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Journal ArticleDOI

A coupled diffusion and cohesive zone modelling approach for numerically assessing hydrogen embrittlement of steel structures

TL;DR: In this article, a review of coupled diffusion and cohesive zone modelling is presented as a method for numerically assessing hydrogen embrittlement of a steel structure, and the model is able to reproduce single experimental results by appropriate fitting of the cohesive parameters, but there appears to be limitations in transferring these results to other hydrogen systems.
About: This article is published in International Journal of Hydrogen Energy.The article was published on 2017-04-20 and is currently open access. It has received 62 citations till now. The article focuses on the topics: Hydrogen embrittlement & Hydrogen.

Summary (3 min read)

1. Introduction

  • Hydrogen induced degradation of mechanical properties, often termed hydrogen embrittlement (HE), is a well recognized threat for structural steels.
  • It manifests as loss in ductility, strength and toughness, which may result in unexpected and premature catastrophic failures.
  • Rather it appears that different mechanisms apply to different systems, and that a combination of mechanisms is more likely in many cases.
  • In recent years, cohesive zone modelling has gained increasing interest as suitable method for modelling hydrogen embrittlement [10, 11, 12, 14, 16], with the possibility of providing increased understanding of the involved process and their interactions combined with reduced time and costs compared to experimental programs.
  • The coupling aspect between hydrogen transport and cohesive zone modelling is discussed and put in conjunction with hydrogen diffusion models in Section 2.

2. Hydrogen transport models

  • The process that results in hydrogen embrittlement includes an important transport stage of hydrogen to the site of degradation.
  • Atomic hydrogen is generally considered to reside either at normal interstitial lattice sites (NILS) or being trapped at microstructural defects like dislocations, carbides, grain boundaries and interfaces.
  • Traps generally reduce the amount of mobile hydrogen, thus decreasing the apparent diffusivity and increasing the local solubility of the system.
  • To date, models of transient hydrogen diffusion generally account for trapping by dislocations and hydrostatic drift.
  • Recent approaches include capturing the effect of multiple trap sites and hydrogen transport by dislocations [13, 21, 22].

2.2. Hydrogen in traps

  • Similarly as for lattice sites, the hydrogen concentra- tion in a specific trapping site can be expressed by [8].
  • The ability of a trap site to hold hydrogen is associated with the trap binding energy, representing the attractive interaction of a trap site compared to a normal lattice site.
  • There have been significant advances in theoretical approaches to capture the effect of traps on hydrogen transport, with models by McNabb and Foster [31] and Oriani [32] describing the process for steel.
  • Generally, the trapped concentration increases with increasing lattice concentration and increasing trap binding energy, until saturation is reached.

2.3. Hydrogen diffusion

  • The main mechanism for hydrogen diffusion in steel is lattice diffusion by interstitial jumps, where the hydrogen atom occupy interstitial sites and move by jumping from one interstitial site to a neighbouring one [38].
  • Chemical potential gradients constitute the main driving force for hydrogen diffusion in steel; hydrogen will diffuse from regions where the chemical potential is high to regions where it is low, and the process ceases once the chemical potentials of all atoms are everywhere the same and the system is in equilibrium [39].
  • Assuming that the diffusion flux is proportional to the concentration gradient, which often is the case, Fick’s laws are the governing equations describing the processes.
  • These laws represent a continuum description and are purely phenomenological.
  • The large scatter observed for ferritic steels is generally considered to be associated with trapping [41].

2.4. Implications of the hydrogen transport model

  • In the following section, the effect of varying the hydrogen solubility, the trap binding energy and the trap density on the total hydrogen distribution, as controlled by the hydrogen transport model in Equation (14), is illustrated.
  • Displacements are enforced on the circular boundary, controlled by the stress intensity factor KI .
  • Figure 6a-d displays the resulting hydrogen profiles in front of the notch tip at the end of loading, for trap binding energies in the range 20-60 kJ/mol and two initial hydrogen concentrations of 0.00034 wppm and 1 wppm, representative of the theoretical solubility of hydrogen in ferrite and a 3 % NaCl aqueous solution [11], respectively.
  • In the plots, CL is therefore included as one single line, representing all the cases considered.
  • For the low trap density model, the maximum attainable trapped concentration is 0.033 wppm, 100 times an initial lattice concentration of 0.00034 wppm.

3. A cohesive zone modelling approach to hydro-

  • Gen embrittlement Cohesive models were first formulated by Barenblatt [44] and Dugdale [45], who introduced finite non-linear cohesive tractions in front of an existing crack, as a mean to overcome the crack tip stress singularity.
  • To date, the cohesive model is extensively applied for crack propagation analysis using the finite element method.
  • Among the various approaches available, it is appealing in that it requires few parameters and in its universality of applicability [46].

3.1. The cohesive model

  • The cohesive theory of fracture is a purely phenomenological continuum framework, not representative of any physical material.
  • Common to most cohesive laws is that they can be described by two independent parameters out of the following three: the cohesive strength σC , the critical separation δC and the cohesive energy ΓC .
  • The area embedded by the curve represents the cohesive energy.
  • Alvaro et al. [15] points out the importance of this in relation to modelling hydrogen embrittlement.
  • Yu et al. [57] have applied the viscosity term by Gao and Bower [56] in a three step, un-coupled, hydrogen in- formed cohesive zone model under constant displacement, and found the viscous regularization to be effective in solving the convergence problem with good accuracy.

3.2. Implementing hydrogen influence

  • Most known attempts of implementing hydrogen influence into the cohesive model is through the HEDE principle [11, 15, 16, 58, 59, 60]; hydrogen reduction of the cohesive energy at fracture.
  • The data fit is illustrated by the red line in Figure 8b.
  • Using the coupling between hydrogen coverage and bulk concentration as supplied by the Langmuir-McLean isotherm, Serebrinsky et al. [11] suggested ∆G0b = 30 kJ/mol, which represents the trapping energy of hydrogen at a Fe grain boundary, yielding a threshold concentration of about 0.001 wppm and an embrittlement saturation level of about 5 wppm.
  • Figure 10b illustrates hydrogen influence, in terms of hydrogen coverage, according to Equation (20), on both the cohesive strength and on the critical separation, for the polynomial cohesive law by Needleman [48].
  • 64], no quantification of any effect of hydrogen on the critical separation is found to date.

3.3. Coupling of diffusion and mechanical models

  • The Langmuir-McLean isotherm defines the necessary coupling between the hydrogen diffusion model in Section 2.3 and the hydrogen-dependent cohesive law described in the previous section.
  • Choosing a ∆G0b level in the lower range may be justified, conforming to the findings by Novak et al. [13] and Ayas et al. [37] that the only possible trap sites associated with hydrogen embrittlement are low-binding energy traps.
  • (Equation (14)) to account for hydrogen transport by dislocations.
  • Brocks et al. [14, 68] have developed a model of hydrogen induced cracking, which in addition to the coupled interactions of hydrogen diffusion and reduced cohesive strength, also includes the effect of surface kinetics on hydrogen absorption and hydrogen induced softening of the local yield strength (HELP mechanism).

5. Conclusion

  • A coupled mass transport and cohesive zone modelling approach for simulating hydrogen induced cracking is described and discussed.
  • Based on calculations, the main findings are summarized as follows: .
  • These levels have again significant influence on hydrogen induced reduction of the cohesive strength.
  • New developments within modelling of mass transport may improve the agreement.
  • Further, transferability may be improved by appropriately identifying the required input parameters for the particular system under study.

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Citations
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Journal ArticleDOI
TL;DR: A numerical code is presented that weakly couples hydrogen diffusion with stress–strain analysis and the formulation of cohesive elements is implemented considering a mechanism of local decohesion with an extensive use of Abaqus user subroutines.

23 citations

Journal ArticleDOI
TL;DR: In this article, the metallurgical changes in the welding of a pipe made from stainless steel or a nickel-based superalloy are studied. And the solidification behavior and microstructure evolution in the weld metal and in the heat-affected zone are further discussed for the different material combinations.
Abstract: In the present work, the metallurgical changes in the welding of clad pipelines are studied. Clad pipes consist of a complex multi-material system, with (i) the clad being stainless steel or a nickel-based superalloy, (ii) the pipe being API X60 or X65 high-strength carbon steel, and (iii) the welding wire being a nickel-based superalloy or stainless steel in the root and hot pass, with a nickel or iron buffer layer, followed by filling with carbon steel wire. Alternatively, the corrosion resistant alloy may be used only. During production of the clad pipe, at the diffusion bonding temperature, substantial material changes may occur. These are carbon diffusion from the carbon steel to the clad, followed by the formation of hard martensite at the interface on cooling. The solidification behavior and microstructure evolution in the weld metal and in the heat-affected zone are further discussed for the different material combinations. Solidification behavior was also numerically estimated to show solidification parameters and resulting solidification modes.

21 citations

Journal ArticleDOI
TL;DR: In this paper, the influence of hydrogen on the mechanical behavior of different quenched and tempered CrMo steels with or without vanadium was investigated by means of tensile tests.

20 citations

Journal ArticleDOI
TL;DR: In this article, a sequentially coupled hydrogen diffusion-cohesive zone modeling approach was applied to the simulation of hydrogen-induced delayed intergranular (IG) fracture in high-strength low-alloy steels.
Abstract: A sequentially coupled hydrogen diffusion-cohesive zone modeling approach was applied to the simulation of hydrogen-induced delayed intergranular (IG) fracture in high-strength low-alloy steels. The effects of multiple hydrogen trap sites and mechanical deformation on the diffusion and cohesive strength of grain boundaries (GB) were taken account, in order to reveal that the hydrogen trapped at GB play a dominant role in the degradation processes of hydrogen of high-strength low-alloy steels, which leads to the IG fracture. The approach was implemented by Abaqus software in the form of a two-steps procedure including the coupled elastoplastic-transient hydrogen diffusion analysis and cohesive stress analysis. To validate the approach, the constant load tests of hydrogen pre-charged AISI 4135 high-strength low-alloy steel notched bars in literature were analyzed. Good agreement is observed between the simulation and experimental data of time to failure. The results confirm that hydrogen-induced IG fracture of high strength low-alloy steels can be related to the hydrogen concentration trapped at GB. The critical hydrogen concentration at GB for crack initiation is independent of the initial hydrogen concentration but depends strongly on the local stress level and stress triaxiality. The critical hydrogen concentration linearly decreases with increasing normalized peak maximal principal stress normalized by the critical cohesive strength in absence of hydrogen.

20 citations

Journal ArticleDOI
TL;DR: In this paper, a numerical investigation of hydrogen-microvoid interactions under the framework of hydrogen enhanced localized plasticity mechanism reveals that the actual effect of hydrogen depends on the stress state as well as on the hydrogen trapping effect.

19 citations

References
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Book
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TL;DR: Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained.
Abstract: Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained

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TL;DR: In this article, a relation between extent of plastic yielding and external load applied was investigated, and panels containing internal and edge slits were loaded in tension and lengths of plastic zones were measured.
Abstract: Y ielding at the end of a slit in a sheet is investigated, and a relation is obtained between extent of plastic yielding and external load applied. To verify this relation, panels containing internal and edge slits were loaded in tension and lengths of plastic zones were measured.

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"A coupled diffusion and cohesive zo..." refers methods in this paper

  • ...gen embrittlement Cohesive models were first formulated by Barenblatt [44] and Dugdale [45], who introduced finite non-linear cohesive tractions in front of an existing crack, as a mean to overcome the crack tip stress singularity....

    [...]

  • ...Cohesive models were first formulated by Barenblatt [44] and Dugdale [45], who introduced finite non-linear cohesive tractions in front of an existing crack, as a mean to overcome the crack tip stress singularity....

    [...]

01 Jan 2008
TL;DR: In this article, fracture mechanics is introduced into finite element analysis by means of a model where stresses are assumed to act across a crack as long as it is narrowly opened, which may be regarded as a way of expressing the energy adsorption in the energy balance approach.
Abstract: A method is presented in which fracture mechanics is introduced into finite element analysis by means of a model where stresses are assumed to act across a crack as long as it is narrowly opened. This assumption may be regarded as a way of expressing the energy adsorption GC in the energy balance approach, but it is also in agreement with results of tension tests. As a demonstration the method has been applied to the bending of an unreinforced beam, which has led to an explanation of the difference between bending strength and tensile strength, and of the variation in bending strength with beam depth.

5,564 citations


"A coupled diffusion and cohesive zo..." refers background in this paper

  • ...[47], a polynomial law suggested by Needleman [48] for ductile materials and, more recently, a versatile trapezoidal law suggested by Scheider [49] also for ductile materials....

    [...]

  • ...[47], Needleman [48] and Scheider [49]....

    [...]

Journal ArticleDOI
TL;DR: In this article, fracture mechanics is introduced into finite element analysis by means of a model where stresses are assumed to act across a crack as long as it is narrowly opened, which may be regarded as a way of expressing the energy adsorption in the energy balance approach.

5,505 citations

Book ChapterDOI
TL;DR: In this paper, the authors present a unified view of the way basic problems in the theory of equilibrium cracks are formulated and discuss the results obtained thereby, and the object of the theory is the study of the equilibrium of solids in the presence of cracks.
Abstract: Publisher Summary In recent years, the interest in the problem of brittle fracture and, in particular, in the theory of cracks has grown appreciably in connection with various technical applications. Numerous investigations have been carried out, enlarging in essential points the classical concepts of cracks and methods of analysis. The qualitative features of the problems of cracks, associated with their peculiar nonlinearity as revealed in these investigations, makes the theory of cracks stand out distinctly from the whole range of problems in terms of the theory of elasticity. The chapter presents a unified view of the way basic problems in the theory of equilibrium cracks are formulated and discusses the results obtained thereby. The object of the theory of equilibrium cracks is the study of the equilibrium of solids in the presence of cracks. However, there exists a fundamental distinction between these two problems, The form of a cavity undergoes only slight changes even under a considerable variation in the load acting on a body, while the cracks whose surface also constitutes a part of the body boundary can expand even with small increase of the load to which the body is subjected.

4,677 citations


"A coupled diffusion and cohesive zo..." refers methods in this paper

  • ...gen embrittlement Cohesive models were first formulated by Barenblatt [44] and Dugdale [45], who introduced finite non-linear cohesive tractions in front of an existing crack, as a mean to overcome the crack tip stress singularity....

    [...]

  • ...Cohesive models were first formulated by Barenblatt [44] and Dugdale [45], who introduced finite non-linear cohesive tractions in front of an existing crack, as a mean to overcome the crack tip stress singularity....

    [...]

Frequently Asked Questions (12)
Q1. What are the contributions in "A coupled diffusion and cohesive zone modelling approach for numerically assessing hydrogen embrittlement of steel structures" ?

The present study presents a review of coupled diffusion and cohesive zone modelling as a method for numerically assessing hydrogen embrittlement of a steel structure. 

For the low trap density model, the maximum attainable trapped concentration of 0.033 wppm corresponds to a hydrogen coverage of 0.29 and a reduction in cohesive strength of 29 %. 

In order to predict the degrading effect of hydrogen on the mechanical properties, it is of fundamental importance to correctly assess the hydrogen distribution in the material. 

Most known attempts of implementing hydrogen influence into the cohesive model is through the HEDE principle [11, 15, 16, 58, 59, 60]; hydrogen reduction of the cohesive energy at fracture. 

Assuming EB = 60 kJ/mol, the effective diffusivity ratio at the notch tip yield 0.62 and 0.005 for the low and high trap density models, respectively, at an initial concentration of 0.00034 wppm. 

Trap sites and trap binding energies can be established experimentally for a microstructure using varies approaches like electrochemical permeation or thermal desorption spectroscopy (TDS), with TDS considered best suited to provide detailed trap characteristics [5, 13, 23]. 

For the high trap density model, the maximum attainable trapped concentration is 10.1 wppm, 30000 times an initial lattice concentration of 0.00034 wppm. 

Using Equation (1) - (5), the dislocation trapped hydrogen concentration, CT , is calculated as a function of the lattice hydrogen concentration, CL, in terms of the trapping models by Kumnick and Johnson [2] and Sofronis et al. [34, 35], assuming VM = 7.106 · 10−6 m3/mol, β = 6, α = 1 and room temperature. 

Using parameters representing of Fe (110); (2γint)0 = 4.86 J/m 2 and Γmax = 5.85 · 10−5 mol/m2 [55], assuming ∆g0i −∆g0s = 74.5 kJ/mol [13], the hydrogen dependent cohesive stress for the fast separation case can be estimated. 

The substantially higher diffusivity in ferrite compared to austenite is due to the lower packing density of bcc metals, reducing the potential energy barrier for jumps. 

when the lattice concentration is increased from 0.00034 wppm to 1 wppm, maintaining a constant trap binding energy level, the effective diffusivity will increase. 

An almost linear decrease in cleavage energy with increasing hydrogen coverage is observed for both Al(111) and Fe(110), as displayed in Figure 8b.