Exploring the Effect of Microstructure and Surface Recombination on Hydrogen Effusion in Zn–Ni‐Coated Martensitic Steels by Advanced Computational Modeling

Ultrahigh‐strength steel (UHSS) structures are plated with Zn–Ni coatings because of their excellent corrosion resistance properties, but the plating process is accompanied by the production of hydrogen. The presence of hydrogen in steel results in hydrogen embrittlement. Hence, during the production of UHSS parts, dedicated outgassing steps are employed to remove the diffusible hydrogen from the steel. In a production environment, the real effect of the outgassing process and the outgassing efficiency is unknown for parts coated with Zn–Ni. Hence, a finite element model is developed to capture the evolution of the hydrogen concentration profile in coated UHSS parts during outgassing to study the influence of coating morphology and microstructural features of steel. In order to develop the geometry of the model, scanning electron microscope images are analyzed to understand the microstructure and morphology of the coating. Numerical samples are generated by combining different coating morphologies with steel substrates of varying microstructural features to attain a series of samples with varying features. The results of the outgassing simulations clearly demonstrate the major role of the coating morphology on the hydrogen flux.


Introduction
Ultrahigh-strength steels (UHSS) are martensitic steels with a minimum strength of 1380 steels with a minimum strength of 1380 MPa, [1] which are used in the automotive, aircraft, and construction industries as they offer reduced weight and increased performance in terms of durability and safety. [2]In the industry, UHSS are primarily coated with cadmium-based coatings because of their excellent anticorrosion properties and are widely accepted as the standard protective coating solution for medium-and high-strength steel structures. [3]Cadmium coatings are not prone to hydrogen embrittlement (HE), show high solderability, and lubricity, all three of which are imperative properties in electroplated coatings for structural high-strength steels. [4]However, the use of cadmium is strictly regulated due to the environmental (CEE recommendation no.91/338/CEE) and health concerns, as cadmium exposure in humans could lead to kidney conditions, liver issues, and anemia and promotes other adverse effects on the body. [5]8] Zinc-based coatings, especially Zn-Ni alloys, exhibit excellent corrosion behavior, [9] as they allow the formation of complex corrosion products that stop the diffusion of corrosion and avert localized corrosion by spreading out the anodic reactions, [10,11] and thus are considered as an effective and benign replacement for cadmium coatings. [12]Zn-Ni alloys with 10-15% weight Ni offer maximum resistance against corrosion [13] and the corrosion properties of Zn-Ni alloys are reported elsewhere. [11]t is known that the electroplating of Zn-Ni is accompanied by the generation of hydrogen as a side reaction during the plating process. [14,15]One of the primary problems associated with UHSS is their susceptibility to HE under critical hydrogen concentrations and environmental conditions.[19] The hydrogen in steels lowers their load-bearing and energy absorption ability. [20]This negative effect on the steel's properties due to hydrogen is termed as HE.HE leads to delayed cracking, which might cause catastrophic failures during the lifetime of the product. [21]he hydrogen produced during the plating process might be at the steel-coating interface or diffuse inward into the steel substrate, which might lead to HE.To reduce the amount of hydrogen in coated UHSS parts, they are subjected to an outgassing process, also known as baking, during the production process. [22]During the outgassing step, the part is held at a high temperature in a furnace for a relatively long time, aerospace industry standard for outgassing is 190 °C, 48 h SAE AMS 2759/9.Although it is assumed that most of the diffusible hydrogen is removed during the outgassing process, the remaining hydrogen concentration after the outgassing process in a production environment is unknown.This is attributed to the coexistence of various coating morphologies in the same part.During the plating process of a complicated sample, the thickness and morphology of the resulting coating might vary due to the current density distribution along the component.Thus, several coating morphologies might coexist in the same part.To address these issues, a detailed study of hydrogen transport mechanisms and trapping in coated UHSS is needed to understand and control the outgassing process, assisted by advanced computational models.This shall allow the establishment of outgassing guidelines for UHSS steels and improve current state of the art based on visual inspection of coating morphologies.
In this work, we consider the effects of the microstructural features of the steel and Zn-Ni coating on the outgassing efficiency.A microstructure generator tool was developed and employed to generate a series of martensitic microstructures in accordance with the analyzed substrate materials.Thereafter, the generated substrate domains were coupled with Zn-Ni coating morphologies, derived from scanning electron microscope (SEM) micrographs, providing the required spatial resolution for the model.Finally, numerical permeation and outgassing simulations were performed on the generated numerical samples to study the effects of the coating and the microstructural features of the steel.

Hydrogen Transport Model
The diffusion of hydrogen in the domain, which includes the steel, coating, and interface, is described with the Fick's second law of diffusion in two dimensions. [23]The equation is given as ∂cððx,yÞ,tÞ ∂t ¼ D∇ 2 cððx, yÞ, tÞ where cððx, yÞ, tÞ is the concentration of atomic hydrogen in the domain and D denotes the diffusion coefficient of hydrogen atoms in the material.Equation ( 1) is solved over the domain Ω, which is divided into two subdomains, Ω steel and Ω coating , corresponding to the steel and the coating, respectively.The metal-coating interface Γ mc is divided into two regions, Γ 1 representing the region of the interface covered by the Zn-Ni coating and Γ 2 representing the region of the interface covered by microcracks in the coating, and is shown in Figure 1.
The individual subdomains are modeled with their unique diffusion coefficients.The microstructural discontinuities, such as grain boundaries (GBs), interface, and microcracks, are represented as quasi-subdomains.Although these features are subdomains in a traditional sense with their unique diffusion coefficients, in this work, they are represented by the smeared approximation approach, detailed later in this section and not with distinct meshes and thus are labeled as quasi-subdomains.

Hydrogen Surface Recombination
The outer surface of the coating is exposed to atmosphere.Here, two reactions are expected to happen: first, the atomic hydrogen in the coating is expected to recombine to form hydrogen molecules and escape into the atmosphere and second, the permeation of atmospheric hydrogen into the metallic coating.
In the work conducted by Moore in ref. [24], it is concluded that the outgassing of hydrogen in stainless steels in vacuum chambers is to be modeled with a recombination limited model.His proposal was accepted by Akaishi et al. in ref. [25], after comparing the outgassing rates obtained experimentally by Nemanič and Šetina. [26]Although the recombination has not yet been reported for Zn-Ni alloys, recombination is assumed on the surface of the coating, leading to the escape of atomic hydrogen from the metal-coating structure.The outgassing rate due to recombination is given by where K r is the recombination rate constant and D c is the diffusion coefficient of the coating.On the coating surface, due to the difference in chemical potential between the atmosphere and the coating, the atmospheric hydrogen might be dissociated and chemisorbed.The dissociated hydrogen atoms form chemical bonds with the adsorption sites of the coating surface before being adsorbed.When M is a representative metal atom, the surface dissociation and adsorption reactions are given as The surface concentration of hydrogen adsorbed on the surface is obtained as a function of the temperature and the hydrogen partial pressure by Sievert's law. [27]Sievert's law is an experimental relationship that determines penetration of hydrogen in a metal by assuming that the adsorbed hydrogen is in equilibrium with the hydrogen gas.For martensitic steels, the concentration of absorbed hydrogen is as given as where P is the partial pressure, R is the gas constant, and T is the temperature in Kelvin.For the full derivation of this expression, refer to ref. [28].

Variational Formulation
The variational form to be solved using the finite element method (FEM) is obtained through the following steps.Equation ( 1) is discretized using the backward Euler scheme: where n is an integer counting the time steps, the time step t n is defined as t n ¼ n Â Δt and the concentration at t n is given as c n and Δt is the time step.The weak form is obtained using the standard procedure, where Equation ( 5) is multiplied by the test function v, applying integration by parts to the terms with second derivatives, utilizing the recombination flux from Equation (2) and replacing the term c nþ1 by c, the bilinear form aðc, vÞ and the linear form L nþ1 ðvÞ of the variational form are obtained as

Diffusive Properties of the Microstructural Features
Dislocations are line defects and hydrogen trapping sites.
The dilatational stress field produced by the dislocation in the lattice attracts hydrogen, keeping it stored at the dislocation core.This is predominantly observed in the edge dislocations due to hydrostatic stresses. [29,30]It is reported that the dislocation densities reach a maximum value of 10 12 dislocations cm À3 due to the presence of dislocations in the laths of the martensite microstructure. [31]Austenite is reported to have a high solubility and low diffusivity of hydrogen, thus acting as a reservoir. [32]he hydrogen diffusion coefficients of austenite and martensite are reported as 5.76 Â 10 À7 Â expðÀ53.6 kJ=RTÞ m 2 s À1 and, 2.82 Â 10 À7 Â expðÀ34.4kJ=RTÞm 2 s À1 , respectively. [33]At room temperature, a difference of three orders of magnitude is observed between the diffusion coefficients of austenite and martensite.In the latter, the presence of retained austenite along the prior austenite GBs will significantly slow down the diffusion process.
We assume that the deep traps are already filled and only the shallow traps play a role in the diffusion process.Traps are classified as deep or shallow depending on their trapping energies, which signifies the amount of energy required to release the trapped hydrogen. [34]Thus, in the martensite microstructure, the martensite laths, retained austenite, and GBs are the main features influencing hydrogen diffusion because they are considered as shallow traps.
In the literature, the diffusive properties of GBs are ambiguous.According to ref. [35], GBs are defined as hydrogen traps because hydrogen accumulates at the GBs due to its high binding energy, hindering the flow of hydrogen in the steel.However, GBs are also regarded as pathways with high diffusivity for hydrogen, thus increasing the effective diffusivity of the steel. [36]his is supported by their low binding energies measured in ref. [37], and GBs are usually modeled with diffusivities three to six orders of magnitude higher than the lattice diffusion coefficient.The ambiguity surrounding the diffusivity of GBs has not been resolved until now.Therefore, in this work, the GBs are split into low angle-and high-angle boundaries.The different types of GBs considered are prior austenite GBs (PAGBs), packet GBs (PGBs), block GBs (BGBs), and lath GBs (LGBs).
LGBs between laths of the same block are low-angle boundaries because the misorientation angle between the laths in the same block is insignificant. [36]Hence, a martensite block is considered as a homogeneous structure with no explicitly modeled internal GBs.The GBs between the blocks and packets, i.e., BGBs and PGBs, appear between crystals with a high angle of misorientation between them and thus are designated as high-angle GBs. [36]GBs and PGBs are modeled with a higher diffusion coefficient; D gb and PAGBs are modeled with the same diffusion coefficient as austenite.In martensitic steels, Du et al. [38] observed a difference of three orders of magnitude between the diffusion coefficients of martensite and GBs.Thus, in the work, the diffusion coefficient of the GBs is assumed to be d mar Â 10 3 .
The diffusion coefficient of the Zn-Ni coating without microcracks was evaluated as 1.81 Â 10 À12 m 2 s À1 using the Kelvin probe-based permeation technique. [39,40]The exit side/Zn-Ni coating side was coated with a Pd film of 100 nm thickness, using physical vapor deposition and hydrogen charging was carried out electrochemically using 0.1 M sulphuric acid solution containing 20 mg LÀ1 thiourea.The charging potential was varied to change the activity of hydrogen at the entry side, to perform a two-step permeation measurement. [41]The calculation of time lag and diffusivity using the Kelvin probe-based technique has been discussed in detail elsewhere. [42]The obtained value of diffusivity is one order lesser than that of martensite and, considering the much lower diffusion coefficient of the interface, the coating will act as a barrier to the flow of hydrogen.Depending on the coating morphology, the Zn-Ni coatings might have microcracks in them.The microcracks in the coating act as pathways for hydrogen to escape into the atmosphere.The reactions leading to the escape of hydrogen through the microcracks are complicated, and modeling these reactions is out of scope of this work.Therefore, at the tip of the microcracks, it is proposed that the atomistic hydrogen recombines to form molecular hydrogen and flows through the microcrack at substantially higher diffusivity.The diffusivity through the microcracks is currently unknown and thus, in this work, microcracks are modeled as regions of high diffusivity and the diffusivity of a microcrack is assumed to be equal to that of a GB.
The metal-coating interface in the case of Zn-Ni coating is a layer of pure nickel (more than 90 wt%). [43]The thickness of this interface has not yet been reported in the literature.Hence, in this work, the thickness of the interface is assumed to be equal to that of a GB.The hydrogen diffusion coefficient of electrodeposited Ni as a function of temperature is reported in ref. [33], and the value is several orders of magnitude lesser than that of martensitic steel.Hence, the metal-coating interface is expected to act as a barrier to the flow of hydrogen.

Modeling of GBs, Microcracks, and Metal-Coating Interface
Traditionally, GBs, microcracks, and metal-coating interface are modeled with explicit meshes.Due to the small size of these features, modeling with explicit meshes will lead to higher number of elements and thus higher computational cost.Hence, in this work, these features are modeled with a smeared approximation function proposed by Nguyen et al. [44] In the domain Ω ∈ ℝ n , let Γ be a curve of dimension n À 1 along the GBs in the domain.In the smeared approximation approach, a scalar function d gb ðXÞ defines the GBs by taking unit value on the GBs Γ and zero in the grains.The area of influence is defined by the characteristic length, l gb .The function d gb ðxÞ is obtained by solving the Equation ( 8)- (10) over the domain: d gb ðxÞ À l gb ðxÞ 2 Δd gb ðxÞ ¼ 0 on Ω (8) ∇d gb ðxÞ:n ¼ 0 on ∂Ω (10)   where Δ is the Laplacian operator, ∇ is the gradient operator, and n is the outward normal to ∂Ω.The weak form of the Equation ( 8) is derived and solved over the domain Ω with the boundary conditions specified in Equation ( 9) and ( 10) using the standard finite element analysis.Upon solving, we obtain a function that goes to 1 on the selected feature (PAGBs, PGBs, BGBs, interface, or microcracks) and zero elsewhere.
The smeared approximation function is solved 5 times (PAGBs, PGBs, BGBs, interface, and microcracks), each resulting in a function whose region of influence is defined by the location of GBs, the interface, or the microcracks, as shown in Figure 2. The smeared approximation function is scaled from ½0, 1 to ½D aus , D mar in the case of PAGBs or ½D mar , D GB in the case of PGBs, BGBs, and microcracks or ½D i , D mar for the interface and if the elements belong to the steel side of the interface or ½D i , D c for the elements that belong to the coating side of the interface.In the regions of intersection, where the different types of GBs or the interface or microcracks might overlap, precedence is given in the following order, microcracks, PAGBs, interface, PGBs, and BGBs.The smeared approximation function is evaluated over the gauss points, and it is important to note here that the diffusion coefficients of the gauss points in the same elements could be different based on the interpolation of the scaled smeared approximation function, and this allows more flexibility with higher mesh sizes.Effects on the atomistic scale (GBs) are not resolved well.However, we believe, at the microscale, the arising properties due to the atomistic-scale effects are captured correctly by the level set method.

Steel Microstructure Generator
The development of the geometry of the simulation domains are detailed in this section.Initially, the microstructure of lath martensite and the diffusion properties of the various features of martensitic steels are discussed.The newly developed microstructure generator tool is discussed in detail.It was used to produce a series of lath martensite microstructures of the experimentally used steel by varying the parameters grain size, block size, and GB density associated with the microstructure.
Finally, the martensite microstructures are coupled with the two types of coating morphologies, also highlighted in this section, to obtain the metal-coating numerical samples for the virtual testing.
Upon rapid cooling of austenite, through diffusionless, displacive, and large distortive shear transformation, martensite is formed. [45]The crystal structure of martensite depends on the carbon content.Steels with a carbon content less than 0.6 wt% have a body centric cubic martensitic crystal structure, while steels with a higher carbon content have a body centric tetragonal martensitic crystal structure. [46]Martensite microstructure is of two types, lath martensite and plate martensite, [47] depending on the carbon content.Steels have a pure lath martensite microstructure when their carbon content is lower than 0.6 wt% or a pure plate martensite microstructure when their carbon content is above 1 wt%.Steels exhibiting a carbon content between 0.6 and 1 wt% have a mixture of both lath and plate martensite microstructure.In this work, we propose a model for martensitic steels with pure lath martensite microstructure representing the coated steels.
The generation of a martensitic microstructure starts with a prior austenite grain structure.The prior austenite grains are divided into packets; the packets are further divided into blocks, which are groups of equivalent martensite laths.All together represents the standard lath martensite microstructure.Martensite laths typically have a width in the range of ½0.2, 0.5 μm [48] .Martensite laths in the same block have the same habit plane and are separated by low-angle boundaries, with less than an angle of 3°misorientation and hence the crystallographic discontinuity between laths in a block is not significant. [49]Thus, it can be concluded that the martensite blocks depict the smallest significant feature.The blocks are separated by high-angle boundaries. [50]A schematic representation of pure lath martensitic microstructure is shown in Figure 3.
In ref. [51], a method to generate lath martensite microstructures has been detailed for a 3D domain populated with voxels to be solved using the finite volume method.Here, a similar method to generate lath martensite microstructures has been developed for a 2D domain to be meshed and solved with the FEM.With this method, all aspects of the microstructure such as the number of packets per prior austenite grain, misorientation angles, and block thickness could be controlled.This enables the controlled study of microstructural feature's effect on hydrogen distribution and transport, and to allocate different empirical diffusion coefficients to the subdomains.
In the developed martensitic microstructure generator tool, a 2D prior austenite grain structure generated by Neper [52] is provided as the input.The average number of packets per prior austenite grain for martensitic steels is arbitrary and does not follow any rules. [51]Hence, prior austenite grains are each divided into three packets using three line segments, which run from the centroid of a prior austenite grain to its periphery and the line segments have an angular distance of 120°between them.The packets are then subdivided into parallel blocks.As the microstructural discontinuity between laths of the block is not significant because of small angle of misorientation between the laths, individual laths are not modeled and the lowest feature of the microstructure is a martensitic block in a packet.The generation of martensite microstructure was achieved with the software GMSH [53] and python scripting, and is represented in

Experimental Assisted Zi-Ni Coating Domain Generation
The geometry of the coating was directly extracted by an imaging tool from SEM cross-sectional micrographs of respective Zn-Ni coatings.Prior to the effusion studies, the coating process was performed multiple times at different plating conditions.The production of Zn-Ni coatings was carried out in a 1 L glass cell using an alkaline low HE Zn-Ni electrolyte.The coatings were applied on 300 M coupons (ϕ ¼ 15 mm) which were mounted on a rotatory electrode (RADIOMETER, EDI101) for an accurate control of the stirring rate during the plating stage.Pure nickel anodes were used as counter-electrode.The required current density range for achieving different coating morphologies was applied by means of a KEYITHLEY (2400 SourceMeter) power supply.The electrolyte was maintained at 30 °C while plating using a thermostatic bath for ensuring homogeneous heating of the electrolyte along the cell.Before plating, the samples were sandblasted and activated in acidic media.After plating, cross sections of selected specimens were produced by cutting and embedding the corresponding samples on hot mounting resin, grinding, and polishing them to mirror-like finishing with diamond paste for cross-sectional observation by field emission scanning electron microscopy (FESEM).The FESEM (CARL ZEISS, ULTRA-PLUS) was operated at 10 keV for obtaining high-resolution images of selected samples.
From the series of produced morphologies, two were selected which best represented the output of the coating process in a production environment.The two selected morphologies are labeled as the compact layer and the open layer morphologies and are shown in Figure 5. Different sections from the FESEM images of the same coating morphology were utilized to generate multiple coating geometry profiles, which were utilized to generate the models for the simulations.By explicitly marking the microcracks in the SEM images, in this work, the enhanced diffusion through the microcracks has been taken into account by modeling the region around the microcrack with increased diffusivity for both the compact layer and open layer morphologies.It is believed that the microcracks, which connect the steel substrate directly to the atmosphere, would act as highways for hydrogen diffusion through the coating.
Within a range of 20-40 μm for the grain size, 5-10 μm for the block size, and sic coating morphologies (four for the compact layer and two for the open layer), 33 different numerical samples were generated through random combination of the grain sizes, block sizes, and coating morphologies by the Latin hypercube sampling method. [54]Two of the selected numerical samples are shown in Figure 6.As a result of the introduced computational domain generation, the following modeling assumptions are fulfilled: 1) The only microstructural features considered for martensitic steels regarding hydrogen interaction are the shallow traps, which include martensite blocks, packets, GBs, and prior austenite GBs. 2) Subsequently, it has been assumed that all the deep traps are filled.3) Here, austenite is present only at the prior austenite GBs. 4) The diffusion coefficient of GBs and microcracks is assumed to have the same magnitude as the diffusion coefficient of martensite, but three orders of magnitude higher, i.e., D gb ¼ D mar Â 10 3 .5) With respect to the computational implementation, the pure nickel metal-coating interface thickness is assumed to be equal to that of a GB.

Virtual Testing Utilizing Boundary Value Problems
The developed models were subjected to two boundary value problems: first, a standard virtual permeation test and second, a virtual outgassing test.To study the influence of the microstructural features on the effective diffusivity, a numerical permeation test with changing microstructure is performed accordingly.The boundary conditions for the permeation test include a constant concentration of 1 ppm applied on the entry side, 0 ppm on the exit side, and an initial concentration of zero was maintained overall.The permeation test is performed on the numerical samples of the metal substrate with and without coating.
The boundary condition relevant to the virtual outgassing test involves the application of a recombination flux boundary condition on the exit side.The surface recombination rate constant has not yet been reported for martensitic steels and Zn-Ni alloy.As this is a study to evaluate the influence of microstructural features and the coating morphology on the diffusivity and outgassing flux, a constant recombination rate constant is assumed for both the metal and the coating.A uniform initial concentration of 10 ppm was assumed in the domain.Subsequently, by application of the values from Table 1 the steel-coating system has been virtually tested for its hydrogen effusion behavior.

Results and Discussion
To evaluate the influence of the microstructural features, such as the grain size and block size on the effective hydrogen diffusivity of metal substrate and the influence of metal substrate, coating morphology and microcrack density on the outgassing flux of the metal-coating structures in Figure 10, a parameter sweep was performed on the developed models with the permeation and outgassing test specified in Section 4. This included numerical permeation and outgassing simulations on the metal substrate and respective outgassing simulations on the metal-coating numerical samples.
Permeation tests were performed on the metal substrate and the effective diffusivities are shown in Figure 7.The hydrogen concentration profile after the permeation test for one selected sample (grain size = 34.8Â 10 À6 m) is shown in Figure 8.The effective diffusivity of the complex steel-coating structure was evaluated using Fick's first law.Fick's first law provides a relation between the flux and concentration gradient.The equation is rearranged to obtain the effective diffusivity as In Equation (11), the denominator is equal to the applied concentration at the entry side, c x¼l ¼ 1, because the concentration on the exit side, c x¼0 , is maintained at 0. Therefore, the effective diffusivity is obtained as the product of flux and length.The evaluated flux at points of the exit surface is multiplied by the length, which is the perpendicular distance between the flat entry side and the point of the exit side, to obtain the diffusivity at those  points.The mean of the diffusivities at the points on the exit surface is reported as the effective diffusivity.
The effective diffusivities ranged from 1.7 Â 10 À12 to 23.5 Â 10 À12 m 2 s À1 , which is in accordance with the effective diffusivities of martensitic steels.No particular trend was observed among the different grain sizes, block sizes, and effective diffusivities evaluated.The parameters influencing the effective diffusivity of the metal are d mar , d aus , the density of GBs, and the orientation of GBs.As d mar and d aus are both constant values, it is proposed that the density of the GBs must be a significant parameter.As this is a 2D simulation, the orientation of the GBs also influences the effective diffusivity.It might be assumed that if the orientation of a GB is along the direction of diffusion, then the diffusion process is significantly faster, as the hydrogen atoms can move along the GB and reach the exit side quicker.But if the GB is oriented perpendicular to the direction of diffusion, although diffusion through the GB is faster, the diffusion is slowed when the hydrogen atoms enter the martensite blocks.Thus, the orientation of GBs is also a significant parameter influencing the effective diffusivity.The angle of orientation of the GBs could not be quantified in any meaningful manner due to the sheer number of GB orientation angles in the domain.Thus, no relationship could be established between the grain size, block size, and effective diffusivity by the current approach.
In the following, the cumulative outgassing flux is evaluated as the ratio of hydrogen removed from the samples and the simulation time.The results of the virtual outgassing test for the metal substrate and the numerical samples with the coating are shown in Figure 9 and 10, respectively.As the metal substrate remains the same in the both set of samples (metal substrate and metal-coating samples), the significant difference between the two set of samples is the coating.Comparing the cumulative outgassing flux of the metal substrate and the samples with the coating, they differ by an order of magnitude three.This large difference in the outgassing flux is apparent of the barrier effects of the Zn-Ni coating and the interface.
In Figure 10, the cumulative outgassing flux is plotted against the grain size and the coating morphologies are highlighted with differently colored markers.It can be observed that the markers are split into two distinct groups, one pertaining to the open layer morphology and the other to the compact layer morphology.Although the diffusivity of the steel varied as observed in Figure 7, it is clearly shown that the coating morphology is much more significant than the metal substrate during outgassing.This means that the grain size and block size, although influence the effective diffusivity of steel, are not factors that affect the outgassing flux in any substantial manner.The results show that the   www.advancedsciencenews.com morphology of the coating influences the outgassing flux the most.It has been previously reported with experimental results that the difference in the effective diffusivity of the coating between compact layer and open layer is due to the presence of microcracks. [55]Although the enhanced diffusion due to microcracks were taken into account, it was not the primary reason for the enhanced outgassing rate in the case of open layer morphology.The open layer morphology allows the faster effusion of hydrogen due to the increased surface area available, since the open layer morphology offers about 17 times more surface area than the compact layer morphology, as reported in Table 2.The average thickness of the open layer morphology is higher than the compact layer morphology.This should decrease the overall diffusivity of the metal-coating structure due to the barrier properties of the coating.On the contrary, an increase in the cumulative outgassing flux is observed.The thickness of the open layer morphology varies greatly, meaning that there are regions where the coating thickness is very low, sometimes less than 1 μm.Diffusion through these regions is much faster, which facilitates the increased outgassing flux as well.Thus, it can be concluded that the coating morphology plays a significant role in the outgassing efficiency for the entire system.As a consequence, the design of the Zn-Ni coating morphology and the Ni-steel interface is crucial for optimal management of the detrimental hydrogen effects on steel-based components (Figure 11).
In this work, all the domains have a thickness of 127 Â 10 À6 m.Upon observing Figure 6, it is clear that the thickness of the metallic region is significantly smaller in the case of open layer because the thickness of the open layer is greater than the thickness of the compact layer.In order to alleviate any issues stemming from the difference of thickness of the metallic region, an additional set of numerical samples were generated with extended thickness of metallic region, where the thickness of the structure was increased from 127 Â 10 À6 to 500 Â 10 À6 .Outgassing simulations were performed with the newly generated elongated samples, and the cumulative outgassing fluxes are shown in Figure 12.These results show that the samples clearly divide into two groups, which are the open and compact layers.This supports the previously derived conclusion that the coating morphology has the biggest impact over the outgassing flux.The size of the markers denotes the block size in the steel substrate.

Conclusions
The hydrogen outgassing process for martensitic steels with Zn-Ni coating after the plating process has been mathematically modeled.A microstructure generator tool was developed and used to produce the martensitic microstructures with varying grain sizes, block sizes, and GB densities.SEM images of the coating were utilized to develop the geometry of the coating for the numerical samples.Geometries of the coating were coupled with the metal substrate samples generated by the microstructure generator tool to obtain a series of coated numerical samples.The smeared approximation approach was utilized to model the GBs, interfaces, and microcracks in an efficient and effective manner.This particular model was developed to study the effects of grain size, block size, and coating morphology on the outgassing flux in virtual tests.By means of numerical permeation and outgassing tests, the influence of the grain sizes, block size, microcrack density, and coating morphologies on the outgassing flux were studied.Gained results contribute to a better understanding of the materials and coating feature contributions to the hydrogen degassing process and enable effusionrelated coating design by revealing: 1) Microscopical properties of the Zn-Ni coatings, respectively, morphology and microcracks, are much more relevant to the outgassing flux than substrate microstructural features because it was observed that the outgassing flux was primarily influenced by the coating morphology, as shown in Figure 2 and 10. 2) Open microstructures are recommended to lower the risk for stress corrosion cracking due to plating-related hydrogen uptake as they facilitate enhanced hydrogen outgassing due to the increased surface area available.
3) It has been observed that the coating's structure has the predominant influence on the outgassing rate.Further fundamental studies are warranted to delve into the hydrogen recombination rate at the surface layer.This area of research holds potential for materials design with controlled recombination reactions.
Upcoming studies have to focus on the hydrogen storage and transport properties of Zn-Ni coating itself.Although it was assumed that the hydrogen was uniformly distributed, further studies have to be performed to obtain the actual spatial distribution of hydrogen after the coating process.Although open layer morphology facilitates the effusion of hydrogen due to the increased surface area available, it is proposed H uptake during the lifetime of the structure is also higher owing to the increased surface area.As the inner Ni layer at the steel-coating interface acts as a barrier to the diffusion of hydrogen, a more detailed investigation on the Ni-rich steel plating interface is recommended.All effects together enable hydrogen related risk mitigation via tailored Zn-Ni plated coating design.

Figure 1 .
Figure 1.Schematic representation of the domain, which includes the bulk steel, interface, and coating with microcracks.The metal-coating interface Γ mc is divided into Γ 1 (marked in blue) and Γ 2 (marked in red), denoting the interface covered by coating and the interface covered by microcracks, respectively.

Figure 3 .
Figure 3. Schematic representation of the martensite grain structure.A prior austenite grain is divided into packets and the packets are divided into blocks, which are populated with martensite laths.The martensite laths are separated by low angle boundaries, and the blocks and packets are separated by high angle boundaries.Retained austenite is present at the prior austenite GBs.

Figure 4 .
Figure 4. Generation of lath martensitic microstructure.Left: Prior austenite grain structure is provided as input, middle: the prior austenite grains are divided into packets, and right: the packets are further divided into blocks.

Figure 5 .
Figure 5.The first row of images shows the compact layer morphology and the bottom row of images shows the open layer morphology.All the images have a physical width of 127 Â 10 À6 m.

Figure 6 .
Figure 6.The geometry of the outgassing simulation domains, which includes the metal substrate, coating, interface, and microcracks.Two selected geometries with the compact layer (left) and open layer (right) combined with metal substrates of different grain and block sizes are shown here.

Figure 8 .
Figure 8. Hydrogen concentration distribution (normalized) over the steel substrate after the permeation test for one selected sample (grain size = 34.8Â 10 À6 m).

Figure 9 .
Figure 9.The cumulative outgassing flux over grain size for outgassing simulations at 230 °C after 1 h performed on the steel substrate.The size of the markers denotes the block size in the steel substrate.

Figure 7 .
Figure 7. Solution space of effective diffusivity for a parameter sweep over grain size and block size for the base steel substrate.The size of the markers signifies the block size.

Figure 11 .
Figure 11.Hydrogen concentration distribution (normalized) over the metal-coating structure after the outgassing test for one selected sample with compact layer and steel substrate with grain size = 34.8Â 10 À6 m.

Figure 12 .
Figure 12.The cumulative outgassing fluxes for metal-coating structures with increased thickness for the metallic region.

Figure 10 .
Figure 10.The cumulative outgassing flux over grain size for outgassing simulations at 230 °C after 2 h performed on the metal-coating structures.The size of the markers denotes the block size in the steel substrate.

Table 1 .
Diffusion parameters used in this work.

Table 2 .
The coating thickness and surface area per unit length, considering unit thickness of sample.