, H–induced latticestrain alone cannot account for the observed solid solution–hardening. However, as suggested by the Snoek–type internalfriction peak [68, 70], the i–s complexes can be associatedwith anisotropic tetragonal distortion. Unlike isotropic latticeexpansion interacting only with edge dislocations, tetragonaldistortion strongly interacts with screw dislocations as well[37], potentially contributing to solid solution–hardening.Moreover, the attractive H–Cr interaction is of particularinterest for advancing and quantifying the diffusion–controlled glide model in Fig. 17. If H–Cr pairing occurswithin the dislocation core, larger energy would be requiredfor the diffusion jump of H to be decoupled from Cr undera given applied stress. This may be one of the reasons forthe correlation between Cr content and H–induced solidsolution–hardening in Fig. 5. Further elucidation of H–Crinteractions are thus highly desired, as they likely playfundamental roles in the strengthening by both segregatedand randomly dispersed H.Referring to Fig. 3(c) again, in the regime below 200Kwhere H diffusion becomes essentially infeasible, themagnitude of H–induced solid solution–hardening iscompletely independent of strain rate, in contrast to thebehavior at room temperature. This fact cannot be explainedby considering only the presence of H as individual dispersedatoms or as H–Cr pairs. One has to consider the possiblecontribution of long–range obstacles that could transformthe strengthening mechanism into an athermal process—forinstance, short–range ordered structures of H–Cr pairs inregions where Cr is stochastically enriched. A systematiccollection of experimental data will be essential to clarify thispossibility.4. Macroscopic Picture and Rate–Controlling Process ofThermally Activated Deformation under the Presenceof H4.1 Modelling deformation behavior by spring–dampersystemIn this section, from a macroscopic perspective, theaugmented stress relaxation via H–induced solid solution–hardening (Fig. 12(a)) and related phenomena are discussedbased on the nature of H as a thermally activatable obstacle.Y. Ogawa et al.398The plastic deformation wherein flow stress contains itstime–dependent component can be modeled as a viscoelasticsystem consisting of a spring and damper (Fig. 19). Thedisplacements of the spring and damper represent the elasticdeformation (Eelastic) and plastic deformation (Eplastic),respectively. The frictional resistance within the damper,which depends on deformation rate, corresponds to theeffective stress required for thermally activated dislocationmotion. In a stress relaxation test, the machine crosshead isarrested after a given amount of deformation. Then, the stressreduction is recorded as a function of time. This operationcorresponds to the illustration in Fig. 19(a-1): under aconstant total strain (Etotal), the gradual contraction of thespring (a decrease in elastic strain) is replaced by thedisplacement in the damper (an increase in plastic strain), asrepresented by stages ②–③ in Fig. 19(a-1).The involvement of H as short–range (thermal) obstaclescan be represented as an increase in the frictional coefficientof the damper—the proportionality constant linking thefrictional resistance with the deformation rate (Fig. 19(a-2)).The variation of such frictional resistance is illustrated by thegradient shading on the right side of Fig. 19(a-2). When atotal strain, Etotal, is applied at a given strain rate, the greaterfrictional coefficient in the H–charged specimen temporarilymakes the spring deformation, Eelastic, larger and the damperdeformation, Eplastic, smaller (Fig. 19(a-2) ②). A greaterEelastic implies that the specimen is subjected to a higherload—emergence of H–induced solid solution–hardening(Fig. 19(a-2) ②). A key point here is the experimentallyobserved increase in strain rate sensitivity, S, in the H–charged specimen (Fig. 14), which is physically equivalentto an increase in frictional coefficient in the damper. Thisindicates that the H–charged specimen exhibits a greaterchange in frictional resistance when the deformation rate ischanged by a given magnitude. Consequently, upon haltingthe crosshead, the slowing down of the deformation rate leadsto a more rapid decrease in frictional resistance. Driven bythe stronger pulling force due to a larger Eelastic, a morepronounced spring contraction then occurs (Fig. 19(a-2) ③).The augmented stress relaxation in Fig. 12(a) virtuallyreflects such a process.The authors reproduced a similar process through room–temperature creep tests on H–charged Type310S steel [91].Unlike stress relaxation with a constant total strain, plasticdeformation proceeds under a constant load in the case ofcreep. This operation corresponds to the illustration inFig. 19(b-1)—a given total strain is first applied, followedby a load–holding. During the load–holding period, thespring part remains fixed, while only the damper partcontinues to deform with time. Until applying the same totalstrain to both non–charged and H–charged specimens(Fig. 19(b-2)), the process is essentially identical to theprevious case shown in Fig. 19(a). However, once the load–holding starts, both the spring deformation (i.e., applied load)and the decreasing rate of the damper’s frictional resistanceare greater in the H–charged specimen than those in thenon–charged specimen—just as in the stress relaxation case.Considering these higher applied load and lower frictionalresistance in the H–charged specimen, one can expect a fastercreep rate.Figures 20(a) and (b) show the stress–strain curve and thecorresponding creep curve in the tests wherein the specimenwas first deformed at a constant strain rate, followed by load–holding. As predicted from Fig. 19(b), when the load washeld at the same total strain, the amount of creep during theholding period was clearly larger in the H–charged specimen.In contrast, Figs. 20(c) and (d) present the creep behaviorof the H–charged specimen when the load was immediatelyreduced to match the level in the non–charged specimenbefore holding. In terms of Fig. 19(b), this procedure(a-1) (a-2)(b-2)(b-1)(a)(b)Fig. 19 Spring-dumper representations of (a) stress relaxation (constant strain) and (b) creep (constant stress) deformation in elasto-plasticsolids. (a-1) and (b-1) represent non-charged state where frictional coefficient of dumper is small, while (a-2) and (b-2) denote H-chargedcondition with large dumper friction owing to solute hydrogen atoms working as thermal obstacles.Phenomenology and Mechanisms of Hydrogen–Induced Solid Solution–Hardening in Fe–Cr–Ni Austenitic Steels 399corresponds to inserting an additional step between stages ②and ③—the spring deformation is restored to the same levelas that in the non–charged specimen. Under such conditions,even at stress levels where pronounced creep is observed inthe non–charged specimen, the creep in the H–chargedspecimen is suppressed dramatically. This suppression ofcreep under an identical load indicates an increase indamper’s frictional coefficient assumed in Fig. 19.4.2 Stress–dependence of rate–controlling factorsIt is worth envisaging that how the series of H–effects onstress relaxation and creep can be represented in the modelcontext in Fig. 17. Figure 21 reproduces the model byviewing it from above the slip plane. In general, junctionswith forest dislocations act as relatively strong and extendedobstacles [92, 96, 121]. Therefore, a moving dislocationmay bow–out between these strong pinning points viasuccessively overcoming weaker, more localized, and closelyspaced obstacles—namely, H atoms—by thermal activation(Fig. 21(a-1)). Let us reconsider the physical sense ofobstacle width in thermal activation. When the same force,F1, acts on both forest dislocation and H atom from a(a) (b)(c) (d)Fig. 20 Room temperature creep behavior of non-charged and hydrogen-charged Type310S austenitic steel [91]. In (a) and (b), 1000 sload holdings were implemented during normal tensile tests, while hydrogen-charged specimen was unloaded to the same flow stresslevel with the non-charged specimen before load holding in (c) and (d). The inset in (d) magnifies the creep curves in H-chargedspecimen.(c) (d)(b)(a)Fig. 21 Schematic illustration of the stress-dependent change of rate-controlled obstacles for thermally activated plastic flow in thepresence of solute H [91]. Mobile dislocation can successively overcome H and forest dislocations at (a) high stress, while surmountingthe latter obstacle type becomes difficult at (b) low stress due to the glide resistance against dislocation by H. (c) and (d) represent thestress-dependence of ¦G in the obstacle profiles with different width. (online color)Y. Ogawa et al.400dislocation line, the thermal energy, ¦G, required toovercome these obstacles is inevitably larger for a moreextended obstacle—forest dislocation (¦Gd)—than for Hatom (¦Gf ) (Figs. 21(c-1) and (c-2)). Consequently, under agiven applied stress, the frequency of which a dislocationsurmounts H atoms is overwhelmingly higher than that forforest dislocations. To shorten the time required forovercoming a forest dislocation to the same level as for H,an extra force, F2, must be supplied (Fig. 21(c-3)), so as toreduce ¦Gd until ¦Gd = ¦Gf. F2 is provided by the linetension force acting on the forest dislocations from thebowing–out segment of the moving dislocation line(Fig. 21(a-1)). As time progresses, the bow–out segmentdecreases its radius of curvature. Once the curvature and linetension force reach a critical level, the mobile dislocationovercomes forest dislocation and exhibits long–range motion.Figure 21(d) illustrates such competition between obstacletypes in terms of the stress–dependence of ¦G. If activationenergies at ¸+ = 0 for forest dislocation and H are denoted as¦G0d and ¦G0f, then assuming ¦Gd > ¦Gf and Vd > Vf(for simplicity, both obstacles are assumed to haverectangular potential profiles), the stress dependence of¦Gd and ¦Gf can be expressed as two straight lines. Theintersection between these two lines corresponds to¦Gd = ¦Gf. A similar schematic diagram was first proposedby Schoeck [122], and later demonstrated in computationalsimulations on solid–solution alloys by Curtin and co–workers [121].As is evident from Fig. 21(d), the deformation kineticsunder high–stress (above the “Critical condition” inFig. 21(d)) is solely governed by ¦Gf, while a smallerbarrier ¦Gd no longer serves as the rate–controlling factor.Consequently, the experimentally measurable activationparameters are also dominated by ¦Gf. The ¦Gf–governeddomain expands with increasing difference between Vd andVf—that is, with increasing H concentration. This accountswell for the experimental trend in the Haasen plot(Fig. 14(a)), where the contribution of forest dislocation toS becomes less apparent (i.e., the slope decreases) as the Hconcentration increases. Meanwhile, as the applied stressdecreases and ¦Gf increases (Fig. 21(c-1)), the dislocationmotion via overcoming H atoms may sharply slow down.This slowdown not only affects the dislocation segmentsconfined between forest junctions. Rather, it also lowers therate at which forest dislocations are surmounted, through adecrease in the line tension force acting on the mobile–forestjunctions. In other words, under low–stress, the rate–controlling process shifts to the stage where mobiledislocations dragging H to overcome forest junctions. Thesuppression of creep at low stresses in H–charged specimens(Figs. 20(c) and (d)) can thus be rationalized on this basis.5. Summary and Future PerspectivesIn Fe–Cr–Ni austenitic steels, interstitial H produces solidsolution–hardening comparable to that achieved by carbon ornitrogen. In the present paper, the phenomenology of suchH–induced solid solution–hardening was addressed, review-ing the principal experimental findings reported to date—namely, that (i) the strengthening exhibits its peak at specifictemperature and strain rate, (ii) it is linearly proportional to Hconcentration, and (iii) it strongly depends on Cr content inthe alloy. Based on the state and diffusivity of H within thematerial, the underlying mechanisms governing H–inducedsolid solution–hardening were discussed in terms of threeessential factors:1). Solute drag of H atmosphere surrounding dislocations(Section 3.1)2). Diffusion–controlled glide of dislocation core with H(Section 3.2)3). Resistance from randomly dispersed H and i–scomplexes (Section 3.3)Although some discussions remain qualitative, we believethat the combination and interplay of these three factors cancollectively account for the phenomenological characteristicsof H–induced solid solution–hardening, the changes inthermally activated deformation behavior, and the “stressequivalence” upon H–addition.Figure 22 summarizes the contributions of these factors1)–3) to solid solution–hardening on a temperature–strainrate map, assuming a mobile dislocation density correspond-ing to the vicinity of yield stress (μm = ³1012/m2). Thegradient shading in the map indicates that, when theresponsible factors are associated with H segregated atdislocations, the local H concentration should decrease atelevated temperatures (Fig. 18), leading to a reducedstrengthening capability. In addition, when the obstacles arethermally activatable in nature, dislocations can more easilyovercome them at higher temperatures and lower strain rates,further diminishing the strengthening. H–induced solidsolution–hardening manifests most effectively when syner-gistic contributions from 1)–3) reach their maximum.According to the authors’ experiments, this optimal conditioncorresponds to deformation at around 300K and strain rateson the order of 10¹5–10¹4/s.The dashed lines in Fig. 22 delineate the temperature andstrain rate ranges experimentally verified in this study, which,however, represent only a small fraction of the overallparameter space. Expanding coverage into the unexploredregions is essential for reinforcing and refining the presentFig. 22 Temperature- and strain rate-dependent changes and synergies ofthe mechanisms responsible for hydrogen-induced solid solution-harden-ing in Fe-Cr-Ni austenitic steels at their yield stress. The fade-out of fillingcolor denotes the weakening contribution of each mechanism. (onlinecolor)Phenomenology and Mechanisms of Hydrogen–Induced Solid Solution–Hardening in Fe–Cr–Ni Austenitic Steels 401framework. In particular, systematic data acquisition below200K—where H diffusivity drops sharply—will be crucialfor clarifying the role of i–s complexes, the most uncertainaspect at present. During post–yield deformation at roomtemperature, where the mobile dislocation density increasesrapidly, and the solute drag regime in Fig. 22 shifts towardhigher strain rates, diffusion–controlled glide is expected todominate. Although the current modeling reproduces theobserved behavior reasonably well, the atomic–scalemechanisms—especially H transport within dislocation coresand the role of alloying elements—remain unresolved. Futureprogress will require quantitative experiments linking theactivation parameters of dislocation motion and H diffusion,the interaction energies between H and substitutional atoms,and the potential profile of H as a short–range obstacle.Complementary computational approaches, such as molecu-lar dynamics simulations, will likewise be indispensable.Moreover, effects unique to FCC alloys (e.g., dislocationdissociation into partials) and deformation–induced defects(e.g., vacancies) are also expected to play a key role. Theseconcerted efforts—including the authors’ forthcomingwork—are anticipated to advance a more comprehensiveunderstanding of H–induced solid solution–hardening.AcknowledgementsThe series of research presented in this paper wassupported by JSPS KAKENHI (Nos. 21K14045 and24K17180), the JFE 21st Century Foundation, the IwataniNaoji Foundation, and the Yoshida–Gakujutu Foundation.The authors would like to express their sincere gratitudeto Prof. Masaki Tanaka and Prof. Emeritus Kenji Higashidaof Kyushu University for their valuable advice and insightfuldiscussions on the topics presented in Section 3.2.Open AccessThis paper is open access and licensed under a CC-BY-NC-ND license. You are free to share or adapt the materialsas long as you follow the license term: Attribution,NonCommercial, and NoDerivatives. To view a copy of thislicense, visit https://creativecommons.org/licenses/by-nc-nd/4.0/.REFERENCES[1] R.P. Gangloff and B.P. Somerday: Gaseous Hydrogen Embrittlementof Materials in Energy Technologies: The Problem, its Character-isation and Effects on Particular Alloy Classes, (WoodheadPublishing, 2012).[2] M. Nagumo: Fundamentals of Hydrogen Embrittlement, 2nd ed.,(Springer, 2023).[3] L. Zhang, M. Wen, M. Imade, S. Fukuyama and K. Yokogawa: Effectof nickel equivalent on hydrogen gas embrittlement of austeniticstainless steels based on type 316 at low temperatures, Acta Mater. 56(2008) 3414–3421.[4] G. Han, J. He, S. Fukuyama and K. Yokogawa: Effect of strain-induced martensite on hydrogen environment embrittlement ofsensitized austenitic stainless steels at low temperatures, Acta Mater.46 (1998) 4559–4570.[5] M. Koyama, T. Ogawa, D. Yan, Y. Matsumoto, C.C. Tasan, K. Takaiand K. Tsuzaki: Hydrogen desorption and cracking associated withmartensitic transformation in Fe-Cr-Ni-Based austenitic steels withdifferent carbon contents, Int. J. Hydrogen Energy 42 (2017) 26423–26435.[6] T. Kanezaki, C. Narazaki, Y. Mine, S. Matsuoka and Y. Murakami:Effects of hydrogen on fatigue crack growth behavior of austeniticstainless steels, Int. J. Hydrogen Energy 33 (2008) 2604–2619.[7] M. Koyama, S. Okazaki, T. Sawaguchi and K. Tsuzaki: HydrogenEmbrittlement Susceptibility of Fe-Mn Binary Alloys with High MnContent: Effects of Stable and Metastable ε-Martensite, and MnConcentration, Metall. Mater. Trans. A 47 (2016) 2656–2673.[8] J. Yamabe, O. Takakuwa, H. Matsunaga, H. Itoga and S. Matsuoka:Hydrogen diffusivity and tensile-ductility loss of solution-treatedaustenitic stainless steels with external and internal hydrogen, Int. J.Hydrogen Energy 42 (2017) 13289–13299.[9] T. Omura, H. Hirata, M. Miyahara and T. Kudo: Effect of chemicalcompositions on embrittlement properties of stainless steels in highlypressurized gaseous hydrogen environments, Zairyo to Kankyo 57(2008) 30–36.[10] S. Takaki, S. Nanba, K. Imakawa, A. Macadre, J. Yamabe, H.Matsunaga and S. Matsuoka: Determination of hydrogen compati-bility for solution-treated austenitic stainless steels based on a newlyproposed nickel-equivalent equation, Int. J. Hydrogen Energy 41(2016) 15095–15100.[11] B.-H. Chi, T. Nakazawa and K. Shibata: Effects of alloying elementson hardening and restoration behavior of 15Cr-15Ni high hardnessnon-magnetic stainless steel, ISIJ Int. 30 (1990) 615–624.[12] K. Oda, N. Kondo and K. Shibata: X-ray absorption fine structureanalysis of interstitial (C, N)-substitutional (Cr) complexes inaustenitic stainless steels, ISIJ Int. 30 (1990) 625–631.[13] N. Ohkubo, K. Miyakusu, Y. Uematsu and H. Kimura: Effect ofAlloying Elements on the Mechanical Properties of the StableAustenitic Stainless Steel, ISIJ Int. 34 (1994) 764–772.[14] M.L.G. Byrnes, M. Grujicic and W.S. Owen: Nitrogen strengtheningof a stable austenitic stainless steel, Acta Metall. 35 (1987) 1853–1862.[15] E. Werner: Solid solution and grain size hardening of nitrogen-alloyed austenitic steels, Mater. Sci. Eng. A 101 (1988) 93–98.[16] A.W. Thompson and J.A. Brooks: The mechanism of precipitationstrengthening in an iron-base superalloy, Acta Metall. 30 (1982)2197–2203.[17] T. Hosoda, Y. Ogawa, O. Takakuwa, S. Motomura, H. Hosoi and H.Matsunaga: Effects of Ni Concentration and Aging Heat Treatmenton the Hydrogen Embrittlement Behavior of Precipitation-HardenedHigh-Mn Austenitic Steel, Tetsu-to-Hagané 108 (2022) 156–172.[18] S. Takaki, S. Tanimoto, K. Tomimura and Y. Tokunaga:Strengthening of Metastable 16–10 Austenitic Stainless Steel byUltra Grain Refining, Tetsu-to-Hagané 74 (1988) 1058–1064.[19] R. Ke, C. Hu, M. Zhong, X. Wan and K. Wu: Grain refinementstrengthening mechanism of an austenitic stainless steel: criticallyanalyze the impacts of grain interior and grain boundary, J. Mater.Res. Technol. 17 (2022) 2999–3012.[20] S. Takaki: Strengthening Mechanisms and Ultimate Strength of Iron,Materia Japan 36 (1997) 675–679.[21] K. Wada, J. Yamabe, Y. Ogawa, O. Takakuwa, T. Iijima and H.Matsunaga: Comparative study of hydrogen-induced intergranularfracture behavior in Ni and Cu–Ni alloy at ambient and cryogenictemperatures, Mater. Sci. Eng. A 766 (2019) 138349.[22] K. Ichii, M. Koyama, C.C. Tasan and K. Tsuzaki: Comparative studyof hydrogen embrittlement in stable and metastable high-entropyalloys, Scr. Mater. 150 (2018) 74–77.[23] Y. Ogawa, H. Hosoi, K. Tsuzaki, T. Redarce, O. Takakuwa and H.Matsunaga: Hydrogen, as an alloying element, enables a greaterstrength-ductility balance in an Fe-Cr-Ni-based, stable austeniticstainless steel, Acta Mater. 199 (2020) 181–192.[24] H. Nishida, Y. Ogawa and K. Tsuzaki: Chemical compositiondependence of the strength and ductility enhancement by solutehydrogen in Fe–Cr–Ni-based austenitic alloys, Mater. Sci. Eng. A836 (2022) 142681.[25] Y. Ogawa: Temperature-sensitive ductilization in hydrogen-alloyedFe-Cr-Ni austenitic steel by enhanced deformation twinning, Scr.Mater. 238 (2024) 115760.[26] Y. Murakami, T. Kanezaki and Y. Mine: Hydrogen Effect againstHydrogen Embrittlement, Metall. Mater. Trans. A 41 (2010) 2548–Y. Ogawa et al.402https://creativecommons.org/licenses/by-nc-nd/4.0/https://creativecommons.org/licenses/by-nc-nd/4.0/https://doi.org/10.1016/j.actamat.2008.03.022https://doi.org/10.1016/j.actamat.2008.03.022https://doi.org/10.1016/S1359-6454(98)00136-0https://doi.org/10.1016/S1359-6454(98)00136-0https://doi.org/10.1016/j.ijhydene.2017.08.209https://doi.org/10.1016/j.ijhydene.2017.08.209https://doi.org/10.1016/j.ijhydene.2008.02.067https://doi.org/10.1007/s11661-016-3431-9https://doi.org/10.1016/j.ijhydene.2017.04.055https://doi.org/10.1016/j.ijhydene.2017.04.055https://doi.org/10.3323/jcorr.57.30https://doi.org/10.3323/jcorr.57.30https://doi.org/10.1016/j.ijhydene.2016.06.193https://doi.org/10.1016/j.ijhydene.2016.06.193https://doi.org/10.2355/isijinternational.30.615https://doi.org/10.2355/isijinternational.30.625https://doi.org/10.2355/isijinternational.34.764https://doi.org/10.1016/0001-6160(87)90131-3https://doi.org/10.1016/0001-6160(87)90131-3https://doi.org/10.1016/0921-5093(88)90054-8https://doi.org/10.1016/0001-6160(82)90140-7https://doi.org/10.1016/0001-6160(82)90140-7https://doi.org/10.2355/tetsutohagane.TETSU-2021-093https://doi.org/10.2355/tetsutohagane1955.74.6_1058https://doi.org/10.1016/j.jmrt.2022.02.056https://doi.org/10.1016/j.jmrt.2022.02.056https://doi.org/10.2320/materia.36.675https://doi.org/10.1016/j.msea.2019.138349https://doi.org/10.1016/j.scriptamat.2018.03.003https://doi.org/10.1016/j.actamat.2020.08.024https://doi.org/10.1016/j.msea.2022.142681https://doi.org/10.1016/j.msea.2022.142681https://doi.org/10.1016/j.scriptamat.2023.115760https://doi.org/10.1016/j.scriptamat.2023.115760https://doi.org/10.1007/s11661-010-0275-62562.[27] T. Boniszewski and G.C. Smith: The influence of hydrogen on theplastic deformation ductility, and fracture of nickel in tension, ActaMetall. 11 (1963) 165–178.[28] S.K. Lawrence, Y. Yagodzinskyy, H. Hänninen, E. Korhonen, F.Tuomisto, Z.D. Harris and B.P. Somerday: Effects of grain size anddeformation temperature on hydrogen-enhanced vacancy formationin Ni alloys, Acta Mater. 128 (2017) 218–226.[29] J.S. Blakemore: The Portevin-Le Chatelier Effect in hydrogenatednickel, Metall. Trans. 1 (1970) 145–149.[30] J.S. Blakemore: The portevin-le chatelier effect in hydrogenatednickel alloys, Metall. Trans. 1 (1970) 151–156.[31] K. Wada and J. Yamabe: The effect of the Ni/Cu ratio on H-inducedductility loss and its mechanism in Cu–Ni binary alloy system, Int. J.Hydrogen Energy 46 (2021) 39577–39589.[32] O. Takakuwa, Y. Mano and H. Soyama: Increase in the local yieldstress near surface of austenitic stainless steel due to invasion byhydrogen, Int. J. Hydrogen Energy 39 (2014) 6095–6103.[33] D.P. Abraham and C.J. Altstetter: The effect of hydrogen on the yieldand flow stress of an austenitic stainless steel, Metall. Mater. Trans. A26 (1995) 2849–2858.[34] C. Sanmarchi: Effects of alloy composition and strain hardening ontensile fracture of hydrogen-precharged type 316 stainless steels, Int.J. Hydrogen Energy 33 (2008) 889–904.[35] M. Koyama, K. Ichii and K. Tsuzaki: Strain Rate and TemperatureEffects on Hydrogen Embrittlement of Stable and Metastable High-Entropy Alloys, Phys. Mesomech. 25 (2022) 385–392.[36] D. Hull and D.J. Bacon: Introduction to Dislocations, 3rd ed.,(Butterworth-Heinemann, 2011) https://doi.org/10.1016/C2009-0-64358-0.[37] P.M. Anderson, J.P. Hirth and J. Lothe: Theory of Dislocations, 3rded., (Cambridge University Press, 2017).[38] Y. Ogawa, O. Takakuwa and K. Tsuzaki: Solid-solution hardening byhydrogen in Fe–Cr–Ni-based austenitic steel: Temperature and strainrate effects, Mater. Sci. Eng. A 879 (2023) 145281.[39] Y. Ogawa, M. Tanaka, T. Fujita and A. Shibata: Thermally activateddislocation motion in hydrogen-alloyed Fe–Cr–Ni austenitic steelrevisited via Haasen plot, Int. J. Hydrogen Energy 74 (2024) 170–182.[40] Y. Ogawa and T. Fujita: Solid solution-hardening by hydrogen in Fe–Cr–Ni-based austenitic steel studied by strain rate sensitivitymeasurement: Contributions of effective stress and solute drag,Mater. Sci. Eng. A 911 (2024) 146941.[41] J. Moriyama, O. Takakuwa, M. Yamaguchi, Y. Ogawa and K.Tsuzaki: The contribution of Cr and Ni to hydrogen absorptionenergy in Fe-Cr-Ni austenitic systems: A first-principles study,Comput. Mater. Sci. 232 (2024) 112650.[42] J.C. Slater: Atomic Radii in Crystals, J. Chem. Phys. 41 (1964) 3199–3204.[43] H.M. Ledbetter and M.W. Austin: Dilation of an fcc Fe–Cr–Ni alloyby interstitial carbon and nitrogen, Mater. Sci. Technol. 3 (1987) 101–104.[44] P. Marshall: Austenitic Stainless Steels: Microstructure and Mechani-cal Properties, (Springer, 1984).[45] K. Shibata, M. Kogita, C.-S. Chen and T. Fujita: Effects of Carbonand Silicon on Softening in Low-cycle Fatigue of Austenitic StainlessSteels, Trans. Iron Steel Inst. Jpn. 28 (1988) 406–412.[46] K. Shibata, N. Namura, Y. Kishimoto and T. Fujita: Low CyclicFatigue Softening of Austenitic Stainless Steels, Tetsu-to-Hagané 69(1983) 2076–2083.[47] T. Ito, Y. Ogawa, W. Gong, W. Mao, T. Kawasaki, K. Okada, A.Shibata and S. Harjo: Role of solute hydrogen on mechanicalproperty enhancement in Fe–24Cr–19Ni austenitic steel: An in situneutron diffraction study, Acta Mater. 287 (2025) 120767.[48] D.G. Ulmer and C.J. Altstetter: Phase relations in the hydrogen-austenite system, Acta Metall. Mater. 41 (1993) 2235–2241.[49] X.W. Zhou, C. Nowak, R.S. Skelton, M.E. Foster, J.A. Ronevich, C.San Marchi and R.B. Sills: An Fe–Ni–Cr–H interatomic potential andpredictions of hydrogen-affected stacking fault energies in austeniticstainless steels, Int. J. Hydrogen Energy 47 (2022) 651–665.[50] C. San Marchi, T. Michler, K.a. Nibur and B.P. Somerday: On thephysical differences between tensile testing of type 304 and 316austenitic stainless steels with internal hydrogen and in externalhydrogen, Int. J. Hydrogen Energy 35 (2010) 9736–9745.[51] K.J. Irvine, T. Gladman and F.B. Pickering: The strength of austeniticstainless steels, J. Iron Steel Inst. 207 (1969) 1017–1028.[52] D. Caillard and J.L. Martin: Thermally Activated Mechanisms inCrystal Plasticity, 1st ed., (Pergamon, 2003).[53] A. Van Den Beukel: Theory of the effect of dynamic strain aging onmechanical properties, Phys. Status Solidi A 30 (1975) 197–206.[54] U.F. Kocks: Kinetics of solution hardening, Metall. Trans. A 16(1985) 2109–2129.[55] X. Zhang, R. Takahashi, T. Akiyama and J. Yagi: Carburization Rateinto Solid Iron at CO-CO2 Atmosphere, Tetsu-to-Hagané 83 (1997)299–304.[56] P. Thibaux, A. Métenier and C. Xhoffer: Carbon DiffusionMeasurement in Austenite in the Temperature Range 500 °C to900 °C, Metall. Mater. Trans. A 38 (2007) 1169–1176.[57] M.I. Ismail, S.S. Iskander and E.B. Saleh: Carburizing of steels, Surf.Technol. 12 (1981) 341–349.[58] A. Kühl, D. Bergner, H.-J. Ullrich, M. Schlaubitz and P. Karduck:Investigations of nitrogen diffusion in austenitic CrNi steels,Mikrochim. Acta 107 (1992) 295–302.[59] R. Hales and A.C. Hill: The diffusion of nitrogen in an austeniticstainless steel, Met. Sci. 11 (1977) 241–244.[60] J. Hirvonen and A. Anttila: Annealing behavior of implanted nitrogenin AISI 316 stainless steel, Appl. Phys. Lett. 46 (1985) 835–836.[61] T. Perng and C.J. Altstetter: Effects of deformation on hydrogenpermeation in austenitic stainless steels, Acta Metall. 34 (1986)1771–1781.[62] Y. Mine and T. Kimoto: Hydrogen uptake in austenitic stainless steelsby exposure to gaseous hydrogen and its effect on tensiledeformation, Corros. Sci. 53 (2011) 2619–2629.[63] C. San Marchi, B. Somerday and S. Robinson: Permeability,solubility and diffusivity of hydrogen isotopes in stainless steels athigh gas pressures, Int. J. Hydrogen Energy 32 (2007) 100–116.[64] O. Takakuwa, J. Yamabe, H. Matsunaga, Y. Furuya and S. Matsuoka:Comprehensive Understanding of Ductility Loss Mechanisms inVarious Steels with External and Internal Hydrogen, Metall. Mater.Trans. A 48 (2017) 5717–5732.[65] J. Moriyama, M. Yamaguchi and O. Takakuwa: Effects ofantagonistic interaction between Cr and Ni on hydrogen solubilityin a Fe-Cr-Ni ternary austenitic system: A first-principles calculation,Mater. Today Commun. 40 (2024) 110059.[66] K. Hirata, S. Iikubo and H. Ohtani: First-principles Calculations ofthe Effects of Mn, Cr, and Ni on Hydrogen Diffusion in BCC, FCC,and HCP Fe, Tetsu-to-Hagané 105 (2019) 231–239.[67] E.J. Song, H.K.D.H. Bhadeshia and D.-W. Suh: Interaction ofaluminium with hydrogen in twinning-induced plasticity steel, Scr.Mater. 87 (2014) 9–12.[68] N. Ide, T. Naito and S. Asano: Internal friction peak in FCC Fe-Cr-Nialloys hydrogen-charged by gas-equilibration method, Jpn. J. Appl.Phys. 44 (2005) 8088–8090.[69] S. Asano, R. Tsunoda and R. Otsuka: Internal Friction due toHydrogen in Austenitic Stainless Steels, J. Japan Inst. Metals 41(1977) 338–344.[70] V.G. Gavriljuk, H. Haänninen, S.Y.U. Smouk, A.V. Tarasenko andK. Ullakko: Internal friction in hydrogen-charged CrNi and CrNiMnaustenitic stainless steels, Metall. Mater. Trans. A 27 (1996) 1815–1821.[71] A.H. Cottrell: Dislocations and Plastic Flow in Crystals, (OxfordUniv. Press, New York, 1953).[72] H.K. Birnbaum and P. Sofronis: Hydrogen-enhanced localizedplasticity—a mechanism for hydrogen-related fracture, Mater. Sci.Eng. A 176 (1994) 191–202.[73] M. Kurkela and R.M. Latanision: The effect of plastic deformation onthe transport of hydrogen in nickel, Scr. Metall. 13 (1979) 927–932.[74] R. Matsumoto, S.T. Oyinbo, M. Vijendran and S. Taketomi:Hydrogen Effect on the Mobility of Edge Dislocation in α-Iron: ALong-Timescale Molecular Dynamics Simulation, ISIJ Int. 62 (2022)2402–2409.[75] A.H. Cottrell and M.A. Jaswon: Distribution of solute atoms round aslow dislocation, Proc. R. Soc. Lond. A 199 (1949) 104–114.[76] R. Fuentes-samaniego, R. Gasca-Neri and J.P. Hirth: Solute drag onPhenomenology and Mechanisms of Hydrogen–Induced Solid Solution–Hardening in Fe–Cr–Ni Austenitic Steels 403https://doi.org/10.1007/s11661-010-0275-6https://doi.org/10.1016/0001-6160(63)90209-8https://doi.org/10.1016/0001-6160(63)90209-8https://doi.org/10.1016/j.actamat.2017.02.016https://doi.org/10.1007/BF02819254https://doi.org/10.1007/BF02819255https://doi.org/10.1016/j.ijhydene.2021.09.140https://doi.org/10.1016/j.ijhydene.2021.09.140https://doi.org/10.1016/j.ijhydene.2014.01.190https://doi.org/10.1007/BF02669643https://doi.org/10.1007/BF02669643https://doi.org/10.1016/j.ijhydene.2007.10.046https://doi.org/10.1016/j.ijhydene.2007.10.046https://doi.org/10.1134/S1029959922050010https://doi.org/10.1016/C2009-0-64358-0https://doi.org/10.1016/C2009-0-64358-0https://doi.org/10.1016/j.msea.2023.145281https://doi.org/10.1016/j.ijhydene.2024.06.113https://doi.org/10.1016/j.ijhydene.2024.06.113https://doi.org/10.1016/j.msea.2024.146941https://doi.org/10.1016/j.commatsci.2023.112650https://doi.org/10.1063/1.1725697https://doi.org/10.1063/1.1725697https://doi.org/10.1179/mst.1987.3.2.101https://doi.org/10.1179/mst.1987.3.2.101https://doi.org/10.2355/isijinternational1966.28.406https://doi.org/10.2355/tetsutohagane1955.69.16_2076https://doi.org/10.2355/tetsutohagane1955.69.16_2076https://doi.org/10.1016/j.actamat.2025.120767https://doi.org/10.1016/0956-7151(93)90393-7https://doi.org/10.1016/j.ijhydene.2021.09.261https://doi.org/10.1016/j.ijhydene.2010.06.018https://doi.org/10.1002/pssa.2210300120https://doi.org/10.1007/BF02670415https://doi.org/10.1007/BF02670415https://doi.org/10.2355/tetsutohagane1955.83.5_299https://doi.org/10.2355/tetsutohagane1955.83.5_299https://doi.org/10.1007/s11661-007-9150-5https://doi.org/10.1016/0376-4583(81)90028-5https://doi.org/10.1016/0376-4583(81)90028-5https://doi.org/10.1007/BF01244484https://doi.org/10.1179/msc.1977.11.7.241https://doi.org/10.1063/1.95901https://doi.org/10.1016/0001-6160(86)90123-9https://doi.org/10.1016/0001-6160(86)90123-9https://doi.org/10.1016/j.corsci.2011.04.022https://doi.org/10.1016/j.ijhydene.2006.05.008https://doi.org/10.1007/s11661-017-4323-3https://doi.org/10.1007/s11661-017-4323-3https://doi.org/10.1016/j.mtcomm.2024.110059https://doi.org/10.2355/tetsutohagane.TETSU-2018-070https://doi.org/10.1016/j.scriptamat.2014.06.007https://doi.org/10.1016/j.scriptamat.2014.06.007https://doi.org/10.1143/JJAP.44.8088https://doi.org/10.1143/JJAP.44.8088https://doi.org/10.2320/jinstmet1952.41.4_338https://doi.org/10.2320/jinstmet1952.41.4_338https://doi.org/10.1007/BF02651931https://doi.org/10.1007/BF02651931https://doi.org/10.1016/0921-5093(94)90975-Xhttps://doi.org/10.1016/0921-5093(94)90975-Xhttps://doi.org/10.1016/0036-9748(79)90322-3https://doi.org/10.2355/isijinternational.ISIJINT-2022-311https://doi.org/10.2355/isijinternational.ISIJINT-2022-311https://doi.org/10.1098/rspa.1949.0128moving edge dislocations, Philos. Mag. A 49 (1984) 31–43.[77] H. Yoshinaga and S. Morozumi: The solute atmosphere round amoving dislocation and its dragging stress, Philos. Mag. 23 (1971)1367–1385.[78] H. Yoshinaga and S. Morozumi: A Portevin-Le Chatelier effectexpected from solute atmosphere dragging, Philos. Mag. 23 (1971)1351–1366.[79] R.B. Sills and W. Cai: Solute drag on perfect and extendeddislocations, Philos. Mag. 96 (2016) 895–921.[80] E.N. Epperly and R.B. Sills: Transient solute drag and strain aging ofdislocations, Acta Mater. 193 (2020) 182–190.[81] Y. Estrin and L.P. Kubin: Local strain hardening and nonuniformityof plastic deformation, Acta Metall. 34 (1986) 2455–2464.[82] T.H. Alden: Theory of mobile dislocation density: Application to thedeformation of 304 stainless steel, Metall. Trans. A 18 (1987) 51–62.[83] T. Zirkle, L. Costello and D.L. McDowell: Crystal PlasticityModeling of Hydrogen and Hydrogen-Related Defects in InitialYield and Plastic Flow of Single-Crystal Stainless Steel 316L, Metall.Mater. Trans. A 52 (2021) 3961–3977.[84] W.G. Johnston and J.J. Gilman: Dislocation velocities, dislocationdensities, and plastic flow in lithium fluoride crystals, J. Appl. Phys.30 (1959) 129–144.[85] H. Saka: Classical Theory of Crystal Dislocations: From Iron toGallium Nitride, (World Scientific Pub Co Inc, 2017).[86] R. Horiuchi, H. Yoshinaga and S. Hama: New Yielding Phenomenonin Some Aluminium Alloys at High Temperatures, Trans. Japan Inst.Metals 6 (1965) 123–130.[87] R. Horiuchi and H. Yoshinaga: Mechanism of the High TemperatureYield Point Phenomenon in Some Aluminium Alloys, Trans. JapanInst. Metals 6 (1965) 131–138.[88] G. Girardin, C. Huvier, D. Delafosse and X. Feaugas: Correlationbetween dislocation organization and slip bands: TEM and AFMinvestigations in hydrogen-containing nickel and nickel–chromium,Acta Mater. 91 (2015) 141–151.[89] S. Wang, A. Nagao, K. Edalati, Z. Horita and I.M. Robertson:Influence of hydrogen on dislocation self-organization in Ni, ActaMater. 135 (2017) 96–102.[90] Q. Sun, J. He, A. Nagao, Y. Ni and S. Wang: Hydrogen-promptedheterogeneous development of dislocation structure in Ni, ActaMater. 246 (2023) 118660.[91] Y. Ogawa and A. Shibata: Plastic flow in Fe-Cr-Ni austenitic steelunder the presence of solute H: A study via room temperature creep,Acta Mater. 285 (2025) 120659.[92] U.F. Kocks, A.S. Argon and M.F. Ashby: Thermodynamics andKinetics of Slip, Prog. Mater. Sci. 19 (1975) 1–291. https://linkinghub.elsevier.com/retrieve/pii/0079642575900055.[93] J.L. Martin, B. Lo Piccolo, T. Kruml and J. Bonneville: Character-ization of thermally activated dislocation mechanisms using transienttests, Mater. Sci. Eng. A 322 (2002) 118–125.[94] P. Groh and R. Conte: Stress relaxation and creep in α-ironfilamentary single crystals at low temperature, Acta Metall. 19(1971) 895–902.[95] P. Spätig, J. Bonneville and J.-L. Martin: A new method for activationvolume measurements: application to Ni3(Al,Hf ), Mater. Sci. Eng. A167 (1993) 73–79.[96] A.G. Evans and R.D. Rawlings: The Thermally ActivatedDeformation of Crystalline Materials, Phys. Status Solidi B 34(1969) 9–31.[97] U.F. Kocks: Superposition of Alloy Hardening, Strain Hardening, andDynamic Recovery, in: Strength of Metals and Alloys, (Elsevier,1979) pp. 1661–1680. https://doi.org/10.1016/B978-1-4832-8412-5.50250–2.[98] R.A. Mulford: Analysis of strengthening mechanisms in alloys bymeans of thermal-activation theory, Acta Metall. 27 (1979) 1115–1124.[99] P. Haasen: Plastic deformation of nickel single crystals at lowtemperatures, Philos. Mag. 3 (1958) 384–418.[100] Y. Dong, T. Nogaret and W.A. Curtin: Scaling of DislocationStrengthening by Multiple Obstacle Types, Metall. Mater. Trans. A41 (2010) 1954–1960.[101] W.A. Curtin: New interpretation of the Haasen plot for solute-strengthened alloys, Scr. Mater. 63 (2010) 917–920.[102] S. Mishra, V.K. Beura, A. Singh and M. Yadava: Effect of obstaclestrength and spacing on the slope of Haasen plot, Mater. Sci. Technol.35 (2019) 403–408.[103] S. Saimoto: The Characterization of Materials by Precision StrainRate Sensitivity, J. Eng. Mater. Technol. 109 (1987) 230–235.[104] S. Saimoto and B.J. Diak: Advanced method for structure-strength-ductility assessment of dispersion-strengthened FCC metals usingactivation work, mean slip distance and constitutive relation analyses:Decoding the Haasen plot, Mater. Sci. Eng. A 828 (2021) 142119.[105] J.A. del Valle, A.C. Picasso and R. Romero: The superposition offlow stress contributions in a precipitate hardened Ni-based alloystudied by strain rate sensitivity measurements, Acta Mater. 51 (2003)6443–6452.[106] H. Mecking and U.F. Kocks: Kinetics of flow and strain-hardening,Acta Metall. 29 (1981) 1865–1875.[107] A.H. Cottrell and R.J. Stokes: Effects of temperature on the plasticproperties of aluminium crystals, Proc. R. Soc. Lond. A 233 (1955)17–34.[108] Z.S. Basinski, R.A. Foxall and R. Pascual: Stress equivalence ofsolution hardening, Scr. Metall. 6 (1972) 807–814.[109] N.F. Mott and F.R.N. Nabarro: Dislocation theory and transient creep,in: Physical Society Bristol Conference Report, (1948) pp. 1–19.[110] R.L. Fleischer: Substitutional solution hardening, Acta Metall. 11(1963) 203–209.[111] R.L. Fleischer: Solution hardening, Acta Metall. 9 (1961) 996–1000.[112] R. Labusch: A Statistical Theory of Solid Solution Hardening, Phys.Status Solidi B 41 (1970) 659–669.[113] J.C. Fisher: Application of Cottrell’s theory of yielding to delayedyield in steel, Trans. ASM 47 (1955) 451–462.[114] R. Kirchheim: Reducing grain boundary, dislocation line and vacancyformation energies by solute segregation. I. Theoretical background,Acta Mater. 55 (2007) 5129–5138.[115] R. Kirchheim: Revisiting hydrogen embrittlement models andhydrogen-induced homogeneous nucleation of dislocations, Scr.Mater. 62 (2010) 67–70.[116] J. Friedel: Dislocations, 1st ed., (Pergamon Press, 1964).[117] A. Atrens, N.F. Fiore and K. Miura: Dislocation damping andhydrogen pinning in austenitic stainless steels, J. Appl. Phys. 48(1977) 4247–4251.[118] Y. Yagodzinskyy, M. Ivanchenko and H. Hänninen: Hydrogen-Dislocation Interaction in Austenitic Stainless Steel Studied withMechanical Loss Spectroscopy, Solid State Phenomena 184 (2012)227–232.[119] R.A. Oriani: The diffusion and trapping of hydrogen in steel, ActaMetall. 18 (1970) 147–157.[120] V.G. Gavriljuk and H. Berns: High Nitrogen Steels Structure,Properties, Manufacture, Applications, (Springer, 1999).[121] Y. Dong and W.A. Curtin: Thermally activated plastic flow in thepresence of multiple obstacle types, Model. Simul. Mater. Sci. Eng.20 (2012) 075006.[122] G. Schoeck: The superposition of thermal activation in dislocationmovement, Phys. Status Solidi A 87 (1985) 571–581.Y. Ogawa et al.404https://doi.org/10.1080/01418618408233426https://doi.org/10.1080/14786437108217008https://doi.org/10.1080/14786437108217008https://doi.org/10.1080/14786437108217007https://doi.org/10.1080/14786437108217007https://doi.org/10.1080/14786435.2016.1142677https://doi.org/10.1016/j.actamat.2020.03.031https://doi.org/10.1016/0001-6160(86)90148-3https://doi.org/10.1007/BF02646221https://doi.org/10.1007/s11661-021-06357-8https://doi.org/10.1007/s11661-021-06357-8https://doi.org/10.1063/1.1735121https://doi.org/10.1063/1.1735121https://doi.org/10.2320/matertrans1960.6.123https://doi.org/10.2320/matertrans1960.6.123https://doi.org/10.2320/matertrans1960.6.131https://doi.org/10.2320/matertrans1960.6.131https://doi.org/10.1016/j.actamat.2015.03.016https://doi.org/10.1016/j.actamat.2017.05.073https://doi.org/10.1016/j.actamat.2017.05.073https://doi.org/10.1016/j.actamat.2022.118660https://doi.org/10.1016/j.actamat.2022.118660https://doi.org/10.1016/j.actamat.2024.120659https://linkinghub.elsevier.com/retrieve/pii/0079642575900055https://linkinghub.elsevier.com/retrieve/pii/0079642575900055https://doi.org/10.1016/S0921-5093(01)01124-8https://doi.org/10.1016/0001-6160(71)90082-4https://doi.org/10.1016/0001-6160(71)90082-4https://doi.org/10.1016/0921-5093(93)90339-Ghttps://doi.org/10.1016/0921-5093(93)90339-Ghttps://doi.org/10.1002/pssb.19690340102https://doi.org/10.1002/pssb.19690340102https://doi.org/10.1016/B978-1-4832-8412-5.50250%E2%80%932https://doi.org/10.1016/B978-1-4832-8412-5.50250%E2%80%932https://doi.org/10.1016/0001-6160(79)90129-9https://doi.org/10.1016/0001-6160(79)90129-9https://doi.org/10.1080/14786435808236826https://doi.org/10.1007/s11661-010-0229-zhttps://doi.org/10.1007/s11661-010-0229-zhttps://doi.org/10.1016/j.scriptamat.2010.07.003https://doi.org/10.1080/02670836.2019.1567043https://doi.org/10.1080/02670836.2019.1567043https://doi.org/10.1115/1.3225969https://doi.org/10.1016/j.msea.2021.142119https://doi.org/10.1016/j.actamat.2003.08.014https://doi.org/10.1016/j.actamat.2003.08.014https://doi.org/10.1016/0001-6160(81)90112-7https://doi.org/10.1098/rspa.1955.0243https://doi.org/10.1098/rspa.1955.0243https://doi.org/10.1016/0036-9748(72)90052-Xhttps://doi.org/10.1016/0001-6160(63)90213-Xhttps://doi.org/10.1016/0001-6160(63)90213-Xhttps://doi.org/10.1016/0001-6160(61)90242-5https://doi.org/10.1002/pssb.19700410221https://doi.org/10.1002/pssb.19700410221https://doi.org/10.1016/j.actamat.2007.05.047https://doi.org/10.1016/j.scriptamat.2009.09.037https://doi.org/10.1016/j.scriptamat.2009.09.037https://doi.org/10.1063/1.323410https://doi.org/10.1063/1.323410https://doi.org/10.4028/www.scientific.net/SSP.184.227https://doi.org/10.4028/www.scientific.net/SSP.184.227https://doi.org/10.1016/0001-6160(70)90078-7https://doi.org/10.1016/0001-6160(70)90078-7https://doi.org/10.1088/0965-0393/20/7/075006https://doi.org/10.1088/0965-0393/20/7/075006https://doi.org/10.1002/pssa.2210870220