This paper is associated with a larger program of research, studying the resistance to hydrogen-induced stress cracking (HISC) of a wrought and a hot isostatically pressed UNS S31803 duplex stainless steel (DSS), with respect to both the independent and interactive effects of the three key components of HISC: microstructure, stress/strain, and hydrogen. In the first part presented here, several material properties such as the three-dimensional microstructure, distribution, and morphology/geometry of the two phases, i.e., ferrite and austenite, and their significance on hydrogen transport have been determined quantitatively, using x-ray computed tomography microstructural data analysis and modeling. This provided a foundation for the study to compare resistance to HISC initiation and propagation of the two DSSs with differing microstructures, using hydrogen permeation measurements, environmental fracture toughness testing of single-edge notched bend test specimens, in Part 2 paper of this study (Blanchard, et al., Corrosion 78, 3 [2022]: p. 258–265).

## INTRODUCTION

**D**uplex stainless steels (DSSs) are high-strength alloys with excellent resistance to corrosive environments. These advantageous properties are conferred by their particular chromium- and molybdenum-rich chemistry, and phase balance close to 50% delta ferrite (δ) and 50% austenite (γ). This combination of chemical composition and phase balance makes them a good material option for harsh conditions and applications, in which a combination of strength, toughness, and corrosion resistance is required. Hence, they are of particular interest in the oil and gas, chemical and petrochemical, marine transportation, power generation, food, and paper industries. This work is particularly relevant to offshore energy and oil and gas applications, and particularly subsea systems. Components made of DSSs are often connected to ferritic alloys, which require cathodic protection (CP) to resist corrosion in seawater. CP can generate monoatomic hydrogen (as a result of the reduction of water at the steel surface), and this can subsequently be absorbed into the metal. When hydrogen has been absorbed into an alloy in a susceptible condition, assisted by the influence of localized straining, the material can become embrittled. Cracking can ensue, via a mechanism known as hydrogen-induced stress cracking (HISC), when a sufficiently high level of stress is applied. This mechanism has been responsible for a large number of major in-service DSS failures.^{1-4 }

Several studies have established the role of the microstructure in terms of phase size distribution, particularly the austenite phase and its “spacing,” in hindering HISC propagation.^{2,5-6 } Austenite spacing is usually defined as the width of austenite islands, along a given direction that is often measured to be perpendicular to the expected cracking direction. As a result, industrial guidelines^{7 } specify an “austenite spacing threshold,” below which the microstructure is deemed “unsusceptible” to HISC. Little information is available with respect to its roles in accommodating deformation, arresting crack growth and hindering hydrogen transport. Recent work, on low-temperature creep behavior^{8 } and environmental fracture toughness testing has suggested that resistance to HISC is related to fundamentally different microstructural responses to localized straining, and is not merely linked to the austenite spacing/size.^{9 } This work used wrought and hot isostatically pressed (HIP) DSSs with comparable austenite spacing/size in the direction in which cracking is normally observed in-service failures. Research on DSSs has shown that HIP materials exhibit superior mechanical properties,^{10 } and resistance to HISC^{11-12 } compared to more conventional product forms, mainly due to the presence of a finer microstructure in the HIP material introducing more obstacles to the HISC path. It has also been demonstrated^{13 } that the fraction and morphology of the austenite phase can create a more tortuous path for the transport of hydrogen, due to its higher solubility in this phase.

These observations underline the shortcomings of two-dimensional (2D) microstructural characterization techniques for linking the “connectivity” of the ferrite phase with high hydrogen diffusivity. They also highlight the importance and influence of the three-dimensional (3D) structure and morphology of the two phases on hydrogen transport, both through the bulk and from the surface. These characteristics of the phase distributions, in turn, control the resistance to the initiation and propagation of HISC, in the presence of stress concentrators, both in service and during laboratory testing.

This paper, i.e., Part 1 of a larger quantified study of the resistance of DSSs to HISC, addresses the significance of the 3D phase distributions and geometrical and morphological properties of the two phases on hydrogen transport, allowing for the Part 2 paper^{14 } to further interpret and relate these findings to the roles of stress raisers, hydrogen transport, and resistance of the two alloys to HISC.

## BACKGROUND AND WORK CONTEXT

It is common practice to assess and quantify the performance of materials, which are directly or indirectly associated with their microstructural parameters, using 2D characterization techniques. However, in reality, materials are 3D aggregates of grains and phases, which respond in a cooperative manner to the conditions encountered during service or testing. Therefore, limiting the quantification of key microstructural parameters to 2D assessments is an over-simplification. This is particularly the case when a hydrogen-assisted cracking (HAC) mechanism such as HISC, with interacting components, is of concern. In this case, the responses of both microstructure, as a function of the morphology of its phases, and hydrogen diffusion, to mechanical loading/cracking, would both be controlled by their three-dimensionally related properties.

The significant progress achieved in 3D materials characterization and quantification techniques has enabled better scrutiny of links between grain structures, phase morphologies and connectivities, and hydrogen transport properties. Currently, three major techniques for 3D microstructural reconstruction of alloys are commonly used: serial sectioning followed by conventional 2D metallographic preparation and imaging, focused ion beam (FIB) milling coupled with electron backscattered diffraction (EBSD) mapping, and x-ray computed tomography (CT). Serial sectioning and FIB milling are destructive and time-consuming methods, with the latter being limited to relatively small sampling volumes.^{15-16 } X-ray CT is a radiographic imaging methodology, and hence, a nondestructive technique, enabling the characterization of larger volumes/specimen sizes. It can be used with different x-ray sources; however, the use of synchrotron radiation allows for high contrast and resolution (i.e., <1 μm) imaging. Given the morphology and the coarseness of the microstructures of the wrought and HIP DSSs, x-ray CT was the most suitable technique to use to produce a 3D reconstruction of the microstructures in question.

_{r}:

^{17 }where σ

_{r}is the relative conductivity, F is the formation factor, ε

_{p}is the porosity volume fraction, and m is the slope of the logarithmic plot F vs. log ε. This relation does not take into account any microstructural parameters, and hence, an Archie’s law has to be established for various types of sediment.

^{18 }and further developed for numerical approaches.

^{19 }This shape-recognition method aims to give a simplified representation of a microstructure, by reducing its dimensions to a set of all points having more than one closest point on the object’s boundary, referred to as the medial axis, leaving only a network with a skeleton, Figure 1. This representation enables each analyzed shape/phase to be simplified to a graph composed of vertices connected by edges, and hence, computation times are drastically reduced.

^{20 }This methodology preserves the tortuosity and connectivity characteristics of the microstructure, which are two essential features for transport properties. However, this model does not account for the “bottleneck effect,” i.e., the possibility for a diffusion path to vary in thickness, over its length, also known as “constrictivity.”

^{21 }

_{eff}, which, due to the complexity of the phase structure, is lower than the intrinsic value for the dense material, σ

_{bulk}. The effect is taken into account through a factor, M, defined as follows:

^{22 }

^{23 }established the following empirical relationship, defining the M-factor according to the morphological parameters of the microstructure, i.e., phase volume fraction, ε; geometrical tortuosity, τ; and constrictivity, β: with a, b, c, and d being morphological exponents. For instance, Stenzel, et al.,

^{24 }have fitted a law on cermet (nickel-yttria stabilized zirconia ceramic–metal composites) reconstructions, which depends on ε, τ

_{geo}, and β of the transporting phase:

This method can be extended to the transport of fluids through porous materials or gas permeation in metals, in a specific direction. The M-factor approach was found to be most suitable for this study and used to characterize the hydrogen transport properties of the ferrite (as the transporting phase) and austenite of the two DSSs studied in this work, as a function of the morphological parameters of their microstructures.

Indeed, the effective conductivity for electric and ionic loads is analogous to “effective diffusivity” for fluids. However, it is important to note that the effective diffusivity, calculated using this approach, only takes into account structural parameters of the transporting phase, i.e., the volume fraction, geometrical tortuosity, and constrictivity. This is distinct from the effective diffusivity, which is measured experimentally using permeation techniques and is also dependent on microstructural parameters, i.e., crystallographic structures, grain boundaries, secondary phases, dislocation densities, the hydrogen trapping effects of such features, etc. Hence, for clarity in this paper, the term “effective diffusivity” will be used to refer to the diffusion coefficient and properties measured using the hydrogen permeation technique, and “effective conductivity” will be used, interchangeably, with “hydrogen transport,” calculated using the M-factor approach.

## EXPERIMENTAL METHODS

### Materials

Materials studied in this work were conventionally manufactured wrought and HIP DSS products. The two materials had the same nominal DSS compositions, consistent with 318 SS (UNS S31803^{(1)}), but had fundamentally different microstructures. The samples consisted of a pipe, manufactured by seam-welding of a rolled plate, and a HIP can, hereafter referred to as “wrought” and “HIP” materials, designated “M1” and “M2,” respectively.

The chemical compositions of the two materials were listed in Table 1. The optical emission spectrometry (OES) technique was used for the analyses, except for the nitrogen and hydrogen contents. Nitrogen was measured by the inert gas fusion technique and diffusible hydrogen was measured by the hot extraction method, using gas carrier analysis at 400°C, in a Bruker G4 Phoenix^{†} hydrogen analyzer. The residual hydrogen content was measured by the melt extraction method, using gas fusion analysis, in an ELTRA ONH 2000^{†} analyzer. The specified composition of UNS S31803 was given in Table 1 for comparison.

### Conventional and Advanced Microstructural Characterization

#### Light Microscopy and 2D Assessment of Key Microstructural Parameters

##### General

A series of 2D micrographs of the two DSSs were produced, using an Olympus BX41M^{†} light microscope, and were used to measure the area fractions of the ferrite phase and the austenite spacing of the alloys, with the methodologies described below. The proportion of ferrite in the microstructure represents one component of the so-called “phase balance” which refers to the relative contents of ferrite and austenite.

##### Ferrite Area Fraction

The area fraction of ferrite in the two materials was measured using manual point counting, based on the point intercept method guidelines given in ASTM E562-11.^{25 } For each material, 32 fields were examined at a final screen magnification of 2,000× (corresponding to a microscope magnification of 500×), using a 25-point grid superimposed on the images.

##### Austenite Spacing

The average austenite spacing was determined manually, using the linear intercept method, in accordance with ASTM E112-12.^{26 } For each direction, 10 random fields were examined. This ensured that the statistical reliability of the results met the requirements of the relevant recommended practice, i.e., DNV-RP-F112.^{7 } For each field, the minimum requirement of 50 intercepts was met. The use of an appropriate magnification ensured that the fields were representative of the microstructure. In the case of the wrought material (M1), the three major planes were examined. For the two planes parallel to the normal direction, the austenite spacing was measured in the through-thickness direction. For the plane perpendicular to the normal direction, the measurements were taken perpendicular to the rolling direction. Due to the homogeneous microstructure of the HIP material (M2), only one representative direction/plane was considered to measure the average austenite spacing.

#### 3D Microstructural Reconstruction Using Phase-Contrast X-Ray Microtomography, and Quantification

##### Measurement Principles

CT involves three steps: the acquisition of the data by x-ray microtomography (XMT); the reconstruction of 2D images of the material from 2D radiographs, using mathematic algorithms; and the 3D reconstruction of the microstructure from the 2D images.^{27 }

Two main XMT techniques exist: absorption tomography, relying on the attenuation of the x-ray beam intensity, and phase contrast tomography (PCT), based on the alteration of the phase of the beam wave while passing through a material. The difference between the attenuation coefficients of austenite and ferrite is very small;^{28 } hence, absorption tomography could not be used to map the two phases, and PCT was adopted instead.

^{29-30 }interfaces within the material create discontinuities in the refractive index which are captured by a detector, positioned beyond the material. In this way, PCT enhances detection of edges, making possible the effective differentiation between phases which have comparable attenuation coefficients.

^{31 }

The specimen is rotated from 0 to 180°, while 2D radiographs are acquired. These radiographs, which do not provide depth information, are treated by mathematical algorithms to generate 2D images of slices of the material.^{27 } Using a volume graphic software, these 2D images are then combined to construct the 3D microstructure.

##### Parameters for Phase Contrast Tomography and Retrieval of 2D Images

The XMT experiment was performed on a SPring-8^{†} undulator beamline (BL20XU). A monochromatic beam of 37.7 keV was produced by a Si(111) double crystal monochromator. The sample was positioned approximately 80 mm away from the x-ray source and the distance between the sample and detector was 300 mm. A complementary metal-oxide semiconductor (CMOS) camera (ORCA Flush 4.0^{†}, Hamamatsu Photonics K. K.) was used to acquire the 2D projections. The exposure time was 0.1 s and 1,800 radiographs were obtained during scanning through 180°. The 2D images of the material were obtained by using conventional filtered back-projection algorithms and isotropic voxels of 0.5 μm^{3} were achieved.

##### Reconstruction of the 3D microstructures

The 3D microstructures were reconstructed using Thermo Scientific™^{†} Amira-Avizo software from the 2D slice images, obtained after image retrieval. For each material, 500 images were loaded, as a stack, and a subvolume of 700 µm × 700 µm × 500 μm was extracted. Median and Deblur filters were applied to the subtracted subvolume, or representative volume (RV).

Once the intensity of each image had been normalized using the “Block Face Correction” module, segmentation between ferrite and austenite was automatically performed, using the thresholding function, and manually corrected for all slices. From those results, the 3D reconstruction of the two phases was possible.

##### Quantification of Microstructural Parameters

The data from the 3D structures of the two phases were used to calculate the M-factors of austenite and ferrite, individually for each phase, in the three principal directions, i.e., the rolling direction (RD), normal direction (ND), and transverse direction (TD). This was achieved using a classical homogenization technique.^{32-34 } The mesh for this finite element method (FEM) of computation was built in “Matlab^{†}” by converting each voxel in one element. The methodology can be summarized in the following major steps:

- The equations of diffusion were solved in the digitized domain (Equation [4]) by imposing uniform gradient of temperature as a boundary condition on the edge of the RV, as described in Kanit, et al.
^{35 }This allowed for the determination of the concentration field through the transporting phase, using: where the scalar σ_{bulk}is the conduction coefficient of the considered phase, C^{local}is the local molar hydrogen concentration, and y_{i}= y_{1}, y_{2}, y_{3}are the RV coordinates. - After the computation of the local concentration field (i.e., ) in the heterogeneous microstructure (cf. Equation [5]), the effective or apparent conductivities for each direction were obtained by equating the volume-average flux to the defined macroscopic one (i.e., ), as described in Wilson, et al.:
^{36 }where V is the volume of the RV, the M-factor for each direction was subsequently calculated using Equation (1), with σ_{bulk}, the intrinsic conductivity of the transporting phase. In the present work, σ

_{bulk}was taken as σ_{bulk}= 1 (whereas the conductivity was set to zero in the complementary phase). This implied that, for the microstructural quantification, the intrinsic conductivities of the austenite and ferrite phases were taken as equal and, as a result of this assumption, the effective conductivity, calculated subsequently from the constructed 3D microstructures, was only dependent on the morphological parameters or the phase shapes.

## RESULTS AND OBSERVATIONS

### 2D Microstructural Characterization

The light micrographs showed that the wrought material (M1) exhibited a ribbon-like microstructure of elongated austenite grains, stretching along the pipe rolling direction, within a ferrite matrix. The HIP material (M2) revealed a microstructure of homogeneously distributed, equiaxed austenite, and ferrite grains. The average ferrite content, standard deviation, and the 95% confidence interval are given in Table 2, alongside the austenite spacing.

For the wrought material (M1), the austenite spacing along the through-thickness direction (the direction in which HISC normally occurs in service), and the grain size of M2 were closely comparable. The phase fraction between austenite and ferrite was very close to 50:50 for M1. In the case of M2, the average ferrite fraction was slightly lower, and measured to be approximately 41%.

### 3D Microstructural Characterization

Figures 4 and 5 highlight the strong directionality of the wrought material in the rolling direction and the layers of austenite grains embedded within the ferrite matrix created by the manufacturing process. Furthermore, the construction of the ferrite phase, Figure 5(a) revealed qualitatively that the connectivity of this phase in the ND direction was not evident.

The phase volume fractions and the M-factors in the three principal directions of the two DSSs (calculated using the data obtained from the XMT 3D microstructural quantification) are given in Table 3. The phase fractions were slightly different from those measured with the 2D methods. In the case of M1, it was observed that both the ferrite and austenite phases were heterogeneously distributed in the three directions, with the phase volume fraction particularly lower in the ND compared to the TD and RD directions. In contrast, the quantification of M2 microstructure showed, as expected, homogeneity of the two phases in all directions. As reflected in the values of the M-factors calculated, the effective conductivity in M1 was higher for ferrite than austenite and vice versa in M2. This is thought to be due to the different volume fractions of the two phases in each material.

The determination of the values of tortuosity and constrictivity for the two materials would have given an idea of the influence of those parameters on the hydrogen diffusion. Unfortunately and despite efforts, it was impossible for us to perform these calculations, as the appropriate numerical tools were not available. Indeed, the development of such codes and their validations for the geometrical tortuosity and constrictivity is not straightforward and onerous. Nevertheless, it is possible to assume in a qualitative manner the following statements when bearing in mind the microstructural morphologies:

For M1, the elongated grains must create a very long path in the ND direction inducing a high geometrical tortuosity factor. Therefore, it can be reasonably proposed that the relatively low value for the M-factor for this direction can be mainly ascribed to this parameter (cf. Equation [3]). In other words, the tortuosity in the ND direction (hydrogen diffusion direction in service) should be the limiting factor for hydrogen diffusion.

For M2, the answer is not that clear due to the high homogeneity of this microstructure. Nevertheless, for this type of two-phase homogeneous microstructure, the geometrical tortuosity tends in general to the unity (cf. articles of Moussaoui, et al.,^{37 } for instance). The M-factor could be thus more related in this case to the bottleneck effect for the hydrogen diffusion in the microstructure.

## DISCUSSION

### Microstructural Characteristics and Parameters

2D and 3D microstructural characterizations were performed for the two DSSs, with similar nominal chemical compositions, but fundamentally different alloy manufacturing routes, which conferred typical wrought (M1) and HIP (M2) microstructures with different phase morphologies. The austenite spacing (grain size in the case of the isotropic HIP material) of both alloys, was measured to be approximately 10 µm in the ND, i.e., the direction along which HISC has been observed in service failures for wrought product forms.

Comparison of the ferrite contents measured in the M1 and M2 DSSs, using the 2D (i.e., conventional point counting) and 3D (i.e., digital XMT) characterization techniques, revealed that the ferrite volume fractions of both materials were approximately 5% higher than their ferrite area fractions (compare Tables 2 and 3). Given the higher resolution and accuracy of the XMT method, and that a more realistic representation of the material was sampled (i.e., a volume of the bulk rather than a planar area), this suggests that simple phase balance measurement techniques, such as ferrite point counting, can report a lower level of ferrite than the true value for the material. In (S)DSSs, the body-centered cubic ferrite phase is known to be primarily susceptible to HISC, resulting in brittle crack propagation predominantly in the ferrite, which has a high hydrogen diffusivity. This might be important when assessing materials with respect to HAC, and particularly HISC, as the significance and impact of borderline 2D measurements, within a 5% range of the upper acceptance limit, on the environmental performance of DSS and its weldments, are not established.

The ferrite volume fractions, measured using the 3D method, were used to calculate the M-factors for both the wrought and HIP DSSs. Given the geometrical nature of this approach, an M-factor can be assigned to both phases, irrespective of their differing properties affecting diffusion, including hydrogen solubility and diffusivity and grain/phase boundary diffusion characteristics. However, in the context of hydrogen embrittlement, this factor has little relevance, as far as austenite is concerned. Therefore, it would be reasonable for any comparative study to use M-factors calculated for ferrite, i.e., the phase through which more active hydrogen transport takes place.

Despite significant anisotropy and asymmetric phase morphology in the M1 material, the ferrite content, i.e., the area fraction measured manually, was ∼50% in all three principal directions. As explained earlier, the M-factor is a function of the morphology and fraction of the phases, so it was not surprising that the M-factors calculated for the wrought DSS, with such apparent directionality, were significantly different in the three principal directions. The M-factor in the RD was calculated to be approximately 5.8 times greater than that in the ND, indicating the lowest conductivity/transport properties in the ND. In contrast, the HIP DSS, with a uniform microstructure, in which the calculated M-factors for the principal directions, were closely similar for both the ferrite and austenite, at ∼0.2 and ∼0.3, respectively. The lower M-factor obtained for the ferrite in the isotropic HIP DSS is thought to be linked to its lower volume fraction.

It should be highlighted that this approach was initially developed to calculate conductivity in porous structures (with conductivity occurring in the matrix) and has been further developed, here, to calculate hydrogen transport in a duplex structure, as function of the shape and nature of the two phases. This treatment is based on the assumption that hydrogen is mainly transported through ferrite, with austenite not playing a significant role in the transport process (see *Hydrogen Permeation* section of Blanchard, et al.,^{14 }).

## CONCLUSIONS

Several studies and guidelines on the resistance of DSSs to HISC have considered austenite spacing (measured in a particular direction) as a single microstructural factor, controlling the cracking. The present investigation, however, demonstrates that the relationship between diverse DSS microstructures and HISC resistance is not as straightforward, and warrants a need for a more comprehensive parameter to account for morphology, continuity, and distribution of the two phases, particularly where microstructural knock-down/derating factors are applied in quantitative assessments.

Despite the presence of a comparable austenite spacing in the measurement direction of the two UNS S31803 DSSs, hydrogen transport properties are understood to rely strongly on the 3D distribution and morphology of the austenite and ferrite phases. The hydrogen transport properties of the two alloys, i.e., the M-factors, calculated as a sole function of the morphological parameters (geometrical tortuosity and constrictivity) and volume fractions of the two phases, were ∼0.21 and ∼0.08, for the HIP and wrought alloys, respectively, giving a difference ratio of approximately 2.6.

The 2D phase balance measurement technique, i.e., point counting, gave ferrite levels 5% lower than those obtained by the 3D XCT high resolution, volumetric method, highlighting the limitations of this conventional technique.

^{(1)}

UNS numbers are listed in *Metals & Alloys in the Unified Numbering System*, published by the Society of Automotive Engineers (SAE International) and cosponsored by ASTM International.

^{†}

Trade name.

## ACKNOWLEDGMENTS

Mike Gittos of TWI Ltd. is gratefully acknowledged for his helpful discussions and contributions. The work was undertaken at the National Structural Integrity Research Centre (NSIRC) established and managed by TWI Ltd. Kasra Sotoudeh and Lisa Blanchard acknowledge funding from the Engineering and Physical Sciences Research Council, Centre for Doctoral Training (EPSRC, CDT Grant No: EP/L016206/1, 2016) in Innovative Metal Processing, also financial support from TWI Ltd. and the School of Engineering at University of Leicester.