Influence of Inhomogeneous Plastic Strain and Crystallographic Orientations on Fatigue-Induced Dislocation Structures in FCC Metals

Abstract

Owing to the differences in crystallographic orientations among individual grains, dislocation structures in polycrystals are inherently inhomogeneous from grain to grain. Since intergranular incompatibility is inevitable during plastic deformation, it may consequently lead to unpredictable plastic strain localization, which in turn facilitates the initiation of fatigue crack. Therefore, to elucidate the mechanisms underlying inhomogeneous deformation in polycrystals, this study systematically examines the fatigue-induced dislocation structures in polycrystalline SUS316L stainless steel. We then directly compare them with those in copper single crystals to clarify the dependence of the dislocation structures on crystallographic orientation. SEM characterization demonstrates that high plastic strain near grain boundaries promotes the formation of secondary cell bands (CBs) overlapping the primary CBs, which is attributable to the simultaneous activation of multiple-slip systems under high plastic strain amplitudes. In addition to strain localization, competition among candidate secondary slip systems strongly governs the dislocation structures. Notably, a new type of deformation band (DB) on the (010) plane is identified in a non-coplanar double-slip-oriented grain, a feature not observed in single crystals, indicating that polycrystals accommodate plastic strain through distinct mechanisms. Detailed dislocation structure analysis provides theoretical guidance for mitigating fatigue crack initiation through the manipulation of dislocations.

1. Introduction

The evolution of dislocation structures during cyclic loading fundamentally governs fatigue damage in metals [1,2]. Extensive research has therefore been devoted to elucidating the dislocation-mediated mechanisms underlying fatigue deformation in face-centered cubic (FCC) metals [3,4,5]. However, the complex microstructures of industrial alloys make their fatigue behavior difficult to characterize with clarity, and quantitative analysis remains challenging. The most conclusive insights into fatigue behavior have been obtained from high-purity FCC metals [6,7], where the influence of extrinsic factors such as grain boundaries and second-phase particles is minimized. Therefore, compared to industrial alloys, investigating the cyclic deformation behavior of single crystals is more feasible to facilitate a clearer understanding of, and potential solutions to, fatigue-related problems. Furthermore, the slip mode in pure FCC metals is primarily governed by stacking fault energy (SFE) [8]. For copper single crystals, with a medium SFE of ~40 mJ/m², cross-slip is readily activated, producing wavy slip that promotes screw dislocation annihilation and leads to the formation of edge multipole veins, which subsequently evolve into persistent slip bands (PSBs), labyrinths, and dislocation cell structures [9,10,11,12]. Based on the above, copper single crystals are the most suitable FCC model material for studying cyclic deformation behavior and the evolution of dislocation structures.

However, with the advancement of industry, SUS316L stainless steel has been widely employed in various applications, owing to its excellent corrosion resistance and mechanical properties [13,14]. As a structural material, polycrystalline SUS316L austenitic stainless steel also suffers from fatigue damage, similar to single crystals, when subjected to cyclic loading that induces irreversible plastic deformation [15]. The inhomogeneous accumulation of plastic strain leads to localized strain-concentrated regions. These regions, commonly located near grain boundaries (GBs) and PSBs, are considered preferential crack initiation sites from which further propagation occurs [16]. The location of these initiation sites is influenced by multiple factors, including the loading axis, strain amplitude, and crystallographic orientation [17,18,19,20,21]. However, the basic conclusions are primarily drawn under low or moderate plastic strain amplitudes, where characteristic dislocation structures have not yet developed. Therefore, elucidating the formation mechanisms of typical dislocation structures under higher plastic strain amplitudes is essential for providing a sound theoretical basis to enhance the fatigue performance of SUS316L stainless steel in practical applications.

Fatigue damage in FCC single crystals is generally initiated at the free surface under cyclic loading; accordingly, the morphology of the surface slip is a key descriptor of fatigue behavior [10,22,23]. Extensive work has shown a strong correlation between surface morphology and crack initiation [24,25,26,27,28,29]. Among the characteristic microstructural features produced by cyclic deformation, deformation bands (DBs) are particularly important and are frequently implicated in crack initiation and early propagation [30]. In fatigued copper single crystals, two mutually orthogonal families of DBs, commonly termed DBI and DBII, are observed [11]. Li et al. [31] examined their habit planes and reported that DBI lies parallel to the primary slip plane, whereas DBII is perpendicular to it. Using three-dimensional reconstruction, Ma et al. [32] further demonstrated that three DB variants can develop in a cyclically deformed [$\overline{1}11$]-oriented copper single crystal, owing to the threefold symmetry of this orientation; the specific variant is dictated by the preferred primary slip plane.

Because dislocation structures are widely regarded as the primary determinants of surface slip morphology, their formation mechanisms have been investigated extensively in fatigued copper single crystals [8,10,33,34]. Winter [35] first reported that ladder structures develop within PSBs, whereas vein structures form in the surrounding matrix of single-slip oriented specimens. Building on this, Ackermann et al. [36] performed cyclic tests on single-slip copper single crystals over plastic strain amplitude of γ_pl = 10⁻⁴–10⁻² and showed that, when γ_pl exceeds 2.0 × 10⁻³, secondary slip systems are activated; concurrently, labyrinth and dislocation cell structures appear at the surface and become progressively more distinct as the amplitude increases. Because activation of secondary slip systems is tightly coupled to structure development, dislocation interactions in double- and multiple-slip orientations are inherently complex, making the resulting morphologies strongly orientation-dependent. Using transmission electron microscopy (TEM), Li et al. [37] examined cyclically deformed coplanar double-slip-oriented copper single crystals and found that dislocation cell structures preferentially form to accommodate larger plastic strains. By contrast, Gong et al. [11] studied a critical double-slip orientation and observed the labyrinth structures produced by the concurrent operation of the critical slip and cross-slip systems during cyclic loading. These results highlight that which secondary system is activated decisively influences whether cells or labyrinths dominate the microstructure.

Building on this orientation dependence, Gong et al. [38] used TEM to examine cyclically deformed [001]-oriented copper single crystals and showed that the labyrinth structure consists of two mutually perpendicular families of dislocation walls: one set with normals along [001] (i.e., walls parallel to the (001) plane) and a second set with normals along the [100] direction. They further noted that wall arrays parallel to the (001) plane are a persistent feature of the [001] orientation. More recently, Ma et al. [39] reported that, at higher plastic strain amplitudes, such labyrinth networks can locally collapse and evolve into typical dislocation cell structures. At lower amplitudes, Li et al. [40] observed two distinctive configurations, the dislocation walls and misoriented cells, in cyclically deformed copper single crystals. In a complementary synthesis, Ma et al. [32] classified multiple types of cell bands (CBs) and concluded that the CB habit plane is perpendicular to the cross-slip plane and parallel to the primary slip direction. For misoriented cells, Ma et al. [39] analyzed crystal rotation in the cell structures formed in [001]-oriented copper single crystals and showed that, at higher plastic strain amplitudes, localized cells emerge from the surrounding labyrinth with only a weak lattice rotation, yielding relatively small misorientation angles. Based on this insight, Pan et al. [41] reported that pre-existing low-angle cell substructures can enhance cyclic strength and mitigate surface roughening by activating an unconventional fatigue-accommodation mechanism. Using multi-plane imaging with high-voltage scanning transmission electron microscopy (HV-STEM), Wang et al. [42] further demonstrated that, at elevated plastic strain amplitudes (γ_pl = 4.0 × 10⁻³), dislocation cells coalesce into well-defined CBs aligned with specific crystallographic planes, thereby accommodating the increased plastic strain. Taken together, these studies clarify the linkage between the slip systems that are activated and the orientations of the resulting dislocation architectures in copper single crystals, and they provide a foundation for analyzing analogous phenomena in polycrystals, where additional factors further modulate structure formation.

In polycrystals, deformation is intrinsically heterogeneous, producing complex dislocation structures within a single specimen. In SUS316L with randomly oriented grains, double- or multiple-slip activation during cyclic loading is expected and underpins the observed diversity of morphologies. Obrtlík et al. [14] reported that, at low plastic strain amplitude (ε_pl), vein structures dominate; with increasing ε_pl, planar dislocation arrangements become prevalent, although PSBs and veins persist in selected grains [43]. This planar character primarily reflects operation of a single primary slip system [44]. Once ε_pl exceeds a threshold, secondary systems are activated and characteristic configurations emerge, such as walls, labyrinths, and cells; this transition is strongly dependent on crystallographic orientation and on which secondary system is engaged [43]. In SUS316L, the conversion from PSBs and veins to walls and cells is typically observed only in certain grains at comparatively high strain amplitudes, roughly an order of magnitude above those required for cell formation in fatigued copper single crystals. Using TEM, Pham et al. [45,46] further documented a cycle-dependent sequence under high ε_pl: planar dislocations, veins and, labyrinth or cell structures, and showed that short fatigue cracks propagate preferentially along dislocation walls [47]. However, the inherently limited field of view of TEM hinders assessment of spatial variability across bulk polycrystals, complicating quantitative links among local orientation, strain localization, and band morphology. These limitations motivate the present use of SEM-electron channeling contrast (ECC) imaging, in concert with electron backscatter diffraction (EBSD), to investigate large areas while preserving crystallographic context.

Despite substantial progress on copper single crystals and polycrystalline SUS316L, the extent to which dislocation structure formation mechanisms are universal versus material specific remains unresolved, particularly regarding the role of inhomogeneous deformation in polycrystals. To address this gap, we compare fatigue-induced dislocation structures in copper single crystals and SUS316L polycrystals under elevated plastic strain amplitudes using SEM-ECC together with SEM-EBSD. High plastic strain amplitudes were selected to ensure that characteristic fatigue-induced dislocation structures developed over larger volume fractions of the fatigued specimens. Elastic deformation is negligible compared with the high plastic strain amplitudes considered in this work and is therefore not further discussed. These findings clarify how plastic-strain inhomogeneity governs the evolution of fatigue-induced dislocation structures in the fatigued metals which subjected to severe loading and processing operations, and provide a comprehensive microstructural framework for dislocation structures, thereby informing dislocation-engineering strategies to enhance the mechanical performance of metallic materials.

2. Materials and Methods

2.1. Preparation of Specimens

Both the [$\overline{1}11$]- and [011]-oriented copper single crystals used in this study were grown by the Bridgman method from high-purity copper (99.99%) at a growth rate of 43 mm/h and a maximum temperature of 1613 K. Their crystallographic orientations were confirmed by the Laue back-reflection technique with an accuracy of ±2°. Fatigue specimens were cut from the as-grown crystals using electrical-discharge machining (EDM, Sodick AD-325L LN1W (Sodick Co., Ltd., Yokohama, Japan)). The stress axis (S.A.) of the near-[$\overline{1}11$] specimen was parallel to the [$\overline{5}66$] direction, deviating by 3.0° from the exact [$\overline{1}11$] orientation, whereas that of the near-[011] specimens was parallel to the [$\overline{1}77$] direction with a 5.7° deviation from the exact [011] orientation. Because these deviations are small, they were regarded as negligible for the development of dislocation structures during fatigue. The S.A. orientations were plotted on the standard stereographic triangle of 001-011-$\overline{1}11$ (Figure 1). Schmid factors (S_F) for the possible slip systems were calculated according to Schmid’s law, S_F = cosλcosφ, where λ is the angle between the S.A. and the slip direction and φ is the angle between the S.A. and the slip plane. The calculated values are summarized in

Table 1. Schmid factors (S_F) of slip systems for the near-[$\overline{1}11$] and near-[011]-oriented copper single crystals used in this study.

	Slip Planes	Slip Directions	SF
[$\overline{5}66$]-oriented specimen	(111) primary	[$\overline{1}01$]	0.32
		[$\overline{1}10$] (coplanar)	0.32
	$(\overline{1}\overline{1}1$) conjugate	[011]	0.25
		[$\overline{1}10$] (coplanar)	0.23
	$(\overline{1}1\overline{1}$) cross	[011]	0.25
		[$\overline{1}01$] (coplanar)	0.23
[$\overline{1}77$]-oriented specimen	(111) primary	[$\overline{1}01$]	0.43
		[$\overline{1}10$] (coplanar)	0.43
	$(\overline{1}11$) critical	[101]	0.37
		[110] (coplanar)	0.37

.

The polycrystalline SUS316L sheet employed in this study was supplied by Aichi Steel Corporation (Aichi, Japan), and its mass-percent chemical composition is provided in

Table 2. Chemical composition of the polycrystalline SUS316L stainless steel (wt.%).

C	Si	Mn	P	S	Ni	Cr	Mo	Co	Fe
0.019	0.47	1.48	0.036	0.002	12.03	16.96	2.03	0.23	Bal.

, measured by the supplier. Fatigue specimens were machined by EDM. Figure 2 illustrates the specimen geometries for both materials. To obtain a homogeneous supersaturated solid solution and a grain size sufficient for intragranular dislocation observation, the specimens were annealed at 1373 K for 6 h in a Koyo KBF828N electric furnace and subsequently water quenched. This treatment increased the average grain size from approximately 30 μm to 100 μm, excluding twin boundaries (TBs). With larger grain size and a reduced fraction of grain boundary regions, the characteristic dislocation microstructures remain essentially the same as those observed in finer grains. GB maps of the annealed specimen are shown in Figure 3a, highlighting the GB distribution, whereas Figure 3b omits coincident site lattice (CSL) Σ3 TBs. High-angle grain boundaries (HAGBs) and low-angle grain boundaries (LAGBs) are indicated in green and red, respectively.

Prior to fatigue testing, impurities and surface oxides were removed from both the copper single crystal and SUS316L stainless steel specimens by mechanical grinding with #220 to #4000 grit emery paper. The SUS316L specimens were subsequently polished with a 1/4 μm diamond paste spray to produce a low-damage surface, facilitating micro crack detection during the fatigue tests.

2.2. Fatigue Tests

Plastic strain-controlled fatigue tests were conducted under uniaxial, symmetric cyclic tension-compression at room temperature (293 K) in air using a Shimadzu Servopulser EHF-LB2-10AL servo-hydraulic testing machine (Shimadzu Corporation, Kyoto, Japan). A Shimadzu Servopulser 4830 shape controller (Shimadzu Corporation, Kyoto, Japan) generated the repeated triangular waveform. Plastic strain amplitudes were monitored with a KFGS-3-120-C1-16 N50C2 strain gauge (Kyowa Electronic Instruments Co., Ltd., Tokyo, Japan) affixed to the center of the specimen gauge section. Detailed fatigue test conditions for the two materials are summarized in

Table 3. Fatigue testing conditions for the specimens examined in this study. C1–C3 represent copper single crystal specimens, whereas S1–S3 represent SUS316L stainless steel specimens, respectively.

Specimen No.	Plastic (Shear) Strain Amplitudes, εpl (γpl)	Saturation Stress Amplitude, $\mathit{\sigma } (\mathit{\tau }$), [MPa]	Frequency, f, [Hz]	Cycle Number, N	Cumulative Plastic Strain, εcum (γcum)
[$\overline{5}66$]-oriented specimen (C1)	γpl = 1.0 × 10−3	36	0.25	10,000	40
[$\overline{1}77$]-oriented specimen (C2)	γpl = 5.0 × 10−3	31	0.05	2000	40
[$\overline{1}77$]-oriented specimen (C3)	γpl = 1.5 × 10−2	40	0.017	220	13.2
S1	εpl = 5.0 × 10−3	320	0.05	2500	50
S2		294		2000	40
S3		324		2800	56

. C1 to C3 denote copper single crystal specimens oriented for the [$\overline{1}11$] and [011] directions, whereas S1 to S3 denote SUS316L stainless steel specimens. At the high plastic strain amplitude of 5.0 × 10⁻³, the tests on specimens S1 and S3 were interrupted at specific cycle numbers because buckling was impending. Before the tests were resumed under identical conditions, each specimen was mechanically repolished to remove surface defects and micro cracks using the same procedure applied before testing, except that emery paper coarser than #1000 was omitted. Cumulative plastic strain (ε_cum) was evaluated using the relation ε_cum = 4Nε_pl (and γ_cum = 4Nγ_pl for shear), where N represents the maximum number of loading cycles and ε_pl (γ_pl) denotes the applied plastic (shear) strain amplitude. To ensure that the total plastic deformation remained comparable and thus exerted no marked influence on the evolution of dislocation microstructures, the cumulative plastic strain was controlled to be as uniform as practicable across all specimens. In the present study, the cumulative plastic strain was controlled to be approximately 40–56 in order to ensure that all specimens had reached saturation and that the dislocation structures had stabilized. Nevertheless, the test on specimen C3 was terminated when γ_cum reached 13.2, because the extremely high plastic shear strain amplitude had already produced a noticeable surface depression. A subsequent secondary fatigue testing was foregone to prevent buckling-related damage. It should also be noted that the cumulative plastic strain is not used here as a universal parameter for describing fatigue strength, but rather as a practical measure under the uniaxial loading conditions of this study.

2.3. Dislocation Characterizations

To eliminate surface roughness generated during fatigue, all specimens were mechanically repolished, strictly following the identical sequence of abrasive papers employed before testing, and were subsequently subjected to an electrolytic polishing step. For copper single crystals and SUS316L stainless steel, electrolytes of CH₃OH:HNO₃ = 4:1 and CH₃COOH:HClO₄ = 9:1, respectively, were employed; detailed conditions appear in

Table 4. Electropolishing conditions for the copper single crystals and SUS316L stainless steel.

	Electrolyte	Voltage	Temperature	Time
Copper single crystals	CH3OH:HNO3 = 4:1	8 V	243 K	30 min
SUS316L stainless steel	CH3COOH:HClO4 = 9:1	35 V	280 K–293 K	2 min

. Characterization was carried out on a field-emission scanning electron microscope (FE-SEM, JEOL JSM-7001F (JEOL Ltd., Tokyo, Japan)). ECC imaging technique, operating at 20 kV with a working distance of 4 mm, was applied to visualize fatigue-induced dislocation microstructures. EBSD was used to obtain Euler angles of selected reference points and thus crystallographic orientation information, employing an accelerating voltage of 15 kV and a 15 mm working distance. For the polycrystalline steel, EBSD measurements were performed in grains of with different orientations within the same sites examined by ECC. The S.A. indices of each grain were determined using the crystal orientation matrix obtained from the EBSD Euler angles, which transforms vectors from the specimen reference frame to the crystal coordinate system.

Because grain orientations in the bulk SUS316L specimens are uniformly distributed, a unified crystallographic analysis scheme is essential to ensure that results from the copper single crystal and the polycrystalline stainless steel are directly comparable. Accordingly, the S.A. of each analyzed grain was remapped into the standard stereographic triangle bounded of 001-011-$\overline{1}11$, so that the primary slip system is unequivocally specified as (111) [$\overline{1}01$]. Consequently, the roster of potentially active slip systems becomes identical for the two materials when their grain orientations coincide, enabling subsequent discussion of deformation mechanisms on a common basis.

3. Results

3.1. Mechanical Response

Figure 4a illustrates the cyclic hardening curves (CHCs) recorded for the fatigued copper single crystal specimens. The blue dashed line corresponds to specimen C1 oriented for the [$\overline{5}66$] direction, whereas the black and red dashed lines trace specimens C2 and C3, respectively, both with the [$\overline{1}77$] direction, but tested at distinct shear strain amplitudes. These amplitudes were deliberately selected to explore amplitude-dependent cyclic strengthening behavior and dislocation microstructures. The shear stress amplitude represents the maximum resolved shear stress on the primary slip system in the single crystals, calculated by multiplying the nominal stress amplitude with the S_F of the (111) [$\overline{1}01$] primary slip system. The general trend of the cyclic stress–strain response agrees with findings reported by Li et al. [40] and Gong et al. [11]. Irrespective of crystallographic orientation, every specimen exhibits a pronounced rise in shear stress amplitude during the first several tens of cycles, reflecting that the rapidly proliferating dislocation becomes an increasingly effective barrier to further glide. The subsequent hardening rates, however, diverge appreciably among the three curves. Although Jin and Winter [48] linked variations in initial hardening rates to the effects of crystallographic orientation in double-slip-oriented copper single crystals, the disparities observed here are attributed mainly to the different shear strain amplitudes imposed during the present investigation. For C3, which experienced the highest shear stress amplitude, the initial cyclic hardening rate far exceeds those of C1 and C2, and this hardening stage is promptly followed by a pronounced stress decline. The drop arises from the formation of new dislocation structures which more effectively accommodate the imposed plastic strain. All three specimens subsequently enter a saturation regime in which the shear stress amplitudes remain nearly constant; the terminal saturation stresses for C1, C2, and C3 are 36 MPa, 31 MPa, and 40 MPa, respectively. Although C3 still exhibits a slight downward trend at the end of testing, the associated softening proceeds at a moderate pace, indicating that saturation has essentially been reached. Throughout this extended plateau constituting the bulk of the fatigue life, the class of dislocation arrangements does not change; instead, only the relative proportions of the various configurations evolve. A previous investigation [32] demonstrated that a larger softening rate promotes extensive formation of cell structures and DBs. Accordingly, the 22.7% softening observed for C3 implies a correspondingly greater volume fraction of such cell structures.

Figure 4b presents the CHCs for the SUS316L stainless steel specimens, S1 to S3 plotted as blue, black, and red solid lines, respectively. As with the copper single crystals, each curve exhibits a swift rise in stress amplitude during the early cycles, followed by a prolonged quasi-steady plateau that persists to the end of testing. This close resemblance in shape is chiefly ascribed to the comparable plastic strain amplitudes applied. None of the stainless steel specimens show the pronounced softening or abrupt stress drop recorded for copper specimen C3, which endured the highest strain amplitude. The stainless steel experiments were ceased after cumulative plastic strain of 50, 40, and 56, respectively. For S1, S2, and S3, the saturation stress which is defined as the final recorded value amounts to 320 MPa, 294 MPa, and 324 MPa, and is in good accord with previous reports [45]. The slightly higher saturation levels observed for S1 and S3 are attributed to the extra hardening imparted by their secondary fatigue tests. Although a tendency toward buckling was noted in S1 and S3, optical microscopy (OM) inspection revealed no actual damage after the first loading segment. Importantly, all three specimens reach essentially identical saturated states at termination, ensuring comparable dislocation microstructures and thereby validating subsequent microstructural comparisons.

3.2. ECC and EBSD Characterization of Dislocation Microstructures

3.2.1. Near-[$\overline{1}11$]-Oriented Copper Single Crystals

Figure 5a displays a strain-concentrated region where DBs are densely developed in the [$\overline{5}66$]-oriented copper single crystal fatigued at a plastic shear strain amplitude of 1.0 × 10⁻³ (specimen C1). A comparable hierarchy of dislocation structures has been reported for crystals of the same orientation, in which CBs evolve together with surrounding vein structures [32,40,49]. Variations in local strain accordingly alter both the number and the nature of activated slip systems, ultimately generating multiple dislocation structures confined to a narrow region, particularly along the specimen edge. Figure 5b presents the [$19 79 \overline{59}$] stereographic projection derived from EBSD data acquired along the observation axis of the ECC image. The transverse direction (TD) [826] and the normal direction (ND) [$19 79 \overline{59}$] were extracted using the crystal orientation matrix calculated from the EBSD-derived Euler angle of the reference point selected in the respective regions. All stereographic projections presented in this work were obtained using the same method. The crystallographic orientations of the DBs, CBs, and vein-like structures are identified in the enlarged ECC micrographs marked in Figure 5a (see Figure 5c,d)). The CBs are found to lie on the ($\overline{2}1\overline{1}$) plane within the ($\overline{1}1\overline{1}$) DBI. Moreover, these DBIs extend toward the interior of the bulk specimen, underscoring a pronounced tendency for strain localization. As the cellular morphology progressively fades, the DBI terminates at distances ranging from several tens to roughly one hundred micrometers from the specimen edge, signaling a relaxation of localized plastic strain. Beyond the DBI, the microstructure is governed by vein-like structures comprising alternating dislocation channels and densely packed bundles. Approaching the DB boundaries, these bundles tighten into wall structures, from which dislocation cells nucleate along the undulating walls. Unlike the vein arrays formed perpendicular to the primary slip plane under single-slip conditions [7,40,50,51], the vein-like structures observed here do not lie on the ($\overline{1}01$) plane; rather, they align parallel to the ($1\overline{1}\overline{2}$) plane. A similar multiple-slip-induced vein geometry was documented by Ma et al. [39] in near-[001]-oriented copper single crystals, closely resembling the present observations. In this [$\overline{5}66$]-oriented specimen, a mixture of vein-like arrays and CBs within the DBs dominates the microstructure at the edges and shoulders, whereas vein structures alone prevail throughout the remainder of the specimen.

3.2.2. Near-[011]-Oriented Copper Single Crystals

For the near-[011] orientation, the dislocation morphology exhibits subtle changes. Figure 6a presents representative arrangements in specimen C2 oriented for the [$\overline{1}77$] direction, captured at a relatively large field of view. Throughout the bulk, dense walls on the exact ($\overline{1}01$) plane constitute the predominant feature, while CBs occasionally nucleate on the (111) primary slip plane and coalesce to form the DBIIs that develop roughly parallel to the primary slip plane. Figure 6b, viewed from the S.A. direction, depicts the same structures from a complementary perspective. This dual-plane observation verifies that the DBIIs are inclined by approximately 15° with respect to the ($\overline{1}01$) plane. This is consistent with Li et al. [7] who reported DBIIs on the ($\overline{1}01$) plane and characterized the accompanying walls as PSB walls. In the present study, however, the DBII consists of CBs rather than the PSB walls described in earlier work. In fact, PSB morphology is seldom encountered in the current specimens; instead, fully developed dislocation walls extend uniformly across the microstructure without segregating into discrete bands. When the applied shear strain amplitude is raised to 1.5 × 10⁻² in specimen C3, as illustrated in Figure 6c,d, the overall dislocation morphology remains essentially unchanged, yet the contrast between adjacent CBs intensifies, indicating a greater concentration of plastic strain within the DB. Concurrently, the DB align strictly parallel to the ($\overline{1}01$) plane, and the cells become markedly elongated rather than equiaxed. Both the channel width separating neighboring walls and the average cell dimension shrink at the higher strain amplitude, with the former decreasing from 1.10 µm to 0.82 µm and the latter contracting from 0.89 µm to 0.56 µm. In addition, the volume fraction occupied by DBII rises appreciably: from roughly 30% to nearly 80% though the macroscopic scale of each DB shows no detectable change.

3.2.3. Polycrystalline SUS316L Stainless Steel

Dislocation structures in cyclically deformed polycrystals exhibit far greater variety than in the single crystals. Because plastic strain is distributed heterogeneously, numerous combinations of slip systems may be activated, yielding distinct structures arrangements even among grains that share similar crystallographic orientations. Typical dislocation structures formed both by single-slip and multiple-slip have been found in SUS316L stainless steel over a wide range of plastic strain amplitude [45,46,47,52]; however, the relationship between crystallographic orientation and dislocation structures have not yet been clarified. In the grain from specimen S1 depicted in Figure 7a, typical DBs develop adjacent to TBs. Remarkably, a narrow ($\overline{1}11$) DBI with roughly 10 µm wide intrudes into a neighboring (111) DBI; both domains are surrounded by the (111) and ($\overline{1}11$) twins. The core region of these DBIs, highlighted by a white dashed rectangle, is enlarged in Figure 7b. For this grain, whose S.A. oriented for the [$22 \overline{67} \overline{71}$] direction, the secondary slip activated is the coplanar slip system. Consequently, once the plastic strain amplitude becomes sufficiently large, CBs emerge [53]. Within the (111) DBI, two arrays of CBs develop on planes whose plane normals differ by only a few degrees, identified as the (111) and (121) planes; the former occupies nearly the entire DB region, whereas the latter appears only occasionally. Notably, the two segments of the (111) DBI separated by the intervening ($\overline{1}11$) DBI contain identical CBs. The narrow ($\overline{1}11$) DBI itself consists of a single family of CBs, although the current viewing geometry precludes a definitive distinction between traces belonging to the ($\overline{1}\overline{1}1$) and ($\overline{2}\overline{1}1$) planes. Despite the coexistence of several CB variants in this heavily deformed grain, the (111) type CBs clearly predominate. Grain reference orientation deviation (GROD) angle maps reveal misorientation angles of ~3° between adjacent CBs inside both the (111) and ($\overline{1}11$) DBIs, confirming their mature development. In certain extreme zones near the twin boundary, several individual cells even exceed a cell-to-cell misorientation of 5°. Concurrent GROD axis maps indicate that these two highly rotated CB sets share an ~<111> rotation axis: specifically [111] for the (111) CBs and <$\overline{1}11$> for those in the ($\overline{1}11$) DBI.

Figure 8a depicts the dislocation structure in a grain whose S.A. lies close to the [011] direction in specimen S2. Within this grain, only cell structures are observed. As in the near-[011] copper single crystal shown in Figure 6a,b, the CBs form on the (111) primary slip plane; however, because the imposed plastic strain amplitude is moderate, they are not heavily elongated. The bands are embedded in a characteristic DBII that lies parallel to the ($\overline{2}11$) plane and penetrating nearly the entire grain. Consequently, dislocation walls or vein structures which are commonly seen in coplanar double-slip grains are absent in this grain vicinity, likely owing to strain localization near the (111) TBs. Figure 8c further reveals that misorientation does not accumulate from CB to the adjacent CBs; instead, it manifests between clusters of CBs, reaching a maximum of ~5°.

To elucidate how subtle differences in crystallographic orientation influence dislocation structure development, we evaluated several grains of nearly identical crystallographic orientation contained within a confined region. Figure 9a shows a low magnification ECC overview of the analyzed area; the target zone is enlarged in Figure 9b, and the triple junction of the GBs is further magnified in Figure 9c. EBSD analysis reveals that these grains, named as G1, G2, and G3, are all oriented close to the [011] direction, favoring activation of the primary-coplanar-critical slip systems. Remarkably, although the S.A. of G1 and G3 locates both nearby the 011-$\overline{1}11$ edge of the stereographic triangle, their dislocation morphologies differ completely. Specifically, Figure 9c shows that G1 contains wall structures on the ($\overline{1}01$) plane, whereas CBs have emerged on the (111) plane immediately adjacent to the GBs. In contrast to previously described CBs, those in G3 are too limited in extent to satisfy any DB criterion. Originating from the GB, the size of the cells grows from ~0.5 µm to ~1 µm within 10 µm away from the boundary and eventually lose their closed geometry. It is also evident that, in G3, PSBs on the (111) primary slip plane with ladder like walls on the ($\overline{1}10$) planes form extensively alongside the CBs (Figure 9b). Such divergence in dislocation morphology likely reflects local variations in plastic strain intensity among the grains, and also confirms that the local stress state within individual grains deviates significantly from the nominal applied stress and therefore cannot be regarded as identical. By contrast, G2, although similarly near-[011]-oriented, has its S.A. located along the 001-011 edge of the stereographic triangle, endowing it with quasi-[001] characteristics. Under these conditions, the ($\overline{1}11$) [101] critical slip system preferentially activates as the secondary system instead of the (111) [$\overline{1}10$] coplanar slip system. As a result, a labyrinthine structure composed of short dislocation walls develops on the (100) and (001) planes, as is similar to the structures reported in the near-[001]-oriented single crystals [39]. Additionally, the spacing between wall segments sharing the same crystallographic index increases with distance from the triple-junction of GBs, while the initial regular arrangement becomes progressively less organized toward the grain center of G2.

When the crystallographic orientation of a grain drifts further toward the [001] direction, both the dislocation structures and the nature of the DBs evolve. Figure 10a displays several grains in specimen S2 in which multiple band-like structures have formed. Within each individual grain, these bands share a uniform orientation and exhibit pronounced contrast in the ECC image, and are therefore identified as DBs. Figure 10b presents an enlarged ECC view of the rectangular area marked in (a) for a particular grain whose S.A. lies on the [$\overline{11} 42 90$] direction, showing a notably high S_F for the ($\overline{1}11$) [101] critical slip system (S_F = 0.46). Orientations are indexed on the stereographic projection corresponding to the viewing direction in Figure 10c. Although the DB boundary is slightly curved, the dark contrast DB is confirmed to lie parallel to the (010) plane. This narrow band, with a roughly 5 µm width, is dominated by labyrinthine structures formed by two families of short walls located on the (001) and (100) planes. In the surrounding matrix bounded by the (111) TBs and ($11\overline{2}$) incoherent twin boundaries (ITBs), PSBs emerge on the (111) primary slip plane and progressively coalesce into continuous dislocation walls on the ($\overline{1}01$) plane, giving the microstructure a consistent appearance. GROD maps demonstrate that the (010) DB is misoriented from the surrounding matrix by roughly 4°, with virtually no orientation gradient inside the band itself. Combined with the stereographic projection, this evidence confirms that the rotation between the DB and matrix occurs precisely about the [010] axis, thereby identifying the DB boundaries as twist in character.

4. Discussion

As summarized in the above results, the dislocation structures revealed by ECC in the copper single-crystal specimens correspond closely to the TEM observation reported in Refs. [50,54,55,56], underscoring the reliability of the present observations. Nevertheless, PSBs are seldom encountered here, they are absent in the [$\overline{5}66$]-oriented crystal (C1) as well as in the two [$\overline{1}77$]-oriented crystals (C2, C3). Because the [$\overline{1}11$] axis typifies a multiple-slip orientation as evidenced by the monotonic rise in saturation stress with increasing shear strain amplitude reported by Li et al. [7], PSBs generated solely by the primary slip system are neither theoretically expected nor experimentally detected in C1 fatigued at ε_pl = 1.0 × 10⁻³. This finding does not contradict earlier studies that reported PSB formation in near-[$\overline{1}11$] crystals at lower amplitudes [57,58], since those specimens experienced more limited shear strain amplitudes. It was also found that once the shear strain amplitude exceeds 1.5 × 10⁻³, an intermediate structure bridging PSBs and dislocation cells, designated PSB cells by Zhou et al. [57], emerges; Li et al. [59] further proposed that fully developed cell structures evolve from PSB ladder walls formed on the {110} planes, an interpretation that aligns with the microstructural transitions observed in our high-amplitude tests. In specimen C1, although no PSBs are detected, single-slip behavior predominates across most of the gauge section, with DBs appearing only near the specimen edges. The orientations of these DBs and of the CBs inside are governed by the locally activated slip systems. As illustrated in Figure 5c,d, the DBs do not originate from the conventional (111) [$\overline{1}01$] primary slip system, which possesses the highest S_F (0.32); instead, they form through activation of the comparable ($\overline{1}1\overline{1}$) [011] system, whose S_F is 0.25 and which therefore becomes the operative primary slip. This explains why the DBI develops on the ($\overline{1}1\overline{1}$) primary slip plane. The geometry of the CBs within the DBI can likewise be rationalized by cross-slip of ($\overline{1}1\overline{1}$) [011] dislocations onto the ($\overline{1}\overline{1}1$) slip plane, which also has a S_F of 0.25. According to the classification proposed by Ma et al. [32], the resulting CBs on the ($\overline{2}\overline{1}1$) plane correspond to the CB-C type. Although shifts in the primary slip system are uncommon, they can occur in regions where plastic strain is distributed inhomogeneously. The vein-like structures of dense dislocation bundles that occupy the region between neighboring DBIs (Figure 5a) can likewise be interpreted through the interaction of two edge dislocation sets resident on the ($\overline{1}1\overline{1}$) primary slip plane: b = a/2 [011] and b = a/2 [$\overline{1}01$], following the equation: a/2 [011] + a/2 [$\overline{1}01$] → [$\overline{1}12$], which is the normal direction of the plane the vein-like bundles lie on. The attendant activation of several slip systems outside the DBI further corroborates that plastic strain is locally higher near the specimen edge than at its center. Moreover, Buque et al. [60] reported a comparable vein-like structures in nickel, describing it as a fragment wall structure oriented nearly perpendicular to the S.A. With increasing shear strain amplitude, the dislocation density is expected to rise, causing these vein-like bundles to coalesce into the dense walls observed between the DBI and the surrounding vein-like bundles in the lower left of Figure 5c.

For the [$\overline{1}77$]-oriented copper single crystals, the primary-coplanar double-slip mode is identical to that in the [$\overline{5}66$] specimens, encouraging DB and CB formation at elevated shear strain amplitudes. The alignment of matrix dislocation walls, however, differs strikingly. In the high strain regime, Gong et al. [11] observed extended walls on the ($\overline{1}01$) plane in a [034]-oriented copper crystal fatigued under a wide shear strain amplitude until 5.0 × 10⁻³, whereas Wang et al. [42,61] reported the ($\overline{1}11$) walls in a near-[$\overline{1}11$]-oriented copper single crystal. At lower shear strain amplitudes, by contrast, veins on the ($\overline{1}01$) plane and PSBs on the (111) primary plane are commonly reported for [$\overline{1}11$] and [011] orientations, respectively. Because the Lomer–Cottrell lock impedes dislocation motions for the [011] orientation, the shear strain threshold for multiple-slip activation is higher. Accordingly, single-slip characters can persist even under comparatively large strain amplitudes. Plastic strain is chiefly accommodated through the development of CBs, with the coplanar slip system preferentially selected as the secondary system because dislocation interactions remain relatively weak [62]. In contrast to the [011] case, the three-fold symmetry of the [$\overline{1}11$] orientation additionally promotes activation of the ($\overline{1}\overline{1}1$) [011] conjugate system apart from coplanar counterpart. As a result, dislocation walls on the ($\overline{1}11$) plane arise through multiple-slip activity.

Another noteworthy observation is that, even though specimen C2 oriented for [$\overline{1}77$] direction is cycled at a substantially higher shear strain amplitude, its saturation stress remains slightly lower than that of specimen C1 oriented for [$\overline{5}66$]. This difference originates from the dominance of single-slip dislocation walls in C2. During cyclic hardening, the primary system first nucleates PSBs, and the stress required for their formation decreases as the imposed amplitude rises [11]. As cumulative plastic strain increases, the PSBs attain the saturation volume fraction predicted by Winter [35] before the coplanar secondary system activates and initiates CB development. Hardening terminates when PSB ladders coalesce into extended walls on the ($\overline{1}01$) plane. Subsequent engagement of the secondary system, accompanied by mild softening, produces both CBs and DBs. By contrast, specimen C1 undergoes multiple-slip systems activation even in the matrix because a larger set of secondary candidates is available. Initial veins therefore transform into multiple-slip vein-like structures or consolidate into dense dislocation walls, both of which necessitate higher shear stress. The ensuing softening behavior in C1 parallels that of C2, as verified by the emergence of CBs.

Compared with C2, specimen C3 oriented for [$\overline{1}77$] direction exhibits similar dislocation morphologies, but with a markedly stronger dark-to-bright contrast, signifying greater misorientation within the CBs. Notably, even at the high shear strain amplitude of 1.5 × 10⁻², single-slip characteristics persist, as evidenced by the ($\overline{1}01$) dislocation walls outside the DBs. Nevertheless, the volume fraction of DBs rises sharply, indicating that these bands accommodate the excess plastic strain and thereby engender the pronounced softening response. Unlike in specimen C1, the CBs in both C2 and C3 form precisely on the {111} primary slip plane rather than on the {211} planes. In light of the findings of Ma et al. [32] and Wang et al. [61] that {211} CBs are closely associated with cross-slip activity, this divergence is attributed to the negligible S_F for cross-slip systems under the [$\overline{1}77$] crystallographic orientation, rather than to the applied strain amplitude.

In addition to the influence of GBs, the SFE also governs the evolution of dislocation structures. Based on the chemical composition of the SUS316L steel employed here, the SFE is estimated at ~26 mJ/m² [44], markedly lower than that of high-purity copper (~40 mJ/m²). Such a reduced SFE promotes planar slip configurations at moderate plastic strain amplitudes, as reported elsewhere [43,52,63,64,65,66]. When the imposed plastic strain amplitude increases, these planar structures persist only during the initial hardening phase. Subsequently, more ordered cell structures emerge with strain localization linked to cross-slip activity [53,67]. In the present work, the plastic strain amplitudes of 5.0 × 10⁻³ lie in Region III of the cyclic stress strain curve (CSSC), according to Polák et al. [68]. Therefore, after saturation the low SFE exerts little additional control over dislocation structures, and microstructural features become broadly comparable to those observed in the copper single crystals.

In this study, we mainly concentrated on grains whose S.A. lie near the 011-$\overline{1}11$ edge of the stereographic triangle, enabling direct comparison with the copper single crystals. When the coplanar slip system operates as the secondary slip system, CBs are readily observed within DBs (see Figure 7a, Figure 8a and Figure 9c). As the S.A. approaches the [011] direction, the ($\overline{1}1\overline{1}$) [101] cross-slip system is generally dormant because of its negligible S_F, so most CBs nucleate on the (111) primary slip planes. A special condition arises when a grain endures excessive plastic strain around grain boundaries, as in Figure 7; deformation twins (DTs) appear in the right portion of Figure 7a, indicating severe strain localization. Under such circumstances, slip system engagement no longer strictly follows their S_F hierarchy, and multiple systems can be activated concurrently. A DBI parallel to the ($\overline{1}11$) slip plane forms locally within the primary (111) DBI, signifying a shift in the primary slip system from (111) [$\overline{1}01$] to the conjugate ($\overline{1}\overline{1}1$) [011] slip system. Despite its modest S_F (0.15), this ($\overline{1}\overline{1}1$) [011] slip system becomes the operative primary slip over the ~5 µm-wide DBI and gives rise to the CBs observed on the ($\overline{1}\overline{1}1$) plane. The elevated plastic strain also causes the (121) CBs to overlap the (111) primary CBs inside the (111) DBI. As discussed previously, even with the low SFE, the high plastic strain eventually activates the ($\overline{1}1\overline{1}$) [$\overline{1}01$] cross-slip system, which, in turn, promotes the formation of these (121) CBs.

Conversely, because neither GBs nor TBs obstruct dislocation glide in the [$\overline{1}77$]-oriented copper single crystals, plastic strain remains microscopically uniform even inside the DBs. As a result, the ($\overline{1}1\overline{1}$) [$\overline{1}01$] cross-slip system is seldom activated, and (121) type CBs do not develop.

Although Kumagai et al. [69] analyzed cell structures in fatigued polycrystalline SUS316L by diffraction line profile techniques and concluded that the cell walls consist predominantly of edge dislocations, we propose that fully matured CBs exhibit twist boundaries formed by primary and coplanar screw dislocations. Supporting evidence is that the rotation axis between neighboring CBs clusters tightly around the {111} direction, independent of which {111} variant the CBs occupy (see Figure 7c–h). These viewpoints are not mutually exclusive when the stage of cell evolution is considered. In Kumagai’s work, although the total strain amplitude reached 1.5 × 10⁻², the tests were terminated after a cumulative strain of 15, corresponding to a cumulative plastic strain estimated at <10, so the specimens remained in the mild hardening regime, prior to complete CB maturation. As observed in the copper single crystals (Figure 5d and Figure 6a), cell structures evolve from pre-existing dislocation walls or vein arrays. At this stage, cell boundaries still retain a substantial fraction of wall remnants, because they have not yet reorganized into well-defined CBs and the edge components likely originate from these residual walls. With continued deformation and full activation of the coplanar screw dislocations, b = a/2 [$\overline{1}10$] and b = a/2 [$0\overline{1}1$] on the (111) plane, a (111) twist boundary ultimately forms between strongly misoriented CBs. The magnitude of this misorientation, governed by the local plastic strain, serves as the defining criterion for CB maturity. In Figure 8c, the low cell-to-cell misorientation shows that the plastic strain remains microscopically homogeneous; consequently, secondary slip systems other than (111) [$\overline{1}10$] are not initiated, and the ($\overline{2}11$) DBII remains the sole band extending from the TB into the grain interior.

The foregoing discussion has shown that plastic strain heterogeneity in polycrystals remarkably influences dislocation structures, and even slight deviations in crystallographic orientation play a decisive role in structure selection. As depicted in Figure 9, grains G1, G2, and G3 are all near-[011]-oriented, among which G3 lies closest to the [011] direction whereas G1 and G2 deviate slightly toward the [$\overline{1}11$] and [001] directions, respectively. Observations reveal that G3 exhibits the same dislocation structures as specimens C2 and C3: single-slip walls dominate the matrix, and CBs emerge locally in regions of elevated strain. When the S.A. tilts toward [$\overline{1}11$] direction, as in G1, single-slip behavior persists, and extended walls on the ($\overline{1}01$) plane even develop at the GB triple junction where local strain is higher. These walls closely resemble those reported in near-[011] copper single crystals subjected to low plastic strain amplitudes. When the S.A. tilts toward the [001] direction; however, the activation of the ($\overline{1}11$) [101] critical system (S_F = 0.47) as the secondary slip and its interaction with the primary dislocations erase the characteristic dislocation structures of [011] feature in G2. In this grain, labyrinth structures comprising short walls on the (100) and (001) planes predominate. These walls arise from reactions between edge dislocations belonging to the primary and critical slip systems, namely: a/2 [$\overline{1}01$] + a/2 [101] → a [001] and a/2 [$\overline{1}01$] + a/2 [$\overline{1}0\overline{1}$] → a [100]. In [011]-oriented copper single crystals, multiple-slip activity involving the ($\overline{1}11$) [101] critical system manifests independently as PSBs on the ($\overline{1}11$) plane, whereas the coplanar slip system normally acts as the secondary mode. Therefore, under moderate plastic strain amplitudes, the competition between critical and coplanar systems dictates the dislocation structures in grains whose crystallographic orientations lie close to the [011] direction. This competition arises from both slight deviations in crystallographic orientation and the inhomogeneous distribution of plastic strain among grains. The latter further results in strain incompatibility between adjacent grains, with grain boundaries eventually serving as preferential sites for crack initiation.

Beyond the conventional DBI and DBII observed in the copper single crystals, another type of DB emerges in a grain whose crystallographic orientation is away from both the [011] and [$\overline{1}11$] directions. Whereas the formation of the usual DB types is closely linked to activation of the coplanar slip system, the dark-contrast band in Figure 10b shows no evidence of such activity. Instead, it is occupied solely by labyrinth structures. Accordingly, the orientation of the band must be attributed to engagement of the ($\overline{1}11$) [101] critical slip system. Dislocations with b = a/2 [$\overline{1}01$] from the (111) [$\overline{1}01$] primary system and b = a/2 [101] from the ($\overline{1}11$) [101] critical system both lie on the (010) plane and intersect at right angles. The screw components thus assemble a twist boundary whose rotation axis is parallel to [010], as illustrated in Figure 10e,f. Consequently, this DB resides on the unique (010) plane, neither parallel nor perpendicular to the primary slip plane, and accommodates a misorientation of approximately 4° relative to the matrix, thereby absorbing local plastic strain. In the surrounding matrix, by contrast, multiple-slip activity has yet to commence, and PSBs with ($\overline{1}01$) ladder walls continue to develop.

The above discussion has elucidated several factors that govern dislocation structures and orientation. However, quantitative characterization of the plastic strain field is still needed to substantiate these interpretations. Future work should therefore prioritize locating plastic strain concentration sites in polycrystals and, in turn, establishing a theoretical framework for enhancing the fatigue performance of polycrystalline alloys.

5. Conclusions

By comparing fatigue-induced dislocation structures captured by SEM-ECC in copper single crystals oriented for coplanar double-slip with those in polycrystalline SUS316L stainless steel, it is clarified how inhomogeneous plastic strain distribution and crystallographic orientation dictate the mechanisms of dislocation structure formation. The major conclusions are as follows:

1. The habit plane on which CBs form is governed by whether cross-slip activity emerges during cyclic deformation. In copper single crystals oriented near the [$\overline{1}11$] direction, activation of cross-slip behavior is favored, resulting in a preferential CB habit plane of the {211}. As the crystallographic orientation drifts away from the [$\overline{1}11$] to the [011] direction on the 011-$\overline{1}11$ edge of the stereographic triangle, cross-slip is suppressed, and CBs instead remain on the {111} planes. In polycrystalline SUS316L, exceptionally high local plastic strain, as adjacent to GB, can still foster the {211} CB, even within grains oriented near [011], which is virtually unattainable in [011] single crystals. Misorientation angle measured between neighboring CBs quantitatively reflects the severity of local strain concentration.

2. Apart from the role of localized plastic strain, subtle deviations in crystallographic orientation strongly influence the dislocation structure of grains oriented near [011]. The competition among candidate secondary slip systems determines whether the resulting dislocation structures exhibit a coplanar double-slip character.

3. In polycrystals, DBs can also arise within grains whose orientations do not favor coplanar double-slip. Their formation is related to the local activation of secondary slip systems, regardless of which type operates. When critical slip system assumes the secondary slip, the resulting DB is composed of labyrinth structures and is bounded by low-angle twist boundaries on the (010) plane, built from two perpendicular screw dislocation sets on the (111) and ($\overline{1}11$) planes. A clear misorientation of several degrees separates the DB from the surrounding matrix. A single-slip feature persists in the matrix under moderate plastic strain amplitude.