In this paper, we have characterized the microstructural evolution and the plastic ow and fracture behaviours of AISI 304L and AISI 316LN stainless steel grades at liquid nitrogen temperature (77 K) and at liquid helium temperature (4 K). Uninterrupted tensile exper- iments, where the sample is continuously deformed under quasi-static loading conditions until fracture, have been carried out with a Single-Section Sample to obtain the stress-strain characteristics of the two grades. Interrupted tensile experiments, in which the sample is unloaded before fracture, have been performed with a novel Double-Section Sample to later characterize the strain-induced martensitic transformation at di erent levels of deformation. The content of martensite has been determined post-mortem, using magnetic induction, elec- tron backscatter di raction and quantitative light optical micrography. The results obtained with the three methods show quantitative agreement, and reveal that the martensitic trans- formation in AISI 304L occurs faster and to a greater extent than in AISI 316LN both at 77 K and at 4 K. To the authors' knowledge, in this paper we provide the rst experimen- tal results for the evolution of the content of strain-induced martensite in AISI 304L and AISI 316LN samples tested at liquid helium temperature. In addition, the experimental data for the evolution of the martensite volume fraction with the strain have been used to identify the temperature-dependent parameters of the martensitic transformation kinetic model pro- posed by Olson and Cohen (1975). Moreover, Mode I fracture tests with fatigue-precracked Compact Samples have been carried out to determine the fracture properties of the two in- vestigated materials using the \resistance curve procedure" (ASTM-E1820-20a, 2020). The crack-growth resistance curves have been obtained with four di erent methods here referred to as ASTM Compliance Method, W-N Compliance Method, Modi ed W-N Compliance Method and ASTM Normalization Method, which is an original methodological contribu- tion of this paper. While the four approaches yield similar results for the fracture toughness, only the W-N Compliance Method and the Modi ed W-N Compliance Method, the latter being proposed in this paper, ful l all the requirements of the standard ASTM-E1820-20a (2020) so that the calculated fracture toughness can be accepted as a material property. The comparison of results for both materials and testing temperatures shows that AISI 316LN displays higher fracture toughness than AISI 304L. Moreover, post-mortem microstructural analysis of the Compact Samples near the fracture surface has revealed that the content of martensite is greater in AISI 304L than in AISI 316LN. Furthermore, for AISI 304L more martensite is formed in the sample tested at 77 K because the plastic deformation near the crack is more than at 4 K. *mariapilar.fernandez@uc3m.es Manuscript published in Engineering Fracture Mechanics 258 (2021) 108042: 10.1016/j.engfracmech.2021.108042 1 Nomenclature Latin characters a crack size: distance from the load-line to the crack tip a0 initial crack size: distance from the load-line to the fatigue precrack tip b0initial remaining ligament: distance from the fatigue precrack tip to the sample back edge ( Wa0) B thickness of the sample Ciconstant parameters used in the de nition of the power law regression line J= C1aC2(i=1,2) D average grain diameter f 0volume fraction of 0-martensite J J -integral JIc plane-strain fracture toughness characterized by J-integral (size-independent JQ) JQcrack initiation toughness characterized by J-integral (at 0.2 mm of crack exten- sion beyond blunting) JR curvecrack extension resistance as a function of stable crack extension K,KI stress intensity factor for Model-I crack KIc plane-strain fracture toughness characterized by K-factor KJIcplane-strain fracture toughness characterized by K-factor converted from JIc(size- independent KJQ) KJQ crack initiation toughness characterized by K-factor converted from JQ P load R load ratio ( R=Pmin=Pmax) t time T temperature v load-line displacement W width of the sample Greek characters body-centred cubic lattice (ferrite) 0body-centred tetragonal lattice (martensite) face-centred cubic lattice (austenite) a crack extension ( aa0)  hexagonal close-packed lattice (martensite)  parameter of the Olson and Cohen model: rate of shear-band formation iparameters to model the temperature-evolution of the Olson and Cohen model parameter(i= 1;2;3) parameter of the Olson and Cohen model: probability of a shear-band intersection forming a martensitic embryo iparameters to model the temperature-evolution of the Olson and Cohen model parameter(i= 1;2;3)  stress (Cauchy) TS ultimate tensile strength Y e ective yield strength ( Y= (YS+TS)=2) YS yield strength (0 :2% o set) " strain (Hencky) _" initial strain rate (Hencky) Acronyms CICC Cable-In-Conduit Conductors 2 EBSD Electron Backscatter Di raction FEG Field Emission Gun LHC Large Hadron Collider SEM Scanning Electron Microscope W-N Weiss-Nyilas (Compliance Method and Modi ed Compliance Method) 1 Introduction Superconducting high- eld magnets have become indispensable in high-energy particle physics accelerators to accurately guide the particle beams, such as at the LHC at CERN (Br uning et al., 2012), and in fusion reactors to con ne and control the plasma, such as ITER (Mitchell et al., 2008). The magnet systems, as they are used in CERN's LHC or ITER, contain coils made of niobium-titanium (NbTi) or niobium-tin (Nb 3Sn) conductors, that need to be cooled to cryogenic temperatures to achieve the superconducting state (Br uning et al., 2012; Apollinari et al., 2015; Mitchell et al., 2008). Superconducting cables allow to apply very high currents that induce strong magnetic elds causing high magnetic forces within the magnet system. These forces have to be counteracted by structural components at the named cryogenic temperatures. Since austenitic stainless steels display stable material properties over the whole temperature operating range of the superconducting magnets, they are the dominant structural materials used for these components (Sgobba, 2006; Barabash et al., 2007). Such components are, for instance, the steel collars of the standard Dipole magnet for the LHC (Bertinelli et al., 2006) and the jacket of the so-called ITER \Cable-In-Conduit Conductors" (CICC) (Devred et al., 2014). The austenitic stainless steels used for the steel collars display at 4 K a yield strength, ultimate tensile stress and elongation higher than 1300 MPa, 1800 MPa and 24%, respectively (Bertinelli et al., 2006; Couturier and Sgobba, 2000); while in the case of the CICC jackets those properties are higher than 700 MPa, 1000 MPa and 20%, respectively (Romano et al., 2016). In both cases stress and deformation values are expressed using the engineering de nition. Austenitic stainless steels generally retain high strength, ductility and toughness at low temperatures, and they are paramagnetic or antiferromagnetic under the N eel temperature in the fully austenitic state. Nevertheless, they are susceptible to develop strain-induced marten- sitic transformation, especially at cryogenic temperatures. The initially undeformed -austenitic phase (face-centred cubic) may be transformed, by di erent transformation mechanisms, either to 0-martensite (body-centred tetragonal) or to -martensite (hexagonal close packed). After a relatively low deformation, the strain-induced 0-martensitic transformation is more extensive than the transformation of -martensite (Mangonon and Thomas, 1970; Seetharaman, 1984; De et al., 2004). Moreover, the 0-martensitic phase is ferromagnetic and becomes brittle at cryo- genic temperatures. For these reasons, the - 0transformation is a major concern due to the high impact on the performance of the structural components used in high- eld magnet systems. A comprehensive analysis of the ow and fracture behaviours of austenitic stainless steels at low temperatures, as applied for the superconducting magnets used at CERN and ITER, is therefore essential. The manuscript is organized as follows. The austenitic stainless steels AISI 304L and AISI 316LN investigated in this work are presented in Section 2, including their chemical composition and the analysis of their microstructure in the as-received condition. A detailed description of the experimental techniques employed to characterize the tensile ow behaviour and microstructural evolution of AISI 304L and AISI 316LN at 300 K, 77 K and 4 K is provided in Section 3, and the analysis of results is performed in Section 4. Moreover, Section 5 describes the Compact Sample used to perform the fracture toughness tests, the four methods employed to construct theJRcrack-growth resistance curves and the optical microscopy technique used to determine the strain-induced martensite formed near the fracture surface during the experiments, while 3 the results of the fracture tests are presented and discussed in Section 6. A summary of the research including the main ndings derived from this investigation is given in Section 7. 2 Materials The materials studied are AISI 304L and AISI 316LN austenitic stainless steels. AISI 304L is a general-purpose grade, while AISI 316LN is selected for applications requiring high strength, or where an increase of magnetic susceptibility might be of concern (Vogt et al., 1991). AISI 304L is the low (L) carbon version of the common iron-chromium-nickel AISI 304. On the other hand, AISI 316LN is a modi cation of the molybdenum-containing grade AISI 316, with low (L) content of carbon and addition of nitrogen (N) (Reed, 1989). The e ect of molybdenum is the improvement of corrosion resistance and a higher stability of the austenite against marten- sitic transformation. Nitrogen also increases austenite stability, and enhances the formation of austenite compared to ferrite. Moreover, nitrogen substantially increases strength and maintains ductility down to cryogenic temperatures (Sgobba, 2006). The speci c chemical compositions of the AISI 304L and AISI 316LN grades investigated in this work are given in Table 1. Both grades show a high purity which is a requirement for products intended for high vacuum purposes at CERN. Special attention is taken in reducing the content of sulphur and phosphorus in order to minimize the risk of micro ssuring in austenitic stainless steel welds (Kujanpaa et al., 1979; Sgobba, 2006). Thus, while AISI 304L is melted in an electric arc furnace followed by secondary metallurgy (vacuum oxygen decarburization), the manufacturing process of AISI 316LN includes an electro-slag remelting which allows to keep the sulphur levels in the ppm range (Chakrabarti, 2006). Grade C S N Cr Ni Mn Si Mo P Co 304L 0:013 0:0003 18:19 10:28 1:27 0:45 0:024 0:024 316LN 0:009<0.002 0:19 17:37 13:09 1:34 0:28 2:61 0:024 0:100 Table 1: Chemical composition of AISI 304L and AISI 316LN (product analysis except for Co 316LN which is heat analysis, weight-% Fe balance). The raw materials were provided in the form of hot rolled and solution annealed plates of 12 mm thickness (surface nish 1D according to the standard EN-10088-2 (2008) as indicated in the corresponding CERN technical speci cations). For AISI 304L the annealing was performed at 1060C for 18 min followed by water quench, while for AISI 316LN it was done at 1110C for 9 min also followed by water quench. Fig. 1 shows the undeformed microstructure of both materials. Rolling direction is horizontal in the micrographs. AISI 304L presents some linear - ferrite (body-centred cubic) precipitations embedded in the austenitic matrix along the rolling direction. The ferritic phase has been identi ed with the selective Murakami's etchant as indi- cated in the standard ASTM-E407-07 (2015). Indeed, according to Sgobba (2006), AISI 304L grade normally retains some ferrite when cooled from solution annealing. Measurements with the Feritscope con rm that the ferrite volume is lower than 0 :5% (see the item Magnetic induc- tion in Section 3.2). On the other hand, AISI 316LN is constituted of 100% austenite, which is expected due to the strong austenite stability provided by the alloying elements. Moreover, the microstructure of both grades, AISI 304L and AISI 316LN, shows some annealing twins which are typically formed in austenitic stainless steels after deformation and subsequent annealing (Jin et al., 2013; Singh, 1996). The average grain size in the undeformed state is D= 89:9m for AISI 304L and D= 53:4m for AISI 316LN. These values were provided by the correspond- ing materials' certi cates, which determined the average grain size according to the standard ASTM-E112-13 (2013). The thermal stability of AISI 316LN was con rmed by immersion in liquid helium for more 4 (a) (b) Figure 1: Light optical microscopy images of the materials' cross-section (through the plate's thickness, along the rolling direction). Rolling direction is horizontal in the micrographs. Images taken after oxalic acid etching (etchant no. 13 in ASTM-E407-07 (2015)): (a) AISI 304L and (b) AISI 316LN. than two hours, after which no ferromagnetic response was detected with the Feritscope thus ruling out a spontaneous martensitic transformation. Regarding AISI 304L, there was not an evident increase of the material's ferromagnetic response neither after immersion in liquid ni- trogen nor in liquid helium. Therefore, the spontaneous transformation of AISI 304L, if any, is negligible. 3 Flow behaviour: experimental techniques 3.1 Mechanical tests Uniaxial tensile tests have been performed at room temperature ( T= 300 K), at liquid nitro- gen temperature ( T= 77 K) and at liquid helium temperature ( T= 4 K), according to the standards ISO-6892-1 (2009), ISO-6892-3 (2015) and ISO-6892-4 (2015), respectively. All the tests have been carried out at CERN in a 100 kN servo-hydraulic testing machine fabricated by MICROTEST. Two Epsilon cryogenic extensometers (3442C-050M-020-LT) have been em- ployed for the tests in their shortest con guration of 12 :5 mm gauge length which maximises the available strain measuring range. All the tests have been performed under displacement control of the machine's cross head at constant speed. For the tests performed at room temperature the samples have been directly attached to the machine's cross head, whereas for the cryogenic tests the in-house developed cryostat described by Avil es-Santillana et al. (2015) and Malik (2021) has been employed. The tensile samples have been extracted from the mid-thickness region of each plate with the tensile axis parallel to the rolling direction (\longitudinal at tension test" according to the standard ASTM-A370-15 (2015)). The thickness of the samples is 4 mm. Two di erent geometries, here referred to as Single-Section Sample and Double-Section Sample, have been used: Single-Section Sample : It has been used in uninterrupted tensile tests where the sample is continuously deformed until fracture. The aim is to obtain the complete stress-strain curve of the material. The design of the Single-Section Sample (Fig. 2) is based on a \non-proportional test piece" according to the standard ISO-6892-4 (2015). For each material, two uninterrupted tensile experiments have been performed for the three di erent testing temperatures. 5 Figure 2: Design of the Single-Section Sample. Dimensions in millimetres. Double-Section Sample : It has been used in interrupted experiments in which the sample is unloaded before frac- ture (see Fig. 6). In a single tensile test both sample's gauge-length sections {which have di erent width{ are simultaneously submitted to a di erent stress level. The aim is to ob- tain two gauge-length sections presenting di erent homogeneous deformation levels when the sample is unloaded, so that we later determine the strain-induced '-martensite (the idea is to decrease the number of experiments to be performed since the cryogenic tests are highly time- and resources-consuming, specially helium). For reasons of comparability, both gauge sections of the Double-Section Sample have the same length, and one of them also the same width as the Single-Section Sample. The width of the other gauge section was selected based on the material's stress-strain curves previously determined by the un- interrupted tensile tests, so that we obtain eight strain levels to measure the 0-martensite (uniformly distributed strain levels over the whole range of homogeneous strain prior the ultimate tensile strength is attained, see Fig. 4) by testing only four Double-Section Sam- ples for each material and testing temperature. Fig. 3 shows the Double-Section Sample designed for AISI 304L and AISI 316LN. The di erent geometry is due to the di erent ma- terials' stress-strain curve. Prior to the execution of the interrupted tensile tests, a prelim- inary assessment of the two geometries was performed. First, tensile test simulations were performed in ABAQUS software (Dassault Syst emes Simulia Corp., RI, United States) by importing the two di erent geometries and the materials' stress-strain curves assessed by the uninterrupted tensile tests. Moreover, one Double-Section Sample for AISI 304L was tensile tested until rupture at room temperature and the full- eld strain was characterized by an in-situ Digital Image Correlation analysis. Both, nite element analysis and Digital Image Correlation, con rmed that the strain distribution in the sample sections is largely homogeneous and that the maximum principal direction of strain is parallel to the tensile axis within each of the two di erent gauge-length sections (these results are not shown here for the sake of brevity). (a) (b) Figure 3: Design of the Double-Section Sample: (a) AISI 304L and (b) AISI 316LN. Dimensions in millimetres. 6 For all performed tensile tests, the stress has been computed using the load values from the machine's load cell (see Fig. 4). The strain values have been calculated using the displacement obtained from the extensometers: a single extensometer in the case of a Single-Section Sample, and two extensometers in the case of a Double-Section Sample. 3.2 Martensite measurements We have used three complementary methods to determine the martensite volume fraction in the tested specimens (post-mortem measurements): magnetic induction, electron backscatter di raction (EBSD) and quantitative light optical micrography. All the measurements have been performed at CERN. The idea is to compare the results obtained with the three approaches and provide consistent data for the evolution of the 0-martensite content with the strain for di erent testing temperatures. Note that Cao and Iwamoto (2017) and Cao et al. (2020) have recently determined the relative magnetic permeability of austenitic stainless steel samples during tensile testing at room temperature at di erent strain rates, thus obtaining a continuous measurement of the evolution of 0-martensite during loading. However, the application of this approach to tests performed at cryogenic temperatures is still pending. Magnetic induction The Feritscope locally determines the content of the ferromagnetic phase in the mate- rial using a magnetic induction probe. The Feritscope Fisher model FMP30 employed in this study was supplied with certi ed ferrite standards which were used for the calibra- tion, and therefore the device provides the measurements in ferrite percent independently of the nature of the ferromagnetic phase. Moreover, according to the Feritscope manual (FERITSCOPE-FMP30, 2008), measurement readings taken at a distance less than 2 mm from the edge of the sample have to be corrected by provided correction curves. Specif- ically, the correction is done by multiplying the device measurements by the respective correction factor provided in the Feritscope's certi cate. The Feritscope measurements have been performed in the mid-width of the section along its longitudinal direction so that, according to Ortwein (2015), when the deformed width of the sample is smaller than 4 mm, the correction has to be applied twice since the mid-width measurement is a ected by the two section's edges. Taking into account that the deformed gauge-length sections present a width range between 3 :25 mm and 4 :42 mm for the di erent strain levels for which the Feritscope analysis is performed, the overall correction factor varies between 1:03 and 1:62. Moreover, the bi-linear calibration curve proposed by Ortwein (2015) is sub- sequently applied to transform the device measurements into 0-martensite content. Eight measurements have been performed on each deformed gauge-length section of the as-tested tensile samples (four measurements per section's side) in order to obtain a representative value of the 0-martensite content. From the eight measurements the average value has been calculated (the maximum deviation from the average is 6 :4% and it corresponds to the samples tested at 4 K). Electron backscatter di raction Electron backscatter di raction (EBSD) can identify and map the phases present in the microstructure based on the di raction of electrons, generated by the scanning electron microscope (SEM), from the speci c crystallographic planes. It allows the visualization of the phases' morphology and the calculation of their respective fraction on the mapped surface. The specimens have been extracted from the gauge length's section of the deformed tensile-test samples. For each section, two cuts perpendicular to the sample's longitudinal direction have been performed to obtain a single 11 mm-long specimen. The surface of the specimens has been prepared by mechanical grinding down to 1200 grit on SiC abrasive grinding papers and mechanical polishing in three steps down to 1 m diamond solution, followed by colloidal silica polishing. For reasons of comparability with the Feritscope measurements, the prepared surface corresponds to one of the longitudinal-width planes 7 of the gauge-length section. In the present study, the EBSD analyses have been performed using a ZEISS Sigma Field Emission Gun Scanning Electron Microscope (FEG-SEM) with a detector of backscattered electrons. The acquired data have been evaluated with the Oxford Instruments AZTEC-EBSD software. The SEM has been operated at 20 kV using an aperture size of 240 m and 16:5 mm of working distance with the specimen tilted by 70. Each map corresponds to an area of approximately 455 x 320 m2which has been acquired at a magni cation of 250 and has been analysed using a step size of 0:75m. One analysis took approximately 10 hours with the before mentioned settings. The analyses reached a pixel indexing between 83 :5% and 99:8%. Note that two databases have been used for the analysis: iron body-centred cubic for martensite, and iron face- centred cubic for austenite. The reason for using body-centred cubic for identifying the martensite is due to the fact that the c/a-ratio of its actual body-centred tetragonal lattice is very close to one (Naraghi, 2009) and the EBSD is not very sensitive to small variations of the crystallographic lattice. The selected batch of analysed specimens consists on 14 specimens which include for each material two deformation levels per tested temperature and a reference specimen in the undeformed state. Moreover, one single analysis has been performed for each specimen, and therefore, each result is based on a sample area of approximately 0 :15 mm2. The volume fraction of martensite is obtained assuming that it is equal to its area fraction. Quantitative light optical micrography Light optical microscopy allows to distinguish between phases with di erent crystallo- graphic structure based on their di erent light re ection from the as-polished specimen's surface. Quanti cation analysis determines the fractions of the phases on the micrographs based on their di erent colour contrast. In the present study, the micrographs have been examined with a Carl ZEISS Optical Microscope connected to the ZEISS AxioCam MRc5 High Resolution Camera. Each micrograph covered an area of about 180 135m2which has been acquired at a magni cation of 500, resulting in a pixel size of 0 :13m. The light optical micrographs show the martensite in dark and austenite in light (see Fig. 19 in Section 6). The correspondence between the two colour-contrasts and the two phases has been obtained by comparing EBSD maps with light optical micrographs covering the same sample area (the comparison is not shown here for the sake of brevity). For the phase quan- ti cation an automatic image analysis using MATLAB software (MathWorks Inc., MA, United States) has been applied on the acquired micrographs. The analysis determines the martensite fraction from binary images which are obtained by image thresholding the processed micrographs. The code used for the determination of the content of martensite is included as Supplementary Material . The specimens used for the quantitative light optical microscopy analysis are the same analysed by EBSD. For this analysis, 24 micrographs per specimen have been acquired. For the sake of reproducibility, each of the 24 micrographs has been taken at approximately the same surface's position on the di erent specimens. From the 24 analyses per specimen, the martensite content for each specimen is based on an a total sample area of approximately 0 :50 mm2. The volume fraction of martensite is obtained assuming that it is equal to its area fraction. 4 Flow behaviour: results The uniaxial tension stress-strain curves, ", obtained from AISI 304L and AISI 316LN samples tested at di erent temperatures, T= 4 K, 77 K and 300 K, are shown in Fig. 4. The stress is the Cauchy stress computed from the machine's load cell and the strain, hereinafter also referred to as raw strain, is the Hencky strain calculated from the displacement values acquired by the extensometer, as mentioned in Section 3.1. The imposed initial strain rate in the experiments is _ "104s1. The results correspond to uninterrupted tests performed with the Single-Section Sample (see Section 3.1). For the sake of clarity in the presentation of data we 8 only show one stress-strain curve per material and testing temperature. In this regard, note that the experiments showed good repeatability and the di erences in the stress-strain characteristics obtained from di erent samples tested at the same temperature are small, and do not a ect the discussion of results presented below. The comparison of the stress-strain curves obtained in this work with data available in the literature is performed in A. Moreover, recall that here we are studying the in uence of temperature on the material mechanical behaviour, and all the samples for each material grade have been produced using the same manufacturing process (see Section 2). The reader is referred to the recent paper of Kvackaj et al. (2020) to obtain insights into the in uence of rolling temperature, ambient or cryogenic, on the mechanical properties of AISI 316LN. 05001000150020002500 0 0.1 0.2 0.3 0.4 0.5 0.6 0.74 77 roomTrue stress, σ (MPa) True strain, εT=4 K T=77 K T=300 KMaterial: AISI 304LMartensite content identification, Figs. 9, 10 and 11 (a) 05001000150020002500 0 0.1 0.2 0.3 0.4 0.5 0.6 0.74 77 roomTrue stress, σ (MPa) True strain, εMaterial: AISI 316 LN T=4 K T=77 K T=300 KMartensite content identification, Figs. 12 13 and 14 (b) Figure 4: Stress-strain curves for three di erent testing temperatures T= 4 K, 77 K and 300 K. The imposed initial strain rate in the experiments is _ "104s1. Results corresponding to: (a) AISI 304L and (b) AISI 316LN. The yellow markers indicate the values of strain corresponding to the EBSD maps of Figs. 7-12. Fig. 4(a) shows the results corresponding to AISI 304L. At room temperature, the material displays an initial 0 :2% o set yield strength of YS300 MPa and quasi-linear strain-hardening, so that the necking forms at a strain of 0:51 and the ultimate tensile strength is TS 1000 MPa (both initial yield stress and ultimate tensile strength are determined following the procedure detailed in ASTM-E8/E8M-15a (2015) converting the values to true stress, necking is assumed to start when the ultimate tensile strength is reached). At 77 K the initial 0 :2% o set yield strength is 350 MPa and the stress-strain characteristic displays a sigmoidal shape, with a sudden increase of the strain-hardening rate at a strain of 0:07. The ultimate tensile strength is 1900 MPa and the necking strain 0:30. The change of curvature of the stress-strain curve and and loss of ductility are typical of a material in which the 0-martensite fraction increases rapidly with strain (Morris Jr et al., 1992; Skocze n, 2001), as it will be shown later (see Fig. 13). At 4 K the stress-strain curve is further shifted upwards, and the plastic ow becomes discontinuous. The transition between continuous and discontinuous plastic ow is observed mainly in face-centred cubic metals and alloys at extremely low temperatures close to absolute zero. It is related to a change in the predominant type of moving dislocation from screw to edge character since the latter needs less thermal energy for its generation and motion. The phenomenon of serrated yielding occurs at suciently low strain rates, so the released heat during deformation can be easily removed by the cryogenic coolant and the motion of dislocation maintains its predominant edge character (Seeger, 1957; Obst and Nyilas, 1991). According to Obst and Nyilas (1991), this phenomenon has a mechanical nature: it is caused by the local catastrophic failure of barriers formed in the weakly excited lattice, whose collapse leads to a massive motion of dislocations. The failure occurs when the edge dislocations pile-ups give rise to stress concentrations which are high enough to overcome the cohesive strength. The massive motion of dislocations occurs locally at the unblocked lattice barriers, then the dislocations move until they reach the next obstacle and the whole process is repeated. Macroscopically, this 9 process leads to simultaneous stepwise increases of strain and abrupt drops of stress, the former consisting in slip bands travelling along the sample (Tabin et al., 2016, 2019). In the course of strain hardening the local breakdown of lattice barriers becomes more dicult (Obst and Nyilas, 1991), thus more pronounced serrations {greater strain increment between individual serrations and higher load drop{ are observed in Fig. 4 for higher strains. Fig. 4(b) shows the results corresponding to AISI 316LN. At room temperature, the stress- strain curve is similar to AISI 304L, with quasi-linear strain-hardening and signi cant ductility, the necking strain and the ultimate tensile strength being 0:32 and900 MPa, respectively. At 77 K the ow stress of AISI 316LN rises signi cantly {the initial 0 :2% o set yield strength and the ultimate tensile strength reaching 700 MPa and2100 MPa, respectively{ while keeping linear strain hardening and large ductility (unlike AISI 304L). Decreasing the testing temperature up to 4 K further increases the material ow stress and decreases the necking strain so that the ultimate tensile strength corresponds to a strain of 0:34. Notice that the ow stress shows serrations for strains greater than 0 :1. Nevertheless, for some of the experiments performed with the AISI 316LN samples at 4 K, the serrated yielding started earlier, for "0:05. 05001000150020002500 00.10.20.30.40.5 0 500 1000 1500stress strain ext strain f strain fTrue stress, σ (MPa)True strain,ε Loading time, t (s)True stress, σ True strain, εzoom Material: AISI 304L T=4 K Δε /Δt=ε.kinkstage II stage I1200130014001500 0.160.170.18 840 850 860 870 880 (a) 05001000150020002500 00.10.20.30.40.5 0 500 1000 1500B C D Loading time, t (s)True stress, σ (MPa)True strain, ε Δε /Δt=ε.Material: AISI 316LN True stress, σ True strain, εT=4 K (b) Figure 5: Temporal evolution of the stress and the strain for experiments performed at 4 K using the Single-Section Sample. The green dashed lines represent the uniform strain on the sample's gauge-length section during plastic deformation (two-stage strain rate for the case of AISI 304L within the range of strains analysed in the gure). Results corresponding to: (a) AISI 304L and (b) AISI 316LN. As already discussed, the discontinuous plastic ow leads to simultaneous stepwise increases of strain and abrupt drops of stress with respect to time during the tests, so that the strain at 4 K is not uniform along the sample's gauge-length but rather has a local nature, as illustrated in Fig. 5 which shows the evolution of the stress (black solid line) and the raw strain (red solid line) with the loading time for the same tests at 4 K presented in Fig. 4. As mentioned before, the raw strain is calculated from the displacement values obtained with the extensometer. The graphs also picture the evolution of the uniform strain which is computed averaging the strain rate over time along the sample's gauge length (green dashed line), where the strain rate is calculated as the ratio between the increase of strain within a time interval. Notice that both AISI 304L and AISI 316LN samples show the same uniform strain rate at the beginning of loading (recall that the initial strain rate is _ "104s1). However, while for AISI 316LN samples the strain rate isroughly constant during the whole loading process {actually, there is a gradual decay of the strain rate due to the sample elongation{, in the case of AISI 304L samples tested at cryogenic temperatures the uniform strain rate suddenly decreases to half of its value at "0:07 (at the kink indicated in Fig. 5(a)). Notice that this is the strain value for which the stress-strain curve changes from concave-downwards to concave-upwards, see Fig. 4(a). The drop of the strain rate occurs because the sections of the sample with " >0:07 need higher stress increment to keep deforming than the sections with a lower strain level, so that the contribution of the sections of the sample beyond the gauge length to the total sample elongation increases. Consequently, since the velocity of the machine's cross-head is constant, the uniform strain rate on the sample's 10 gauge length decreases. Fig. 6 shows experimental results for AISI 304L obtained at 77 K with the Double-Section Sample. Notice that the stress-strain curves computed from interrupted tests performed with the Double-Section Sample {coloured lines{ and from uninterrupted tests carried out with the Single-Section Sample {black lines{ are very similar. Solid coloured lines correspond to the results of the 4 mm width gauge-length section of the sample, and dashed coloured lines to the 4 :5 mm width section. Each colour corresponds to the results obtained from a given Double-Section Sample. As anticipated in Section 3.1, performing four interrupted tests enables to obtain a set of eight distributed strain levels to measure the 0-martensite content in the samples before the ultimate tensile strength of the material is attained: two levels of strain at the end of each test, corresponding to the two gauge-length sections of the sample. Similar observations are derived from the tests performed at 4 K and 300 K, and also from the interrupted experiments conducted with the Double-Section Sample designed for AISI 316LN. 0400800120016002000 0 0.1 0.2 0.3 0.4True stress, σ (MPa) True strain, εT=77 K Material: AISI 304L unloadingUninterrupted tests InterruptionInterrupted tests: 4.5 mm width gauge-length sectionInterrupted tests: 4 mm width gauge-length section Figure 6: Experimental results for AISI 304L at 77 K. Comparison between stress-strain curves obtained from interrupted tests performed with the Double-Section Sample {coloured lines{ and from uninterrupted tests carried out with the Single-Section Sample {black lines{. Solid coloured lines correspond to the results of the 4 mm width gauge-length section, and dashed coloured lines correspond to the 4 :5 mm width section. Each colour corresponds to the results obtained from a given Double-Section Sample. The EBSD maps obtained from Double-Section Samples, which were used in interrupted experiments performed at di erent testing temperatures, are shown in Figs. 7-12. The results for AISI 304L are pictured in Figs. 7-9, and the results for AISI 316LN in Figs. 10-12, respectively. The colour coding of the EBSD maps is such that the martensite is in blue and the austenite is in red. The observed morphology of the 0-martensite phase consists of the low-carbon lath- type martensite. The laths tend to align parallel to one another forming a packet arrangement. Moreover, several lath-packages with di erent orientations normally coexist in a single austenite grain (Vander Voort et al., 2004; Naraghi, 2009). From the EBSD maps analysed here, the lath- packages are distinguishable for specimens containing relative small contents of martensite (up to approximately 30%). Specimens containing a high content of martensite (higher than 80%) show austenite grains which are quasi-fully transformed into martensite. It can be observed that the 0-martensite phase tends to form at or nearby stacking faults, which are recognized as parallel black lines inside the austenite grains (see Fig. 10(b) where the quasi-monochromatic 11 red map allows an easy identi cation of the stacking faults). The density of stacking faults is noted to be increased with increasing strain. Moreover, the EBSD maps corresponding to high level of deformations show grains greatly deformed with a tendency to elongate along the rolling direction (Figs. 7(b)-12(b)). Figs. 7(a)-(b) show images for an AISI 304L sample tested at 300 K corresponding to two values of strain, 0 :25 and 0:43, respectively. While the amount of martensite is not large, these images make apparent the increasing formation of martensite in AISI 304L due to the accumula- tion of plastic deformation at room temperature. On the other hand, the amount of martensite signi cantly increases at cryogenic temperatures. Figs. 8(a)-(b) show EBSD maps corresponding to a sample tested at 77 K, which reveal a large martensite content for a relatively low strain of0:12, and quasi-complete transformation of the austenite grains into martensite at a strain of0:24. Moreover, the results obtained from the tests performed at 4 K, see Figs. 9(a)-(b), are similar to the EBSD maps of the tests at 77 K with the material becoming almost fully martensitic for strains greater than 0 :2. 200 m (a) 200 m (b) Figure 7: EBSD maps of deformed AISI 304L Double-Section Sample tested at 300 K. Rolling direction is horizontal in the micrographs. Colour coding: martensite in blue and austenite in red. The maps correspond to di erent values of strain indicated in Fig. 4(a) with yellow markers: (a)"0:25 and (b) "0:43. 200 m (a) 200 m (b) Figure 8: EBSD maps of deformed AISI 304L Double-Section Sample tested at 77 K. Rolling direction is horizontal in the micrographs. Colour coding: martensite in blue and austenite in red. The maps correspond to di erent values of strain indicated in Fig. 4(a) with yellow markers: (a)"0:12 and (b) "0:24. 12 200 m(a) 200 m (b) Figure 9: EBSD maps of deformed AISI 304L Double-Section Sample tested at 4 K. Rolling direction is horizontal in the micrographs. Colour coding: martensite in blue and austenite in red. The maps correspond to di erent values of strain indicated in Fig. 4(a) with yellow markers: (a)"0:16 and (b) "0:22. Figs. 10(a)-(b) shows EBSD maps for an AISI 316LN sample tested at 300 K which reveal that, unlike in the case of AISI 304L, negligible amount of martensite is formed in this steel grade at room temperature. On the other hand, decreasing the testing temperature promotes the martensitic transformation, yet, the content of martensite in AISI 316LN samples tested at cryogenic temperatures is signi cantly lower than in the case of AISI 304L. Namely, the results presented in Figs. 11(a)-(b) for a test carried out at 77 K show that for a strain of 0:20 the martensite content is virtually negligible, and that increasing the material straining up to 0 :36 only causes a modest portion of austenite to transform into martensite. Moreover, the EBSD maps of Figs. 12(a)-(b) show that the formation of martensite at 4 K starts at a lower level of strain in comparison with the test performed at 77 K (compare Figs. 11(a) and 12(a)), and the transformation seems to be faster (compare Figs. 11(b) and 12(b)). 200 m (a) 200 m (b) Figure 10: EBSD maps of deformed AISI 316LN Double-Section Sample tested at 300 K. Rolling direction is horizontal in the micrographs. Colour coding: martensite in blue and austenite in red. The maps correspond to di erent values of strain indicated in Fig. 4(b) with yellow markers: (a)"0:23 and (b) "0:32. Quantitative measurements for the evolution of the martensitic transformation with the strain (elastic strains are neglected, so that all the strain is considered to be plastic) are shown in Figs. 13 and 14. The data correspond to measurements obtained with all the three methods: magnetic induction, electron backscatter di raction and quantitative light optical micrography (black, red and green markers, respectively). Notice that the results obtained with the three 13 200 m(a) 200 m (b) Figure 11: EBSD maps of deformed AISI 316LN Double-Section Sample tested at 77 K. Rolling direction is horizontal in the micrographs. Colour coding: martensite in blue and austenite in red. The maps correspond to di erent values of strain indicated in Fig. 4(b) with yellow markers: (a)"0:20 and (b) "0:36. 200 m (a) 200 m (b) Figure 12: EBSD maps of deformed AISI 316LN Double-Section Sample tested at 4 K. Rolling direction is horizontal in the micrographs. Colour coding: martensite in blue and austenite in red. The maps correspond to di erent values of strain indicated in Fig. 4(b) with yellow markers: (a)"0:18 and (b) "0:31. methods are similar, for the three testing temperatures (300 K, 77 K and 4 K) and both ma- terials, which shows the robustness and reliability of the measurements. The comparison of the martensite content obtained in this work with data available in the literature is performed in A. Fig. 13 pictures the results corresponding to AISI 304L. At room temperature the martensitic transformation starts at "0:05 and increases with the strain so that for "0:4 the volume fraction of martensite f 0reaches5%. The evolution of the martensite content with the strain is very similar for 77 K and 4 K, with the martensite volume fraction f 0reaching70% for a strain of0:2 (see Figs. 8(b) and 9(b)). The rapid martensitic transformation displayed by AISI 304L at cryogenic temperatures explains the sigmoidal shape of the stress-strain curves shown in Fig. 4, so that the higher strength of the martensitic phase, in comparison with the austenite, is responsible for the sudden increase of the strain-hardening rate of the material. To the authors knowledge these are the rst measurements available in the open literature for the martensite content in 304L tensile samples tested at 4 K. To the authors' knowledge it is also the rst time the evolution of the martensite content with the strain shows almost an equal behavior when reducing the temperature, as it is the case of the results obtained in this work for AISI 304L at 77 K and 4 K. This fact seems to indicate that for this grade the transformation process is already saturated at 77 K, so the formation of martensite cannot occur either earlier 14 05101520 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7Fer EBSD LOM OC GSVolume fraction of martensite, fα(%) True strain,ε' T=300 KMaterial: AISI 304L Magnetic induction Electron backsactter diffraction Quantitative light optical micrography Olson and Cohen model(a) 020406080100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7Fer EBSD LOM OC GSVolume fraction of martensite, fα(%) True strain,ε' T=77 KMaterial: AISI 304L Magnetic induction Electron backsactter diffraction Quantitative light optical micrography Olson and Cohen model (b) 020406080100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7B D F H JVolume fraction of martensite, fα(%) True strain,ε' T=4 KMaterial: AISI 304L Magnetic induction Electron backsactter diffraction Quantitative light optical micrography Olson and Cohen model (c) Figure 13: Evolution of the volume fraction of martensite f 0with the strain "in AISI 304L samples tested at di erent temperatures: (a) 300 K, (b) 77 K and (c) 4 K. The experimental data correspond to measurements obtained with all the three methods: magnetic induction, electron backscatter di raction and quantitative light optical micrography (black, red and green markers, respectively). The solid line corresponds to the kinetic relation of Olson and Cohen (1975) which has been tted to the experimental data (see Tables 2 and 3). or develop faster at 4 K. Fig. 14 presents the results for AISI 316LN. The three measurement methods detected martensite formation at room temperature lower than 0 :3% (which is within the error of the experimental measure), which evidences the higher stability of this material, in comparison with AISI 304L, against martensitic transformation (see Fig. 10 versus Fig. 7). Moreover, unlike in the case of AISI 304L, there are signi cant di erences in the kinetics of the martensitic transfor- mation at 77 K and 4 K, so that the formation of martensite starts earlier and develops faster at the lower temperature. Namely, at 77 K the volume fraction of martensite for "= 0:2 and 0:3 is 2% and 15%, while at 4 K is 7% and 25%, respectively. Nevertheless, the rate of the trans- formation and the volume fraction of austenite transformed into martensite are smaller than in the case of AISI 304L. In this regard, Morris Jr et al. (1992) and Skocze n (2001) stated that a slow martensitic transformation does not produce a signi cant change on the strain-hardening rate of the material and enhances tensile ductility, in agreement with the stress-strain curves shown in Fig. 4(b) {compare the results with Fig. 4(a) for AISI 304L{. To the authors knowl- edge these are the only measurements available in the literature for the martensite formation in 316LN samples tested at 4 K. It is noticeable that, for both grades, the maximum deviation from the average content between the eight measurements performed using the magnetic induction method has been obtained in the case of samples tested at 4 K (see item Magnetic induction in Section 3.2). It indicates that the local nature of the strain at 4 K, as already discussed in a previous paragraph, 15 05101520 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7MI EBDS LOM OC GSVolume fraction of martensite, fα(%) True strain,ε' T=300 KMaterial: AISI 316LN Magnetic induction Electron backsactter diffraction Quantitative light optical micrography Olson and Cohen model(a) 020406080100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7B D F H JVolume fraction of martensite, fα(%) True strain,ε'Material: AISI 316LN T=77 K Magnetic induction Electron backsactter diffraction Quantitative light optical micrography Olson and Cohen model (b) 020406080100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7MI EBSD LOM OC GSVolume fraction of martensite, fα(%) True strain,ε'Material: AISI 316LN T=4 K Magnetic induction Electron backsactter diffraction Quantitative light optical micrography Olson and Cohen model (c) Figure 14: Evolution of the volume fraction of martensite f 0with the strain "in AISI 316LN samples tested at di erent temperatures: (a) 300 K, (b) 77 K and (c) 4 K. The experimental data correspond to measurements obtained with all the three methods: magnetic induction, electron backscatter di raction and quantitative light optical micrography (black, red and green markers, respectively). The solid line corresponds to the kinetic relation of Olson and Cohen (1975) which has been tted to the experimental data (see Tables 2 and 3). leads to a less homogeneous distribution of martensite along the sample's gauge-length section in comparison with the samples tested at 77 K and 300 K where the plastic ow is continuous (see Fig. 4). The experimental data for the evolution of the martensite volume fraction with the strain (recall that elastic strains are neglected) are tted using the sigmoidal-type kinetic relationship proposed by Olson and Cohen (1975), see Figs. 13 and 14. Olson and Cohen model is given by equation (1), where the parameter represents the rate of shear-band formation and indicates the probability that an intersection of shear bands will result in the nucleation of martensite. f 0= 1e(1e("))4:5 (1) The values of the model parameters are given in Tables 2 and 3. The identi cation process has been carried out by assuming a temperature-evolution function for each parameter. The selected functions are based on the former experimental data provided by Olson and Cohen (1975), who showed a dependence of the parameters andon temperature {see Fig. 2 therein{ which in this work are approximated with a half sigmoid and a full sigmoid function, respectively, see equation (2). =2 1 +e[3(T1)]2 2;=2 1 +e[3(T1)];10;20;30;20;30 (2) 16 AISI 304L AISI 316LN T=300 K T=77 K T=4 K T=300 K T=77 K T=4 K  4:49 7 :81 7 :81 0:37 2 :64 3 :38  0:10 3 :74 3 :74 0:00 1 :80 2 :08 Table 2: Identi cation of the parameters corresponding to the kinetic relation of Olson and Cohen (1975), see equation (1), used in the tted curves shown in Fig. 13 and Fig. 14. AISI 304L AISI 316LN 1 3:361023:36102 2 1:561019:32102 33:661024:36105 1 2:711021:24102 2 3:74 2:10 31:251013:73102 Table 3: Identi cation of the parameters corresponding to the kinetic relation of Olson and Cohen (1975), see equation (2), used in the tted curves shown in Fig. 13 and Fig. 14. 5 Fracture behaviour: experimental techniques 5.1 Mechanical tests Elastic-plastic fracture toughness tests with fatigue-precracked Compact Samples for the opening mode of loading (i.e. Mode I) have been carried out at liquid nitrogen temperature ( T= 77 K) and at liquid helium temperature ( T= 4 K), according to the standard ASTM-E1820-20a (2020). All the fatigue pre-cracking and fracture toughness tests have been performed at CERN. The tests have been used to compute crack-growth resistance JRcurves following the so-called \resistance curve procedure" (see ASTM-E1820-20a (2020)), i.e. using a single Compact Sample to obtain the complete JRcurve. Experiments at room temperature have not been performed since, for the two analysed materials, samples with thickness greater than 12 mm, that is the thickness of the plates from which all samples tested in this work are extracted (see Section 2)), are needed to obtain fracture toughness values that are independent of the sample size (the threshold thickness for AISI 304L is estimated to be around 25 :4 mm based on the work of Sa et al. (2005)). Additionally, since here we are only considering fracture toughness of Mode I, the reader is referred to the recent paper of Wang et al. (2020) to obtain insights into the fracture behaviour of metals under mixed mode loading. The same servo-hydraulic testing machine and cryostat used for the uniaxial tensile tests (Section 3.1) have been employed to perform the fatigue pre-cracking and the fracture toughness experiments. The basic design lines of the tension testing clevis were presented by Malik (2021). Moreover, the design of the Compact Sample consists of an \alternative specimen" according to ASTM-E1820-20a (2020), with a width-to-thickness ratio of W=B = 4 (W= 40 mm and B= 10 mm, see the corresponding dimensions in Fig. 15). The Compact Samples have been extracted from the mid-thickness of each material plate with the load-line axis parallel to the rolling direction (L-T direction according to the standard ASTM-E1823 (2020)). They have been machined using spark-erosion for the in-plane geometry and subsequent milling to obtain the pin holes and the desired thickness. Fatigue pre-cracking of the Compact Samples has been carried out at room temperature according to the standard ASTM-E1820-20a (2020), following the same procedure for both 17 50 40 10 10 G728.451.7° 48A 0.05 A A10-00.05 44.410 2 x R1 2 x 25° ±1°2 x R15710.440°+-10° 10° R0.13 max.23 2.5-00.5SHARP NOTCH SHARP EDGESSHARP EDGES0.05 A 0.05 A 0.05 AEE A 2:10.05 AFigure 15: Design of the Compact Sample used in the fracture toughness tests. materials, with the purpose of obtaining a sharp precrack. Monitoring of the precrack has been performed with a portable optical microscope (Wi-Fi Digital Microscope RS PRO 913-2478). The precrack has been produced by cyclic loading the sample with a sinusoidal waveform at a maximum frequency of 30 Hz under force control using a load ratio of R= 0:1. The rst step of the pre-cracking has been conducted using a maximum load of 1 kN. The transition to the second step has been done when the number of cycles is 105. For the second step a maximum load of 4 kN has been selected. The test was stopped at the moment in which the precrack reached approximately 3 mm (from the sharp notch, see Fig. 15), which corresponds to an initial crack size of a00:65W26 mm (distance from load-line to fatigue precrack tip, see Fig. 15). Hence, the remaining ligament is b0Wa014 mm. Next, side grooves with a total thickness reduction of approximately 2 mm were machined. The machining has been performed using spark-erosion since, according to Weiss and Nyilas (2006), it leads to a straighter crack front during the fracture toughness test. The elastic-plastic fracture toughness tests have been performed according to the standard ASTM-E1820-20a (2020), following the \resistance curve procedure" (as mentioned before). The load was applied under displacement control of the machine's cross head at a speed of 0:5 mm/min, and it was measured by the machine's load cell. A number of unloading-reloading sequences have been performed along the test every 0 :14 mm of the machine's cross-head dis- placement, with a force reduction range of 2 kN, see Fig. 16. A cryogenic clip gage (Epsilon 3541-005M-040M-LT) has been used to measure the load-line displacement. While the load and load-line displacement values have been continuously measured during the tests, the crack size and J values have been calculated a posteriori when computing the crack-growth resistance JRcurves (as discussed in a later paragraph). As mentioned before the cryogenic test setup described in Section 3.1 has been employed for all the tests. Three fracture toughness tests per material and testing temperature have been conducted. The tests are stopped shortly after the point of maximum force is exceeded, which is an indication that the crack has propagated, and before the clip gage reaches the maximum measuring range of 5 mm. The nal crack size after testing has been marked by heat tinting the sample at 400C for 1 hour. Subsequently, the sam- ple has been fractured in order to analyse the crack. Identi cation of the initial and nal crack sizes has been conducted using an optical microscope. The initial crack size corresponds to the end of the at fatigue precracked area, while the nal crack size is marked by the colouration from heat tinting (see Fig. 18). The load and load-line displacement measurements obtained from the fracture toughness experiments have been used to compute the crack-growth resistance JRcurves. From each 18 JRcurve the fracture toughness parameter JQhas been determined according to the standard ASTM-E1820-20a (2020). If all the quali cation requirements of the standard are ful lled a quali ed value of JQis obtained, which represents the crack growth resistance near the onset of ductile and stable crack extension (at 0.2 mm of crack extension beyond initial crack tip blunting, see Fig. 17). This parameter quali ed as size-independent plane-strain JIc(crack- extension resistance under conditions of crack-tip plane-strain) provided that the size criteria speci ed in Sections A9.10.1 and A9.10.2 of the standard ASTM-E1820-20a (2020) are also met. Moreover, Section A9.11 of the standard provides an equation which allows to obtain the stress intensity factor KJIccalculated from JIc:KJIc=p (EJIc)=(12), where here the Young's modulus and Poisson's ratio are E= 206 GPa and = 0:3, respectively. This formula makes possible an estimation of the crack-extension resistance near the onset of stable crack extension under dominant elastic conditions, which is very useful for predominantly-elastic applications when the sample tests do not yield valid KIcresults (Joyce and Tregoning, 2000). To be noted the di erence between KJIcandKIc, where the former is evaluated using JIcand the latter is directly measured (the reader is referred to the standard ASTM-E399 (2020) for a direct determination of KIc). As mentioned before, four di erent methods have been used for the calculation of the JR curves, which is an original methodological contribution of this paper: ASTM Compliance Method . The ocial procedure provided by the standard ASTM- E1820-20a (2020) is an elastic-compliance approach based on the assumption that as the crack grows the sample becomes less sti , leading to an increase of the unloading compli- ance with respect to the previous unloading. The crack length is related to the unloading compliance using the equations provided in the Appendix of the standard ASTM-E1820- 20a (2020) devoted to the Compact Sample (Appendix 2 - Special requirements for testing compact specimens), which includes an adjustment procedure to improve the estimation of the initial crack size. The adjustment is based on a third-order polynomial regression tting of crack size versus Jvalues (Section A9.3 therein). W-N Compliance Method . This approach was developed in the works of Nyilas et al. (1998) and Weiss and Nyilas (2006), and includes two improvements with respect to the ASTM Compliance Method. On the one hand, it proposes a solution for the so-called apparent negative crack extension (a problem not addressed by the ASTM Compliance Method), which results from an experimentally-measured continuously increasing sti ness with respect to previous unloadings at the initial stage of the test (Voss, 1983; Rosenthal et al., 1990; Seok, 2000). While there is not a general consensus about the causes behind the apparent negative crack extension, Nyilas et al. (1998) and Weiss and Nyilas (2006) mainly attributed the initial increase of the sample's sti ness to the strain hardening of the plastic zone ahead of the precrack tip during blunting, which does not imply actual crack growth. Thus, the W-N Compliance Method identi es the crack initiation when the overall sti ness changes from an increasing to a decreasing behaviour, i.e. when the blunted precrack turns into ductile tearing. The data points before the designated crack initiation are not included in the JRcurve, and therefore, no negative crack growth is predicted. On the other hand, the W-N Compliance Method improves the estimation of the crack lengths, replacing the experimentally-measured compliances by the so-called \corrected compliance function" of load-line displacement, which results from the construc- tion of a second-order polynomial regression of sti ness versus displacement at the onset of unloading. The speci c form of the polynomial regression is determined by imposing three conditions: (i) the displacement at the onset of the last unloading is associated with the compliance calculated with the equation (A2.11) of the standard ASTM-E1820-20a (2020) using the measured nal crack length, (ii) the displacement at the crack initiation is associated with the compliance calculated with the equation (A2.11) of the standard ASTM-E1820-20a (2020) using the measured initial crack length, and (iii) the maximum of the polynomial regression corresponds with the displacement associated to the crack 19 initiation. Note that the measured initial crack length rather corresponds to the sharp precrack than to the blunted precrack. However, since the sharp precrack is readily mea- surable using optical microscopy, see Fig. 18, the \corrected compliance function" directly associates the sharp precrack with the crack initiation for the sake of simplicity. Generally, the di erence between the blunted precrack and the sharp precrack is between 50 m and 400m (Tarafder and Tarafder, 2006). Moreover, the W-N Compliance Method relates the values of Jwith the improved estimation of the crack extensions and the entire JR curve is shifted so that the crack initiation point coincides with the \construction line" (also referred to as blunting line). After the shifting, the computed value for the initial crack length is calculated as the crack length corresponding to a crack extension  a= 0 (see Fig. 20), which is smaller than the experimental measurement of the initial crack length due to the simpli cation of associating the sharp precrack with the crack initiation point. Modi ed W-N Compliance Method . This approach is an original contribution of this paper, and the main di erence with respect to the W-N Compliance Method is that the values ofJare re-calculated using the improved estimation of the crack lengths obtained from the \corrected compliance function" of displacement. Moreover, the \corrected com- pliance function" associates the crack initiation with the blunted precrack, instead of with the sharp precrack, using an iterative procedure. The iterative procedure starts assuming that the blunted precrack is equal to the sharp precrack, the simpli cation used in the W-N Compliance Method. Once the JRcurve is obtained, instead of performing the shifting to the blunting line, a new estimation of the blunted precrack is calculated as the sum of the measured initial crack length and the ratio between the Jvalue of the current crack initiation point and the slope of the blunting line, indicated in Fig. 17(a). The iterative process is then re-started, so that in each iteration, \corrected compliance function", crack lengths, Jvalues,JRcurve and blunted precrack are updated. The iterative process ends when the di erence between current and previous estimation for the blunted precrack is lower than 105mm, so that this iterative process ensures that the crack initiation point coincides with the blunting line and the computed initial crack length equals the measured initial crack length. ASTM Normalization Method . The Normalization technique enables direct estima- tion of the crack lengths from a test performed under continuous displacement increase, so that unloading-reloading sequences are not needed and estimations of intermediate crack lengths are based on the load versus load-line displacement record, as well as on the initial and nal measured crack sizes (Herrera and Landes, 1990; Landes et al., 1991; Lee, 1995; Joyce, 2001). The Normalization method which has been used in this work is described in Annex 15 of the standard ASTM-E1820-20a (2020). Since the fracture toughness tests presented in this paper have been performed according to the \resistance curve proce- dure", the data of the unloading-reloading sequences had to be removed. Speci cally, we have retrieved for the analysis the whole record of load and displacement until the onset of the rst unloading, one data-point between each unloading sequence, and the point corresponding to the onset of the last unloading, see Fig. 16. The code used for construction of the crack-growth resistance JRcurves, and the identi - cation of the fracture toughness parameters JQandKJQ, is included as Supplementary Material . The Potential Di erence Method has not been used in this work due to the diculty that it presents to accurately di erentiate the potential drop signal caused by crack extension from the one caused by plasticity for a ductile crack growth (Zhu and Joyce, 2012; Park et al., 2019), as well as due to the high time- and resources-consumption that the calibration of this method implies at cryogenic temperatures (because it is necessary to relate potential drop with the crack size). Moreover, recall that all the fracture toughness tests are performed at low loading rate, so that the reader is referred to the recent papers of Pham and Iwamoto (2015, 2018) to obtain 20 insights into the in uence of rate e ects on the fracture behaviour of 304 austenitic stainless steel. 5.2 Martensite measurements Light optical micrography inspections have been carried out to investigate the extent of the 0-martensitic transformation near the fracture surface of the Compact Samples after testing. The analysis encompasses samples of both materials, AISI 30L and AISI 316LN, tested at 77 K and 4 K. The samples selected for the analysis have been cut into two parts along their mid- thickness plane. One cutting plane for each specimen has been metallographically prepared. The cut and metallographic preparation have been carried out at CERN following the same procedure described in the item Electron backscatter di raction of Section 3.2. The as-polished state of the surface has been used for the inspection. The micrographs have been acquired with the equipment described in the item Quantitative light optical micrography of Section 3.2. Stitching images composed by individual micrographs taken at the high magni cation of 200 have been obtained in order to have a global image of the distribution of 0-martensite. Each stitching covers a region of about 7 mm along the fracture surface and 4 mm below it, see Fig. 19. The stitching's length includes the fracture surface corresponding to the nal part of the fatigue pre-cracking and the total length of the crack developed in the fracture toughness tests. 6 Fracture behaviour: results Fig. 16 shows the load versus load-line displacement record of one of the performed fracture toughness tests for AISI 304L at 4 K. The graphic also includes the intermediate points selected for the ASTM Normalization Method (see Section 5.1) {blue lled circles{ as well as the points identi ed as the onset and end of each unloading {red star symbols{, values which are needed for the construction of the JRcurve using the compliance methods (ASTM, W-N and Mod- i ed W-N Compliance Methods). Notice that, since the test is performed at 4 K, the loading curve shows serrated yielding (see Section 4) which gets more pronounced as the displacement increases. Special attention is paid during the identi cation of the aforementioned points so that none of the serrations is recognized as an unloading sequence, otherwise false points in the construction of the JRcurve might in uence the determination of the fracture toughness parameters. On the other hand, it might happen that an unloading sequence is carried out just after a serration takes place, in that case an underestimated load value for the corresponding unloading onset point is obtained (see for example the second unloading which is shown on the magni ed area in Fig. 16). Nevertheless, as it is discussed in a following paragraph (see Table 4), the similarity between the results obtained with the Modi ed W-N Compliance Method and the ASTM Normalization Method suggests that, for the tests analysed in this work, the under- estimated load of these individual points has a negligible in uence on the determination of the fracture toughness parameters. The fracture toughness experimental results for AISI 304L and AISI 316LN are shown in Fig. 17. The crack-growth resistance JRcurves are computed with the ASTM Normalization Method. Filled and empty symbols represent data points that fall inside and outside the \Region of Quali ed Data", which is determined according to Fig. A9.2 of the standard ASTM-E1820- 20a (2020). Large darker symbols indicate the fracture toughness JQ, which is obtained from the intersection of the power law regression line with the \0 :2mm o set line" (Section A9.6.6 of the standard ASTM-E1820-20a (2020)). The power law regression line is de ned by tting the expressionJ=C1aC2, where ais the crack extension and C1andC2are constants, to the data that fall into the \Region of Quali ed Data", and it is pictured with solid lines in the g- ure. Dashed lines correspond to the \construction line" (blunting line) and the \0 :2mm o set line", as indicated in the graph, with the slope being 2 Y=YS+TS(using the engineering de nition of stress) according to the standard ASTM-E1820-20a (2020). Results corresponding to three di erent experiments (i.e., three di erent realizations for the same material and testing 21 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Load-line displacement, v (mm)02000400060008000100001200014000Load, P (N) Raw data Initial point unloading Final point unloading Selected points for Normalization Method Figure 16: Load versus load-line displacement record corresponding to a fracture toughness test for AISI 304L performed at 4 K. Blue lled circles represent the individual points used for the ASTM Normalization Method. Red star symbols represent the onset and end of each unloading. conditions) indicated with circular, square and triangular symbols are included in each graph. Speci cally, Figs. 17(a) and 17(b) picture the results for AISI 304L tested at 77 K and 4 K, respectively, and Fig. 17(c) shows the results for AISI 316LN tested at 4 K. Notice that, in the three graphs, the results obtained with the three realizations are similar, which shows the robustness and repeatability of the measurements. The comparison of results for both materi- als and testing temperatures shows that AISI 316LN displays higher fracture toughness than AISI 304L (check Figs. 17(b) and 17(c)), and for AISI 304L the fracture toughness decreases with decreasing testing temperature (check Figs. 17(a) and 17(b)). No results for AISI 316LN at 77 K are provided as during the three performed fracture toughness tests the crack did not propagate for displacements within the clip gage measuring range, so that no data points within the \Region of Quali ed Data" were obtained. The comparison of the crack-growth resistance JRcurves obtained in this work with data available in the literature is performed in B. Optical micrographs of the fracture surface for experiments performed with AISI 304L sam- ples tested at 77 K and 4 K and AISI 316LN samles at 4 K are presented in Fig. 18. The sharp notch, the surface corresponding to the pre-cracking, and the surface corresponding to the frac- ture toughness test are indicated in the pictures. A close view of the blunting zone is enlarged on the left bottom part of Fig. 18(a). In the case of AISI 304L, Figs. 18(a)-(b), the crack front presents the so-called tunnelling e ect (Weiss and Nyilas, 2006), with much shorter crack exten- sion near the sample's edges. In contrast, notice that for the AISI 316LN sample, the tunnelling e ect is less pronounced. Irrespective of the di erent crack front shapes, the crack front of all tested samples ful ls the requirements of the standard ASTM-E1820-20a (2020) (see Sections 9.1.4.1, 9.1.4.2 and 9.1.5.1 therein). Moreover, the optical micrographs make evident the forma- tion of a neck in the samples {pointed out in the pictures{ that leads to a reduction of thickness of5:5%,3% and 5% for AISI 304L tested at 77 K, AISI 304L at 4 K and AISI 316LN at 4 K, respectively. Even though the reduction of thickness is signi cant, the plane-strain conditions stated in the standard ASTM-E1820-20a (2020) ( B > 10JQ=Yandb0>10JQ=Yaccording to Sections A9.10.1 and A9.10.2) are ful lled for all the samples tested in this work, as it is also discussed in a following paragraph. Additionally, the fracture surfaces of all tested samples show symmetry with respect to the middle-thickness plane (see Fig. 18) which together with the fact that the crack developed along the sample's middle-height plane (see Fig. 15) indicate 22 050010001500 0 0.5 1 1.5 2 2.5J-integral, J (kJ/m2) Crack extension, Δa (mm)0.2-mm offset line construction line Material: AISI 304LT=77 K2σY(a) 050010001500 0 0.5 1 1.5 2 2.5J-integral, J (kJ/m2) Crack extension, Δa (mm)Material: AISI 304LT=4 K0.2-mm offset lineconstruction line (b) 050010001500 0 0.5 1 1.5 2 2.5J-integral, J (kJ/m2) Crack extension, Δa (mm)Material: AISI 316LNT=4 K0.2-mm offset lineconstruction line (c) Figure 17: Fracture toughness experimental results for AISI 304L and AISI 316LN. Crack- growth resistance JRcurves computed with the ASTM Normalization Method. Filled and empty symbols represent data points that fall inside and outside the \Region of Quali ed Data", respectively. Large darker symbols indicate the fracture toughness JQ. Solid lines represent the power law regression tting. Dashed lines correspond to the \construction line" (blunting line) and the \0:2mm o set line", as indicated in the graphs. Results corresponding to three di erent experiments indicated with circular, square and triangular symbols are included in each graph: (a) AISI 304L tested at T= 77 K, (b) AISI 304L tested at T= 4 K and (c) AISI 316LN tested atT= 4 K. a good alignment and Mode I loading dominance (negligible contribution of Mode II and Mode III) during fatigue pre-cracking and fracture toughness tests. Fig. 19 shows stitched micrographs obtained by light optical microscopy of the fractured samples near the fracture surface for the same samples investigated in Fig. 18. The surfaces corresponding to the pre-cracking and the fracture toughness test are indicated in the pictures. A close view of the fracture toughness area is enlarged on the bottom part of the images in order to illustrate the lath-type 0-martensite morphology. Note that the martensite appears in black, and the austenite in grey, as indicated in the legend located in the bottom left part of the micrographs. The highest concentration of martensite is located next to the fracture surface, decreasing towards the bulk, most likely due to decreasing plastic strain. The content of marten- site seems to be greater in AISI 304L specimens, which is consistent with the results reported in Figs. 13 and 14 of Section 4, which showed that the martensitic transformation is faster and more important in AISI 304L than in AISI 316LN. Note that for AISI 304L, more martensite is observed in the sample tested at 77 K, most likely because the plastic deformation near the crack is greater than at 4 K. Furthermore, the AISI 304L specimens show more regular and plane crack path in comparison with the results obtained with AISI 316LN, as can be anticipated from Fig. 18(c) where the fracture surface of the AISI 316LN sample shows a rough and granular ap- pearance. This can be attributed to the higher amount of the martensitic phase shown by the 23 1000 m~100 m sharp notch pre-craccking areafracture toughness areanecking(a) 1000 m sharp notch pre-cracking areafracture toughness areanecking (b) 1000 m sharp notch pre-cracking areafracture toughness areanecking (c) Figure 18: Optical micrographs of the fracture surface for: (a) AISI 304L tested at T= 77 K, (b) AISI 304L tested at T= 4 K and (c) AISI 316LN tested at T= 4 K. The neck, the sharp notch, the surface corresponding to the pre-cracking, and the surface corresponding to the fracture toughness tests are indicated in the pictures. Moreover, a close view of the blunting zone is also enlarged on the left bottom part in the picture corresponding to AISI 304L tested at T= 77 K. AISI 304L specimens (the martensite being less ductile than the austenite). Moreover, Fig. 19(a) also makes evident the blunting pro le in the transition between the pre-cracking area and the fracture toughness area of AISI 304L at 77 K (see Fig. 3.25(b) from Anderson (2017)), recall that the blunting is also noticeable from a top view of the fracture surface as it is shown in Fig. 18(a). Based on the experimental tests it is not possible to provide further conclusions regarding the contribution of the martensitic transformation and of the blunting to the fracture toughness results. For this purpose, the reader is referred to the nite element calculations performed by Iwamoto and Tsuta (2002) for Compact Samples subjected to Mode I loading, which evalu- ate the fracture toughness for an austenitic material (AISI 304) with and without martensitic transformation. The comparison between the results obtained with the four approaches described in Section 5.1 to compute the crack-growth resistance JRcurves (ASTM Compliance Method, W-N Compliance Method, Modi ed W-N Compliance Method and ASTM Normalization Method) is performed in Fig. 20. As in Fig. 17, lled and empty symbols represent data points that fall inside and outside the \Region of Quali ed Data", respectively. Large darker symbols indicate 24 (a) (b) (c) Figure 19: Stitched micrographs obtained by light optical microscopy of the fractured specimens near the fracture surface. (a) AISI 304L tested at T= 77 K, (b) AISI 304L tested at T= 4 K and (c) AISI 316LN tested at T= 4 K. For the image corresponding to AISI 304L tested at 77K, the crack pro le in the transition between the pre-cracking area and the fracture toughness area is indicated with a yellow dashed line and the blunting is pointed out with a yellow arrow. the fracture toughness JQ, the power law regression tting being represented by solid lines. Each colour corresponds to the results obtained with a given method, see the legend in the bottom right part of the graph. There are noticeable di erences between the crack-growth resistance JRcurves obtained with the four di erent methods. For instance, while the values of J computed with the Modi ed W-N Compliance Method and the ASTM Normalization Method are similar, they lie above the data obtained with the W-N Compliance Method. Moreover, note that, in comparison with the other three approaches, the ASTM Compliance Method greatly underestimates the value of JQ: the negative crack extension causes two points with J0 to fall into the \Region of Quali ed Data" so that the power law regression line does not properly represent the JRevolution obtained for most of the data points. Additional quantitative comparison between the results obtained with the four approaches used to compute the JRcurves is provided in Table. 4 which displays the stress intensity factor KJQcalculated for AISI 304L at 77 K and 4 K and for 316LN at 4 K for the three experiments performed per material-temperature combination. The results are expressed in terms of the fracture toughness parameter KJQinstead ofJQas the former is widely used in the literature. Nevertheless, the same discussion for KJQ(andKJIc) is valid for JQ(andJIc) since, as discussed in Section 5.1, the two parameters are directly related by the formula KJQ=p (EJQ)=(12) (andKJIc=p (EJIc)=(12), see Sections A9.11 of the standard ASTM-E1820-20a (2020)). 25 050010001500 0 0.5 1 1.5 2 2.5J-integral, J (kJ/m2) Crack extension, Δa (mm)Material: AISI 304LT=77 K0.2-mm offset line construction line Red: ASTM Compliance Method Green : W-N Compliance Method Yellow : Modified W-N Compliance Method Grey : ASTM Compliance MethodFigure 20: Fracture toughness experimental results for AISI 304L tested at T= 77 K. Crack- growth resistance JRcurves computed with the four approaches described in Section 5.1: ASTM Compliance Method, W-N Compliance Method, Modi ed W-N Compliance Method and ASTM Normalization Method. Filled and empty symbols represent data points that fall inside and outside the `Region of Quali ed Data", respectively. Large darker symbols indicate the frac- ture toughness JQ. Solid lines represent the power law regression tting. Each colour corresponds to the results obtained with a given method. Dashed lines correspond to the \construction line" and the \0:2mm o set line". Notice that for some experiments the tests data do not ful l the requirements established by the standard for KJQto be considered the actual stress intensity factor. To be highlighted that ifKJQis the actual stress intensity factor (i.e. it ful ls all the requirements of the standard), we have that KJQ=KJIc(size-independent plane-strain stress intensity factor), since the size criteria,B > 10JQ=Yandb0>10JQ=Yaccording to Sections A9.10.1 and A9.10.2 of the standard ASTM-E1820-20a (2020), are ful lled for all the tests performed in this work. For instance, none of the KJQvalues which have been obtained using the ASTM Compliance Method ful l all the requirements listed in ASTM-E1820-20a (2020) because the quali cation requirements included in Sections A9.3.3.2, A9.4 and 9.1.5.2 and Note A9.1 are repeatedly breached. Note A9.1 indicates that anomalies at the beginning of the test, due to the apparent negative crack extension in the experiments performed in this work, cause points with low J to fall within the \Region of Quali ed Data" providing an unreasonable low value of KJQ (where Note A9.1 is mentioned in Table 4, the resulting KJQvalue is not included as it is not consistent with the corresponding JRcurve, see Fig. 20). Furthermore, since the ASTM Compliance Method does not address the negative crack extension phenomenon, see the item ASTM Compliance Method in Section 5.1, the adjustment procedure to obtain an improved estimation of the initial crack size is not e ective to evaluate the data obtained from most tests. Speci cally, the correlation coecient of the data which resulted from the adjustment procedure is lower than 0 :96, so that the test data are invalid according to Section A9.3.3.2 of ASTM-E1820-20a (2020). In addition, for some tests the adjustment procedure underestimates the initial crack size by more than 0 :5 mm with respect to the measurements obtained with optical microscopy, making the result invalid according to Section A9.4 of ASTM-E1820-20a (2020). The large di erence between estimated and measured initial crack size is most likely due to the defective estimation of the crack size using the compliance equations rather than a consequence of the adjustment procedure, so that for some of the experiments the di erence between predicted and measured crack extension is larger than the maximum value accepted in Section 9.1.5.2 of ASTM-E1820-20a (2020). In contrast, the W-N Compliance Method addresses the problem related to the negative crack 26 extension and corrects the estimation of the crack lengths, see the item W-N Compliance Method in Section 5.1. Furthermore, despite the estimation of the initial crack length does not match with the measurement obtained with optical microscopy, the di erence is lower than 200m, it is acceptable according to Section A9.4 of the standard ASTM-E1820-20a (2020) so that the values of KJQqualify asKJIc. For the Modi ed W-N Compliance Method all the resulting KJQvalues also qualify as KJIc. The quantitative di erences with the results obtained with the W-N Compliance Method {which yields lower values for KJQ{ are most likely due to the re-calculation of the values of Jusing the improved values of the crack sizes, see the item Modi ed W-N Compliance Method in Section 5.1. Moreover, the iterative process implemented for the estimation of the crack sizes predicts that the crack extension caused by blunting is approximately 100 m, 30m and 80m for AISI 304L at 77 K, AISI 304L at 4 K and AISI 316LN at 4 K, respectively. Note that the predictions for AISI 304L nd reasonable agreement with the experimental measurements presented in Fig. 18. Regarding the ASTM Normalization Method, some of the tests do not comply with the additional restriction included in Section A15.2.4 of the standard ASTM-E1820-20a (2020) which states that the measured crack extension should not exceed the lesser of 4 mm or 15% of the initial uncracked ligament. Nonetheless, the other additional requirements included in the standard are met, so that the values of the stress intensity factor obtained from the tests are assumed to qualify as KJIc. Furthermore, while this approach does not require to carry out a series of unloading-reloading sequences during the fracture toughness tests, which makes the ASTM Normalization Method more sound and practical to analyse as compared to the other three compliance methods (see the item ASTM Normalization Method in Section 5.1), the results obtained for KJQare very similar, qualitatively and quantitatively, to the ones computed with the Modi ed W-N Compliance Method. This also suggests that breaching the additional requirement included in Section A15.2.4 of the standard ASTM-E1820-20a (2020) does not have an important in uence for the determination of KJQ. 27 ASTM Compliance Method W-N Compliance Method Modi ed W-N Compliance MethodASTM Normalization Method KJQ (MPapm)Invalid requirementsKJQ (MPapm)Invalid requirementsKJQ (MPapm)Invalid requirementsKJQ (MPapm)Invalid requirements 385.56 Section A9.3.3.2 Section A9.4 Section 9.1.5.2348.62 - 389.60 - 399.04 - - Section A9.3.3.2 Section A9.4 Section 9.1.5.2 Note A9.1369.87 - 404.71 - 413.11 -AISI 304L T=77 K 367.57 Section A9.4 Section 9.1.5.2353.43 - 393.06 - 405.93 - - Section A9.3.3.2 Section A9.4 Section 9.1.5.2 Note A9.1273.31 - 286.37 - 298.03 Section A15.2.4 264.46 Section A9.3.3.2 247.41 - 251.11 - 276.21 Section A15.2.4AISI 304L T=4 K - Section A9.3.3.2 Note A9.1270.34 - 272.82 - 287.19 Section A15.2.4 - Section A9.3.3.2 Section A9.4 Section 9.1.5.2 Note A9.1414.35 - 434.23 - 456.89 - - Section A9.3.3.2 Section A9.4 Note A9.1425.93 - 444.84 - 436.66 Section A15.2.4AISI 316LN T=4 K - Section A9.3.3.2 Section A9.4 Note A9.1419.20 - 448.35 - 458.97 - Table 4: Stress intensity factor KJQresults obtained from the fracture toughness tests (three experiments per material-temperature combination) with the four approaches described in Section 5.1 to compute the crack-growth resistance JRcurves: ASTM Compliance Method, W-N Compliance Method, Modi ed W-N Compliance Method and ASTM Normalization Method. The requirements of the standard that are not met are indicated for each test. 28 7 Concluding remarks In this paper, we have performed a comprehensive experimental characterization of the mi- crostructural evolution and the mechanical behaviour and fracture of AISI 304L and AISI 316LN austenitic stainless steels at cryogenic temperatures. For that purpose, we have devised an ex- perimental methodology which includes uniaxial tensile experiments and Mode I fracture tests in liquid nitrogen (77 K) and liquid helium (4 K). We have shown that both AISI 304L and AISI 316LN display a signi cant increase of the ow stress with decreasing testing temperature and discontinuous plastic ow at 4 K. On the other hand, while AISI 316LN retains quasi-linear strain hardening and large ductility at cryo- genic temperatures, the stress-strain characteristic of AISI 304L displays a sigmoidal shape and a drop in ductility of nearly 50% as compared to room temperature. Note that we have designed a novel Double-Section Sample to perform interrupted tensile tests in which the sample is un- loaded before fracture to measure the martensite content at di erent strain levels. Post-mortem microstructural analysis of the tensile samples using magnetic induction, electron backscatter di raction and quantitative light optical micrography allowed to determine the evolution of the martensitic transformation with the strain. The code developed for the determination of the con- tent of martensite from light optical micrographs is included as Supplementary Material . The results obtained with the three methods show the same general trends and reasonable quantita- tive agreement, bringing out that the martensitic transformation in AISI 304L occurs faster and to a greater extent than in AISI 316LN both at 77 K and at 4 K. To the authors' knowledge, in this paper we provide the rst experimental results for the evolution of the content of strain- induced martensite in AISI 304L and AISI 316LN samples tested at liquid helium temperature. Moreover, note that for AISI 304L the evolution of the martensite content at 77 K and 4 K is very similar, which seems to indicate that for this grade the transformation process is already saturated at 77 K, which is an original result of this paper. In addition, the experimental data for the strain-induced martensite fraction have been used to identify the temperature-dependent parameters of the transformation kinetic model proposed by Olson and Cohen (1975). Moreover, the fracture tests data have been used to determine the crack-growth resistance JRcurves and the fracture toughness of the investigated materials using four di erent meth- ods here referred to as ASTM Compliance Method, W-N Compliance Method, Modi ed W-N Compliance Method (which is proposed in this work) and ASTM Normalization Method, which is an original methodological contribution of this paper. Out of these four approaches, only the JRcurves computed with the W-N Compliance Method and the Modi ed W-N Compliance Method ful l all the requirements of the standard ASTM-E1820-20a (2020) so that the calcu- lated fracture toughness can be considered a material property. On the other hand, note that the results obtained with ASTM Normalization Method are very similar to the crack-growth resis- tance curves and the fracture toughness computed with the Modi ed W-N Compliance Method, the main advantage of the ASTM Normalization Method being the simpler procedures required for the test performance and the analysis of test data. The codes developed for the construction of the crack-growth resistance JRcurves, and the identi cation of the fracture toughness are included as Supplementary Material . The experiments have shown that AISI 316LN has higher fracture toughness than AISI 304L, and for AISI 304L the fracture toughness decreases with decreasing testing temperature. The results are in good agreement with the experimental data available in the literature. In addition, post-mortem optical micrography examination of the fracture samples has shown that the amount of austenite transformed into martensite near the fracture surface is greater for AISI 304L than for AISI 316LN. On the other hand, for AISI 304L there is more martensite formed in the sample tested at 77 K because the plastic deformation near the crack is greater than at 4 K. 29 Acknowledgements The authors would like to thank A. Gallifa-Terricabras (CERN) for performing the analysis with Digital Image Correlation and A. T. P erez-Fontenla (CERN) for the help with the SEM imaging. Thanks are also owed to K. Weiss (KIT) for the helpful discussions about fracture toughness. The research leading to these results has received funding from the European Union's Hori- zon2020 Programme (Excellent Science, Marie Sk lodowska-Curie Actions) under REA grant agreement 777896 (Project QUANTIFY). Supplementary material In the following links we provide access to the code developed for the determination of the content of martensite from light optical micrographs: https://doi.org/10.21950/OX2ZFR; and to the codes developed for the construction of the crack-growth resistance JRcurves, and the identi cation of the fracture toughness: https://doi.org/10.21950/XTQRTZ. A Flow behaviour: comparison with experimental data available in the literature Figs. 21 and 22 show a comparison between the stress-strain curves obtained in this work for AISI 304L and AISI 316LN, and results for the same grades available in the literature with chemical composition given in Table 5. Note that all the experimental data for AISI 304L and AISI 316LN available in the literature showed discontinuous plastic ow at 4 K, however, we just display the upper envelop in Figs. 21(c) and 22(c) to facilitate the comparison of results. Generally, there is good qualitative and quantitative agreement between the stress-strain char- acteristics obtained in this work and the experimental evidence used for comparison. Fig. 23 shows a comparison between the results for the evolution of the volume fraction of martensite f 0with strain "obtained in this work and experimental data available in the litera- ture for tests performed at 300 K and 77 K for the same steel grades with chemical composition given in Table 5. Generally, there is good qualitative and quantitative agreement between the results obtained in this work and the experimental evidence used for comparison. However, no results are available in the literature for AISI 304L and AISI 316LN samples tested at 4 K so that we could compare the martensite volume fraction measurements presented in this paper. No graph is included for AISI 316LN tested at room temperature because, in agreement with other authors, see Botshekan et al. (1998) and Pattanayak (1984), the martensitic transformation is negligible. 30 05001000150020002500 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7B D F H JTrue stress, σ (MPa) True strain, εT=300 K Material: AISI 304L This work Yanushkevich et al. (2017) Spencer et al. (2004) Cooper et al. (2018) DeMania (1995)(a) 05001000150020002500 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7B D F H JTrue stress, σ (MPa) True strain, εT=77 K Material: AISI 304L This work Spencer et al. (2004) Mei and Morris Jr (1990), Fultz and Morris Jr. (1986) Behjati et al. (2011) Ogata et al. (1985), Ogata et al. (1990) (b) 05001000150020002500 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7B D FTrue stress, σ (MPa) True strain, εT=4 KMaterial: AISI 304L This work Behjati et al. (2011) Ogata et al. (1985), Ogata et al. (1990) (c) Figure 21: Comparison between the stress-strain curves obtained in this paper for AISI 304L and experimental results taken from the works of Yanushkevich et al. (2017), Spencer et al. (2004), Cooper et al. (2018), DeMania (1995), Mei and Morris Jr (1990), Fultz and Morris Jr (1986), Behjati et al. (2011), Ogata et al. (1985) and Ogata et al. (1990). Data corresponding to tensile samples tested under quasi-static loading at di erent temperatures: (a) T= 300 K, (b)T= 77 K and (c) T= 4 K. 31 05001000150020002500 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7B D F H JTrue stress, σ (MPa) True strain, εT=300 K Material: AISI 316LN This work Wang et al. (2008), Wang et al. (2010) Botshekan et al. (1997), Botshekan et al. (1998) Obst and Pattanayak (1982), Pattanayak (1984) Czarkowski et al. (2011)(a) 05001000150020002500 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7B D F H JTrue stress, σ (MPa) True strain, εT=77 K Material: AISI 316LN This work Wang et al. (2008), Wang et al. (2010) Botshekan et al. (1997), Botshekan et al. (1998) Obst and Pattanayak (1982), Pattanayak (1984) Czarkowski et al. (2011) (b) 05001000150020002500 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7B D F HTrue stress, σ (MPa) True strain, εT=4 KMaterial: AISI 316LN This work Obst and Pattanayak (1982), Pattanayak (1984) Park et al. (2011) Couturier and Sgobba (2000) (c) Figure 22: Comparison between the stress-strain curves obtained in this paper for AISI 316LN and experimental results taken from the works of Wang et al. (2008), Wang et al. (2010), Botshekan et al. (1997), Botshekan et al. (1998), Obst and Pattanayak (1982), Pattanayak (1984), Czarkowski et al. (2011), Park et al. (2011) and Couturier and Sgobba (2000). Data corresponding to tensile samples tested under quasi-static loading at di erent temperatures: (a) T= 300 K, (b) T= 77 K and (c) T= 4 K. 32 01020 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7B D F H J LVolume fraction of martensite, f α (%) True strain, ε' T=300 KMaterial: AISI 304L Magnetic induction Electron backsactter diffraction Quantitative light optical micrography Angel (1954) - Note: AISI 304 Behjati et al. (2011) Mei and Morris Jr (1990), Fultz and Morris Jr. (1986)(a) 020406080100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7B D F H J L NVolume fraction of martensite, f α (%) True strain, ε' T=77 KMaterial: AISI 304L Magnetic induction Electron backsactter diffraction Quantitative light optical micrography Angel (1954) - Note: AISI 304 Behjati et al. (2011) Spencer et al. (2004) Mei and Morris Jr (1990), Fultz and Morris Jr. (1986) (b) 020406080100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7B D F HVolume fraction of martensite, f α (%) True strain, ε' Magnetic induction Electron backsactter diffraction Quantitative light optical micrography Botshekan et al. (1997), Botshekan et al. (1998)T=77 KMaterial: AISI 316LN (c) Figure 23: Comparison between the evolution of the volume fraction of martensite f 0with strain"obtained in this paper and experimental results taken from the works of Angel (1954), Behjati et al. (2011), Fultz and Morris Jr (1986), Mei and Morris Jr (1990), Spencer et al. (2004), Botshekan et al. (1997) and Botshekan et al. (1998). Data corresponding to tensile samples tested under quasi-static loading: (a) AISI 304L tested at T= 300 K, (b) AISI 304L tested at T= 77 K and (c) AISI 316LN tested at T= 77 K. 33 AISI 304L Source C S NCr Ni Mn SiMo PCo Cu Nb Yanushkevich et al. (2017) 0.04 0.04 - 18.20 8.80 1.70 - - 0.05 - 0.50 0.05 Spencer et al. (2004) 0.02 - 0.07 18.22 9.03 1.85 0.56 0.34 - 0.13 0.35 - Cooper et al. (2018) 0.03 - - 19.40 9.65 1.65 0.57 0.35 - - - - DeMania (1995) 0.02 - 0.04 18.37 9.31 1.39 0.42 0.35 0.02 - 0.39 - Mei and Morris Jr (1990) 0.02 0.01 0.07 18.70 8.64 1.63 0.51 - 0.02 - - - Fultz and Morris Jr (1986) Behjati et al. (2011) 0.03 0.03 - 18.00 10.00 2.00 1.00 - 0.04 - - - Ogata et al. (1985) 0.02 0.01 - 18.24 10.03 1.52 0.67 - 0.03 - - - Ogata et al. (1990) AISI 316LN Source C S NCr Ni Mn SiMo PCo Cu Nb Wang et al. (2008) 0.01 - 0.14 15.30 12.54 1.48 0.21 2.50 0.01 - - - Wang et al. (2010) Botshekan et al. (1997) 0.03 0.03 0.16 17.2 13.5 2.00 1.00 2.50 0.05 - - - Botshekan et al. (1998) Obst and Pattanayak (1982) 0.03 0.02 0.16 16.70 13.70 1.26 0.41 2.68 0.02 - - - Pattanayak (1984) Czarkowski et al. (2011) 0.02 0.01 0.15 17.10 12.60 1.15 0.53 2.66 0.07 - 0.16 - Park et al. (2011) 0.01 - 0.16 17.27 13.55 1.70 0.15 2.56 0.02 0.02 - - Couturier and Sgobba (2000) 0.02 - 0.16 17.33 13.03 1.26 0.61 2.61 0.03 - - - Table 5: Data source and chemical composition of the reference materials presented in Fig. 21, 22 and 23 (weight-%, Fe balance). 34 B Fracture behaviour: comparison with experimental data avail- able in the literature Figs. 24 shows a comparison between crack-growth resistance JRcurves computed in this paper with the ASTM Normalization Method and experimental results taken from the works of Lee et al. (1998), Murase et al. (1993) and Nyilas and Yanagi (1989) (chemical composition given in Table 6). For the experiments performed in this work lled and empty symbols represent data points that fall inside and outside the \Region of Quali ed Data", respectively, large darker symbols indicate the fracture toughness JQ, solid lines represent the power law regression tting, and dashed lines correspond to the \construction line" and the \0 :2mm o set line". Data are shown for AISI 304L tested at 77 K and 4 K in Figs. 24(a) and 24(b), respectively, and for AISI 316LN tested at 4 K in Fig. 24(c). There is qualitative agreement between the experimental results obtained in this work and the data available in the literature {higher fracture toughness for AISI 316LN, and decreasing fracture toughness with decreasing testing temperature for AISI 304L{, and also quantitative agreement for AISI 304L tested at 4 K and for AISI 316LN tested at 4 K. 050010001500 0 0.5 1 1.5 2 2.5J-integral, J (kJ/m2) Crack extension, Δa (mm)Grey : This work Red: Lee et al. (1998)0.2-mm offset lineconstruction line Material: AISI 304LT=77 K (a) 050010001500 0 0.5 1 1.5 2 2.5J-integral, J (kJ/m2) Crack extension, Δa (mm)0.2-mm offset lineconstruction line Material: AISI 304LT=4 KGrey : This work Red: Lee et al. (1998) Green : Murase et al. (1993) (b) 050010001500 0 0.5 1 1.5 2 2.5J-integral, J (kJ/m2) Crack extension, Δa (mm)0.2-mm offset lineconstruction line Material: AISI 316LNT=4 K Grey : This work Green : Murase et al. (1993) Purple : Nyilas and Yanagi (1989) (c) Figure 24: Comparison between crack-growth resistance JRcurves computed in this paper with the ASTM Normalization Method and experimental results taken from the works of Lee et al. (1998), Murase et al. (1993) and Nyilas and Yanagi (1989). For the experiments performed in this work lled and empty symbols represent data points that fall inside and outside the \Region of Quali ed Data", respectively, large darker symbols indicate the fracture toughness JQ, solid lines represent the power law regression tting, and dashed lines correspond to the \construction line" and the \0 :2mm o set line". Data corresponding to fracture toughness tests: (a) AISI 304L tested at T= 77 K, (b) AISI 304L tested at T= 4 K and (c) AISI 316LN tested atT= 4 K. 35 Fig. 25 shows the evolution of the fracture toughness KJIcwith the initial 0 :2% o set yield strength of the material YSfor the tests presented in this paper (solid markers). The experi- mental results are compared with data available in the literature for AISI 304L and AISI 316LN tested at 77 K and 4 K, and with the NIST trend line for 300 series austenitic stainless steels at 4 K taken from McRae et al. (2017). The general trend is that the fracture toughness de- creases as the yield strength of the material increases, the data obtained in this paper being in reasonable qualitative agreement with the experiments taken from the literature. 0100200300400500 0 500 1000 1500 2000Fracture toughness, K JIc (MPa m1/2) 0.2% offset yield strength of the material, σYS (MPa)Red: AISI 304L - T=77 K Green : AISI 304L - T=4 K Yellow : AISI 316LN - T=4 KNIST trendline 300. Figure 25: Fracture toughness KJIcversus 0:2% o set yield strength of the material YS. Com- parison of the results obtained in this work for AISI 304L and AISI 316LN with experimental data taken from the works of Shimada et al. (1987), Lee et al. (1998), Purtscher and Read (1987), Park et al. (2019), Morris Jr et al. (1992), Murase et al. (1993), Nyilas and Mitterbacher (2010), Chan et al. (1994), Drexler et al. (1994), Krauth and Nyilas (1980), Mazandarany et al. (1980), Muster and Elster (1990), Nyilas and Yanagi (1989) and Ogata et al. (1992). The experiments taken from the literature and the results obtained in this work are represented with empty and lled symbols, respectively. The dashed line corresponds to the NIST trend line for 300 series austenitic stainless steels at 4 K, taken from McRae et al. (2017). AISI 304L Source C S NCr Ni Mn SiMo PCo Cu Nb Lee et al. (1998) 0.01 - - 18.22 9.15 1.19 0.42 - 0.03 - - - Murase et al. (1993) 0.02 - - 18.36 9.67 0.82 - - - - - - AISI 316LN Source C S NCr Ni Mn SiMo PCo Cu Nb Murase et al. (1993) 0.02 - 0.18 17.88 11.16 0.84 - 2.62 - - - - Nyilas and Yanagi (1989) 0.02 0.02 0.17 17.60 12.60 1.60 0.24 3.03 0.03 - - - Table 6: Data source and chemical composition of the reference materials presented in Fig. 24 (weight-%, Fe balance). 36