Finite element analysis of hydrogen diffusion/plasticity coupled behaviors of low-alloy ferritic steel at large strain

Hydrogen embrittlement is commonly considered as a typical failure mechanism for low-alloy ferritic steel under high pressure hydrogen environment. Currently, the hydrogen enhanced localized plasticity theory has been largely recognized for studying the hydrogen embrittlement mechanism by introducing the localized plastic flow and the hydrogen induced strain concept. However, the hydrogen induced strain and the plastic strain are often solved respectively in this theory, which may weaken the effect of hydrogen on the plastic deformation. The purpose of this paper is to propose a modified theoretical model from the microstructural level by emphasizing the coupling mechanism between the hydrogen diffusion and the plastic deformation at large strain, where the hydrogen induced strain is superimposed on the equivalent plastic strain instead of on the strain components. Fully implicit backward Euler algorithm by finite element analysis (FEA) under the corotational configuration is used to implement the proposed model, where the hydrogen induced strain is involved in the stress return process within each iteration, indicating a more direct interaction between them than existing works. FEA by using finite element software ABAQUS-UMAT subroutine is performed for the smooth tensile specimen and the notch specimen respectively under slow tensile strain rate loading and different hydrogen pressure. Developed direct coupling model is expected to further gain insight into the hydrogen embrittlement effect on the plastic deformation, especially at the trapping sites.     

Understanding microstructural influences on hydrogen diffusion characteristics in martensitic steels using finite element analysis (FEA)

A two-fold approach is considered to study hydrogen (H) diffusion characteristics in martensitic steels. Initially, a multi-trap stress coupled H diffusion finite element model was developed to investigate the role of various trap states on effective H trapping during a four point bend test. The calculations show that high angle boundaries are more influential in controlling H diffusion in presence of low initial (bulk) H concentrations, while dislocations can have more pronounced impact, when the bulk H concentration is higher. A microstructural model comprising of prior austenite grains and packets was further developed. The study highlights the importance of packet boundaries (PBs) moderating H diffusion in martensite microstructure. The presence of retained austenite content affecting H diffusion paths was also studied. Overall, this parametric study presents complementary techniques in numerical modeling, as well as implications on the role of various microstructural entities affecting H diffusion.     

Transient hydrogen diffusion analyses coupled with crack-tip plasticity under cyclic loading

The effect of hydrogen on the material strengths of metals is known as the hydrogen embrittlement, which affects the structural integrity of a hydrogen energy system. In the present paper, we developed a computer program for a transient hydrogen diffusion–elastoplastic coupling analysis by combining an in-house finite element program with a general purpose finite element computer program to analyze hydrogen diffusion. In this program, we use a hypothesis that the hydrogen absorbed in the metal affects the yield stress of the metal.     

Comparison of hydrogen transport through pre-deformed synthetic polycrystals and homogeneous samples by finite element analysis

This study aims at comparing the hydrogen transport in polycrystals and in equivalent homogeneous material, with 3D FE simulations accounting for stress-assisted diffusion and trapping due to plastic strain, in order to examine the hydrogen concentration fields consistency in multi-scale simulations. The effective diffusion features are compared for various sizes of iron polycrystals. For trapping free diffusion, it is shown that hydrogen concentration fields are consistent between scales. When trapping is accounted for, effective diffusion in polycrystals and in homogeneous materials are different, underlying the importance of the trap density function formulation at different scales.     

An effective finite element model for the prediction of hydrogen induced cracking in steel pipelines

This paper presents a comprehensive finite element model for the numerical simulation of Hydrogen Induced Cracking (HIC) in steel pipelines exposed to sulphurous compounds, such as hydrogen sulphide (H₂S). The model is able to mimic the pressure build-up mechanism related to the recombination of atomic hydrogen into hydrogen gas within the crack cavity. In addition, the strong couplings between non-Fickian hydrogen diffusion, pressure build-up and crack extension are accounted for. In order to enhance the predictive capabilities of the proposed model, problem boundary conditions are based on actual in-field operating parameters, such as pH and partial pressure of H₂S. The computational results reported herein show that, during the extension phase, the propagating crack behaves like a trap attracting more hydrogen, and that the hydrostatic stress field at the crack tip speed-up HIC related crack initiation and growth. In addition, HIC is reduced when the pH increases and the partial pressure of H₂S decreases. Furthermore, the relation between the crack growth rate and (i) the initial crack radius and position, (ii) the pipe wall thickness and (iii) the fracture toughness, is also evaluated. Numerical results agree well with experimental data retrieved from the literature.     

Influence of grain boundary misorientation on hydrogen embrittlement in bi-crystal nickel

Computational techniques and tools have been developed to understand hydrogen embrittlement and hydrogen induced intergranular cracking based on grain boundary (GB) engineering with the help of computational materials engineering. This study can help to optimize GB misorientation configurations by identifying the cases that would improve the material properties increasing resistance to hydrogen embrittlement. In order to understand and optimize, it is important to understand the influence of misorientation angle on the atomic clustered hydrogen distribution under the impact of dilatational stress distributions. In this study, a number of bi-crystal models with tilt grain boundary (TGB) misorientation angles (θ) ranging between 0°≤ θ ≤ 90° were developed, with rotation performed about the [001] axis, using numerical microstructural finite element analysis. Subsequently, local stress and strain concentrations generated along the TGB (due to the difference in individual neighbouring crystals elastic anisotropy response as functions of misorientation angles) were evaluated when bi-crystals were subjected to overall uniform applied traction. Finally, the hydrogen distribution and segregations as a function of misorientation angles were studied. In real nickel, as opposed to the numerical model, geometrically necessary dislocations are generated due to GB misorientation. The generated dislocation motion along TGBs in response to dilatational mismatch varies depending on the misorientation angles. These generated dislocation motions affect the stress, strain and hydrogen distribution. Hydrogen segregates along these dislocations acting as traps and since the dislocation distribution varies depending on misorientation angles the hydrogen traps are also influenced by misorientation angles. From the results of numerical modelling it has been observed that the local stress, strain and hydrogen distributions are inhomogeneous, affected by the misorientation angles, orientations of neighbouring crystal and boundary conditions. In real material, as opposed to the numerical model, the clustered atomic hydrogens are segregated in traps near to the TGB due to the influence of dislocations developed under the effects of applied mechanical stress. The numerical model predicts maximum hydrogen concentrations are accumulated on the TGB with misorientation angles ranging between 15°< θ < 45°. This investigation reinforces the importance of GB engineering for designing and optimizing these materials to decrease hydrogen segregation arising from TGB misorientation angles.     

Combined effects of stress and temperature on hydrogen diffusion in non-hydride forming alloys applied in gas turbines

Hydrogen plays a vital role in the utilisation of renewable energy, but ingress and diffusion of hydrogen in a gas turbine can induce hydrogen embrittlement on its metallic components. This paper aims to investigate the hydrogen transport in a non-hydride forming alloy such as Alloy 690 used in gas turbines inspired by service conditions of turbine blades, i.e. under the combined effects of stress and temperature. An appropriate hydrogen transport equation is formulated, accounting for both stress and temperature distributions of the domain in the non-hydride forming alloy. Finite element (FE) analyses are performed to predict steady-state hydrogen distribution in lattice sites and dislocation traps of a double notched specimen under constant tensile load and various temperature fields. Results demonstrate that the lattice hydrogen concentration is very sensitive to the temperature gradients, whilst the stress concentration only slightly increases local lattice hydrogen concentration. The combined effects of stress and temperature result in the highest concentration of the dislocation trapped hydrogen in low-temperature regions, although the plastic strain is only at a moderate level. Our results suggest that temperature gradients and stress concentrations in turbine blades due to cooling channels and holes make the relatively low-temperature regions susceptible to hydrogen embrittlement.     

Sensitivity analysis in thermoelastic problems using the complex finite element method

This article presents the complex finite element method (ZFEM) for the sensitivity analysis of thermoelastic systems. ZFEM, based on the complex Taylor series approach, performs finite element procedures using complex variables such that the response variables (temperature, stress) and their sensitivities with respect to an input parameter of interest (shape, mechanical and thermal properties, loading) are obtained simultaneously. ZFEM offers significant advantages over alternative sensitivity analyses that require direct derivations of the sensitivity formulae, multiple runs, and/or remeshing. To verify the numerical implementation, a hollow cylinder with convective boundary conditions on the inside and outside surface was considered. First-order derivatives of the stress fields were compared with exact solutions to demonstrate the accuracy of ZFEM sensitivities. The results indicate that the ZFEM-based derivatives are of high accuracy, thereby showing its applicability in the design and analysis of thermoelastic problems.     

Optimizing the mass transport phenomenon around micro-electrodes of an enzymatic biofuel cell inside a blood artery via finite element analysis method

Two different orientations of an enzymatic biofuel cell (EBFC) chip, involving highly dense and three-dimensional cylindrical micro-electrodes arrays, have been studied with the finite element method. Mass transport phenomenon around the micro-electrodes of an EBFC chip inside a blood artery has been simulated. The stability of the chip to its position and blood flow pattern surrounding it are also investigated. The comparison between horizontal position (HP) and vertical position (VP) reveals that the chip can be more stable in VP rather than in HP. In VP, the diffusive flux and convective flux values are bigger compared to HP, but both these fluxes are non-uniform around all electrodes in both the positions. In addition to that in case of HP, the electrodes located at different positions on a chip receive different amount of glucose. A novel designed chip with holes through the substrate has enhanced the diffusive and convective flux in the HP of a chip and also all micro-electrodes on a chip receives similar amount of glucose uniformly throughout from the top to the bottom.     

A finite element analysis modeling tool for solid oxide fuel cell development: coupled electrochemistry, thermal and flow analysis in MARC

A 3D simulation tool for modeling solid oxide fuel cells is described. The tool combines the versatility and efficiency of a commercial finite element analysis code, MARC^®, with an in-house developed robust and flexible electrochemical (EC) module. Based upon characteristic parameters obtained experimentally and assigned by the user, the EC module calculates the current density distribution, heat generation, and fuel and oxidant species concentration, taking the temperature profile provided by MARC^® and operating conditions such as the fuel and oxidant flow rate and the total stack output voltage or current as the input. MARC^® performs flow and thermal analyses based on the initial and boundary thermal and flow conditions and the heat generation calculated by the EC module. The main coupling between MARC^® and EC is for MARC^® to supply the temperature field to EC and for EC to give the heat generation profile to MARC^®. The loosely coupled, iterative scheme is advantageous in terms of memory requirement, numerical stability and computational efficiency. The coupling is iterated to self-consistency for a steady-state solution. Sample results for steady states as well as the startup process for stacks with different flow designs are presented to illustrate the modeling capability and numerical performance characteristic of the simulation tool.     

Increase in the local yield stress near surface of austenitic stainless steel due to invasion by hydrogen

In order to determine the effect of hydrogen on the local yield stress near the surface of austenitic stainless steel, an indentation test combined with inverse problem analysis was employed. For austenitic stainless steel, the indentation test is an effective method since the hydrogen is distributed near to the surface because of its high solubility and low diffusion coefficient. Although uniaxial tensile tests can also provide useful data, greater variations in the mechanical properties due to the presence of hydrogen can be detected through indentation tests. In this study, Secondary Ion Mass Spectrometry (SIMS) was used to measure hydrogen depth profiles in order to establish the relationships between the hydrogen absorption depth and the effects due to hydrogen evaluated using the indentation test. The results showed that the yield stress doubled due to hydrogen absorption and then reverted to its initial state due to hydrogen desorption at room temperature. Also, hardening due to the presence of hydrogen, which was determined using an indentation test, was found to be dependent on the relationship between the plastic deformation depth and the hydrogen absorption depth.     

Three-dimensional finite element analysis to predict the effects of SAW process parameters on temperature distribution and angular distortions in single-pass butt joints with top and bottom reinforcements

Achieving adequate top and bottom reinforcement is important to minimize angular distortions in single-pass submerged arc welded (SAW) butt joints. This is achieved in the present work by using a reusable flux-filled backing strip and proper SAW process parameters without resorting to costly distortion mitigation techniques. The butt joints were made without edge (square butts) preparation. The process was also modeled by using three-dimensional finite element analysis by incorporating the top and bottom reinforcements into the modeling. Filler material deposition was also simulated. Temperature distributions and angular distortions obtained from the modeling closely matched with the experimental values. Thus, the cost effective experimental methodology established in the present work can be utilized for minimizing angular distortions in SAW square butts. The modeling methodology adopted can be used for predicting the angular distortions in SAW square butts with top and bottom reinforcements.     

A thermomechanical model for the analysis of disc brake using the finite element method in frictional contact

Abstract

In this work, a numerical simulation of the transient thermal analysis and the static structural one was performed here sequentially, with the coupled thermo-structural method using the ANSYS software. Numerical procedure of calculation relies on important steps such that the CFD thermal analysis has been well illustrated in 3D, showing the effects of heat distribution over the brake disc. This CFD analysis helped in the calculation of the values of the thermal coefficients (h) that have been exploited in the 3D transient evolution of the brake disc temperatures. Three different brake disc materials were selected in this simulation and comparative analysis of the results was conducted in order, to derive the one with the best thermal behavior. Finally, the resolution of the coupled thermomechanical model allows to visualize other important results of this research such as; the deformations, and the equivalent stresses of Von Mises of the disc, as well as the contact pressure of the brake pads. Following our analysis and results we draw from it, we derive several conclusions. The choice makes it possible to deliver the best brake rotor so as to ensure and guarantee the good braking performance of the vehicles.     

Determination of the autofrettage pressure and estimation of material failures of a Type III hydrogen pressure vessel by using finite element analysis

The autofrettage process of a Type III hydrogen pressure vessel for fuel cell vehicles with preset winding pattern was simulated by finite element analysis (FEA). For a precise finite element analysis, the ply based modeling technique was used for the composite layers; a contour function was derived for the fibers at the dome part to determine the exact winding angle; and the exact composite thickness was also considered. In order to determine the most appropriate autofrettage pressure, stress analysis of the pressure vessel according to its internal pressure was carried out with consideration of the international regulations about pressure vessel design. The minimum stress ratio, the permanent volumetric expansion and the generated residual stress were investigated, and the failure of the pressure vessel under minimum burst pressure was predicted by application of various failure criteria of anisotropic composites.     

A generic methodology to evaluate economics of hydrogen production using energy from nuclear power plants

Hydrogen, the deemed future transportation fuel can be produced from nuclear assisted energy sources. Assessment of economics of hydrogen production using energy from nuclear power plants is vital for asserting its competitiveness with competing technologies. A generic method is presented in this paper to evaluate Levelised Hydrogen Generation Cost, based on the discounted cash flow analysis. The method is illustrated by consideration of a typical case of hydrogen production via conventional electrolysis using electrical energy supplied from a pressure tube type boiling light water cooled heavy water moderated reactor concept.     

Numerical investigation on optimization of thermal analysis due to immersion of hybrid nanostructures in a fluid of shear dependent viscosity using the finite element method

This article considers the dispersion of hybrid and mono nanoparticles in a fluid with viscosity (Williamson) dependent on shear rate, over a heated surface moving with nonuniform velocity and exposed to a magnetic field in the presence of an applied current. Extensive modeling leads to complex coupled mathematical models that are solved numerically via the finite element method (FEM). Convergent simulations are run to investigate the role of parameters on the dynamics of flow fields. The magnetic field intensity plays a role in controlling the magnetohydrodynamic boundary layer thickness (BLT) and thermal radiation controls the thickness of thermal boundary layers (TBL). However, the magnetic field intensity is responsible for an increase in BLT. In contrast to this, thermal radiation plays a role in controlling the thickness of the TBL. The impact of shear rate dependent viscosity on velocity is remarkable for both fluids. The motion of both of the fluids slows down when viscosity varies as a function of shear rate. Viscosity depending on the shear rate has a significant impact on wall shear stress. It is observed from simulations that wall shear increases when the parameters appearing in the model for shear rate dependent viscosity are increased. However, this increase in wall shear stress associated with a hybrid nanofluid is greater than the increase in wall shear stress associated with a mono nanofluid.