Cryogenic spatiotemporal characteristics and microevolution of 316LN discontinuous plastic flow

Abstract

Alloys exhibit discontinuous plastic flow (DPF) at cryogenic temperatures; however, the mechanism is not fully understood. The DPF on 316LN stainless steel is investigated via the digital image correlation (DIC) technique. Serrated plastic flow was accompanied by the formation of slip bands with widths of 1–2 mm and showing both downward and upward split propagation. According to the DIC results, localized microscopic observations revealed that the occurrence of slip bands was accompanied by a change in texture and the expansion of the dislocation blocks; this produced deformation twins and caused recrystallization of the α′-martensite nanocrystals in a short time. The temperature rise caused by the slip bands was ~10 K, and the heat effect suppresses the propagation of the slip bands. These findings provide new concepts for material structure design in engineering applications at cryogenic temperatures.

Introduction

Low-temperature sawtooth deformation is a common behavior of metals such as titanium alloys, stainless steel, and aluminum alloys under ultracold deformation^1,2, which is also known as discontinuous plastic flow (DPF)^3,4,5 and results in stress oscillation. This accelerates irreversible damage to materials as a precursor to the leakage site of liquid hydrogen or helium equipment^6,7. Therefore, studying the mechanism of DPF and suppressing the stress oscillations can improve the reliability and service life of cryogenic-temperature equipment in the fields of liquid hydrogen transportation and deep space exploration.

The manifestation of DPF on the stress‒strain curve is observed as a serrated yielding segment, and based on the stress‒strain curve, DPF can be divided into four stages: quasi-elastic loading, plastic flow, stress drop (SD), and stress relaxation⁸. The DPF releases heat energy and works in the form of sound in the sudden stress stage and absorbs the heat energy into the deformation energy in the quasi-elastic loading stage⁵. The temperature during the tensile process and different strain rates influences thermal instability; this changes the shape and frequency of the DPF⁹. As deformation continues, the SD caused by DPF increases, and a rising temperature peak is detected¹⁰. Moreover, an environment with a relatively high cooling capacity enhances the frequency of the DPF behavior in the stress‒strain curve, such as in superfluid helium (2.18 K) versus liquid helium (4.2 K) or liquid hydrogen (20 K) versus helium gas (20 K)^11,12. The above behavior of the DPF shows that a strong correlation exists between its cause and temperature. Moreover, DPF can occur in various crystal structures, such as face-centered cubic (FCC), hexagonal close-packed (HCP), and body-centered cubic (BCC) structures, both in single crystals and polycrystalline materials^13,14,15; thus, the occurrence of DPF is independent of the crystal structure. The positions where DPF occurs during tensile loading have been calculated, and the statistical results show that the positions are not uniformly distributed but are localized in individual locations in a certain manner¹.

Currently, several theoretical hypotheses have been proposed to explain DPF. Recent research indicated that with decreasing temperature, the difficulty of dislocation cross-slip increased, leading to widespread diffusion of dislocations and a decrease in stress¹⁶. A previous study indicated that heat accumulated locally and could not be conducted at cryogenic temperatures; this resulted in a rapid increase in the temperature and a sudden drop in the flow stress¹⁰. Some investigations attribute DPF to strain rate softening instability, where the flow stress responds positively to sudden increases in the strain rate, followed by stress relaxation to a steady-state asymptotic value; this is a typical manifestation of dynamic strain aging (DSA)¹⁷. Experimental studies have also shown that the DPF behavior of metals at cryogenic temperatures can be attributed to the twinning plastic deformation mechanism¹⁸. The twinning formed by the FCC->HCP phase transformation will lead to the instability of the dynamic evolution of the system, thereby forming unstable stress flow¹⁹. Another perspective proposes that DPF results from the behavior of dislocation motion. Edge dislocation is the main type of active dislocation at cryogenic temperatures, and when the critical state is reached, barriers collapse, releasing dislocations for unrestricted sliding from the LC locks and delaying groups of edge dislocations, with stress changes^20,21,22. Studies have shown that solute atom‒dislocation interactions can contribute to DPF and establish problems capable of locking dislocations and leading to pile-ups²³. In general, DPF involves special deformation under the dynamic motion of the dislocation, multiplication, and special properties of the dislocation interacting with each other at cryogenic temperatures.

At present, in extreme cryogenic environments, DPF research is limited to one-dimensional stress‒strain curves and temperature measurements^7,9,24. The digital image correlation (DIC) technique is an optical, noncontact deformation method that analyzes the grayscale patterns of speckle images²⁵ and is widely used in the study of material deformation^26,27,28 and thermoelastic materials^29,30,31. We developed a DIC-based visual apparatus for observing full-field strains and temperatures during tensile processes at cryogenic temperatures to clarify the real-time dynamic mechanisms underlying the mechanical behavior of DPF. As a widely used stainless steel at low temperature^32,33, 316LN was selected as the experimental material. The different shapes of the slip bands of DPF were observed, and the propagation trends of DPF combined with microstructure evolution were analyzed.

This work experimentally demonstrates a bidirectional splitting propagation mode in cryogenic slip bands with 316LN via DIC technology. The propagation behavior provides critical mechanistic insights into the rules of DPF, particularly revealing the priority order of synchronized dislocation activity at grain boundaries and establishing a framework for stress flow by cooperatively mediating strain localization under cryogenic conditions. Meanwhile, the observation of network-structured dislocation pile-ups in microscopic characterization provides evidence for dislocation activity as the primary origin of DPF at cryogenic temperatures. Furthermore, this work establishes a quantitative framework for analyzing the thermal characteristics associated with slip band formation, providing experimental validation of the energy dissipation pathways during both slip band nucleation and subsequent microstructural evolution.

Results

DIC measurement

The tensile experiment was conducted when the specimen was stabilized at 12 K (Fig. 1a and Supplementary Fig. 1b), and ε_yy of the Green-Lagrange strain tensor measured by DIC was recorded (Supplementary Movie 1). The yield strength and tensile strength are 883 MPa and 1482 MPa, respectively, and the elongation is 48.5%. In the DPF, the specimen underwent a series of SD processes, and the SDs were ~50–100 MPa in the early stage and 200 MPa in the later stage. Simultaneously, a traversing region with more evident strain than the other surrounding areas appeared in the strain field ε_yy of the SD process (Fig. 1c); this is referred to as the slip band of DPF³. The occurrence of a slip band was accompanied by stress relaxation, leading to a contraction in the tensile direction of other subregions; this also corresponds to the pseudo-elastic stage⁵ after the end of the stress relaxation stage (Supplementary Fig. 1c–e). In the later stage of DPF, the slip band exhibited more directionality, with a fixed inclined shape, more engineering strain steps, and its time interval became longer (Supplementary Fig. 2a, b).

Fig. 1: Analysis of slip band and coupled thermo-mechanical responses during cryogenic tensile deformation.

a Engineering stress‒strain and temperatures of the Top, Middle, and Bottom positions (Supplementary Fig. 4f) with the time curve during the tensile process. b Temperature fluctuations caused by the slip band (8074–8081 s) and reconstructed via the FEA method (Supplementary Fig. 4d). c Digital ε_yy strain cloud maps at two moments A (8073.5 s) before and B (8074 s) after the slip band occurs in Fig. 1d. d Engineering stress‒strain curves and temperatures over time (8000–8150 s). Δt₁, Δt₂, and Δt₃ are, respectively, the time intervals from when the mechanical sensor detects the stress drop to when the temperature rise is detected by the thermometers at the Top, Middle, and Bottom positions. e Three types of Δε_yy local images of the slip band throughout the entire tensile process.

After the experiment commenced, during the elastic stage, the temperature consistently increased (Fig. 1a). The red, blue, and yellow curves respectively represent the recorded temperature variations of the thermometers located at the top, middle, and bottom during the tensile process (Supplementary Fig. 3f). Coupled with heat release during the elastic process, the temperature rapidly increased. After entering the plastic stage, a new thermodynamic equilibrium was established, and a new temperature gradient was formed. The temperature fluctuations caused by the formation of a slip band (8074 s) (Fig. 1d) revealed differences in the response times (Δt₁, Δt₂, and Δt₃) captured after SD; thus, the slip bands formed before the temperature fluctuation. The generated temperature increase could locally increase the temperature to ~10 K, and heat diffused across the entire specimen surface; this led to an overall increase in that temperature that lasted for ~2 s (Fig. 1b). By integrating the temperature fluctuations, the heat released during the generation of the slip band could be obtained, and the energy was far less than the input load work in the SD process (Supplementary Fig. 4e); therefore, the material absorbed energy in the process of forming a barrier to reach the stress minimum.

The formation of slip bands exhibited prominent features (Supplementary Fig. 5); based on the Green-Lagrange strain increments Δε_yy, the slip bands could be classified into three types (Fig. 1e). Type I and Type III slip bands collectively constitute a minor proportion of the total DPF events, exhibiting stochastic spatial distributions without discernible propagation tendencies, where Type 1 manifests during the initial DPF stage, whereas Type 3 emerges in the terminal DPF stage (Supplementary Fig. 6). In Type I, the region with the maximum Δε_yy was centered. This type was more likely to occur in the early stage of DPF because of the insufficient sliding distance of dislocations, which could not propagate to the edge. Type II constituted the majority of the slip bands and featured a horizontally inclined slip line penetrating the surface; here, in the region with the maximum ε_yy, this distinctive band structure formed with a clear Δε_yy gradient. For type III, the region with the maximum Δε_yy originated from the center and traversed one side, with a substantial Δε_yy gradient. The fundamental physical origin of slip band formation stems from a unified dislocation-mediated mechanism; however, the distinct morphological manifestations (three types of slip bands) arise from microstructural constraints during DPF, where localized variations in defect-dislocation interactions mediate the transition between different slip band types. Type II slip bands result from fully activated dislocation activity, which induces a localized strain increase propagating across the specimen surface. Conversely, both type I and type III slip bands did not penetrate the surface; however, type I slip bands occurred because the dislocation behavior that caused the ε_yy step could not expand through the surrounding region with a lower dislocation density, whereas type III slip bands contributed to internal obstacles, preventing the expansion of the slip band^34,35. In addition, the slip direction was not always the same direction, and slip bands in the opposite direction also appeared. There are several possible reasons for the emergence of reverse slip bands here. On the one hand, slip band directionality is decided by the configurations of dislocations, and there is a possibility of special reaction in the dislocations, which leads to the formation of reverse slip bands in DPF. On the other hand, the reverse slip band may come from the source of slip band generation outside the measurement range of DIC. Over time, the shape and direction of the Δε_yy of the slip bands gradually aligned, and their magnitudes progressively increased.

Spatiotemporal properties of the slip bands

The regions of the slip bands are arranged in chronological order (Supplementary Fig. 7), and the distribution of the slip bands in DPF does not exhibit a distinct continuous propagation in either time or space. Some studies propose that the uneven spatial distribution of slip bands is associated with strain-induced martensitic transformation and that the nucleation of martensite impedes the formation of slip bands^4,36. However, other studies claim that twinning and martensite nucleation have no influence on DPF¹⁶. When the centers of all slip bands are placed on the time axis (Fig. 2a), a strong spatiotemporal relationship is attained. Three starting points are selected: starting point 1 (SP 1), starting point 2 (SP 2), and starting point 3 (SP 3). SP 2 exhibits an upward propagation path, SP 3 a downward propagation path, while SP 1 occurs in both directions. These paths form intersections, and the slip bands at these intersections have splitting characteristics and propagate upward and downward at the same time; for example, points propagating downward in path 4 can follow the yellow arrow to find the split path propagating upward. When the positions of the slip bands in space-time are connected, they spread in crossed paths, and the occurrence of each slip band is associated with the slip bands located on either side of it that were previously generated. Moreover, almost all positions can be classified in this way; thus, the propagation of the slip bands has two directions. Other repeated experiments also revealed the same result (Supplementary Fig. 8a, b). Slip bands with different tilt directions (red and blue) occur in a concentrated space-time, and at their junction (such as Region I) (Fig. 2a), they appear as a transition region where no slip bands occur for a certain period of time; this potentially occurs because the threshold of slip band occurrence increases when slip bands with different glide angles meet, resulting in other low threshold regions occurring first.

Fig. 2: The distributed and propagation behavior of the slip bands.

a Temporal distribution of the centers of the slip bands. The slip bands of different orientations are represented by red and blue, respectively. There are special zones between slip bands in different directions, such as Region I. Taking the three points SP 1, SP 2, and SP 3 as the starting points, four paths for slip band propagation, Upward1, Upward2, Downward1, and Downward2, were selected. b Temporal distribution of the centers of the slip bands in the actual location in the tensile process. c Propagation velocity of the slip band along paths Upward1, Upward2, Downward1, and Downward2. d Changes in Δσ and Δε of the engineering strain-stress curve of the slip bands with time.

At room temperature or high temperature, the PLC bands also appear during the tensile process of the alloy, which is similar to the slip band. Additionally, according to the stress‒strain curve, the PLC bands can be divided into three types: types A, B, and C³⁷ (Supplementary Fig. 9). Among them, the type C bands are most similar to the slip band that occurs at cryogenic temperature in both frequency and amplitude. Distinct PLC band types exhibit characteristically divergent propagation modes. In contrast to the well-documented propagation modes of PLC bands—where type A and B typically demonstrate unidirectional, splitting, and reflective propagation while type C shows random spatial distribution—the slip bands under cryogenic conditions display unique morphological features, most notably frequent splitting events coupled with simultaneous bidirectional propagation. Interestingly, Type C bands are observed in tensile experiments at relatively high temperatures³⁸, and slip bands occur at low temperatures¹⁶. The production of PLC bands contributes to the dynamic interaction between the dislocation and the solute atoms, which is also called DSA²⁶; moreover, with more activation energies (higher temperatures) in the diffusion processes of atoms, the dislocation is pinned and released by the solute atoms, and PLC bands subsequently change into Type C bands³⁸.

According to the rules of network propagation, considering clarity and sufficient path length, two lines propagating from the bottom up (Upward1 and Upward2) and two lines propagating from top down (Downward1 and Downward2) in actual distance are connected (Fig. 2b), and the propagation speed of the four slip band lines is calculated by dividing the positions of the centers of adjacent slip bands on the path by their time intervals (Fig. 2c). The propagation velocity of the slip bands gradually decreases with time in both directions, reaches 10 × 10⁻⁶ ms⁻¹ at the beginning and decreases to ~1 × 10⁻⁶ ms⁻¹ at the later stage of DPF; these results indicate that more time is needed for the dislocation pile-up to accumulate to meet the threshold value of release. Not only can the SD Δσ caused by the slip band be observed on the engineering stress curve, but also the step Δε can be observed on the engineering strain curve (Supplementary Fig. 1a). The variations in Δσ and Δε are caused by slip bands with time (Fig. 2d), and the value of both gradually increases with respect to time. The increases in Δσ and Δε are related to the scale of the dislocation pile-up chain release and the time of repining.

Microstructure

The initial microstructure and X-ray diffraction (XRD) pattern of 316LN SS are shown in Supplementary Fig. 10a, b. The average grain size of the annealed alloy is 94 μm, and a large number of annealing twins are observed in the inverse pole figure (IPF) map. The XRD pattern shows that the annealed 316LN SS has the FCC phase. Notably, the slip bands exhibit a serrated depression (Fig. 3a) across the entire specimen. Ductile dimples are observed in the fracture morphology of the tensile specimens (Supplementary Fig. 11). Four slip bands are clearly visible, and their traces are found in the yellow zone of the ε_yy strain field. The first slip band is closest to the fracture and was selected for examination; additionally, electron backscatter diffraction (EBSD) was used to observe the two places with different ε_yy within (61 %, sampling 1) and outside (53 %, sampling 2) of the slip bands (Supplementary Fig. 12).

Fig. 3: Specialized characterization of microstructure based on DIC.

a Frontal image of the fractured specimen, full-field ε_yy strain image of the fractured sample measured by DIC, and the locations of the sampling 1 and sampling 2 points in the specimen. Residual traces of previously formed slip bands are clearly observed on the specimen surface. The slip bands traverse the entire specimen at an angle of ~60°, with a width of 1 mm. EBSD micrographs of deformation microstructures for sampling 1 and sampling 2, and the magnified images in the white rectangle. b IPF maps of sampling 1. c IPF map of sampling 2. d IPF map of sampling 2 of Grain 1. e BC maps of sampling 1. f BC maps of sampling 2. g BC maps of Grain 1. h Grain orientation transformation during the occurrence of slip bands. i ODFs identified in the sampling 1 and sampling 2: (i1) (i2) γ-austenite, φ₂ = 90°. (i3) (i4) α′-martensite, φ₂ = 90°. j TKD and TEM at Grain 1: (j1) BC map. (j2) (j3) (j4) Images of the boundaries of α′-martensite and γ-austenite. (j5) FFT pattern of (j4).

At sampling 1, α′-martensite (BCC, 70.5%) and γ-austenite (FCC, 29.5%) are observed in the phase maps. Prior investigations have demonstrated that cryogenic plastic deformation induces stress-assisted martensitic transformation in austenitic stainless steels such as 316LN and 316L, where the phase transitions coupled with dislocation-transformation interactions contribute to enhanced strength characteristics through multiphase strengthening mechanisms^39,40. High-stress dislocation blocks are present and cannot be marked around the grains (Fig. 3b, c); these blocks are a mixture of edge, screw, and mixed components and are related to the cross-slip motion of dislocations^41,42. These dislocation blocks are interconnected to form a large-scale dislocation block network on the right side of the IPF maps (Fig. 3e), and their high stress causes severe deformation of the surrounding grains^43,44. To cushion against high stress, most γ-austenites in the dislocation block network are transformed into martensite to resist extrusion^45,46,47. At sampling 2, the area of the dislocation blocks clearly decreased, no continuous dislocation block network was observed (Fig. 3f), and the ratio of α′-martensite decreased to 60.2%.

In the orientation distribution function (ODF) of sampling 2, γ-austenite has two concentrated orientations, {011} <111> and {011} <100>, along the RD direction (Fig. 3i1); this is a typical texture for tensile deformed FCC metals and alloys⁴⁸. For sampling 1 (Fig. 3i2), the orientation of the γ-austenite changed and focused on {012} $< \bar{2}11 >$ and {001} $< \bar{1}\bar{2}0 >$; these results show that the orientation changed before and after the formation of slip bands. On the basis of the Kurdjumov‒Sachs mechanism, the first shear deformation in the martensitic phase transition is parallel to {111} and deforms to $< \bar{2}11 >$; this leads to the presence of γ-austenite in the $< \bar{2}11 >$ direction⁴⁹. The orientation $< \bar{1}\bar{2}0 >$ is the deformation twin produced by $< \bar{1}00 >$ since the angle between them is 60°. α′-Martensite is oriented in the {014} $< 0\bar{4}1 >$ directions at sampling 2 (Fig. 3i3) and in the {001} <100> and {012} $< 42\bar{1} >$ directions at sampling 1 (Fig. 3i4). The α′-martensite with a $< 42\bar{1} >$ orientation originates from the γ-austenite with a < 111> orientation formed after the second shear deformation contributes to the K‒S mechanism. Similarly, $< 0\bar{4}1 >$ is the 60° deformation twin produced by $< 42\bar{1} >$, and it is located in Grain 1 (Fig. 3d, g); these results indicate that α′-martensite grains generate deformation twins in two directions to relieve the internal stress under dislocation blocks⁵⁰. The {001} <100> orientation shows recrystallization⁵¹, with the formation of new subgrains. These findings demonstrate that during the DPF, the interplay between cyclic tensile stress loading and slip band nucleation drives periodic crystallographic reorientation of grains (Fig. 3h). Microstructural characterization performed inside (Sampling 1) and outside (Sampling 2) slip bands revealed distinct differences in grain orientations. This difference originates from changes in dislocation pile-ups responsible for the SDs in DPF; dislocation pile-ups expansion leads to strain increase, causing grain orientations to evolve differently under periodic stress relaxation in DPF compared to typical cryogenic strain-induced martensitic transformation. Outside slip bands (Sample 2), orientations concentrated at {011} <111> and {011} <100>, typical for austenite under tension. Inside slip bands (Sample 1), grains exhibited orientations concentrated in the first shear strain of martensitic transformation, indicating rapid martensite formation within slip bands in DPF occurrence to accommodate the increase of strain, thus preserving significant residual first shear strain {012} $< \bar{2}11 >$ and {001} $< \bar{1}\bar{2}0 >$ in the austenite grain orientation. Similarly, Sample 1 contained martensite grains with orientations corresponding to the second shear strain at {012} $< 42\bar{1} >$, indicating rapid martensitic transformation within slip bands. Both results demonstrate substantial martensitic transformation during slip band occurrence due to stress-strain oscillations. Additionally, the presence of {001} <100> oriented grains indicates that slip bands not only induce martensitic transformation but also trigger recrystallization. After the slip band, these grain orientations revert to those resembling Sample 2 during continued tension until the next slip band forms.

The FIB technique was used to analyze a 4 × 4 μm region inside Grain 1, and transmission Kikuchi diffraction (TKD) is conducted to identify the microevolution (Supplementary Fig. 13). Both α′-martensite and γ-austenite exist in the grains, and their different orientations affect each other at subgrain boundaries (Fig. 3j1); this results in greater differences in orientation and leads to the formation of nanoscale grains⁵². Moreover, the violent rotation of the grains caused by the slip bands and obstacles helps the low-temperature dynamic recrystallization⁵³ and contributes to the formation of new subgrains. The grains of α′-martensite become broken under the action of the dislocation blocks during the generation of the slip bands and decompose into twins. Furthermore, this region is observed by transmission electron microscopy (TEM) along the <011> band axis (Fig. 3j2–5). A clear subgrain boundary is formed between γ-austenite and α′-martensite, with a large number of dislocation blocks near the boundary. These dislocation blocks accumulate, expand, and cause the grain edges to bulge and form a new complete grain boundary⁵⁴.

In summary, large-scale expansion of dislocation blocks occurs with the slip bands; this promotes the transformation of γ-austenite to α′-martensite in a short time and forms a subgrain boundary between them to produce nanocrystals. In the process of rapid transformation, deformation twins form, and the simultaneous existence of twin and subgrain boundaries also accelerates the process of grain breakage.

Discussion

Formation

Based on the experimental results observed in the tensile test of 316LN at 12 K, the cause of DPF lies in the dislocation behavior. With decreasing temperature, the stacking fault energy (SFE) decreases, the dislocation core further expands, and the dislocation density increases^55,56. The dislocations have difficulty escaping and accumulate at the grain boundaries or subgrain boundaries to form dislocation blocks⁴⁴. At cryogenic temperatures, the threshold of the thermal activation energy of sliding systems increases, and the number of sliding systems activated is limited⁵⁷; this cannot meet the demand of stress release through sliding deformation. In this case, γ-austenite relieves stress through the martensitic transformation and deformation twinning, and many deformation twins are present in α′-martensite. This results in a large number of subgrain boundaries and twin boundaries in the grains, and these areas become the core of the formation of new dislocation blocks due to poor dislocation mobility¹⁶. The simulation reveals that dislocations aligned linearly along identical Burgers vectors maintain equilibrium, while generating substantial shear stress differentials across both sides of this linear configuration (Fig. 4b). When the shear stress differential regions generated by adjacent dislocation pile-ups progressively interconnect and reach convergence during plastic deformation, they collectively overcome the local stress threshold through coordinated dislocation motion, initiating large-scale slip events that propagate through the crystalline lattice via dislocation activation and annihilation processes. This cascade of plastic activity leads to strain localization within preferential slip planes, where the accumulated shear strain eventually stabilizes as distinct macroscopic slip bands (Fig. 4c); when this occurs, a large number of dislocations lose control and move at high speed into other grains and dislocation blocks, and their release causes dislocation structure collapse in other areas and results in a chain reaction, which is also called the “avalanche” effect^58,59 (Fig. 4a). The stress release caused by this dislocation behavior has disastrous effects on the grain structure; γ-austenite undergoes martensitic transformation and produces many twins in a short period of time, which increases the disorder and provides the opportunity for further reactions of the “avalanche” effect. Finally, the movement stops after sufficient recrystallization of the martensitic nanocrystals from the dislocation blocks and broken grains, and the newly formed martensite has disordered dislocation structures and twins; these can effectively stabilize the dislocation block region.

Fig. 4: Dislocation “avalanche” process.

a Dislocation blocks, gradually expands, reaches the stress threshold, causes the “avalanche” effect, recrystallizes, and retains part of the dislocation blocks. b Stress field that forms on both sides of a dislocation when its direction converges. c When multiple dislocation blocks are connected, if the direction of dislocation tends to be the same, it produces a stress difference in the surrounding area and reaches the limit of the dislocation blocks. d Energy change of the dislocation as it is pinned by the solute atom until release. E_v is the kinetic energy of the dislocation, E_b is the barrier energy of the solute atom, and E_a is the external activation energy. e Variation in the dislocation stacking energy E after the slip bands occur. E_d denotes the energy dissipation associated with dislocation pile-ups following slip band formation, while E_c corresponds to the excess energy accumulation beyond the critical “avalanche threshold” within dislocation pile-ups.

Spatiotemporal characteristics

When an “avalanche” occurs, the newly formed martensitic nanocrystals reform a stress field to prevent deformation and improve the threshold of the “avalanche”; however, dislocation blocks still remain and are more likely to become new points of “avalanche” at the edge of the region. A decrease in SFE during cryogenic conditions leads to severe dislocation blocks, their critical lengths increase, the connectivity of the dislocation blocks in the same direction also overcomes the threshold, and devastating “avalanches” are triggered. Therefore, a new event of “avalanche” is more likely to occur between the old ones; this creates a spatial connection between the slip bands propagating bidirectionally across the specimen. The propagation speed of all propagation paths constantly decreases, which can be attributed to the following two aspects: (1) α′-Martensite can hinder the spread of dislocation blocks. (2) α′-Martensite nanocrystals increase the threshold of the “avalanche” effect. The increases in the values of the SD and ε_yy step caused by the slip bands with time are potentially related to the decrease in γ-austenite during the tensile process. Due to the strengthening of the material by α′-martensite nanocrystals, the formation of slip bands becomes more difficult; this increases the time interval of the occurrence of the slip bands and the critical dislocation length that triggers the “avalanche” effect. A greater stress difference occurs on both sides of the dislocation line and contributes to more significant SD and ε_yy steps in the later stage of DPF.

Energy analysis

Whether a dislocation is pinned or detached from a solute atom depends on the relative magnitude of the kinetic energy E_v of the dislocation, the barrier energy E_b of the solute atom, and the external activation energy E_a⁶⁰. Typically, the generation of slip bands is also related to similar pile-up behaviors between the solute atoms and dislocations. At high temperatures, the barrier energy E_b increases with increasing molecular thermal motion, resulting in more dislocation accumulation at the solute atoms. However, at low temperatures, the cross-slip behavior of dislocations decreases, and the activation energy increases E_a; this is the main reason for dislocation pile-up.

From the perspective of energy, when the kinetic energy and activation energy of a dislocation are less than the barrier energy (${{{E}}}_{{{v}}}+{{{E}}}_{{{a}}} < {{{E}}}_{{{b}}}$), the dislocation is pinned by the solute atoms. As the number of pinned dislocations increases, the pile-up energy E increases by absorbing the kinetic energy of the dislocation to escape the solute atom, and the dislocation collapses and releases the surrounding dislocations (Fig. 4d). After the solute atoms are free, the pile-up energy E_d is reduced, and the dislocation can be repinned by it. The dislocations released by the pile-up have a high kinetic energy E_v, and their addition triggers the release behavior of other pile-ups in advance; this process results in a large-scale pile-up chain reaction. The stopping condition of the chain release is that the released dislocations are repinned, and all kinetic energy is consumed and converted into potential and heat energy; thus, temperature fluctuations are observed after the occurrence of the slip band.

Based on the distribution of the slip bands, as the material is deformed, the dislocations are continuously pinned at the solute atoms. Slip bands occur when the sum of the energy of the pile-up E and the activation energy E_a exceeds the barrier energy E_b that the pile-up can withstand. After the first slip band occurs, the pile-up energy is released, and E_d is reduced to keep the level low. Owing to the release of the dislocations, which have a relatively high kinetic energy E_v, the pile-up energy in the surrounding environment increases E_c (Fig. 4e), and more easily reaches the critical value to release the dislocations. The pile-up between the two slip bands has the highest energy due to the absorption of energy released by both; this point becomes the most likely location for a new slip band. Between the two opposite direction slip bands, the dislocation energy released cannot be absorbed by the pile-up; thus, the lower energy of the pile-up continuously pins the dislocations and does not preferentially occur in the slip band. As the engineering strain increases, the Δσ and Δε caused by the slip band gradually increase, which means when the number of slip bands increases, more pile-up energy E is needed, more energy E_d is lost with the release of the dislocations, more released dislocations are formed, a higher kinetic energy E_v is attained and the time of repinning dislocations increases.

From a macroscopic perspective, the input of the load work needs to be in the deceleration stage of the ε_yy step, and a local heating phenomenon with a temperature rise of ~10 K occurs after the slip bands are generated; thus, adiabatic heating is not the precipitating factor in the occurrence of slip bands. In particular, sawtooth fluctuations only occur again after the temperature decreases back to the base temperature; here, the temperature rise has an inhibitory effect on the propagation of the slip bands (Fig. 1a). The heat energy provided by the load work reduces the activation energy E_a of the dislocation; hence, it is easier to break away from the pinning of the solute atom and the grain boundary. Therefore, the dislocation is difficult to capture by the solute atoms at high temperatures for the formation of the dislocation blocks. On the other hand, the thermal energy is more conducive to recrystallization in the dislocation blocks and has an inhibitory effect on the propagation of the slip bands.

In summary, in this study, the macroscopic behavior and temperature fluctuations of DPF via the DIC technique are reported, and the formation mechanism and propagation mechanism of slip bands are analyzed from a microscopic perspective. We recorded the shape characteristics and spatial distribution of the slip band in the DPF stage at cryogenic temperatures; this distribution exhibited a bidirectional propagation trend on the specimen surface, its propagation speed gradually decreased, and the SD gradually increased with increasing tensile strength. This propagation behavior reveals core mechanisms of DPF through demonstrating the sequence of synchronized dislocation avalanches and constructing a stress flow model regulated by synergistic strain localization under cryogenic conditions. Microstructural identification of networked dislocation pile-ups corroborates dislocation-mediated DPF initiation as temperature decreases. Comparisons of crystallographic orientation evolution across slip bands, combined with analysis of stress variations induced by dislocation avalanches on microstructural evolution, have been conducted to elucidate the mechanistic relationship between localized stress redistribution and cyclic oscillation patterns in DPF. These findings collectively demonstrate that suppression of stress fluctuations in cryogenic alloy structural materials can be achieved through strategic regulation of dislocation motion pathways and density distribution. Specifically, increasing the concentration of solute atoms elevates the critical threshold for dislocation pile-up and constrains dislocation mobility during “avalanche” events, thereby effectively diminishing both the frequency and amplitude of stress oscillations. Concurrently, based on the relationship between the propagation of slip bands and martensitic transformation, setting up partition structures may help reduce or even eliminate the mobility of slip bands. Furthermore, this work found that the heat effect suppresses the propagation of the slip bands; thus, sawtooth fluctuations occur more frequently under better cooling conditions, and the indirect local heating strategy can effectively avoid the formation of slip bands.

Methods

Sample preparation

The experimental specimens were machined from a 316LN SS plate with dimensions of 20 mm thickness, 300 mm length, and 150 mm width. The plate underwent solution annealing at 1050 °C for 140 min, followed by water quenching. The samples were extracted from the solid solution-treated plate without undergoing any subsequent heat treatment. The elemental composition of 316LN was determined using direct reading spectrometry. Due to the direct impact of carbon (C) and nitrogen (N) on the stability of the internal austenite in steel, chemical analysis involving both the carbon sulfur analysis and the oxygen nitrogen analysis was conducted to accurately determine the contents of C and N in 316LN. The chemical composition of the 316LN is listed in Supplementary Table 1. 316LN SS was processed into plate samples according to ISO 6982-4; the measurement range of the standard distance was 28 × 6 mm in the middle part of the specimen, and the front side of the specimen laser-engraved met the grayscale requirements for DIC (Supplementary Fig. 3f).

Mechanical experiments

The cryogenic-temperature tensile platform used in the experiment enables stable temperature control in the range of 4 K to 300 K, ensuring temperature fluctuations at both ends of the specimen within 5 mK (Supplementary Fig. 3a, b). Temperature control is achieved through the combination of a refrigeration unit and a heating unit, and the refrigeration unit consists of two GM cryocoolers (Sumitomo model RDK-415D). Both the vacuum layer and the shielding layer are equipped with optical windows for DIC measurement. The mechanical test system employs a universal testing machine (Instron model 5985). We previously provided a detailed description of the device’s structure in our earlier work⁶¹. To enhance the observation of DPF during the plastic deformation process of 316LN, a slower strain rate of 6 × 10⁻⁵ was employed.

Temperature measurement

Three Cernorx-1050-SD-HT thermometers were arranged within the marked distance on the back of the specimen and designated top (A), middle (B), and bottom (C) (Supplementary Fig. 3c, d, f). All thermometers could measure temperatures in the range of 1.4 K to 325 K, had dimensions of 1.08 × 1.905 × 3.175 mm (Supplementary Fig. 14a), and were secured using VGE-7031. To correspond to the changes in the full-field ε_yy strain and temperature fluctuations, the data from the three thermometers located in the sample were separately collected by Model 240-8P with a high frequency of 100 ms to avoid conflicts with the temperature acquisition channel in the temperature control system.

To obtain the full heat changes in DPF, a one-dimensional heat diffusion model enabled the reconstruction of the temperature variations in response to thermal effects of the DPF slip bands using the three temperature measurement points. The temperature changes were divided into two parts. The first part consisted of the baseline temperature plane of the specimen formed by different cooling effects and the continuous stretching heat source. The baseline temperature curves of the three temperature points are shown in Supplementary Fig. 4a. This temperature gradient slowly changed over time and could be considered a quasistatic process. Here, the 1D steady-state conduction equation was used.

$$0=\lambda (T)\frac{\partial {T}^{2}}{{\partial }^{2}x}+\dot{\phi }$$

(1)

where $\lambda$ represents the thermal conductivity, and $\dot{\phi }$ denotes the internal heat source resulting from the load-induced work. Combined with the three temperature points at each moment, the temperature distribution along the tensile direction and the average internal heat source could be obtained (Supplementary Fig. 4c).

The second part involves the thermal fluctuations generated by the DPF. The temperature fluctuations caused by the formation of a single slip band are shown in Supplementary Fig. 4b; here, differences in the response times and peak values captured by the three thermometers are observed. The response time for the temperature fluctuations to propagate to different locations can be used to determine the position of the slip bands. Using DIC, the time of the slip band occurrence, along with its specific position and width on the specimen surface, can be obtained. Combining one-dimensional finite element analysis (FEA) allows the solution of the temperature variations after the slip band occurs. The FEA adopts the fully implicit discrete method, as follows:

$$\rho {c}_{{{{\rm{p}}}}}\frac{{T}_{{{{\rm{i}}}}}^{n+1}-{T}_{{{{\rm{i}}}}}^{n}}{\varDelta t}=\lambda \frac{{T}_{{{{\rm{i}}}}+1}^{n+1}+{T}_{{{{\rm{i}}}}-1}^{n+1}-2{T}_{{{{\rm{i}}}}}^{n+1}}{\varDelta {x}^{2}}+\dot{\phi }$$

(2)

An iterative algorithm based on FEA is designed to solve for the peak value of the DPF using the temperature measurements from the three thermometers (Supplementary Fig. 4d). Since the thermal resistance between the thermometer and the specimen affects the thermal response rate of the thermometer, and based on Fourier’s law of heat conduction, the following equation can be used:

$$\frac{dT}{dt}=-\lambda \frac{dT}{dx}\frac{A}{m{c}_{{{{\rm{p}}}}}}$$

(3)

where c_p represents the temperature-dependent specific heat capacity, and m and A denote the mass and contact area of the thermometer, respectively. The heat capacity, size, and cryogenic thermal conductivity of Cernorx-1050-SD-HT are shown in Supplementary Fig. 14c–e. The proposed iterative algorithm demonstrates temperature deviations within 3% relative to experimental measurements at both the Bottom and Top monitoring points (Supplementary Fig. 4f, g).

DIC measurement

In the experiment, VIC-Snap was used to capture images of the 316LN specimen using a CCD camera. These images were then imported into VIC-2D software to calculate the two-dimensional ε_yy strain field of the specimen, with an ε_yy strain measurement accuracy of 5 × 10⁻⁹. To ensure the quality of the image acquisition, the DIC system adopted an acquisition frequency of 500 ms. Moreover, the accuracy of DIC measurement was validated with the engineering strain-stress curve measured by the contacting-extensometer, which has been verified in our previous works, and the result showed that the one-dimensional engineering strain-stress curve measured by DIC is consistent with that of the contacting-extensometer in both the elastic and plastic stages, and there is only a difference in the fracture stage, which contributes to the drop of the contacting-extensometer due to vibration⁶². The quality of DIC strain field measurements is strongly correlated with an adequate light source. To eliminate the influence of light source reflection and refraction on DIC measurement, the 0.05 mm-thick Indium Tin Oxides film with high transmittance was applied to the optical window (Supplementary Fig. 3e, g). Relevant work can be found in our previous work⁶³. However, to maintain a cryogenic environment, the shape of the optical window needed to remain slender to prevent excessive radiation heat loss; this led to a loss at the edges of the 2D strain field. To increase the effectiveness and resolution of the strain field, the DIC results were repaired by the strain of the surroundings and converted into digital images based on an interpolation-based repair method derived from plasticity theory during the post-processing stage. This approach establishes a dual-objective optimization framework that simultaneously preserves the weighting characteristics of raw measurements and enforces strict compliance with the governing physical equations of strain fields:

$$\min {L}_{{{{\rm{data}}}}}+\lambda {L}_{{{{\rm{physics}}}}}$$

(4)

$${L}_{{{{\rm{data}}}}}=\frac{1}{N}\sum {({\varepsilon }_{{{{\rm{yy}}}}}^{{{{\rm{pre}}}}}-{\varepsilon }_{{{{\rm{yy}}}}}^{\exp })}^{2}$$

(5)

$${L}_{{{{\rm{physics}}}}}={\lambda }_{1}\cdot (\nabla \sigma +f)+{\lambda }_{2}\cdot (\nabla \cdot \sigma )+{\lambda }_{3}\cdot (\nabla \cdot \varepsilon )$$

(6)

The loss function consists of two components: L_data quantifies the residual between repaired and measured data points, while L_physics enforces physical consistency through three governing constraints: (a) stress equilibrium equations, (b) stress field smoothness, and (c) strain field smoothness. This dual-loss architecture establishes a physics-informed regularization framework where L_data preserves measurement fidelity and L_physics maintains mechanical rationality.

All ε_yy strain digital images are based on the subregions defined by DIC, and these subregions do not represent the actual dimensions during tensile testing. The varying ε_yy strain sizes in different subregions of the digital images indicate the actual size differences in those subregions.

Structural and compositional characterization

The crystalline phase was identified using XRD (D8 Advanced). The topography of the fracture was characterized via scanning electron microscopy (HITACHI*S-4300). The microstructure evolution in and out of the slip band area was analyzed by EBSD (Thermo Fisher Verios 5UC). The TEM foil samples were cut from the fractured pieces and thinned to electron transparency using focused ion beam (FIB) milling (Thermo Fisher Helios 5UX). TKD (Oxford symmetry S2) was performed on the same instrument using an accelerating voltage of 30 keV with the foil positioned at −20 °C relative to the plane normal to the incident beam, and data processing was performed with Aztec crystal analysis software. The deformation microstructures were characterized via high-resolution transmission electron microscopy (HRTEM, Thermo Fisher Talos F200X) and aberration-corrected scanning TEM (STEM, JEOL JEM-ARM300F2).

Dislocation stress field

The main types of dislocations active at cryogenic temperatures are edge dislocations, and the stress field of edge dislocations can be calculated by the following formula⁶⁴:

$$\left\{\begin{array}{c}{\sigma }_{x}=\frac{{\tau }_{0}by(3{x}^{2}+{y}^{2})}{{({x}^{2}+{y}^{2})}^{2}} \hfill\\ {\sigma }_{y}=\frac{{\tau }_{0}by({x}^{2}-{y}^{2})}{{({x}^{2}+{y}^{2})}^{2}} \hfill \\ {\sigma }_{z}={{{\rm{v}}}}({\sigma }_{x}+{\sigma }_{y})\end{array}\right.$$

(7)

$$\left\{\begin{array}{c}{\tau }_{xy}=\frac{{\tau }_{0}by({x}^{2}-{y}^{2})}{{({x}^{2}+{y}^{2})}^{2}}\\ {\tau }_{xz}={\tau }_{yz}\hfill\end{array}\right.$$

(8)

$${\tau }_{0}=\frac{G}{2\pi (1-v)}$$

(9)

Here, x, y denote the coordinates in a two-dimensional orthonormal coordinate system with the edge dislocation line as the origin and its Burgers vector b aligned along the x-axis, where G represents the shear modulus, v represents the Poisson’s ratio, σ_x, σ_y, and σ_z represent the normal stress components, and τ_xy, τ_xz, and τ_yz represent the shear stress components associated with the edge dislocation field. Figure 4b describes a local τ_xy stress field formed by the arrangement of multiple dislocations along their Burgers direction. The shear stress difference between the two sides of the overlong edge dislocation alignment will lead to the pile-up of the dislocation blocks, eventually reaching the failure limit.