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[Kazuho Okada](https://orcid.org/0000-0003-0183-4528), [Kaneaki Tsuzaki](https://orcid.org/0000-0003-2400-7605), [Eri Nakagawa](https://orcid.org/0000-0002-8784-0138), [Akinobu Shibata](https://orcid.org/0000-0001-8577-6411)

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[Fatigue Limit Doubling in High‐Strength Martensitic Steel through Crack Embryo Engineering–Cyclic‐Training‐Driven Self‐Optimization](https://mdr.nims.go.jp/datasets/5c55ac6f-2b75-41d3-92f5-216fcfd1c891)

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Fatigue Limit Doubling in High‐Strength Martensitic Steel through Crack Embryo Engineering–Cyclic‐Training‐Driven Self‐OptimizationRESEARCH ARTICLEwww.advancedscience.comFatigue Limit Doubling in High-Strength Martensitic Steelthrough Crack Embryo Engineering–Cyclic-Training-DrivenSelf-OptimizationKazuho Okada,* Kaneaki Tsuzaki, Eri Nakagawa, and Akinobu ShibataAchieving superior fracture resistance under cyclic loading–specifically, ahigh-fatigue limit–is crucial for ensuring structural safety and supporting asustainable society. This study demonstrates a breakthrough in overcomingthe conventional fatigue limit ceiling in high-strength as-quenchedmartensitic steel by enhancing resistance to crack initiation. In theas-heat-treated state, high-angle boundaries with large elastic misfits andplastic incompatibility served as precursory sites for intrusions/extrusions(these are defined as “crack embryos”), eventually leading to fatigue crackinitiation. Remarkably, after the pre-fatigue training, surface crack initiation isentirely suppressed, doubling the fatigue limit with minimal change in tensilestrength. A novel concept of “crack embryo engineering” is introduced, whichtargets the prevention of crack embryo formation by extracting intrinsicmicrostructural self-optimization against fatigue deformation: macroscopichardness homogenization and selective nano-hardening of the precursorysites. This self-optimization strategy offers a versatile approach to improvingfatigue limit in general steels, providing an effective alternative to temperingheat treatment that inevitably sacrifices tensile strength.1. IntroductionTo achieve a safe and sustainable society, the durability and re-liability of metallic components, in addition to high-strength,are crucial across various industries—from aerospace and au-tomotive to infrastructure and manufacturing. Cyclic loadingcan cause catastrophic failures at much lower stresses thanthose under monotonic loading, known as fatigue fracture.[1,2]Safety and reliability alone would suggest making metallic com-ponents thicker and heavier. However, thin and lightweightcomponents are essential for adopting environmentally friendlyK. Okada, K. Tsuzaki, E. Nakagawa, A. ShibataResearch Center of Structural MaterialsNational Institute for Materials Science (NIMS)Tsukuba 305-0047, JapanE-mail: okada.kazuho@nims.go.jpThe ORCID identification number(s) for the author(s) of this articlecan be found under https://doi.org/10.1002/advs.202504165© 2025 The Author(s). Advanced Science published by Wiley-VCHGmbH. This is an open access article under the terms of the CreativeCommons Attribution License, which permits use, distribution andreproduction in any medium, provided the original work is properly cited.DOI: 10.1002/advs.202504165solutions through energy savings and re-ducing carbon emissions in such indus-tries as automotive. To simultaneouslymeet these demands, establishing designguidelines for materials with high fa-tigue resistance is crucial.[3–6] As shown inFigure 1a, the fatigue limit (𝜎W, expressedby stress amplitude) of steel increasesproportionally with tensile strength (𝜎B),following 𝜎W = 0.42𝜎B at a stress ra-tio (R) of 0 for furnace/air-cooled steels[7](plus marks) and tempered martensiticsteels[7c,8,9] (cross marks). However, when𝜎B exceeds ≈1.4 GPa, further increasesin 𝜎B do not improve or rather decrease𝜎W, that is, the “fatigue limit ceiling”.Consequently, the practical application ofultra-high-strength steel is restricted.[10]Generally, 𝜎W equals the higher of the“crack initiation limit” and “crack non-propagation limit”. The crack initiationlimit is defined as the maximum stress be-low which no cracks initiate. On the otherhand, the crack non-propagation limit isthe maximum stress where cracks can initiate but do not prop-agate to final rupture. For most steels, the ceiling of the non-propagation limit becomes that of 𝜎W since the non-propagationlimit is higher than the initiation limit. Extensive research oncrack propagation/termination behaviors has demonstrated thequantitative correlation between the non-propagation limit andthe macroscopic mechanical properties, such as hardness andtensile/yield strength.[11–16] These properties correlate positivelywith the non-propagation limit because the hardness/strengthof the crack-front matrix is one of the controlling factors incrack-termination. These results indicate that the upper limit sizeof the non-propagation crack, necessary for achieving the 𝜎W–𝜎B proportional relationship, decreases with increasing the 𝜎Band becomes submicron size when 𝜎B > ≈1.4 GPa (see “Up-per limit size of non-propagation crack” and Figure S1, sup-porting information). Terminating submicron cracks is chal-lenging since there is insufficient prior plastic deformation forcrack closure.[17] This indicates an intrinsic ceiling of the non-propagation limit, while the theoretical ceiling of the crack ini-tiation limit has not been reported. Thus, improving the crackinitiation limit holdsmore potential to overcome the fatigue limitceiling.[18,19] However, a systematic framework for designing ma-terials with superior crack initiation resistance has been lacking.Adv. Sci. 2025, 12, e04165 e04165 (1 of 14) © 2025 The Author(s). Advanced Science published by Wiley-VCH GmbHhttp://www.advancedscience.commailto:okada.kazuho@nims.go.jphttps://doi.org/10.1002/advs.202504165http://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/http://crossmark.crossref.org/dialog/?doi=10.1002%2Fadvs.202504165&domain=pdf&date_stamp=2025-06-29www.advancedsciencenews.com www.advancedscience.comFigure 1. Significant improvement of fatigue limit by suppressing crack initiation via pre-fatigue deformation in as-quenched martensitic steels. a) Re-lationship between tensile strength (𝜎B) and 107 cycles fatigue limit at a stress ratio of 0 (𝜎W(0), expressed as stress amplitude). Solid black circles,green squares, and blue and red triangles indicate the non-deformed, pre-constant-loaded, pre-fatigued, and pre-fatigued + coaxing specimens, respec-tively. Furnace/air-cooled steels[7] (plusmark), temperedmartensitic steels[7c–9] (cross mark), and as-quenchedmartensitic steels[24,25,30,31] (open blackmark) are cited from the open-source database and literature. Contrary to the conventional concept that 𝜎W corresponds to the crack non-propagationlimit, the present study aimed at improving 𝜎W by controlling the stages before intrusion/extrusion (crack embryo) formation and improving the crackinitiation limit. b) Number of cycles to failure against maximum stress (smax) in the fatigue test at R = 0.1, in which the crack initiation site for eachtest is indicated with specific symbols: at the surface matrix (open mark), surface inclusion (open triangle with extended corners), subsurface inclusion(solid triangle), or non-fractured (open mark with arrow). The smax corresponding to the fatigue limit (smax-W) is converted to 𝜎W(0) using the modifiedGoodman diagram and plotted in (a).To date, conventional research on structuralmetals and alloys hasprimarily focused on the balance between tensile strength andelongation,[20–22] and the tensile properties (bulk average prop-erties) are closely related to the non-propagation limit becausecrack termination can occur throughout a material.[11–16] In con-trast, crack initiation occurs at the weakest domain in a mate-rial, which cannot be evaluated from the bulk average propertiesand is highly microstructure-dependent; thus, designing crack-initiation-resistantmaterial holds an immense potential to utilizethe microstructure.It is well known that shot peening can improve the crack initi-ation limit.[23] The compressive residual stress, introduced in thenear-surface layer, substantially reduces the effective stress dur-ing fatigue loading and suppresses crack initiation at the surface.Adv. Sci. 2025, 12, e04165 e04165 (2 of 14) © 2025 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2025, 33, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/advs.202504165 by National Institute For, Wiley Online Library on [04/09/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comHowever, in as-quenchedmartensitic steel, vital for high-strengthlow/medium-carbon steels, shot peening merely shifts the crackinitiation site from surface matrix to subsurface matrix (not toinclusion), with only a slight improvement in the 𝜎W: from 𝜎W =0.25𝜎B to 0.26𝜎B.[24] This would be due to the stress gradient in-troduced by shot peening from the surface to the interior actingas a new weak domain. A novel microstructure design strategyfor improving crack initiation resistance throughout the samplefrom surface to subsurface is crucial.Due to the low fracture resistance of as-quenched martensiticsteels, tempered martensitic steels with sacrificed 𝜎B are appliedfor structural components. Wider application of as-quenchedmartensitic steels in their highest strength would contribute toa sustainable society. In martensitic steels, the fatigue cracksinitiate from intrusions/extrusions formed along specific grainboundaries (GBs).[25,26] While intrusions/extrusions have not yetbecome cracks, the local stress concentration caused by surfaceroughness promotes local plastic deformation, leading to crackinitiation. Therefore, we newly defined intrusions/extrusions as“crack embryos”. Controlling the formation of crack embryoswould suppress crack initiation. However, it remains unclearwhy localized plastic deformation forms intrusions/extrusions atspecific GBs in martensitic structures. In the submicron/nano-crystalline materials, the intrusions/extrusions do not originatefrom persistent slip bands (PSBs) because the grain size is toosmall for the dislocation activity leading to PSB.[27,28]This study demonstrates a fatigue limit doubling, overcom-ing the conventional fatigue limit ceiling, in high-strength as-quenched martensitic steel by improving crack initiation resis-tance throughout the sample from surface to subsurface via pre-fatigue training. Additionally, we elucidated the mechanism ofi) crack initiation and ii) suppression of crack initiation in pre-fatigued specimens. Specifically, we identified sites that could po-tentially form intrusions/extrusions, that is “precursory sites ofcrack embryos”, and demonstrated successful strategies for deac-tivating them, introducing “crack embryo engineering” as a noveldesign concept for superior fatigue resistance. As shown on theright side of Figure 1a, conventional studies have primarily fo-cused on crack propagation/termination, lacking a framework tothoroughly understand and suppress crack initiation. The crackembryo engineering newly subdivides the crack initiation pro-cess into “precursory site → embryo → crack” and aims to sup-press crack initiation by systematically understanding and con-trolling the stages before crack embryo formation, unlocking anew potential of the microstructure. This study specifically tar-gets the fatigue limit at 107 cycles though the very-high-cycle fa-tigue property is also an important topic.2. Results and Discussion2.1. Significant Improvement of Fatigue Limit by Pre-FatigueDeformationIn this study, non-deformed specimens (Fe-3Mn-0.2C (wt.%)) inthe as-quenched condition served as the basematerial, alongwiththree specimens subjected to different pre-deformations: pre-constant-loaded, pre-fatigued, and pre-fatigued + coaxing. Thenon-deformed specimen exhibited 𝜎B and 0.2% proof stress (𝜎0.2)of 1615 and 1118 MPa, respectively. In the pre-deformations, themaximum stress (smax) for both the pre-constant-loaded and pre-fatigued specimens was 1000 MPa, but the stress amplitude dif-fered: 0 MPa for the pre-constant-loaded and 50 MPa for thepre-fatigued. Figure 1b shows the number of cycles to failureagainst smax in the fatigue test at R = 0.1, with crack initiationsites marked by specific symbols. The smax at the fatigue limit(smax-W) was 675, 725, and 1025 MPa in the non-deformed, pre-constant-loaded, and pre-fatigued specimens, respectively. Thepre-fatigued specimen tested at the original smax-W was furtherrepeated with the repolish/fatigue test procedure, incrementallyincreasing smax by 25–100 MPa every 107 cycles until reaching1250MPa (seemethods and Figure S2, Supporting Information):the pre-fatigued + coaxing specimen with an extraordinary highsmax-W of 1300 MPa. The term “coaxing” is used in reference tothe “coaxing effect,” where a specimen fatigued at 𝜎W does notfracture even after additional fatigue tests at slightly higher stresslevels. However, the degree and mechanism of the present coax-ing is completely different from the conventional one as dis-cussed in the following sections. The 𝜎B of the non-deformed,pre-constant-loaded, and pre-fatigued specimens were ≈1.6 GPa(Figure S3, Supporting Information). Though the pre-fatigued+ coaxing specimen showed slight softening, the softening wasminimal, maintaining a 𝜎B ≥ 1.5 GPa. The smax-W was convertedto 𝜎W at R = 0 (𝜎W(0)) using the modified-Goodman diagram[29]and plotted in Figure 1a. As-quenchedmartensitic steels typicallyexhibit 𝜎W = ≈0.27𝜎B or lower[24,25,30,31] (open black circle), no-tably lower than tempered martensitic steels. The non-deformedspecimen (solid black circle) showed a similar trend, with 𝜎W =0.20𝜎B. The 𝜎W significantly improved in the pre-fatigued (bluetriangle, 𝜎W = 0.31𝜎B) and pre-fatigued + coaxing (red triangle,𝜎W = 0.43𝜎B) specimens, successfully overcoming the fatiguelimit ceiling. However, improvement was minimal in the pre-constant-loaded specimen (green square, 𝜎W = 0.22𝜎B). The re-sults suggest that fatigue deformation, conventionally consideredharmful, can enhance fatigue resistance.2.2. New Coaxing Effect on Crack InitiationIn carbon steels, the coaxing effect has been attributed to dy-namic strain aging of carbon,[32,33] which hardens the non-propagation crack tip and enhances crack-termination ability.Conventionally, the coaxing effect is effective only with smallstress increments (below ≈5 MPa). In contrast, the stress incre-ments in this study were exceptionally large (up to 100MPa), sug-gesting a new mechanism. Figure S4 (Supporting Information)shows montages of ≈1700 optical microscopy images of the en-tire gauge part of the non-deformed specimen tested at the smax-W.The dark contrasts are contamination (enlarged in Figure S4e,Supporting Information), and no surface crack was observed.Similarly, no surface cracks appeared in any non-fractured pre-deformed specimens tested at their smax-W. Therefore, we con-cluded that the fatigue limit of the as-quenched martensiticsteels corresponded to the crack initiation limit, not the non-propagation limit. This suggests that pre-fatigue deformationand subsequent repolishing induced a novel coaxing effect oncrack initiation. Understanding this novel coaxing effect wouldestablish new design concepts for superior fatigue crack initia-tion resistance.Adv. Sci. 2025, 12, e04165 e04165 (3 of 14) © 2025 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2025, 33, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/advs.202504165 by National Institute For, Wiley Online Library on [04/09/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comFigure 2. Initiation site of the main fatigue crack in the high-strength martensitic steel. SEM images of the fracture surface around the a) surface crackinitiation site in the non-deformed specimen tested at smax = 700 MPa and b) subsurface crack initiation site in the pre-fatigued + coaxing specimentested at smax = 1325 MPa. c–e) Replication of surface crack initiation/propagation behavior in the non-deformed specimen using the surface FRASTAmethod. SEM images of the upper/lower side surfaces corresponding to the enlarged fracture surface in (a) were used. The cracked region is highlightedin yellow. f) EBSD orientation map corresponding to the white broken rectangle in (e), where the color of each martensite variant (V) represents thecrystallographic orientation along the loading direction (LD). Prior austenite grain boundaries (PAGBs), packet boundaries, and block boundaries areindicated by white broken, yellow, and black lines, respectively. g) Stereographic triangle showing Young’s modulus in each tensile orientation (Ehkl). h)Stereographic projection showing the in-lath-plane primary slip systems in V13&16 and V14&17.2.3. Mechanism of Surface Crack InitiationFigure 2a shows an SEM image of the fracture surface of thenon-deformed specimen tested at smax = 700 MPa (just abovesmax-W). Radial patterns spread out from the enlarged rectangulararea. The enlarged view reveals striated patterns on the smoothsurface propagating from the lower left to the upper right, in-dicating crack initiation at the lower left surface. In contrast,the crack initiated at a subsurface inclusion in the pre-fatigued+ coaxing specimen (Figure 2b). Since the fatigue limit of thepresent martensitic steels corresponded to the crack initiationlimit, the results suggest that suppressing surface crack initia-tion significantly improved the fatigue limit. Namely, the crackinitiation limit at the surface was improved and surpassed thatat the subsurface. We emphasize that repolishing after the pre-deformation is equivalent to cutting out smaller specimens froma pre-deformed material (see Experimental Section), which dif-fers from merely retarding crack initiation. In materials withcoarse grains (∼ tens of micrometers), cracks initiate from in-trusions/extrusions formed along slip bands within a grain. Re-moving these intrusions/extrusions by slight polishing forcesthe material to undergo the same process of re-forming intru-sions/extrusions before crack initiation, thereby extending fa-tigue life.[34] However, the crack initiation mechanism remainsunchanged; the slip bands within a grain re-develop into intru-sions/extrusions and further cracks. No improvement in the fa-tigue limit was reported in the previous study. Namely, the previ-ous report is the mere retardation, not the suppression, of crackinitiation. On the other hand, this study is the first to report thatpre-fatigue training and subsequent repolishing fundamentallysuppresses and changes the crack initiation mechanism, leadingto the significant improvement in the fatigue limit.To identify the exact crack initiation site in the non-deformedspecimen, the surface crack initiation/propagationwas replicatedusing the surface FRASTA method (see Experimental Section)(Figure 2c–e). SEM images of the upper/lower side surfaces cor-responding to the enlarged fracture surface in Figure 2a wereused. The cracked region is yellow-highlighted. The crack initi-ation site, indicated by a black arrow in Figure 2c, matches thelocation identified in Figure 2a. Figure 2f is the EBSD orientationmap corresponding to the white broken rectangle in Figure 2e,where the color of each martensite variant (V) represents thecrystallographic orientation along the loading direction (LD). Thefatigue crack was initiated within the mixed region of V13&16(red) and V14&17 (blue) in the upper left prior austenite grain(PAG), propagating parallel to their block boundaries. This re-sult aligns with our previous report that fatigue cracks prefer-entially initiate at high-angle GBs in as-quenched martensiticsteel.[25] Figure 2g is a stereographic triangle showing Young’smodulus in each LD (Ehkl). The Ehkl in any orientation wasAdv. Sci. 2025, 12, e04165 e04165 (4 of 14) © 2025 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2025, 33, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/advs.202504165 by National Institute For, Wiley Online Library on [04/09/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comcalculated from the elastic stiffness coefficients measured by insitu neutron diffraction under tensile loading (see Experimen-tal Section, Figure S5a–c, Supporting Information). The maxi-mum and minimum Ehkl are 250 GPa (E111) and 164 GPa (E100),respectively. The Ehkl of V13&16 was 168 GPa, much smallerthan that of V14&17 (241 GPa), demonstrating a significant elas-tic misfit. Slip deformation, governed by the stress concentra-tion due to elastic anisotropy rather than the Schmid factor (Sf),has shown by elastoplastic self-consistent modeling[35] and 3Dcrystal plasticity finite element analysis.[36] When two dissimilarmaterials are bonded, an abnormally high-stress field (a singu-lar stress field) arises at their interfaces, especially at intersec-tions with free surface.[37] A significant difference in Ehkl meansthat the neighboring variants are elastically “dissimilar” in theLD, generating a large singular stress field at the GBs, espe-cially at their intersection with the specimen surface. There-fore, we presume that the singular stress field due to the elas-tic misfit between adjacent variants caused local yielding even atthe smax (700 MPa), well below the 𝜎0.2 (1118 MPa). In marten-sitic steel, the slip system parallel to the lath (habit) plane (in-lath-plane slip system) is preferentially activated at small strainregimes (below 8%).[38,39] For the {011}<111> slip systems, theprimary in-lath-plane systems in V13&16 and V14&17 were (1-10)[-1-11] (Sf = 0.444) and (1-10)[111] (Sf = 0.388), respectively(Figure 2h). The 63.4° angle between these slip directions demon-strates significant plastic incompatibility. At the surface, due tothe lower geometrical constraint from adjacent variants, eachvariant is expected to deform into a shape strongly influenced bythe activity of the primary in-lath-plane slip system. Therefore,greater plastic incompatibility leads to more pronounced sur-face roughness—i.e., intrusions/extrusions—at high-angle GBs,which gradually accelerates crack initiation autocatalytically viaadditional stress concentration originating from the geometricalroughness.[25] Similarly, we confirmed that the main cracks wereinitiated along the surface high-angle GBs with significant elas-tic misfit and plastic incompatibility in the pre-constant-loaded(Figure S6, Supporting Information) and pre-fatigued (FigureS7, Supporting Information) specimens tested just above theirsmax-W. In the pre-fatigued specimens at smax = 1025 MPa, oneoutlier (short-life ≈7 × 106 cycles, blue triangle with extendedcorners in Figure 1b) was confirmed. This would be attributed tothe crack initiation at a surface inclusion (Figure S8, SupportingInformation). Otherwise, the crack initiation sites were surfacehigh-angle GBs in all the pre-fatigued, pre-constant-loaded, andnon-deformed specimens. Therefore, in the pre-fatigued speci-men, the increase in the crack initiation limit at surface high-angle GBs improved the fatigue limit; however, the increase wasinsufficient to change the crack initiation mechanism. On theother hand, in the pre-fatigued + coaxing specimen, the crackinitiation limit at surface high-angle GBs increased sufficientlyto surpass that at subsurface inclusions, changing in the crackinitiation mechanism.The elastic misfit and plastic incompatibility across intru-sion/extrusion (Figure 3a,b) and microcrack (Figure 3c,d) wereinvestigated in the fractured non-deformed specimen (smax =800 MPa). To discuss the relationship between the fatigue limitand crack initiation mechanisms, specimens tested at stress lev-els close to the smax-W must be analyzed. Unfortunately, since thesmax-W of the non-deformed specimen is 675 MPa and no micro-cracks or intrusions/extrusions other than the main crack wereobserved at stress levels below 800 MPa, all features in the spec-imens tested at 800 MPa were analyzed. To minimize the stressconcentration effects due to main crack propagation, observa-tions were made over 2 mm away from the fracture surface. Toquantify elastic misfit, we introduced the elastic misfit factor (fE),ranging from 0 (no misfit) to 1 (maximum misfit), defined asfollows:fE =|||E𝛼 − E𝛽|||E111 − E100(1)where E𝛼 and E𝛽 are Ehkl of variants adjacent to the intru-sion/extrusion or crack. Plastic incompatibility was quantifiedby the angle between primary in-lath-plane slip directions (𝜃S).In Figure 3a,b, the intrusion/extrusion, indicated by a black ar-row, was formed along the PAGB between V2&5 in PAG(i) andV14&17 in PAG(ii), with fE = 0.87 and 𝜃S = 70.1°. Similarly, the fEand 𝜃S of 14 other intrusions/extrusions were analyzed and plot-ted in Figure 3e (plus marks). The microcrack along the PAGB(Figure 3c,d) included 8 variant boundary segments (5 variantcombinations), whose fE and 𝜃S, along with those of the maincrack initiation sites (Figure 2, and S7, Supporting Information),are plotted in Figure 3e. Most data points are concentrated in thelarge fE and 𝜃S region, statistically supporting the crack initia-tion mechanism significantly affected by the elastic misfit andplastic incompatibility. In contrast, segments 1 and 8 arrestedthe microcrack, and the crack width was exceptionally narrow atsegment 4 (Figure 3c), suggesting that these segments retardedcrack initiation/propagation. These segments are the PAGB be-tween V9&12 in PAG(i) and V9&12 in PAG(ii), with exceptionallysmall fE (0.07). This further highlights the significance of elasticmisfit.Therefore, the singular stress field due to the elastic misfit be-tween the adjacent variants induces local yielding, and, especiallyat the surface, plastic incompatibility causes intrusion/extrusion(crack embryo) formation. Additional stress concentration origi-nating from the geometrical roughness of intrusions/extrusionsaccelerates crack initiation. Namely, the precursory sites of crackembryos are the high-angle GBs with large elastic misfits in LDand plastic incompatibility.2.4. Mechanism of Crack Initiation SuppressionThe increase in smax-W does not align with the trends in tensileproperties, such as 𝜎B, proof stresses, and elastic limit, indicat-ing they are not responsible for the crack initiation suppression(Figure S3, Supporting Information). The residual stress relativeto the non-deformed specimen (𝜎res), obtained by neutron diffrac-tion (see Experimental Section and Figure S5, Supporting Infor-mation), decreases as smax-W increases. However, the reductions(50–100MPa) are too small to account for the significant increasein smax-W (up to 625 MPa). The results demonstrate that crack ini-tiation, locally occurring in the weakest regions, cannot be ex-plained by macroscopic average properties.The macroscopic hardness distribution across microstruc-ture and the nano-hardness corresponding to lath martensiticstructure were examined through 1681 micro-Vickers and 1200Adv. Sci. 2025, 12, e04165 e04165 (5 of 14) © 2025 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2025, 33, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/advs.202504165 by National Institute For, Wiley Online Library on [04/09/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comFigure 3. Elastic misfits and plastic incompatibility at the high-angle grain boundaries where intrusion/extrusion and microcrack were formed. a,c)SEM images and b,d) corresponding EBSD orientation maps of the side surface more than 2 mm away from the fracture surface in the non-deformedspecimen tested at smax = 800 MPa: (a, b) and (c, d) show an intrusion/extrusion and a microcrack, respectively. e) Elastic misfit factors and anglesbetween the primary in-lath-plane slip systems at the high-angle boundaries where main cracks (open marks), intrusions/extrusions (plus marks), andmicrocracks (cross marks) were initiated.nanoindentation tests, respectively (see Experimental Sectionand Figure S9, Supporting Information). The average Vick-ers hardness (Hvave) varied little between the specimens andshowed no correlation with smax-W (Figure S10a,b, Supporting In-formation). However, hardness distribution was homogenizedby pre-deformations, visualized in Figure 4a–d with all datapoints colored by its difference from Hvave. The smax-W increasedwith decreasing the standard deviation of hardness distribution(Figure 4e). Microstructures with wide-range hardness distribu-tions, such asmartensitic-ferritic dual-phase steel, lead to the cor-responding stress/strain concentrations; softer ferrite undergoeslarger plastic deformation, while harder martensite bears higherstress.[40,41] Naturally, in the present martensitic steel, the softerareas undergo larger plastic deformation and larger work hard-ening than the harder areas. Additionally, the reduction in stan-dard deviationwithout a change in the average value indicates notonly the hardening of soft areas but also the softening of hard ar-eas. Therefore, it is possible that the plastic deformation of thesofter area released internal residual stress in the harder areas,contributing to hardness homogenization. The local deformationbehavior of martensite is affected by the internal residual stressintroduced during the martensitic transformation; the release ofinternal residual stress leads to local softening.[42,43] Therefore,one can easily imagine that the hardness homogenization sup-pressedmacro/mesoscale concentration of effective stress/strain(including internal residual and external), suppressing crack ini-tiation.All nano-hardnesses properties were classified as “withinlath”, “on lath boundaries”, or “on high-angle GBs” (see Exper-imental Section and Figure S10c–f, Supporting Information).The standard deviations of nano-hardness were minimally af-fected by pre-deformations. However, smax-W increased linearlyAdv. Sci. 2025, 12, e04165 e04165 (6 of 14) © 2025 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2025, 33, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/advs.202504165 by National Institute For, Wiley Online Library on [04/09/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comFigure 4. Microstructural self-optimizations: hardness homogenization and selective local work hardening of precursory site. a–d) Vickers hardnessdistribution maps where 1681 data points are colored based on the difference from their average value. Relationship between the smax-W and e) thestandard deviation of Vickers hardness distribution (Hvst.dev) or f) the average nano-hardness on high-angle GB (Hnhigh-GB). Relationship between theelastic misfit factor and the Hnhigh-GB in the g) non-deformed and h) pre-fatigued + coaxing specimens; all data points (open marks) are plotted withthe average values (solid lines). i–n) Schematic illustrations showing the mechanism of the new coaxing effect on crack initiation; i,j) At high-angle GBswhere Ehkl of the adjacent variants have a large gap (i.e., precursory sites), elastic misfit originates the singular stress field. k) This causes local plasticdeformation, forming intrusion/extrusion (i.e., crack embryos). l) Additional stress concentration due to surface roughness leads to crack initiation inthe non-deformed specimen. m,n) However, in the pre-fatigued (+coaxing) specimens, the crack embryos were removed by repolishing before theybecame cracks. The precursory sites were deactivated and no longer can become crack embryos because they were selectively work hardened, improvinglocal plastic deformation resistance.Adv. Sci. 2025, 12, e04165 e04165 (7 of 14) © 2025 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2025, 33, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/advs.202504165 by National Institute For, Wiley Online Library on [04/09/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comwith the average nano-hardness on high-angle GBs (Hnhigh-GB)(Figure 4f). To correlate the increase in Hnhigh-GB with the crackinitiation mechanism, all Hnhigh-GB are plotted against fE for thenon-deformed (Figure 4g, 355 points) and pre-fatigued+ coaxing(Figure 4h, 377 points) specimens, with their average values indi-cated by solid lines. The increases in the average and minimumHnhigh-GB were more pronounced at high-angle GBs with largerfE. Figure 5a–d shows the kernel average misorientation (KAM)maps of the nanoindentation-tested regions obtained by EBSD.KAM value represents the average misorientation around eachmeasurement point relative to its nearest neighbors. Figure 5eshows the correlation between the average KAM value and av-erage Hnhigh-GB. As the orientation change increases, the aver-age Hnhigh-GB also increases. Notably, despite the same maxi-mum load during pre-deformations, the pre-fatigued specimenexhibits greater orientation changes than the pre-constant-loadedspecimen. This demonstrates that cyclic loading promoted lo-cal plastic deformation, suggesting local work hardening as theorigin of the nano-hardening. The nano-hardening is unlikelydue to the release of internal residual stress. The release of in-ternal residual stress, introduced by the martensitic transforma-tion, leads to a decrease in nano-hardness.[43] The redistributionof carbon, originating from dynamic strain aging, is also un-likely to be the cause of the nano-hardening. Since carbon atomsare supersaturated in the as-quenched martensite matrix, the re-distribution of carbon is expected to form stable states ratherthan a further increase in supersaturation:, e.g., dislocation pin-ning or carbide formation. Dislocation pinning by carbon atomsshould increase the critical load for activating dislocation mo-tion (pop-in load obtained from nanoindentation tests, Pc). How-ever, the average Pc on high-angle GBs was largely unaffectedby the pre-deformations (Figure 5f) and the fE (Figure 5g,h). Therepresentative load–penetration depth curves on high-angle GBsobtained by the nanoindentation tests are shown in Figure 5i,with the Hnhigh-GB of 8.12 (black, non-deformed) and 8.97 (red,pre-fatigued + coaxing), consistent with each specimen’s aver-age. While the Pc remains similar, work-hardening behavior dif-fers. Carbide formation would reduce thematrix hardness, whichcontradicts the nano-hardening; additionally, no carbide was ob-served in the scanning transmission electronmicroscopy (STEM)images (Figure 5j–m). Figure 5j–m shows STEM images of sam-ples prepared by focused ion beam (FIB) pickup from lathsadjacent to the nanoindentation-tested high-angle GBs shownin Figure 5i: non-deformed (j and k) and pre-fatigued + coax-ing (l and m). The observation regions were ≈5 μm below thenanoindentation-tested surface. Figure 5i–l were observed usingg-vectors to visualize dislocations with Burgers vectors either par-allel or not parallel to the laths, respectively. No characteristic dis-location structures, such as dislocation cells, were observed inthe pre-fatigued + coaxing specimen. The detailed dislocation-related mechanism of nano-hardening could not be fully eluci-dated. However, we conclude that the high-angle GBs (and neigh-boring matrix) with larger fE undergo greater local plastic defor-mation to accommodate the singular stress fields, resulting ingreater local work hardening.We propose the mechanism of the new coaxing effect; the pre-cursory sites of crack embryos (surface high-angle GBs) wereselectively plastic-deformed by a singular stress field, originat-ing from elastic misfit (Figure 4i,j). The local plastic defor-mation and possibly the resultant release of internal residualstress contributed to the macroscopic hardness homogenization.On the specimen surface, plastic incompatibility led to intru-sions/extrusions with considerable magnitude, and at this point,precursory sites became crack embryos — consequently, addi-tional stress concentration by surface roughness led to crackinitiation (Figure 4k,l). However, in the pre-fatigued (+coaxing)specimens, the surface layer including crack embryos was re-moved by repolishing before they became cracks (Figure 4m).These precursory sites were deactivated and no longer can be-come crack embryos because theywere selectively work hardenedin nano-scale. The macroscopic hardness homogenization miti-gated the macro/mesoscale stress/strain concentrations (includ-ing both internal residual and external), further contributing tothe deactivation. Namely, crack initiation was suppressed by theimproved local plastic deformation resistance and the reductionin effective localized stress (Figure 4n).2.5. Crack Embryo EngineeringWeakest-link theory, a common framework for statistical fractureanalysis, posits that the fracture strength of a material is deter-mined by its weakest domains having a certain cracking resis-tance distribution.[44] The domains with a resistance lower thanmacroscopic load can be cracked. When the fatigue limit cor-responds to the crack initiation limit, no domain should havea crack initiation resistance lower than the macroscopic load atthe fatigue limit. This study identifies the weakest domains—i.e., precursory sites of fatigue crack embryos—as the surfacehigh-angle GBs with significant elastic misfit and plastic incom-patibility in martensitic steel. Figure 6a illustrates the distribu-tion of crack initiation resistance against macroscopic load forsurface high-angle GBs in the non-deformed specimen. Beforethe fatigue test (gray line), all surface high-angle GBs can, tosome degree, be regarded as precursory sites, with resistancesvarying by microstructural factors such as fE and 𝜃S. Once aload is applied, intrusions/extrusions are, to some extent, formedalong the weak precursory sites; the resultant geometrical rough-ness causes additional stress concentration. Consequently, dur-ing/after the fatigue test (black line), the resistance distributionbroadens toward smaller macroscopic loads due to this enhancedlocal stress. Due to the plastic deformation localization, the pre-cursory sites with resistance below the macroscopic load be-come crack embryos, which autocatalytically become cracks at thesame load. Conversely, the precursory sites with resistance abovethe macroscopic load do not form cracks—even if minor intru-sions/extrusions are formed—as elastic misfit and plastic incom-patibility (and the resultant roughness-enhanced stress concen-tration) are not sufficiently large. Thus, the lowest point of the re-sistance distribution corresponds to 𝜎W, leading to nearly singlecrack initiation just above the 𝜎W (Figure 6b, gray star). Underlarger loads, many precursory sites can become crack embryos(Figure 6c, gray area), resulting in multiple simultaneous crackinitiations. No secondary cracks were found in the non-deformedspecimen tested at smax = 700 MPa (just above smax-W), whilemany secondary cracks and intrusions/extrusions appeared atsmax = 800 MPa (Figure 3). Therefore, the goal of “crack em-bryo engineering” is to elevate the lowest point of the resistanceAdv. Sci. 2025, 12, e04165 e04165 (8 of 14) © 2025 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2025, 33, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/advs.202504165 by National Institute For, Wiley Online Library on [04/09/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comFigure 5. Mechanismof selective nano-hardening of the precursory sites. a–d) KAMmaps of the nanoindentation-tested regions. e) Relationship betweenthe average KAM value and average Hnhigh-GB. f) Average pop-in load (Pc) on high-angle GBs in each specimen. Relationship between the elastic misfitfactor and the Pc on high-angle GBs in the g) non-deformed and h) pre-fatigued + coaxing specimens; all data points (open marks) are plotted withthe average values (solid lines). i) Typical load–penetration depth curves on the high-angle GBs in the non-deformed (black) and pre-fatigued + coaxing(red) specimens obtained by the nanoindentation tests. The load–penetration depth curves around the pop-in (gray broken rectangle) are enlarged. TheHnhigh-GB was 8.12 and 8.97 in the non-deformed and pre-fatigued + coaxing specimens, respectively, which are consistent with the averageHnhigh-GB ineach specimen. j–m) STEM images within laths neighboring to the high-angle GBs tested in (i): (j, k) non-deformed and (l, m) pre-fatigued + coaxing.The observation regions are located ≈5 μm below the nanoindentation measurement surface. (i, k) and (j, l) were observed using g-vectors where onlydislocations with Burgers vectors parallel or not parallel to the laths were visible, respectively; Kikuchi diffraction patterns are shown below or right-sideof each image. All the dislocations having a/2<111> Burgers vectors are visible in one of the STEM images. The visible Burgers vectors are indicated inblack arrows in each stereographic projection.Adv. Sci. 2025, 12, e04165 e04165 (9 of 14) © 2025 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2025, 33, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/advs.202504165 by National Institute For, Wiley Online Library on [04/09/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comFigure 6. Schematic illustrations showing the crack embryo engineering. a) Schematic illustrations of the distribution of crack initiation resistanceagainst macroscopic load for surface high-angle GBs in the non-deformed specimen: before the fatigue test (gray line) and during/after the fatigue test(black line). Schematic illustrations of the resistance distributions at macroscopic stresses corresponding to the fatigue limit of the b) non-deformedand c) pre-fatigued + coaxing specimens. The surface high-angle GBs (precursory sites) corresponding to the resistance distribution lower than themacroscopic load become crack embryos (intrusions/extrusions) and eventually cracks. Crack embryo(s) corresponds to (b) the lowest point of theresistance distribution just above the fatigue limit loading (gray star) and (c) a certain area under a larger loading (gray area). As indicated by redlines, the lowest point of the pre-fatigued + coaxing specimen was increased by the hardness homogenization and selective local hardening, thereby,deactivating the precursory sites. The red broken line in (b) illustrates the decomposed effect of only the hardness homogenization. Under the fatiguelimit loading of the pre-fatigued + coaxing specimen, macroscopic load corresponds to the lowest point of the resistance distribution for subsurfaceinclusions (blue line and star).distribution. Namely, a fatigue-crack-initiation-resistant mi-crostructure minimizes localized plastic deformation at specificsites—either by reducing the effective local stress or enhancingthe local plastic deformation resistance of precursory sites—bothof which directly influence the resistance distribution.Controlling the intrinsic fE and 𝜃S of a material could greatlyinfluence the resistance distribution but requires crystallogra-phy control by novel alloy design, thermomechanical treatments,or both. In contrast, the present study used pre-fatigue defor-mations for controlling the resistance distribution and demon-strated two effective crack embryo engineering strategies applica-ble to general high-strength steels. First, homogenizing macro-scopic hardness distribution (Figure 4a–e) narrowed the resis-tance distribution, elevating its lowest point without changingthe mean value (Figure 6b, red broken line). Since the averageHv remained constant, the average resistance did not improve.However, the hardness homogenization resulted from plastic de-formation (and work hardening) of relatively soft regions duringpre-deformation, and possibly from the release of internal resid-ual stress, reducing variations in intrinsic plastic deformation re-sistance and effective stress/strain concentration (including in-ternal residual and external) in the macro/mesoscale. Second,the plastic deformation resistance of the weak precursory siteswas selectively increased by the nano-hardening (Figure 4f–n), di-rectly elevating the lowest point. The combination of these effectssignificantly elevated the lowest point and deactivated the weakprecursory sites (Figure 6b, red solid line), thereby suppressingthe plastic deformation localization at these sites—that is, thecyclic-training-driven self-optimization. These self-optimizationeffects should intrinsically occur in the non-deformed speci-mens during fatigue test, while being offset by the crack em-bryos (i.e., surface roughness and resultant stress concentra-tion). The amplitude of intrusions/extrusions (crack embryos)formed in an initial few cycles significantly impacts the fatiguelimit.[45] This study successfully isolated the self-optimization ef-fects by removing crack embryos. Consequently, the lowest pointfor surface high-angle GBs exceeded that for subsurface inclu-sions (Figure 6c, blue line), changing the crack initiation mech-anism (Figure 2a,b). The detailed mechanism of fatigue crackinitiation at subsurface inclusions remains unclear. However,since this study did not adopt an approach to remove subsur-face crack embryos, the crack initiation limit at subsurface in-clusions would not be improved by the pre-deformations. Thus,controlling the lowest point of the resistance distribution is cru-cial for improving crack initiation resistance, not necessarily re-quired to change themacroscopic average properties, such as ten-sile strength, ductility, etc. It is essential to deeply understand andsuppress the formation mechanism of crack embryos among thecrack initiation process of “precursory site → embryo → crack”;this is the essence of crack embryo engineering. Revealing “whatAdv. Sci. 2025, 12, e04165 e04165 (10 of 14) © 2025 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2025, 33, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/advs.202504165 by National Institute For, Wiley Online Library on [04/09/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comconstitutes a crack embryo” in the crack initiation at subsurfaceinclusion (precursory site) would further allow for controlling thesubsurface crack initiation.3. ConclusionThis study proposes a novel strategy, crack embryo engineering,to improve crack initiation resistance, demonstrating a break-through in overcoming the conventional fatigue limit ceilingin high-strength as-quenched martensitic steel; the maximumstress corresponding to the fatigue limit significantly increasedfrom 675 to 1300 MPa by pre-fatigue training with minimalchange in tensile strength. In the as-heat-treated state, high-angleboundaries with large elastic misfits and plastic incompatibilityserved as precursory sites for intrusions/extrusions (crack em-bryos), eventually leading to crack initiation. However, after thepre-fatigue training and subsequent repolishing, surface crackinitiation was entirely suppressed by the intrinsic microstruc-tural self-optimization of (pre-)fatigue deformation: macroscopichardness homogenization and selective nano-hardening of theprecursory sites. The self-optimization deactivated the precursorysites, i.e., the formation of intrusion/extrusion was suppressed,effectively controlling the lowest point of the resistance distribu-tion for crack initiation. Crack embryo engineering is a novel ma-terial design framework that subdivides the crack initiation pro-cess into “precursory site → embryo → crack” and aims to sup-press crack initiation by systematically understanding and con-trolling the stages before crack embryo formation. The presentmicrostructural self-optimization against fatigue deformation isa successful crack embryo engineering strategy, doubling thefatigue limit with minimal change in the macroscopic averageproperties. This demonstrates that fatigue deformation, conven-tionally considered harmful, can be a beneficial and versatile ap-proach to enhancing fracture resistance in general steels, provid-ing an alternative to tempering heat treatment that inevitably sac-rifices tensile strength.4. Experimental SectionMaterial: A Fe-3Mn-0.2C ingot (Mn: 3.02, C: 0.18, Si: 0.01, Al: 0.002, S:0.001, P: <0.002, N: 0.002, O: 0.001, and Fe: balance (wt.%)) was used inthe present study. The hot-rolled plate was cold-rolled from 18 to 1.8 mmin thickness (reduction: 90%). The cold-rolled sheet was austenitized at900 °C for 30 min, ice brine quenched, and then sub-zero cooled in liquidnitrogen for 10 min.Fatigue and Tensile Tests: Figure S2a (Supporting Information) showsthe pre-deformation procedures. Sheet-type smooth specimens with agauge length of 8 mm, width of 4 mm, and thickness of 1 mm were fab-ricated from the as-heat-treated specimen (Figure S2b, Supporting Infor-mation). The specimens were mechanically wet-polished using emery pa-per from #80 to #4000 and finished by electrochemical polishing in anaqueous solution of 450 ml CH3COOH + 50 ml HCLO4 at 22 V for 90 s(referred to as non-deformed specimen). The non-deformed specimenswere uniaxially fatigue-deformed at maximum stress (smax) of 1000 MPa,frequency of 50 Hz, and stress amplitude of 50 MPa (referred to as pre-fatigued specimen) or that of 0 MPa (referred to as pre-constant-loadedspecimen) for 107 cycles (2 × 105 s). A 20–30 μm surface layer was re-moved by mechanical and electrochemical repolishing, followed by a fa-tigue test at a frequency of 50 Hz and stress ratio (R) of 0.1. It is impor-tant to emphasize that, given that a martensite lath (a single crystal) issubmicron in size, repolishing the 20–30 μm surface layer is equivalentto cutting out new small specimens from a larger pre-deformed mate-rial. As a result, the surface-specific plastic deformation history (includ-ing geometrical roughness) during pre-deformation was removed, and allgrains from the surface to the subsurface in the repolished specimen wereoriginally inside the material during the pre-deformations, having experi-enced (macroscopically) uniform training. This is fundamentally distinctfrom methods like shot peening, which induces a residual stress gradi-ent from the surface to the interior. Due to the limited load capacity ofthe testing machine, repolishing was performed for each specimen. Asshown in Figure 1b, the smax corresponding to the fatigue limit (smax-W) ofthe non-deformed, pre-constant-loaded, pre-fatigued specimenswere 675,725, and 1025 MPa, respectively. For the pre-fatigued specimens tested attheir smax-W, the repolish/fatigue test procedure with an increase in smax by25–100 MPa was repeated every 107 cycles until they fractured. The pre-fatigued specimens finally fractured at smax ≥ 1325 MPa. The pre-fatiguedspecimen tested up to smax = 1250MPa was used as the initial microstruc-ture of the pre-fatigued + coaxing specimen. Consequently, the smax-W was1300 MPa in the pre-fatigued + coaxing specimen. For comparison, the𝜎W of the present martensitic steels at R = 0.1 was converted to those atR = 0 using the modified Goodman diagram,[29] plotted in Figure 1a.𝜎W(x) = 𝜎W(−1)(1 −𝜎m(x)𝜎B)(2)where 𝜎B is tensile strength, 𝜎m(x) and 𝜎W(x) are the average stress andstress amplitude, respectively, corresponding to the fatigue limit at R =x. The fatigue test at the fatigue limit was repeated twice to confirm nofracture below that load. Uniaxial tensile tests were also performed at aninitial strain rate of 10−4 s−1 to evaluate tensile strength, proof stresses,and elastic limit. The elastic limit was defined as the nominal stress wherethe nominal stress–nominal strain curve fell by more than 5 MPa below astraight line extrapolated from the slope between 50 and 250 MPa.It should be noted that an R-value of 0.1 was selected to preserve thefracture surface morphology. At R ≤ 0, upper/lower fracture surfaces maycome into contact and deform during unloading or compression, whichcould significantly reduce the accuracy of the fracture surface topographyanalysis (FRASTA)method explained later. It was also noted that the sheet-type specimen, rather than the round-bar specimen, was intentionally usedbecause the flat surface facilitate the analysis of surface crack initiationbehavior using optical microscopy, scanning electron microscopy (SEM,ZEISS: sigma), and electron backscattered diffraction (EBSD). While edgestress concentration in the sheet-type specimen may lower the 𝜎W, it doesnot lead to an overestimation of 𝜎W, ensuring the reliability of the excellent𝜎W of the pre-fatigued + coaxing specimen shown in Figure 1.Surface FRASTA Method: FRASTA is a methodological approach thatcomputationally reconstructs microscopic fracture processes by analyzingthe topographic characteristics of corresponding areas on opposing frac-ture surfaces.[46,47] Typically, FRASTA utilizes reconstructed 3D geometrydata of the fracture surfaces. However, when the sample surface serves asthe crack initiation site, identifiable from the fracture surface, 3D data wasunnecessary. This study introduced the “surface FRASTA method” specif-ically for analyzing surface crack initiation. SEM images of upper/lowersurfaces around the crack initiation site were used. These images weresuperimposed until aligned with no visible gap, after which the relativedistance between them was incrementally increased, resulting in the ap-pearance of gaps between the two conjugate surface images. The ap-peared gaps likely correspond to fractured regions, enabling the repli-cation of surface crack initiation/propagation by sequentially increasingthe relative distance. The surface crack initiations/propagations, shownin Figure 2c–e, Figures S6b–d, S7b–d, and S8c–e (Supporting Informa-tion), were replicated using the surface FRASTA method. The fracturedregions were yellow-highlighted. The crystallographic orientations of thecorresponding areas were measured using EBSD. The EBSD measure-ment (step size: 0.1 μm, acceleration voltage: 15 kV) and analysis wereperformed with the Bruker QUANTAX-EBSD system and the TSL OIMAnalysis program, respectively. Additionally, for the specimens that didnot fracture after the fatigue test, the absence of surface cracks was con-firmed using optical microscopy (OLYMPUS: DSX1000). The entire gaugeAdv. Sci. 2025, 12, e04165 e04165 (11 of 14) © 2025 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2025, 33, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/advs.202504165 by National Institute For, Wiley Online Library on [04/09/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.compart was examined by stitching together ≈1700 images (each ≈240 μmsquare) of the front, back, left, and right surfaces (Figure S4, SupportingInformation).Lath Martensitic Structure and Variant Analysis: The lath martensitestructure is a characteristic microstructure in high-strength low/medium-carbon steels. It is well known that lathmartensite satisfies the Kurdjumov-Sachs (K-S) orientation relationship relative to parent austenite, given by{111}A//{011}M and<101>A//<111>M, where the subscripts A andMde-note austenite andmartensite, respectively. In the K-S orientation relation-ship, twenty-four equivalent crystallographic variants can be transformedfrom a single austenite grain.[48,49] This diversity of crystallographic vari-ants leads to the subdivision of an austenite grain into several struc-tural units with different size scales, namely lath, sub-block, block, andpacket.[50,51] A martensite lath is a single crystal of martensite ≈0.2 μmthick, withmisorientation between adjacent laths being less than 5°. A sub-block is an aggregation of laths of an identical variant. A block consists ofa specific combination of two variants with a small misorientation, suchas V1-V4, V2-V5, or V3-V6. The boundaries between adjacent laths (habitplanes) or adjacent blocks correspond to crystallographic planes approx-imately parallel to {011}, satisfying the parallel plane relationship in theK-S orientation relationship. A packet comprises six variants (V1 to V6, V7to V12, V13 to V18, or V19 to V24) that exhibit the same parallel planerelationship in the K-S orientation relationship. Typically, several packetsare present within each prior austenite grain (PAG). Due to the distinctcrystallographic orientations of the martensite variants, crystallographicanalysis can precisely characterize the lath martensite structure. In thisstudy, block boundaries, packet boundaries, and PAG boundaries (PAGB)were classified as high-angle boundaries. It did not differentiate betweensub-block and lath boundaries, as sub-block boundaries were not clearlydistinguishable after deformation. The average PAG size of the presentmartensitic steel measured by the line-interception method was 62 μm.In Situ Neutron Diffraction Experiment During Tensile Loading: In situneutron diffraction experiments were conducted during tensile loading tomeasure elastic constants and residual stress of the martensitic steels.These experiments were performed at the Materials and Life Science Ex-perimental Facility (MLF) of the Japan Proton Accelerator Research Com-plex (J-PARC), using the Engineering Materials Diffractometer, TAKUMI.At this facility, it was possible to measure both the lattice spacing (d) inthe loading direction (LD), which expands under tensile stress, and thatin the transverse direction (TD), which shrinks under tensile loading. De-tailed information about the TAKUMI can be found in the literature.[52] Auniaxial tensile test was conducted on the non-deformed specimen at aninitial strain rate of 1.3 × 10−5 s−1. The tensile load was held constant for5 min at various stress levels from 0 to 550 MPa. The specimen surfacewas randomly sprayed with a black pattern, which was captured every 5 sto accurately calculate the nominal strain in the LD using the digital im-age correlation (DIC) method. The diffraction profiles in the LD (FigureS5a, Supporting Information) and TD (Figure S5b, Supporting Informa-tion) for each holding stage are shown with true stress indicated on theright side. The lattice strains of each lattice plane (𝜖hkl) were calculated bythe following equation:𝜀hkl =dhkl − d0−hkld0−hkl(3)where d0-hkl is the d at 0 MPa. The d of each lattice plane was determinedby fitting the diffraction profiles to a Voigt function. The 𝜖hkl as a functionof true stress in the LD and TD are shown in Figure S5c (Supporting Infor-mation). Young’s modulus (Ehkl) and Poisson’s ratio (𝜈hkl) of each latticeplane were determined from least-squares fit slopes, as summarized inTable S1 (Supporting Information). The bulk Young’s modulus (Ebulk) andPoisson’s ratio (𝜈bulk) were calculated to be 213.6 GPa and 0.293, respec-tively, using the following equations:Ebulk =∑hklILD−hklEhkl (4)𝜈bulk =∑hklITD−hkl𝜈hkl (5)where ILD-hkl and ITD-hkl are the normalized integrated intensities of eachhkl profile in the LD and TD, respectively. Below 550 MPa, plastic defor-mation wasminimal, so the ILD-hkl and ITD-hkl remained unchanged. Elasticstiffness coefficients (s11, s12, and s44) were determined from the followingsimultaneous equations:[53]1Ehkl= s11 − ah2k2 + k2l2 + l2h2(h2 + k2 + l2) (6)a = 2s11 − 2s12 − s44 (7)1 − 2𝜈bulkEbulk= s11 + 2s12 (8)The Equation (6) was solved by the least-squares approximation usingall Ehkl in Table S1 (Supporting Information). The obtained values were s11= 6.074, s12 = -2.065, and s44 = 10.063 TPa−1. Finally, Ehkl for any arbi-trary LD was calculated using the following equations[54] and is shown inFigure 2G, Figures S6f, and S7f (Supporting Information).Ehkl =1s11 + (2s12 − 2s11 + s44)H2(9)H2 = h2k2 + k2l2 + l2h2(h2 + k2 + l2) (10)Neutron diffraction experiments were also performed on the pre-deformed specimens in the unloaded state. As illustrated by the 110peaks in Figure S5d (Supporting Information), the d0 values of the pre-deformed specimens were clearly reduced. The relative residual stressesof each lattice plane (𝜎res-hkl) and bulk average (𝜎res-bulk) relative to thenon-deformed specimen were calculated using the following equations:𝜎res−hkl =d′0−hkl − d0−hkld0−hklEhkl (11)𝜎res−bulk =∑hklILD−hkl𝜎res−hkl (12)where d’0-hkl is the lattice spacing in the pre-deformed specimens in theunloaded state. The residual stresses are presented in Figure S5e (Sup-porting Information). The 𝜎res value is 0 in the non-deformed specimenand is not shown in Figure S5e (Supporting Information) because it is thereference value.Multiscale Hardness Tests: The macroscopic distribution of hardnessacross microstructure and the nano-hardness corresponding to lathmartensitic structure were examined by conducting the micro-Vickersand nanoindentation tests, respectively. The micro-Vickers tests were per-formed with a maximum load of 490.3 mN and a holding period of 10s, using the SHIMADZU HMV-G test machine. The resultant indentationsize was ≈13 μm, which was larger than the average block width of ≈3 μm.A total of 1681 hardness measurements were taken for each specimen,with tests conducted every 50 μm within a 2 mm square area. Optical mi-croscopy images of the entire measurement area and an enlarged viewof it in the non-deformed specimen are shown in Figure S9a,b (Support-ing Information), respectively. For the nanoindentation testing, the BrukerHysitron Triboindenter TI950, equipped with a Berkovich indenter, wasused. The tests were conducted in load-control mode with a maximumload of 1000 μNand a loading rate of 50 μNs−1, resulting in an indentationsize of ≈300 nm. A total of 1200 tests were performed for each specimen,with tests conducted every 7 μm within the area (203 × 273 μm) that wasmeasured by EBSD in advance (Figure S9c, Supporting Information). Sub-sequently, 300 backscattered electron (BSE) images of the correspondingarea were captured, each containing four indentations. By comparing theBSE images (Figure S9d, Supporting Information) with the correspondingEBSD orientation maps (Figure S9e, Supporting Information), the posi-tion of each indentation was classified into within lath, on lath boundaries,Adv. Sci. 2025, 12, e04165 e04165 (12 of 14) © 2025 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2025, 33, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/advs.202504165 by National Institute For, Wiley Online Library on [04/09/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comor on high-angle GBs. It should be noted that the affected areas aroundthe nanoindentations were not considered, and the indentations overlap-ping with the boundaries were classified as “on the boundary”. Using afocused ion beam (FIB, ZEISS: Crossbeam), thin foils were lifted out fromthe nanoindentation-tested surface. The lifted-out samples were observedby scanning transmission electron microscopy (STEM, JEOL: JEM-2800)at an acceleration voltage of 200 kV.Supporting InformationSupporting Information is available from the Wiley Online Library or fromthe author.AcknowledgementsThe authors are very grateful to Dr. Takahito Ohmura and Dr. Seiichiro Iiat the National Institute for Materials Science (NIMS) for providing withopportunities to conduct the nanoindentation tests. The authors also ap-preciate Dr. Hideaki Nishikawa and Dr. Kentaro Wada in NIMS for ad-vising the fatigue test methods and specimen geometry. The neutrondiffraction experiment at the Materials and Life Science Experimental Fa-cility of the J-PARC was performed under a user program (Proposal No.2023B0198). K.O. was financially supported by the Japan Science and Tech-nology Agency ACT-X (JPMJAX23D5) and the Japan Society for the Promo-tion of Science KAKENHI (JP23K13541). A.S. was financially supported bythe Japan Society for the Promotion of Science KAKENHI (JP23K26410).Conflict of InterestThe authors declare no conflict of interest.Author ContributionsK.O., K.T., and A.S. performed conceptualization and methodology. K.O.and E.N. performed investigation and data analysis. K.O. and A.S. per-formed funding acquisition and Project administration. K.T. and A.S. per-formed supervision. K.O. performed wrote the original draft. K.T., E.N.,and A.S. performed wrote, reviewed, edited the draft.Data Availability StatementThe data that support the findings of this study are available from thecorresponding author upon reasonable request.Keywordscrack initiation, elastic anisotropy, fatigue limit, martensitic steel, plasticincompatibility, self-optimization, trainingReceived: April 24, 2025Revised: May 23, 2025Published online: June 30, 2025[1] H. Mughrabi, Philos. Trans. R. Soc. A 2015, 373, 20140132.[2] A. Pineau, D. L. McDowell, E. P. Busso, S. D. 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Advanced Science published by Wiley-VCH GmbH 21983844, 2025, 33, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/advs.202504165 by National Institute For, Wiley Online Library on [04/09/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.com Fatigue Limit Doubling in High-Strength Martensitic Steel through Crack Embryo Engineering9040�Cyclic-Training-Driven Self-Optimization 1. Introduction 2. Results and Discussion 2.1. Significant Improvement of Fatigue Limit by Pre-Fatigue Deformation 2.2. New Coaxing Effect on Crack Initiation 2.3. Mechanism of Surface Crack Initiation 2.4. Mechanism of Crack Initiation Suppression 2.5. Crack Embryo Engineering 3. Conclusion 4. Experimental Section Supporting Information Acknowledgements Conflict of Interest Author Contributions Data Availability Statement Keywords