Anisotropy of cold-worked Type-304 austenitic stainless steel: Focus on the hydrogen diffusivity

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Anisotropy of cold-worked Type-304 austenitic stainless steel: Focus on the hydrogen diffusivity Jean-Gabriel Sezgin a,*, Daichi Takatori b, Junichiro Yamabe a,b,* a

AIST-Kyushu University Hydrogen Materials Laboratory (HydroMate), National Institute of Advanced Industrial Science and Technology (AIST), 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan b Department of Mechanical Engineering, Fukuoka University, 8-19-1 Nanakuma, Jonan-ku, Fukuoka, 814-0180, Japan

article info

abstract

Article history:

Anisotropic nature of effective hydrogen diffusivity was investigated on a cold-worked

Received 27 March 2019

(CW) Type-304 stainless steel. The material was characterized by using disk-shaped

Received in revised form

specimens sampled from two directions of steel plates with various rolling ratio. The

17 May 2019

thickness direction of the disks was parallel to the rolling direction for SL specimens and

Accepted 22 May 2019

perpendicular for LT ones. Electromagnetic induction (EMI) and electron backscatter

Available online 18 June 2019

diffraction (EBSD) clarified the content and distribution of strain-induced martensite (SIM). The effective diffusivities and solubilities were jointly determined by desorption method

Keywords:

and thermal desorption analysis (TDA) in H-charged specimens with high-pressure gas.

Austenitic stainless steel

The increase of SIM with CW ratio and the differences of SIM distribution observed be-

Hydrogen diffusion

tween LT and SL specimens could justify the anisotropic effective diffusivities. Finite

Finite element method (FEM)

element method (FEM) was used to simulate permeation tests based on multiple EBSD

Cold-working

maps. Simulations supported the experimental findings: at the CW ratio of 60%, the CW

Strain-induced martensite

process increased the diffusivity by twenty and the diffusivity was five time greater in the

transformation

SL specimen than the LT one. The inhomogeneous SIM distribution justified the modifications of diffusion properties by CW in both specimens. © 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.

Introduction The turnover currently operating in the energy industry tends to develop carbon neutral systems. In this context, the use of hydrogen as an energy carrier is considered as a viable path to contribute to this objective. However, the exposure of the material to aggressive environment raises the question of hydrogen embrittlement (HE), which was previously defined in [1e5] as the degradation of the material properties by the

presence of hydrogen in solution. The embrittlement of metallic alloys has contributed to the failure of various types of components and cannot be explained by a unique mechanism. Depending on the type of hydrogen (intrinsically present in the alloy or consequence of hydrogen charging) and the related conditions of solicitation, the failure of the structure has been explained by using multiple mechanisms. The following mechanisms have been proposed in the literature and justify most of the observed failures: hydrogen-enhanced localized plasticity (HELP) [6], hydrogen-enhanced decohesion

* Corresponding authors. AIST-Kyushu University Hydrogen Materials Laboratory (HydroMate), National Institute of Advanced Industrial Science and Technology (AIST), 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan. E-mail addresses: [email protected] (J.-G. Sezgin), [email protected] (J. Yamabe). https://doi.org/10.1016/j.ijhydene.2019.05.175 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.

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(HEDE) [7], adsorption-induced dislocation emission (AIDE) [8], the defactant concept [9], the hydrogen-enhanced straininduced vacancies (HESIV) [10] and the hydrogen induced cracking (HIC) [11]. In a context of fuel cell vehicles (FCVs) and hydrogen stations, standards and regulations suggest the use of stable austenitic stainless steels because of their excellent resistance to HE [12]. For instance, the relative reduction in area (RRA) of Type-316L austenitic stainless steels, measured by slowstrain-rate tensile (SSRT) tests, is greater than 0.8 [13,14]. The RRA is defined as the ratio of reduction in area (RA) in presence of hydrogen to the RA in absence of hydrogen and is usually used to quantify the sensitivity of a material to HE. Some comprehensive dataset concerning several aspects of these alloys are available in the literature [15] as well as the eventual interactions with crystallographic defects [16,17]. The characterization of anisotropic diffusion properties in materials being crucial, various studies have considered, in regards with the specificity of each materials, multiple ways to measure them such as, electrical coupling [18], X-ray diffraction [19], microhardness [20,21] or permeation techniques [22]. From a thermodynamic viewpoint, the allotropic phase stable at low temperature is the a' phase (BCC), i.e. martensitic phase. Under specific conditions, some ε martensite (HCP phase) could be eventually created as reported in [23]. In case of AISI 304, the ε martensite could be created under low strain rate (in the order of few percent), but higher strain rates result in the formation of a' phase [24]; this finding implies that the ε phase is likely to transform into a' with the increasing strain rate. Previous studies [25] have found that a' phase is predominant for the conditions in scope of the present paper (e.g. high rolling ratio up to 60%). In consequence, the austenitic phase is unstable and some environmental factor can result in the creation of such martensitic phase. This martensitic transformation will be detailed hereafter. The degradation of 300series austenitic stainless steels by hydrogen depends on the composition of the alloy and it has been established that the resistance to HE increases with the stability of austenite [26,27]. This statement supports a higher sensitivity to HE of Type-304 stainless steel compared to Type-316L stainless steel. Therefore, the HE operates in a different manner according to the composition and the loading conditions. The Type-304 stainless steel shows a hydrogen-induced slow crack growth during SSRT tests [28,29]. In the case of fatigue, this alloy presents a reduction of the stress intensity factor range and an acceleration of the fatigue crack growth (FCG) rate [29e35]. However, these observations have been recently refined since it has been established that even though the FCG rate is substantially increased by hydrogen, the steel has an upper bound of the hydrogen-accelerated FCG rate within a wide range of testing frequencies [36,37]. In [36], it has been established that no reduction of the fatigue limit can be attributed to hydrogen for both Type-316L and Type-304 austenitic stainless steels. On the basis of this experimental fact, it has been proposed to extend the eligibility of the Type304 steels for use in systems involving high-pressure hydrogen based on design by rule (i.e. infinite-life design) or design by analysis (i.e. finite-life design). In general, the martensitic transformation is initiated at a temperature equal to Ms. This temperature, also called

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temperature of martensitic transformation, could be modified by several parameters related to composition, temperature, yield-stress, and grain size [38]. Since the martensitic transformation does not require any diffusion process, the composition of the newly formed martensite does not differ from the one of the parent austenitic phase. Then, the resulting structure could be modified by the parent composition [39]. It is for example agreed that the martensite with a carbon content lower than 0.6 mass % mainly contains laths. In case of metastable austenite, e.g. Type-304 steels, the martensitic transformation can be initiated by the environmental stress condition at low temperature [40]. The transformation requiring an uptake of Gibbs energy under the form of external load is called strain-induced martensite transformation (SIMT) [41]. Manufacturing process, such as coldworking or cyclic load, could be at the origin of the SIMT [42,43]. It is not clear whether the applied stress or the actual strain affects the SIMT. In [44], an expression linking the Gibbs energy of SIMT to the applied stress has been proposed. It has also been shown in [45] that from the thermodynamic viewpoint, the correlation between martensite content and plastic strain is the consequence of the applied stress. In other words, these findings suggest a predominant effect of stress on the SIMT. At a local scale, the martensite resulting from SIMT is observable at the vicinity of microslip bands and translates a potential interaction with local defects [46]. [47]. Previous studies investigated the effect of hydrogen on the fatigue behavior of Type-304 steels and a peculiar test frequency dependence of the FCG rate has been observed in high-pressure hydrogen [48]. The influence of hydrogen on both the fatigue behavior and tensile properties [49] have been discussed in terms of migration of hydrogen. Then the hydrogen content and mobility in austenitic stainless steel became a key topic to get insight on the HE mechanism observed in such steels. The difference of diffusivity between the martensite and the austenite is four to six orders of magnitude. This fact suggests that the martensite acts as a preferred path for hydrogen diffusion in the material; such an effect have been previously reported as hydrogen highway effect [15]. On the other hands, the effects of the rolling ratio on the Type-316L and Type-310S steels have previously been investigated [50]. This study concluded that the cold rolling process does not have a significant influence on the measured diffusivity. This fact could be quantitatively translated by the variation of hydrogen diffusivity due to the pre-strain of the material. A pre-strain of
0.92 results in an increase of one order of magnitude in the case of Type-304 steels but a variation between 3% and 9% for the Type-310S and Type-316L, respectively. The present paper targets to clarify the effect of the coldworking ratio applied on the Type-304 steels on the hydrogen diffusivity and more specifically its effect on the direction of diffusion. First of all, a material characterization has been performed in order to gather various properties. The fraction of martensite resulting from the CW has been quantified by electromagnetic induction (EMI) method and its distribution by electron backscatter diffraction (EBSD) observations. The correspondence between CW ratio and fraction of strain-induced martensite being available, the hydrogen diffusivities and solubilities in two directions have

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been measured. Secondly, the experimental results are then reproduced by finite-element method by simulating a permeation test. This analysis being only based on a continuum approach of the problematic, the results provided do not account for the crystallographic singularities (e.g. dislocations, lattice defects …). The simulation is performed on the representative distribution of martensite based on the EBSD observations. The results from experiments and simulation are then discussed.

Experimental characterization Material The material in interest in this study is the JIS-SUS304 stainless steel, referred hereafter as Type-304. This alloy has the particularity to be metastable which means that under certain conditions, the strain-induced martensite (SIM) transformation can occur. The composition of this alloy is given on Table 1. The 30 mm thick Type-304 plate has been hot-rolled prior applying a solution treatment (at 1080  C for 3 min followed by a water cooling). The plates are then cold-rolled at room temperature to reach the targeted thickness. The resulting cold working ratio (called CW ratio) is included in the [0%; 60%] range, with increments of 15% (leading to 5 CW ratios in total). This rolling reduction ratio rcw is usually calculated by the following expression (1): rCW ¼


 t0 et1 x 100 t0

(1)

Where t0 and t1 are respectively the initial and the final thicknesses. The investigations on this material have been performed on the basis of disk-shaped specimen withdrawn from the cold rolled plates along the LT and SL planes for each rolling ratio involved in this study. The dimensions of the specimens could be described by their diameter, 5 mm, and their thickness, 0.5 mm. The specimens with the thickness direction perpendicular to the rolling direction are called LT specimen and, oppositely, the specimens with a thickness direction parallel to the rolling direction are called SL specimen. The specimens have then been polished by emery paper #600.

Experimental protocol To characterize the material, several experiments will be performed on both the LT and SL specimens. The experiments target to access to the martensite content, the martensite distribution, the effective diffusivity as well as the hydrogen content of the biphasic material.

The electromagnetic induction (EMI) method is adapted to measure the volume fraction of the martensitic phase a'. The measurements have been performed on a rectangular partition of the initial specimen (cut from the cold-rolled plates) as illustrated on Fig. 1 by using a Fischer MP30 Feritscope. After cutting, the surface of measurement have been prepared by using #2000 emery paper. In a practical manner, the Feritscope uses a probe (diameter in the orders of the mm2) that measures locally the ferrite content by magnetic induction. The expected accuracy on ferrite content is in the order of 0.1%. Previous measurements using a different technique (saturation magnetization) [51,52] have provided some coherent results with a difference in the order of 0.5% (compared to EMI). This point suggests that this technique provides a sufficient accuracy for the present study. To ensure the relevance of the a' volume fraction measurements, 35 points have been considered, distributed in the whole cut surface (in 7 lines and 5 points per line). For example, in case of a CW ratio of 0%, the lines were distant of 20 mm and the points distant of 5 mm for a total area of 120  20 mm2. The phase distribution has been identified on the basis of EBSD (electron backscatter diffraction) maps. The EBSD acquisition has been carried out under an acceleration voltage of 15 kV on a JEOL SEM-FEG (JSM-7001FKM) apparatus. Both the LT and SL specimens have been mapped after processing the surface with colloidal silica to reach the expected requirement for this technique. The diffusivity measurements are performed on the disk specimens preliminarily exposed to 100 MPa high pressure hydrogen gas at 270  C for 200 h to ensure a uniform concentration profile of hydrogen in the whole volume of the specimen. The hydrogen content is then monitored using gas chromatography-mass spectroscopy (JTF-20W, J-SCIENCE LAB Co., Ltd., Japan) while controlling the heating temperature (constant or ramp). In the present case, the specimen has been heated at a rate of 100  C/h. By fitting the measured residual hydrogen contents (CR) at several constant temperatures to the proper analytical solution, a value of the effective diffusivity of the material can be deduced. Setting the hydrogen content of the non-charged specimen, CH0, here assumed to be zero, the residual hydrogen content CR, can be expressed by series of parameters, including diffusivity [53e55]. This expression is recalled in (2) " #9 8  9 8 > ð2nþ1Þ2 p2 DtR > > > Db2m tR > > > > exp
2 > > > > exp z 2 > > > b ð2n þ 1Þ > > > > m > > ; > n¼0 > : m¼1 : ;

(2)

Where tR is the holding time in the mass spectroscopy, AR the constant determined by fitting from the measurements of saturated hydrogen content [54], D the diffusivity, r0 the radius

Table 1 e Chemical composition [mass %]. Material SUS304 JIS

C

Si

Mn

P

S

Ni

Cr

0.05 0.08

0.58 2.00

1.25 1.00

0.026 0.045

0.0018  0.030

8.07 8.00~10.50

18.56 18.00~20.00

JIS: Japanese Industrial Standards, JIS G 4304 (2012).

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Fig. 1 e Illustration of the sampling of disk specimens according to the rolling direction. The disks, sampled for a CW ratio of 0%, 15%, 30%, 45%, and 60%, have a diameter of 5 mm and a thickness of 0.5 mm.

of the specimen, z0 the thickness of the specimen and bm the root of the zero-order Bessel function. In order to get insight on the solubility, some measurements with thermal desorption analysis (TDA) have been carried out. The specimens used for this experiment are identical to the ones involved in the diffusion measurements. These measurements consist in monitoring the amount of desorbed hydrogen under a constant heating rate using a gas chromatography mass spectroscopy. The hydrogen in solution can be decomposed into diffusible and trapped hydrogen, the proportion of hydrogen in each state being governed by an equilibrium. Usually, the trapping sites correspond to the crystallographic defects such as dislocations, grain boundaries … The equilibrium has been formalized by Oriani [56] and is described by a trapping energy. In TDA measurements, the applied ramp provides energy to the system and contributes to release progressively the trapped hydrogen. The resulting desorption spectrum then translates qualitatively the different trapping sites by analyzing the associated temperatures. If the dataset includes different heating temperatures, the TDS spectra are able to provide a quantitative estimation of the trapping energy by using the Choo-Lee formula [57]. However, quantitative measurements have not been carried out in the present study.

Rolling ratio dependence of the martensite Fig. 2 presents the evolution of the martensite content in the cold-worked material measured by EMI. The represented data corresponds to the averaged value of martensite volume fraction (the acquisition have been done on 35 points uniformly distributed on the surface of the material). This graph clearly shows an increase of the martensite content with the CW ratio. This increase of the martensite content can be attributed to the SIM transformation. According to the graph, the maximal martensite content is 25% and is reached for a CW ratio of 60%. The dashed line connecting the experimental data is the result of the smoothing and mainly targets to illustrate the trend of this dependence to CW ratio. The nominal composition of this alloys suggests that the SIM transformation is more likely to lead to lath martensite since the carbon content is lower than 0.6%. The EMI method only provides information about the fraction of martensite at a mesoscopic scale. In consequence, these measurements translate the average value of martensite contained in a

Fig. 2 e Rolling ratio dependence of the martensite content measured by EMI method.

characteristic volume of material and do not account for the distribution of the martensite isles in the material. The error bars show the increasing dispersion of the measurements with the augmentation of the CW ratio. This increase translates the heterogeneous nature of the distribution of martensite phase. However, this distribution of the martensite is a key parameter required to investigate the changes in diffusivity.

Distribution of the martensitic phase The distribution of the martensitic phase has been investigated by using the EBSD analysis. The EBSD maps are given in Fig. 3 for LT and SL specimen. Two CW ratio have been considered. The maps on Fig. 3(aeb) are related to the CW ¼ 15% specimens whereas the Fig. 3(ced) refer to a CW ratio of 60%. On these maps, the austenite is represented in green and the a' phase in red. For a CW ratio of 15%, the EBSD maps show no significant difference between the LT specimen (a) and the SL specimen (b). The repartition of the martensitic phase in the material is not clearly characterizable on the basis of these micrographs. The martensite isles are located on the grain boundaries as well as in the center of grains which means that the a' phase can be considered as homogeneously distributed. For a CW ratio of 60%, a strong

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Fig. 3 e Phase map illustrating the martensite content and its repartition for 15% and 60% rolling ratio in LT and SL planes.

difference between LT (c) and SL (d) specimens is observable. The map of the LT specimen shows that a' phase is distributed in elongated islands parallel to the rolling direction. The amount of martensite being greater, the distance between islands is reduced. The difference in diffusivity between the austenitic and martensitic phase being a few orders of magnitude, the martensite is likely to behave as a preferred path for hydrogen diffusion. Some additional effects may affect the hydrogen diffusivity such as dislocations and crystallographic defects. A subsequent increase of the effective diffusivity is then expected as well as a complex hydrogen redistribution.

Diffusivity measurements The diffusivity measurements have been carried out on the specimens previously described. The results are summarized by Fig. 4 which shows the temperature dependence of the effective diffusivity. The graph in (a) is related to the LT specimens whereas the graph in (b) shows the results of the SL specimen. On both graphs, the data have been fitted by an Arrhenius’ law and compared to a reference related to unprocessed 300-series austenitic stainless steels available in [14]. As expected, the diffusivity measurements carried out on the Type-304 specimens provide identical values for LT and SL specimens for CW ratio of 0%. Moreover, in all cases, the increase of CW ratio promotes the mobility of hydrogen in the material. For instance, this effect could be observed on the relatively high value of hydrogen diffusivity in the case of a CW ratio of 60% which has increased by more than one order of magnitude. If both directions are compared, the difference of diffusivity is about one order of magnitude greater in case of SL specimen. This fact could be explained by diverse factors such as the martensite distribution, lattice defects … The

contribution of the distribution of the martensitic phase remains to be assessed by the simulation.

Hydrogen content measurements In order to get more insight on the modifications brought by the cold-rolling process in terms of hydrogen content, some TDA measurements have been performed for all the rolling ratio and for both LT and SL directions. The results are given by Fig. 5 and show some interesting tendencies. The spectra in a) are related to the LT specimens whereas the spectra in b) are related to the SL direction. In both cases, a notable decrease of peak intensities and untrapping temperatures are observed for an increasing rolling-ratio. This tendency translates a modification of the hydrogen redistribution and suggests an increased diffusivity resulting from the rolling ratio. Furthermore, the decrease of the area under the curve (translated by a lower amount of hydrogen in solution, see Table 2) indicates that the total content of hydrogen is strongly affected by the cold rolling process. This fact can be explained by the increase of the fraction of the SIM (up to 25% for a CW ratio of 60%) since the solubility of hydrogen is about two orders of magnitude greater in FCC compared to BCC structure. The comparison of the LT and SL spectra reveals a slight modification of around 45  C of the relative positions of peaks for a CW ratio of 45% and 60% which suggests an anisotropic nature of the material properties. However, these discrepancies do not necessarily translate some different trapping properties (this point requires some additional measurements performed with different heating rates) This fact supports the assumption that the change in diffusivity is the result of the martensite distribution. In such experiment, the integration of the spectra provides the cumulated quantity of desorbed hydrogen from the specimen in the considered temperature range. Assuming

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Fig. 4 e Diffusivity measurements performed on several CW ratio for both specimen: LT (a) and SL (b). The results have been compared to the reference available in [14].

Fig. 5 e Results of the TDA measurements performed at a constant heating rate of 100  C h¡1 for both specimens, LT (a) and SL (b), for various rolling ratio.

that the entire amount of hydrogen desorbs in the temperature (i.e. no irreversible traps exists at a temperature greater than 800  C), the measured value could be assimilated to the concentration involved in Sievert's law. The main results of the diffusivity measurements and the TDA are summarized in Table 2 for various CW ratio and both LT and SL specimens. These values indicate that an increase of the apparent diffusivity occurs with the cold-working process and this effect intensifies with the martensite content. The diffusivities at CW ¼ 0% for LT and SL specimens are equal which means that the presence of martensite in the material is a key factor. Then, if the values are compared at CW ¼ 60% the diffusivity

Table 2 e Amount of hydrogen and effective diffusivity measured for three rolling ratios and in both directions  cised (the conditions of pressure and temperature are pre in the header). CW ratio

0% 15% 60%

Cs (100 MPa, 270  C)

Deff measured at 143  C

LT/SL direction

LT

97.2 mass ppm 94.6 mass ppm 69.3 mass ppm


13

SL 2


1

1.06 10 m s 1.29 10
13 m2 s
1 2.05 10
13 m2 s
1 4.15 10
13 m2 s
1 1.86 10
12 m2 s
1

in the SL specimen is about 5 times greater compared to the LT directions at 143  C. This table also provides the decreasing value of the concentration of hydrogen in solution in the metal. Knowing the pressure of exposure and the temperature, the value of the actual fugacity could be calculated by using a real gas equation of state (Abel-Noble model for example). For instance, at a temperature of 270  C, the fugacity corresponding to 100 MPa is 142 MPa (the molar co-volume being 1.584 10
5 m3.mol
1). The solubilities of the material for a CW ratio of 0%, 15% and 60% are then 8.15 mass ppm.MPa
0.5, 7.94 mass ppm.MPa
0.5 and 5.81 mass ppm.MPa
0.5, respectively.

Modelling of hydrogen diffusion in the heterogeneous medium To verify the interpretation of the experimental results, the values of the equivalent diffusivity have been simulated for various CW ratio for LT and SL specimens. In order to be as accurate as possible, the simulation domain have been built for all cases in respect with the EBSD maps. Considering the diffusivities of pure materials as input parameters, the aim is to simulate the resulting diffusivity of the cold-worked material and compare the values to the experimental values. In

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case of a good agreement with the experiment, the assumptions involved to build the model are likely to provide information on the predominant phenomena governing the variation of the diffusivity resulting from CW.

Domain definition and methodology The simulation domains have been defined on the basis of a set of EBSD maps. The EBSD images have been preliminarily processed prior constructing the model as illustrated in Fig. 6. Several EBSD maps have been obtained in different areas. The EBSD maps only show some local aspects of the materials. It is then necessary to perform the FEM analysis on multiple areas in order to supply results as accurate as possible. For this reason, the underlaying image processing, as well as the construction of the FEM model, steps have been performed using a routine. Prior building the FEM model, some modifications of the map have to be realized. First of all, a dithering algorithm have been applied. Such a filter targets to reassign the color scale of a 32-bits image to a customized palette. In the present case, the processed image has to be composed by two color only, one for each phase. Then, the images have been rescaled to decrease the total number of pixels in order to optimize the size of the model for finite element model (FEM) and its efficiency. Finally, the material properties shown in Table 3 are assigned to a FEM mesh on the basis of the EBSD mapping (for a given set of pixels, the proper material is assigned on the FEM grid if its proportion exceeds 50%). This procedure to define the FEM model on the basis of the experimental EBSD maps is summarized in Fig. 6. This figure shows an example of the post-processing implemented to

Table 3 e Hydrogen diffusion properties used for FEM simulation given at 143  C. Phase

Diffusivity [m2.s
1]

Solubility [ppm.MPa
0.5]

Reference

g a'

1.06  10
13 2.32  10
8

8.5 8.4  10
2

Type-304 steel [14] Low-alloy steel [54]

generate the FEM model and also locates the direction of diffusion relatively to the rolling direction. A look at the Fig. 3(ced), which presents the phase distributions for a CW ratio of 60% in both LT and SL specimens, shows that the a' isles in these specimens are elongated following two orthogonal axis. Furthermore, the isles observed in the LT specimen of the Fig. 3c) have a slightly different distribution as compared to the ones observed on SL specimens. This point could be justified by the bidimensional and local view of the EBSD maps. For this reason, the FEM domains for both specimens will be based upon the same EBSD maps, considering different boundary conditions. The EBSD maps are then selected in order to be representative of the actual material. The maps issued from the SL specimens are then preferred since the martensitic isles are clearly separated by the austenitic phase. In contrast, an interconnectivity of the martensitic isles may result in an overestimated value of the diffusivity. To avoid such an artifact, the permeation test is simulated with a diffusion in the Xdirection, to calculate the hydrogen diffusivity of the LT specimens. Oppositely, the permeation test is simulated considering a diffusion in the Y-direction for the SL specimen. In a practical manner, the direction of diffusion is imposed by

Fig. 6 e Construction of the FEM model based on the EBSD maps and illustration of the direction of diffusion used in the simulations of permeation tests for LT and SL specimens.

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modifying the boundary conditions of the domain. The position of the entry face and outgassing face are indicated in the Fig. 6. In a general viewpoint, EBSD maps provide a local view of the material which means that these maps have to be carefully selected. For instance, the maps locally showing a fraction of martensite greater than 0.40 are not considered

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because of the excessively high fraction of martensite compared to the fraction measured by the Feritscope. The EBSD maps presenting a continuous path to connect entry and outgassing bounds are also evicted since such arrangement results in an excessively enhanced effective diffusivity (artifact). The set of EBSD maps actually used in this study is presented in Fig. 7. On these maps, the martensite repartition

Fig. 7 e EBSD maps used to create the FEM model.

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is judged as representative of the average repartition observed in the experimental specimens. Slightly different martensite contents are expected in all these maps since EBSD analysis only provides local and bidimensional observations. The effect of the variable martensite content on the calculated diffusivity is observable in the result section. The maps of the cases 2 and 4 were taken at lower magnification compared to the other cases. The corresponding martensite contents are then 25.5% and 26.9% respectively. These cases are then more likely to provide results in accordance with the experimental results. In the FEM model, the properties of the pure phases have been assigned. For the austenitic phase, the diffusivity and the solubility measured on the Type-304 steel have been considered. The properties of the martensitic phase have been measured on specimens made of low-alloy steels. The values of diffusivity and solubility at 143  C as well as their reference in the literature are provided in Table 3. After constructing the FEM grid, the simulation of the permeation test consists in the application of two Dirichlet boundary condition: a unitary concentration on the charging bound and a concentration equal to zero on the outgassing face (corresponding to a hydrogen partial pressure of hydrogen equal to 0 MPa). According to the load case, the position of the entry face and outgassing face are adapted whether the diffusion occurs on the X direction and the Y direction (corresponding to SL and LT specimens respectively). The desorption flux is then calculated to determine the effective diffusivity of this dual phase material. The effective diffusion coefficient is determined by a time-lag based method. The hydrogen entering in solution in the material at a given time desorbs on the other end of the specimen in a delayed manner. This delay is usually called time-lag. This

time-lag is calculated by extrapolation of the asymptotic behavior of the cumulated desorption flux curve, as illustrated hereafter. This method has been explained in details in [58,59]. After determining the actual time-lag, the following expression have been used to calculate the effective diffusivity (3). D¼

l2 6tD

(3)

Where D is the effective diffusivity of the specimen, l is the thickness of the material in the direction of diffusion and tD the time-lag calculated on the basis of the asymptotic behavior cumulated desorption flux.

Simulation results The results of the FEM simulations are presented from Figs. 8e10. Fig. 8 shows the repartition of hydrogen in the dual phase material at steady state for cases 2 and 4 in both direction of diffusion. The martensite fractions in both cases 2 and 4 are close to the ones measured during the experimental measurements. The difference of solubility between both materials results in a heterogeneous repartition of the hydrogen content. The reason of the observed discontinuity of hydrogen resides in the continuity of the mass flux and the chemical potential of hydrogen in the material. The martensite isle modifies the repartition of hydrogen and then the effective diffusivity of the material. In cases 2 and 4, the fractions of martensite determined with the EBSD maps are respectively 25.5% and 26.9%. The experimental value being equal to 25%, the cases 2 and 4 could then be considered as relevant enough to build the FEM models from these maps.

Fig. 8 e Concentration fields of hydrogen obtained in both X and Y direction for cases 2 and 4.

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Fig. 9 e Definition of the time-lag determined on the cumulated permeation curve: example of the case 4. The graph (a) is related to the permeation test in the X-direction whereas the (b) graph refers to the Y-direction.

Fig. 9 provides the cumulated desorption curve for the case 4. The martensite fraction (and its arrangement) of case 4 is quite close to the one experimentally measured by the Feritscope. These conditions lead to a quite good agreements with the experimental tendencies as shown hereafter. The time-lag is defined on the basis of the asymptotic behavior of the system. The steady-state curve has been extrapolated to obtain the intersection with the time axis. The time-lags in the X and Y directions are 11 500 s and 5300 s, respectively. According to the expression (3), the corresponding diffusivities are 4.53 10
13 m2 s
1 and 1.07 10
12 m2 s
1. Fig. 10 summarizes the simulation results obtained in all the cases presented in Fig. 7. This graph contains the results of the effective diffusivities simulated for various martensite fractions, due to the variability of the EBSD maps on this aspect. The circle shaped markers refer to the diffusivities resulting from the permeation tests in the X-direction whereas the diffusivities represented by the cross shaped markers are issued from the permeation tests in the Y-direction. The experimental data are represented in diamond

shaped markers (blue and red for the X- and Y-direction, respectively). This graph suggests a strong dependence of the diffusivity to the martensite volume fraction. The diffusivity increases with the martensite fraction for both directions. The scattering of the values of diffusivity is the consequence of the experimental EBSD maps. These simulated data are in interest since the actual tridimensional repartition of the martensitic phase is not available. Then, the simulations performed for various bidimensional EBSD maps provide an envelope translating the expected tendencies. It is noteworthy noticing that the experimental data are contained in the tendencies of the simulation results. This graph also shows that the anisotropic nature of the material increases with the fraction of martensite. Knowing that the highest fraction of martensite is reached in case 5 (33%), the ratio of diffusivity in both directions diverges compared to the other cases. The simulation results are consistent with the experimental value, especially in the X-direction (which corresponds to the SL specimens). For instance, the simulation of the case 4 results in a relative error of 9.13% in the X-direction (SL specimens) and 42.4% in the Y-direction (LT specimens).

Discussion

Fig. 10 e Orientation dependent diffusivity simulated for cases 1 to 5. This graph presents the values of the diffusivity in X and Y directions for different martensite fraction (as measured on the EBSD maps).

The experimental investigations have shown that the CW process results in a formation of martensitic elongated island. The fraction of martensite of reversion increases with the CW ratio until reaching 25% for a ratio of 60%. The EBSD maps suggest some differences in the repartition of the martensite between LT and SL specimen, especially for high CW ratio, which could be translated by different path for diffusible hydrogen. A significant difference of diffusivity between LT and SL specimens is then expected for high rolling ratio but expected to be negligible for low rolling ratio. The anisotropic behavior of the CW material has been confirmed by the diffusivity measurements. These measurements have revealed a strong influence of the cold-working process on the diffusivity as well as its anisotropic nature. Since various parameters are known to influence the effective diffusivity of the material such as the distribution of the martensitic phase, the crystallographic defects, the composition of the alloy and its cleanliness, the plastic field resulting from CW. It is then of

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Fig. 11 e Austenitic (green) and martensitic (red) partitions assembled in series. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

great importance to clarify this anisotropy by considering the appropriate modelling. The TDA experiments suggest a variation of the total hydrogen content in case of CW. This fact translates a modification of the solubility by the CW. Some analytical expressions exist to predict the effective diffusivity of a multiphase media; however, neither the effect of solubility nor the transient regime are taken into account in these expressions. The validity of the analytical expressions has been verified numerically by simulating a permeation test on a hypothetical FEM model containing successively some multiphase areas assembled in series as illustrated in Fig. 11. The diffusivities inputted in the model are 10
7 m2 s
1 and 10
8 m2 s
1; respectively applied to the first (green) and the second (red) domain. The proportion of the second phase has been taken equal to 25%. The analytical solution has been calculated for a ratio of solubility of 1. The diffusivity is 3.08  10
8 m2 s
1. The results of the FEM simulations conducted for several solubility ratio are summarized in Table 4. The error is also calculated relatively to the analytical solution. These simulations show that a heterogeneous solubility significantly modifies the effective diffusivity. For this reason, the modification of the effective diffusivity by the CW process cannot be investigated analytically. The FEM simulations based on the experimental EBSD maps rely on a continuum and macroscopic approach of the diffusion process. More accurately, these simulations only account for the distribution of martensite and a macroscopic description of each phase (e.g. diffusion parameters). The good agreement with the experimental tendencies proves that the anisotropy is mainly the consequence of the specific distribution of the martensitic phase. In the present case, the martensite acts as a diffusion highway for diffusible hydrogen, meaning that the diffusion process preferentially operate through the martensite isles (the diffusivity of the pure martensite being about five orders of magnitude higher than the pure austenite). As mentioned before, the SIMT does not involve any diffusion process. The composition of the

Table 4 e Effective diffusivities simulated for various ratio of solubility. The relative error is also calculated.   DD Solubility ratio, S1/S2 DFEM [m2 s
1]   [%] D 1 0.1 0.01 10 100

3.08 2.92 4.76 5.30 5.63

    


8

10 10
8 10
9 10
9 10
10

0.20 5.04 84.5 82.8 98.2

martensite of reversion is then nearly equal to the one of the parent austenite. The diffusivity of such phase is not straightforward to determine experimentally and an assumption has then been considered in the FEM simulations since the inputted diffusivity and solubility for a' phase have been taken equal to the ones of the low-alloy steel. For this reason, the variation of hydrogen diffusivity in a' phase remains to be quantified as well as its effect on the effective diffusivity of the CW material. In addition, the use of experimental EBSD maps is likely to introduce some incertitude since the information of martensite content and distribution are limited to some slices of the initial volume. The simulation conducted in three dimensions must lead to more realistic values of diffusivities. However, the construction of the FEM model requires some additional observations based on 3DEBSD, for example. In a more general manner, the present study shows the effect of the distribution of martensitic phase in a CW Type-304 stainless steel. The anisotropic diffusivity observed and simulated may be in great interest for various topics including acid pickling, heat treatment, welding or hydrogen induced cracks. Such problematics deal with the entry, repartition and outgassing of hydrogen and thus require an accurate understanding of the hydrogen diffusion in either heterogeneous or homogenized materials.

Conclusion Effect of sampling directions on the effective hydrogen diffusivity in a cold-rolled Type-304 austenitic stainless steel has been investigated using a joint experimental and simulation analysis. The diffusivity has been measured in both LT and SL directions for five cold-worked (CW) ratios up to 60% which provide materials containing various martensite contents (up to 25%). The LT specimens are characterized by a thickness perpendicular to the rolling direction and the SL specimens could be described by a thickness parallel to the rolling direction. The difference of diffusivity in the LT and SL directions for several CW ratios suggests that the inhomogeneous repartition of martensite is a key feature to clarify the hydrogen diffusion in such alloys. This study has resulted in the following conclusions: 1. In Type-304 steels, a cold-working step applied during manufacturing process results in the formation of straininduced martensite in relation with the CW ratio. This ratio of a' phase has been measured by the electromagnetic induction (EMI) method and ranges from 5% to 25%, for a CW ratio of 15% and 60% respectively.

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2. The difference between the repartition of martensite in SL and LT specimens is observable on the electron backscatter diffraction (EBSD) maps and increases with the rolling ratio. 3. For a CW ratio of 60%, the measured diffusivity in SL direction is about five times higher as compared to the LT direction. The comparison with the reference state (i.e. CW ratio of 0% and a martensite content of 0%) shows that the effective diffusivity measured at CW ¼ 60% is increased by about 20 times in case of SL specimens. 4. The necessity of the FEM simulations has been justified by verifying the error resulting from the use of an analytical expression of diffusivity association in composite media. Since the analytical models neither take into account the solubility nor the transient behavior of the material, the error introduced by a solubility ratio of 100 is around 100% for analytical expressions. 5. A permeation test has been simulated on the basis of EBSD maps for multiple representative arrangements and fraction of martensite, corresponding to both LT and SL specimens. The simulations reproduced accurately the tendencies experimentally observed. The simulated diffusivities only involved assumptions based on a phenomenological description of the problem (e.g. Fickian diffusion). This means that the phenomena involving a local description of the material (e.g. crystal defects, dislocations …) are inherently neglected.

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