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Characteristics of environmental stress cracking of PE-HD induced by biodiesel and diesel fuels
(2024)
In the context of the increasing effect of carbon dioxide emissions on the global climate biodiesel produced from renewable sources has emerged as a promising contender replacing fossil fuels, especially in long-range transport vehicles, using existing engines and infrastructure.
High-density polyethylene is one of the prevailing materials for pipe and container applications for storage and transport of such fuels, both, from fossil and renewable resources. The contact with the respective fuels raises questions concerning material compatibility as biodiesel exhibits significant differences compared to conventional diesel fuel affecting its sorption and plasticization behavior in polyethylene. In this study, its behavior with respect to environmental stress cracking, considered one of the most frequent damage mechanisms leading to failure of polymer parts and packaging, was evaluated using the well-established Full Notch Creep Test. This
approach allows for a detailed fracture surface analysis using imaging techniques, such as optical and laser scanning microscopy, as well as infrared spectroscopy. Comparing the environmental stress cracking behavior in standard surfactant solutions with that in biodiesel and diesel, respective crack propagation rates, showing different levels of acceleration, were determined and details of the underlying mechanisms could be revealed.
Furthermore, the specific infrared absorption of the biodiesel’s ester functionality allows its semi-quantitative determination on the fracture surface of the tested specimens after failure. Thus, a preferred uptake of sorptive fluids in the fracture zone due to local morphological changes of the polyethylene could be directly evidenced by infrared spectroscopy.
Relation of craze to crack length during slow crack growth phenomena in high‐density polyethylene
(2024)
The craze‐crack mechanism occurring in high‐density polyethylene (HDPE) causing slow crack growth and environmental stress cracking is investigated in detail with respect to the relation of crack length and the related craze zone. This is essential for the understanding of the resulting features of the formed fracture surface and their interpretation in the context of the transition from crack propagation to ductile shear deformation. It turns out that an already formed craze zone does not inevitably result in formation of a propagating crack, but could also undergo ductile failure. For the examination, the full notch creep test (FNCT) was employed with a subsequent advanced fracture surface analysis that was performed using various imaging techniques: light microscopy, laser scanning microscopy, scanning electron microscopy, and X‐ray micro computed tomography scan. FNCT specimens were progressively damaged for increasing durations under standard test conditions applying Arkopal, the standard surfactant solution, and biodiesel as test media were used to analyze the stepwise growth of cracks and crazes. From considerations based on well‐established fracture mechanics approaches, a theoretical correlation between the length of the actual crack and the length of the preceding craze zone was established that could be evidenced and affirmed by FNCT fracture surface analysis. Moreover, the yield strength of a HDPE material exposed to a certain medium as detected by a classic tensile test was found to be the crucial value of true stress to induce the transition from crack propagation due to the craze‐crack mechanism to shear deformation during FNCT measurements.
Highlights
- Progress of crack formation in high‐density polyethylene is analyzed by different imaging techniques
- Determined growth rates depend on distinction between craze zone and crack
- The ratio of the present crack to the anteceding craze zone is validated theoretically
- The transition from crack propagation to ductile shear deformation is identified
- An already formed craze zone may still fail by ductile mechanisms
A widespread recovery of waste heat requires a cost‐effective production of thermoelectric generators. Thermoelectric oxides are predestined for use at high temperatures. For manufacturing reasons, a multilayer generator design will be easily scalable and cost‐effective. To evaluate the potential of ceramic multilayer technology for that purpose, a multilayer of the promising thermoelectric oxides calcium cobaltite (Ca3Co4O9), calcium manganate (CMO, CaMnO3), and glass–ceramic insulation layers is fabricated. Cracks and reaction layers at the interfaces are observed in the microstructure. The compositions of these reaction layers are identified by energy‐dispersive X‐ray spectroscopy and X‐ray diffraction. Mechanical and thermal properties of all layers are compiled from literature or determined by purposeful sample preparation and testing. Based on this data set, the internal stresses in the multilayer after co‐firing are calculated numerically. It is shown that tensile stresses in the range of 50 MPa occur in the CMO layers. The reaction layers have only a minor influence on the level of these residual stresses. Herein, it is proven that the material system is basically suitable for multilayer generator production, but that the co‐firing process and the layer structure must be adapted to improve densification and reduce the tensile stresses in the CMO.
The current lack of quantitative knowledge on processing-microstructure–property relationships is one of the major bottlenecks in today’s rapidly expanding field of additive manufacturing. This is centrally rooted in the nature of the processing, leading to complex microstructural features. Experimentally-guided modeling can offer reliable solutions for the safe application of additively manufactured materials. In this work, we combine a set of systematic experiments and modeling to address creep anisotropy and its correlation with microstructural characteristics in laser-based powder bed fusion (PBF-LB/M) additively manufactured Inconel-738LC (IN738LC). Three sample orientations (with the tensile axis parallel, perpendicular, and 45° tilted, relative to the building direction) are crept at 850 °C, accompanied by electron backscatter secondary diffraction (EBSD), scanning electron microscopy (SEM) and transmission electron microscopy (TEM) investigations. A crystal plasticity (CP) model for Ni-base superalloys, capable of modeling different types of slip systems, is developed and combined with various polycrystalline representative volume elements (RVEs) built on the experimental measurements. Besides our experiments, we verify our modeling framework on electron beam powder bed fusion (PBF-EB/M) additively manufactured Inconel-738LC. The results of our simulations show that while the crystallographic texture alone cannot explain the observed creep anisotropy, the superlattice extrinsic stacking faults (SESF) and related microtwinning slip systems play major roles as active deformation mechanisms. We confirm this using TEM investigations, revealing evidence of SESFs in crept specimens. We also show that the elongated grain morphology can result in higher creep rates, especially in the specimens with a tilted tensile axis.
Extended X-ray absorption fine structure (EXAFS) conducted on an equiatomic MoNbTaW bcc medium-entropy alloy that was annealed at 2273 K reveals unexpectedly small 1st and 2nd shell element-specific lattice distortions. An experimental size-mismatch parameter, δexp, is determined to be ca. 50% lower than the corresponding calculated value. Around W, short-range order (SRO) preferring 4d elements in the 1st and 2nd shells persists. A Nb-W ordering is found, which is reminiscent of ordering emerging at lower temperatures in the B2(Mo,W;Ta,Nb)- and B32(Nb,W)-phases. With high-temperature ordering preferences in fcc also foreshadowing low-temperature phase, these findings suggest a general feature of high-temperature SRO.
A density-based phase field model is developed where the free energy functional is explicitly linked with molecular dynamics and is referred to as the Molecular Phase Field Method (MoPF). MoPF simulations involve expressing interatomic potentials in terms of density to form a density based free energy functional. Inputs to this functional are taken from atomistics such that the phase field density profile matches the corresponding density profile from atomistic simulations. We analyze our results by comparing the MoPF calculated excess interfacial energies with excess interfacial energies calculated using molecular dynamics associated with several nickel grain boundaries. Additionally, a comparison is made between our results and the interfacial energies of a \Sigma7 boundary across a variety of FCC systems simulated using density functional theory. The MoPF method is able to successfully predict grain boundary free energy trends between grain boundary and material types offering an atomistically informed mesoscale formulation for studying grain boundary physics.
Mean-field modeling and phase-field simulation of grain growth under directional driving forces
(2024)
Directional grain growth is a common phenomenon in the synthetic and natural evolution of various polycrystals. It occurs in the presence of an external driving force, such as a temperature gradient, along which grains show a preferred, yet competitive, growth. Novel additive manufacturing processes, with intense, localized energy deposition, are prominent examples of when directional grain growth can occur, beneath the melting pool. In this work, we derive a phenomenological mean-field model and perform 3D phase-field simulations to investigate the directional grain growth and its underlying physical mechanisms. The effect of the intensity of driving force is simulated and systematically analyzed at the evolving growth front as well as various cross-sections perpendicular to the direction of the driving force. We found that although the directional growth significantly deviates from normal grain growth, it is still governed by a power law relation <R> α tⁿ with an exponent n ~ 0.6–0.7. The exponent n exhibits a nontrivial dependence on the magnitude of the directional driving force, such that the lowest growth exponent is observed for intermediate driving forces. We elaborate that this can originate from the fact that the forces at grain boundary junctions evolve out of balance under the influence of the directional driving force. With increasing the driving forces, the growth exponent asymptotically approaches a value of n ≈ 0.63, imposed by the largest possible grain aspect ratio for given grain boundary energies. The current combined mean-field and phase-field framework pave the way for future exploration in broader contexts such as the evolution of complex additively manufactured microstructures.
A giant Zn segregation transition is revealed using CALPHAD-integrated density-based modeling of segregation into Fe grain boundaries (GBs). The results show that above a threshold of only a few atomic percent Zn in the alloy, a substantial amount of up to 60 at.% Zn can segregate to the GB. We found that the amount of segregation abruptly increases with decreasing temperature, while the Zn content in the alloy required for triggering the segregation transition decreases. Direct evidence of the Zn segregation transition is obtained using high-resolution scanning transmission electron microscopy. Base on the model, we trace the origin of the segregation transition back to the low cohesive energy of Zn and a miscibility gap in Fe-Zn GB, arising from the magnetic ordering effect, which is confirmed by ab-initio calculations. We also show that the massive Zn segregation resulting from the segregation transition greatly assists with liquid wetting and reduces the work of separation along the GB. The current predictions suggest that control over Zn segregation, by both alloy design and optimizing the galvanization and welding processes, may offer preventive strategies against liquid metal embrittlement.
Density-based phase-field (DPF) methods have emerged as a technique for simulating grain boundary thermodynamics and kinetics. Compared to the classical phase-field, DPF gives a more physical description of the grain boundary structure and chemistry, bridging CALPHAD databases and atomistic simulations, with broad applications to grain boundary and segregation engineering. Notwithstanding their notable progress, further advancements are still warranted in DPF methods. Chief among these are the requirements to resolve its performance constraints associated with solving fourth-order partial differential equations (PDEs) and to enable the DPF methods for simulating moving grain boundaries. Presented in this work is a means by which the aforementioned problems are addressed by expressing the density field of a DPF simulation in terms of a traditional order parameter field. A generic DPF free energy functional is derived and used to carry out a series of equilibrium and dynamic simulations of grain boundaries in order to generate trends such as grain boundary width vs. gradient energy coefficient, grain boundary velocity vs. applied driving force, and spherical grain radius vs. time. These trends are compared with analytical solutions and the behavior of physical grain boundaries in order to ascertain the validity of the coupled DPF model. All tested quantities were found to agree with established theories of grain boundary behavior. In addition, the resulting simulations allow for DPF simulations to be carried out by existing phase-field solvers.
Liquid-metal embrittlement (LME) of galvanized (Zn-coated) advanced high-strength steels is a long-known problem in materials science. Here we reveal the initial microstructural processes underneath the Zn-coating that lead to LME-microcrack initiation in the steel substrate. We track the microstructural evolution during the first tens of milliseconds and find pronounced signatures of Fe-Zn intermetallic precipitation in both ferrite grain boundaries and at internal ferrite-oxide phase boundaries. In concert with novel CALPHAD-integrated density-based thermodynamic modelling, we demonstrate that Zn-rich intermetallic phase-nucleation can occur at markedly low processing temperatures due to a segregation transition. We show that a small Znenrichment caused by Zn bulk-diffusion during the initial temperature rise in a joining process is sufficient to induce the segregation transition and subsequent nucleation of Fe-Zn intermetallic grain-boundary phases, which the experiments link to crack initiation sites. These findings direct focus onto LME-controlling microstructural and thermodynamic phenomena at temperatures below the ductility trough and the austenite formation temperature.
The embrittlement of metallic alloys by liquid metals leads to catastrophic material failure and severely impacts their structural integrity. The weakening of grain boundaries by the ingress of liquid metal and preceding segregation in the solid are thought to promote early fracture. However, the potential of balancing between the segregation of cohesion-enhancing interstitial solutes and embrittling elements inducing grain boundary decohesion is not understood. Here, we unveil the mechanisms of how boron segregation mitigates the detrimental effects of the prime embrittler, zinc, in a Σ5 [0 0 1] tilt grain boundary in α −Fe (4 at.% Al). Zinc forms nanoscale segregation patterns inducing structurally and compositionally complex grain boundary states. Ab-initio simulations reveal that boron hinders zinc segregation and compensates for the zinc induced loss in grain boundary cohesion. Our work sheds new light on how interstitial solutes intimately modify grain boundaries, thereby opening pathways to use them as dopants for preventing disastrous material failure.
Crack propagation under low cycle fatigue and thermomechanical fatigue is characterized by high plastic and creep strains that extend over large regions around the crack, so that concepts of linear-elastic fracture mechanics cannot be applied. In these cases, the cyclic crack tip opening displacement 𝛥CTOD is a promising loading parameter to quantify crack growth. In this work, suitable definitions and Finite Element techniques are investigated and compared for an accurate calculation of 𝛥CTOD under cyclic mechanical and/or thermal loading. A viscoplastic temperature dependent material model of Chaboche-type is used along with large strain settings, specified for the austenitic cast iron Ni-resist. Extensive two-dimensional analyses of Single Edge Notch Tension specimens revealed that collapsed special crack tip elements are superior compared with commonly used regular quadrilateral 8-node elements. At the same level of accuracy of 𝛥CTOD, they require an about ten times coarser mesh and show less sensitivity
w.r.t. element size for both stationary and propagating cracks. In order to simulate fatigue crack growth, an efficient, fully automated FE-technique is developed for an incremental crack propagation by successive remeshing, whereby the deformations and internal state variables are mapped from the old mesh onto the new one. Recommendations are made regarding important numerical control parameters like optimal size of crack tip elements, length of crack growth increment in relation to plastic zone size and 𝛥CTOD value.
This contribution contains the raw data used to compare experimental results with thermodynamic calculations using the CALPHAD method, which is related to the research article “The AlMo0.5NbTa0.5TiZr refractory high entropy superalloy: experimental findings and comparison with calculations using the CALPHAD method” [1] , and therefore this article can be used as a basis for interpreting the data contained therein. The AlMo0.5NbTa0.5TiZr refractory superalloy was characterized in the cast and annealed condition (1400 °C for 24 h) in order to measure grain size and to identify and measure the size and area fraction of the phases present. The raw data of this article include X-ray diffraction (XRD) measurements, microstructural characterization by scanning and transmission electron microscopy (SEM and TEM), and elemental analysis by energy dispersive X-ray spectroscopy (EDX). XRD includes the determination of phases and the lattice parameters (A2, B2, and hexagonal structure). Microstructural analysis by scanning and transmission electron microscopy includes (1) identification of composition, size, and volume fraction of the present phases and (2) determination of grain size. Based on these experimental data, it is possible to identify similarities and discrepancies with the data calculated using the CALPHAD method for the alloy under study in Ref. [1] , which provides the basis for better and more efficient development of reliable databases.
Aero-engine turbine disks are safety-relevant components which are operated under high thermal and mechanical stress conditions. The actual part qualification and certification procedures make use of spin-tests conducted on production-similar disks. While these tests provide, on the one hand, a reliable definition of the critical conditions for real components, on the other hand they represent a relevant cost item for engine manufacturers. The aim of this work is to present two alternative burst speed assessment methods under development based on the Failure Assessment Diagram (FAD) and a global stability criterion, respectively. In the scope of the fracture mechanics assessment, the failure modes hoop-burst and rim-peeling are investigated with semicircular surface cracks modelled at the critical regions on the turbine disk. The comparison of the predicted critical rotational speed shows good agreement between the assessment methods.
Along with the desire for developing novel multi-principal element alloys, also known as high-entropy alloys, the concern about their safe application is also increasingly growing. This relates to the alloys’ phase stability, in particular, the control required over unexpected phase decompositions resulting from solute segregation at grain boundaries. Yet, the mechanisms of co-segregation and grain boundary phase decomposition in multi-component alloys are rather challenging to explore. In fact, quantitative investigation of grain boundary behaviors is mostly conducted for binary and a few ternary alloys. In this work, we apply the recently introduced CALPHAD-integrated density-based formalism [RSC Advances 10 (2020) 26728-26741] for considering co-segregation phenomena in alloys with an arbitrary number of components —the term ‘co-segregation’ here refers to co-evolution and any mutual interplay among the solute atoms during their interaction with a grain boundary. Quaternary Fe-Co-Mn-Cr alloy system is studied. We present two major advances beyond previous results: First, a co-segregation-induced multi-component grain boundary spinodal decomposition is quantitatively simulated for the first time. We found that in addition to its low cohesive energy and asymmetrical mixing enthalpy due to magnetic ordering, Mn plays a leading role in triggering interfacial phase decomposition by having a relatively large, concentration-dependent atomic mobility. Second, as an alternative to grain boundary phase diagrams proposed for binary and ternary alloys, we introduce the concept of co-segregation maps for grain boundary segregation screening and design in multi-component alloys. Applying the co-segregation maps, the nonlinear Mn and Cr co-segregation are discussed. Depicted on the alloying composition and phase space, the co-segregation maps enable the required insights to guide a safer, more controlled design of high-entropy alloys.
Grain boundaries (GBs)’s role in determining the functional and mechanical properties of polycrystalline materials is inscribed in both their structure and chemistry. Upon solute segregation, the structure and composition of a GB can change concurrently. We study the co-evolution of GB’s structure and segregation by enhancing the density-based phase-field model to account for the in-plane structural variations in the GB. Significant mutual coupling is revealed between the GB’s chemical and structural states during Mn segregation in Fe-Mn alloys. We found that the structural degrees of freedom in a GB (the ability of the GB structure to respond to the chemical variation) amplifies Mn segregation transition, even when the GB structure stays unchanged. When the GB structure is not uniform, that is the usual case, the coupling between GB structure and segregation evolution also enables the spinodally formed low- and high-Mn phases (upon segregation transition) to co-exist within the GB region. These findings explain the stabilizing mechanism of pronounced interfacial segregation fluctuations, experimentally evidenced in Fe-Mn GBs, and give new insights on the structural sensitivity of GBs’ segregation phenomena and the mutual chemo-structural interplay.
The large surface-to-volume ratio of nanoparticles is understood to be the source of many interesting phenomena. The melting temperature of nanoparticles is shown to dramatically reduce compared to bulk material. Yet, at temperatures below this reduced melting point, a liquid-like atomic arrangement on the surface of nanoparticles is still anticipated to influence its properties. To understand such surface effects, here, we study the coalescence of Au nanoparticles of various sizes using molecular dynamics simulations. Analysis of the potential energy and Lindemann index distribution across the nanoparticles reveals that high-energy, high-mobility surface atoms can enable the coalescence of nanoparticles at temperatures much lower than their corresponding melting point. The smaller the nanoparticles, the larger the difference between their melting and coalescence temperatures. For small enough particles and/or elevated enough temperatures, we found that the coalescence leads to a melting transition of the two nominally solid nanoparticles, here discussed in relation to the heat released due to the surface reduction upon the coalescence and the size dependence of latent heat. Such discontinuous melting transitions can lead to abrupt changes in the properties of nanoparticles, important for their applications at intermediate temperatures.
Detailed microstructural characterization of the AlMo0.5NbTa0.5TiZr refractory high entropy superalloy in the as-cast state is reported for first time and compared with the state annealed at 1400 oC for 24 h. The former shows a dendritic structure, with a mixture of A2/B2 phases < 20 nm in both the dendritic and interdendritic regions. A mostly amorphous phase, rich in Al and Zr, is found within the interdendritic region. The annealed state reproduced the combination of A2/B2/Al-Zr-rich phases reported previously. Calculations from two relevant ThermoCalc databases were compared with the experimental results. Equilibrium calculations were compared with results for the annealed alloy, whereas solidification paths calculated using Scheil-Gulliver model were used for comparison with the as-cast alloy. A previously hypothesized spinodal decomposition during cooling as the mechanism responsible for the patterned A2/B2 microstructure is confirmed via the CALPHAD calculations, pointing to its use as an efficient design tool for such alloys. Finally, the comparison between the experimental and computational findings allowed better understanding the solidification path and equilibrium stability of this alloy, giving a base to make better decisions on the field of new refractory superalloy design.
Grain boundaries (GBs) are planar lattice defects that govern the properties of many types of polycrystalline materials. Hence, their structures have been investigated in great detail. However, much less is known about their chemical features, owing to the experimental difficulties to probe these features at the atomic length scale inside bulk material specimens. Atom probe tomography (APT) is a tool capable of accomplishing this task, with an ability to quantify chemical characteristics at near-atomic scale. Using APT data sets, we present here a machine-learning-based approach for the automated quantification of chemical features of GBs. We trained a convolutional neural network (CNN) using twenty thousand synthesized images of grain interiors, GBs, or triple junctions. Such a trained CNN automatically detects the locations of GBs from APT data. Those GBs are then subjected to compositional mapping and analysis, including revealing their in-plane chemical decoration patterns. We applied this approach to experimentally obtained APT data sets pertaining to three case studies, namely, Ni-P, Pt-Au, and Al-Zn-Mg-Cu alloys. In the first case, we extracted GB specific segregation features as a function of misorientation and coincidence site lattice character. Secondly, we revealed interfacial excesses and in-plane chemical features that could not have been found by standard compositional analyses. Lastly, we tracked the temporal evolution of chemical decoration from early-stage solute GB segregation in the dilute limit to interfacial phase separation, characterized by the evolution of complex composition patterns. This machine-learning-based approach provides quantitative, unbiased, and automated access to GB chemical analyses, serving as an enabling tool for new discoveries related to interface thermodynamics, kinetics, and the associated chemistry-structure-property relations.
Single-crystal components made of nickel base superalloys contain pores after casting and homogenization heat treatment. Hot isostatic pressing (HIP), which is carried above the γ' -solvus temperature of the alloy, is industrially applied to reduce porosity. A modeling of HIP based on continuously distributed dislocations is developed in a 2D setting. Glide and climb of straight-edge dislocations, as well as vacancy diffusion, are the deformation mechanisms taken into account.
Thereby, dislocation glide is controlled by dragging a cloud of large atoms, and climb is controlled by vacancy diffusion. Relying on previous investigations of the creep behavior at HIP temperatures, it is assumed that new dislocations are nucleated at low-angle boundaries (LAB) and move through subgrains until they either reach the opposite LABs or react with other dislocations and annihilate.
Vacancies are created at the pore surface and diffuse through the alloy until they are either consumed by climbing dislocations or disappear at the LABs. The field equations are solved by finite elements. It is shown that pore shrinking is mostly controlled by vacancy diffusion as the shear stresses at the LABs are too low to
nucleate a sufficient amount of dislocations.
The formation of pores in CMSX-4 nickel based superalloys is detrimental to the service life of the material. A way to avoid the problem is to treat the superalloys under Hot Isostatic Pressing (HIP), which enables a large volume fraction of pores to be annihilated. This paper aims to understand the contribution of plastic activity related to the gliding of dislocations on the pore annihilation. Simulations based on a phase-field model of dislocation are performed and make it possible to consider the strong anisotropy of the CMSX-4 under HIP conditions in conjunction to the strong elastic heterogeneity introduced by the pore. For pores with a radius of few micrometers, it is shown that edge parts of dislocation lines that present an extra half atomic plane oriented towards the pore are stacked above and under it in the direction which is perpendicular to their slip-planes, causing an increase of the number of dislocation along the four octahedral directions of the FCC single crystal which intersect the pore center. Results are streamlined within the isotropic elastic theory of dislocations. Effects of elastic anisotropy and dislocation reactions are also investigated in order to specify what would be the dislocation configuration around a pore in CMSX-4 under HIP conditions. Notably, the elastic anisotropy is shown to significantly modify the arrangement of dislocations close to the pore equator. Simulations also allow for the characterization of pore/dislocation interactions when dislocations are involved in Low Angle Boundaries as experimentally observed.
The elastic energy of mixing for multi-component solid solutions is derived by generalizing Eshelby's sphere-in-hole model. By surveying the dependence of the elastic energy on the chemical composition and lattice misfit, we derive a lattice strain coefficient λ*. Studying several high-entropy alloys and superalloys, we propose that most solid solution multi-component alloys are stable when λ*<0.16, generalizing the Hume-Rothery atomic-size rule for binary alloys. We also reveal that the polydispersity index δ, frequently used for describing strain in multi-component alloys, directly represents the elastic energy e with e=qδ², q being an elastic constant. Furthermore, the effects of (i) the number and (ii) the atomic-size distribution of constituting elements on the phase stability of high-entropy alloys were quantified. The present derivations and discussions open for richer considerations of elastic effects in high-entropy alloys, offering immediate support for quantitative assessments of their thermodynamic properties and studying related strengthening mechanisms.
A γ-analogue of the superalloy CMSX-4 that does not contain the strengthening γ′ -phase and only consists of the γ-solid solution of nickel has been designed, solidified as single-crystals of different orientations, and tested under creep conditions in the temperature range between 1150 and 1288 °C. The tests have revealed a very high creep anisotropy of this alloy, as was previously found for CMSX-4 at supersolvus temperature of 1288 °C. This creep anisotropy could be explained by the dominance of 〈011〉{111} octahedral slip. Furthermore, the analysis of the creep data has yielded a high value of the creep activation energy, Qc≈442 kJ/mol, which correlates with the high activation energy of Re diffusion in Ni. This supports the hypothesis that dislocation motion in the γ-matrix of Re-containing superalloys is controlled by the diffusion of the Re atoms segregating at the dislocation core. The Norton stress exponent n is close to 5, which is a typical value for pure metals and their alloys. The absence of γ′ -reprecipitation after high-temperature creep tests facilitates microstructural investigations. It has been shown by EBSD that creep deformation results in an increasing misorientation of the existing low angle boundaries. In addition, according to TEM, new low angle boundaries appear due to reactions of the a/2 〈011〉 mobile dislocations and knitting of new networks.
The phase-like behavior of grain boundaries (GBs), recently evidenced in several materials, is opening up new possibilities in the design of alloy microstructures. In this context, GB phase diagrams are contributing to a predictive description of GB segregation and (interfacial) phase changes. The influence of chemo-mechanical solute-GB interactions on the GB phase diagram remains elusive so far. This is particularly important for multi-component alloys where the elastic interactions among solute atoms, of various sizes and bonding energies, can prevail, governing a complex co-segregation phenomenon. Recently, we developed a density-based model for GB thermodynamics that intrinsically accounts for GB elasticity in pure elements. In this work, we incorporate the homogeneous and heterogeneous elastic energies associated with the solutes into the density-based framework. We derive the multi-component homogeneous elastic energy by generalizing the continuum misfitting sphere model and extend it for GBs. The density-based free energy functional directly uses bulk CALPHAD thermodynamic data. The model is applied to binary and ternary Al alloys. We reveal that the elastic energy can profoundly affect the GB solubility and segregation behavior, leading to Cu segregation in otherwise Cu-depleted Al GBs. Consequently, GB segregation transition, i.e., a jump in the GB segregation as a function of alloy composition, is revealed in Al-Cu and Al-Cu-Mg alloy systems with implications for subsequent GB precipitation in these alloys. CALPHAD-informed elasticity-incorporated GB phase diagrams enable addressing a broader range of GB phenomena in engineering multi-component alloys.
For more than half a century, spinodal decomposition has been a key phenomenon in considering the formation of secondary phases in alloys. The most prominent aspect of the spinodal phenomenon is the lack of an energy barrier on its transformation pathway, offering an alternative to the nucleation and growth mechanism. The classical description of spinodal decomposition often neglects the influence of defects, such as grain boundaries, on the transformation because the innate ability for like-atoms to cluster is assumed to lead the process. Nevertheless, in nanocrystalline alloys, with a high population of grain boundaries with diverse characters, the structurally heterogeneous landscape can greatly influence the chemical decomposition behavior. Combining atom-probe tomography, precession electron diffraction and density-based phase-field simulations, we address how grain boundaries contribute to the temporal evolution of chemical decomposition within the miscibility gap of a Pt-Au nanocrystalline system. We found that grain boundaries can actually have their own miscibility gaps profoundly altering the spinodal decomposition in nanocrystalline alloys. A complex realm of multiple interfacial states, ranging from competitive grain boundary segregation to barrier-free low-dimensional interfacial decomposition, occurs with a dependency upon the grain boundary character.
Initially, as-cast and homogenized single crystals of nickel-base superalloy CMSX-4 are subjected to hot isostatic pressing at 1288 °C. Two series of experiments are conducted: under the same pressure of 103 MPa but with different durations, between 0.5 and 6 h, and under different pressures, between 15 and 150 MPa, but for the same time of 0.5 h. The porosity annihilation is investigated metallographically and by high-resolution synchrotron X-ray tomography. The obtained experimental results are compared with the predictions of the vacancy model proposed recently in the group. Herein, the model is further refined by coupling with X-ray tomography. The model describes the evolution of the pore arrays enclosed in the 3D synchrotron tomograms during hot isostatic pressing and properly predicts the time and stress dependences of the pore annihilation kinetics. The validated model and the obtained experimental results are used for selecting the optimal technological parameters such as applied pressure and processing time
Results of an extended TMF test program on grade P92 steel in the temperature range of 620 °C - 300 °C, comprising in-phase (IP) and out-of-phase (OP) tests, partly performed with symmetric dwells at Tmax/Tmin, are presented. In contrast to previous studies, the low-strain regime is also illuminated, which approaches flexible operation in a power plant with start/stop cycles. At all strain amplitudes, the material performance is characterized by continuous cyclic softening, which is retarded in tests at lower strains but reaches similar magnitudes in the course of testing. In the investigated temperature range, the phase angle does not affect fatigue life in continuous experiments, whereas the IP condition is more detrimental in tests with dwells. Fractographic analyses indicate creep-dominated and fatigue-dominated damage for IP and OP, respectively. Analyses of the (micro)hardness distribution in the tested specimens suggest an enhanced microstructural softening in tests with dwell times for the low- but not for the high-strain regime. To rationalize the obtained fatigue data, the fracture-mechanics-based D_TMF concept, which was developed for TMF life assessment of ductile alloys, was applied. It is found that the D_TMF parameter correlates well with the measured fatigue lives, suggesting that subcritical growth of cracks (with sizes from a few microns to a few millimeters) governs failure in the investigated range of strain amplitudes.
The onset of plasticity in a single crystal C60 fullerite was investigated by nanoindentation on the (111) crystallographic plane. The transition from elastic to plastic deformation in a contact was observed as pop-in events on loading curves. The respective resolved shear stresses were computed for the octahedral slip systems ⟨011¯¯¯⟩{111}, supposing that their activation resulted in the onset of plasticity. A finite element analysis was applied, which reproduced the elastic loading until the first pop-in, using a realistic geometry of the Berkovich indenter blunt tip. The obtained estimate of the C60 theoretical shear strength was about 1/11 of the shear modulus on {111} planes.
A phase field model of brittle fracture has been developed to simulate the Hertzian crack induced by penetration of a rigid sphere to an isotropic linear-elastic half-space. The fracture formation is regarded as a diffusive field variable, which is zero for the intact material and unity if there is a crack. Crack growth is assumed to be driven by a strain invariant. The numerical implementation is performed with the finite element method and an implicit time integration scheme. The mechanical equilibrium and the phase field equations are solved in a staggered manner, sequentially updating the displacement field and the phase field variable. Numerical examples demonstrate the capability of the model to reproduce the nucleation and growth of the Hertzian cone crack.
The effectiveness of the mechanism of precipitation strengthening in metallic alloys depends on the shapes of the precipitates. Two different material systems are considered: tetragonal γ′′ precipitates in Ni-based alloys and tetragonal θ′ precipitates in Al-Cu-alloys. The shape formation and evolution of the tetragonally misfitting precipitates was investigated by means of experiments and phase-field simulations. We employed the method of invariant moments for the consistent shape quantification of precipitates obtained from the simulation as well as those obtained from the experiment. Two well-defined shape-quantities are proposed: (i) a generalized measure for the particles aspect ratio and (ii) the normalized λ2, as a measure for shape deviations from an ideal ellipse of the given aspect ratio. Considering the size dependence of the aspect ratio of γ′′ precipitates, we find good agreement between the simulation results and the experiment. Further, the precipitates’ in-plane shape is defined as the central 2D cut through the 3D particle in a plane normal to the tetragonal c-axes of the precipitate. The experimentally observed in-plane shapes of γ′′-precipitates can be quantitatively reproduced by the phase-field model.
Simulation of the θ′ Precipitation Process with Interfacial Anisotropy Effects in Al-Cu Alloys
(2021)
The effects of anisotropic interfacial properties and heterogeneous elasticity on the growth and ripening of plate-like θ′-phase (Al2Cu) in Al-1.69 at.% Cu alloy are studied. Multi-phase-field simulations are conducted and discussed in comparison with aging experiments. The precipitate/matrix interface is considered to be anisotropic in terms of its energy and mobility. We find that the additional incorporation of an anisotropic interfacial mobility in conjunction with the elastic anisotropy result in substantially larger aspect ratios of the precipitates closer to the experimental observations. The anisotropy of the interfacial energy shows comparably small effect on the precipitate’s aspect ratio but changes the interface’s shape at the rim. The effect of the chemo-mechanical coupling, i.e., the composition dependence of the elastic constants, is studied as well. We show that the inverse ripening phenomenon, recently evidenced for δ’ precipitates in Al-Li alloys (Park et al. Sci. Rep. 2019, 9, 3981), does not establish for the θ′ precipitates. This is because of the anisotropic stress fields built around the θ′ precipitates, stemming from the precipitate’s shape and the interaction among different variants of the θ′ precipitate, that disturb the chemo-mechanical effects. These results show that the chemo-mechanical effects on the precipitation ripening strongly depend on the degree of sphericity and elastic isotropy of the precipitate and matrix phases.
Phase diagrams are the roadmaps for designing bulk phases. Similar to bulk, grain boundaries can possess various phases, but their phase diagrams remain largely unknown. Using a recently introduced density-based model, here we devise a strategy for computing multi-component grain boundary phase diagrams based on available bulk (CALPHAD) thermodynamic data. Fe-Mn-Cr, Fe-Mn-Ni, Fe-Mn-Co, Fe-Cr-Ni and Fe-Cr-Co alloy systems, as important ternary bases for several trending steels and high-entropy alloys, are studied. We found that despite its solute segregation enrichment, a grain boundary can have lower solubility limit than its corresponding bulk, promoting an interfacial chemical decomposition upon solute segregation. This is revealed here for the Fe-Mn-base alloy systems. The origins of this counter-intuitive feature are traced back to two effects, i.e., the magnetic ordering effect and the low cohesive energy of Mn solute element. Different aspects of interfacial phase stability and GB co-segregation in ternary alloys are investigated as well. We show that the concentration gradient energy contributions reduce segregation level but increase grain boundary solubility limit, stabilizing the GB against a chemical decomposition. Density-based grain boundary phase diagrams offer guidelines for systematic investigation of interfacial phase changes with applications to microstructure defects engineering.
A phenomenological criterion for an optical assessment of PE-HD fracture surfaces obtained from FNCT
(2021)
The full-notch creep test (FNCT) is a common test method to evaluate the environmental stress cracking (ESC) behavior of high-density polyethylene (PE-HD), e.g. for container materials. The test procedure as specified in ISO 16770 provides a comparative measure of the resistance against ESC using the time to failure of PE-HD specimens under constant mechanical load in a well-defined liquid test environment. Since the craze-crack damage mechanism underlying the ESC phenomenon is associated with brittle failure, the occurrence of a predominantly brittle fracture surface is a prerequisite to consider an FNCT measurement as representative for ESC, i.e. a time to failure dominated by craze-crack propagation.
The craze-crack propagation continuously reduces the effective residual cross-sectional area of the specimen during the test, which results in a corresponding increase of the effective mechanical stress. Thus, a transition to ductile shear deformation is inevitable at later stages of the test, leading usually to a pronounced central ligament.
Therefore, an optical evaluation of FNCT fracture surfaces concerning their brittleness is essential. An enhanced imaging analysis of FNCT fracture surfaces enables a detailed assessment of craze-crack Propagation during ESC. In this study, laser scanning microscopy (LSM) was employed to evaluate whether FNCT fracture surfaces are representative with respect to craze-crack propagation and ESC. Based on LSM height data, a phenomenological criterion is proposed to assess the validity of distinct FNCT measurements. This criterion is
supposed to facilitate a quick evaluation of FNCT results in practical routine testing. Its applicability is verified on a sample basis for seven different commercial PE-HD container materials.
The elastic properties of the single-crystal nickel-base superalloy CMSX-4 used as a blade material in gas turbines were investigated by the sonic resonance method in the temperature interval between room temperature and 1300 °C. Elastic constants at such high temperatures are needed to model the mechanical behavior of blade material during manufacturing (hot isostatic pressing) as well as during technical accidents which may happen in service (overheating). High reliability of the results was achieved using specimens of different crystallographic orientations, exciting various vibration modes as well as precise measurement of the material density and thermal Expansion required for modeling the resonance frequencies by finite element method. Combining the results measured in this work and literature data the elastic constants of the gamma and gamma' phases were predicted.
This prediction was supported by measurement of the temperature dependence of the gamma'fraction.
All data obtained in this work are given in numerical or analytical forms and can be easily used for different scientific and engineering calculations.
The aluminum alloy 2618A is applied for engine components such as radial compressor wheels which operate for long time at elevated temperatures. This results in coarsening of the hardening precipitates and degradation in mechanical properties during the long-term operation, which is not taken into account in the current lifetime prediction models due to the lack of quantitative microstructural and mechanical data. To address this issue, a quantitative investigation on the evolution of precipitates during long-term aging at 190 °C for up to 25,000 h was conducted. Detailed transmission electron microscopy (TEM) was combined with Brinell hardness measurements and thorough differential scanning calorimetry (DSC) experiments. The results showthat GPB zones and S-phase Al2CuMg grow up to < 1,000 h during which the GPB zones dissolve and S-phase precipitates form. For longer aging times, only S-phase precipitates coarsen, which can be well described using the Lifshitz–Slyozov Wagner theory of ripening. A thorough understanding of the underlying microstructural processes is a prerequisite to enable the integration of aging behavior into the established lifetime models for components manufactured from alloy 2618A.
Segregation to grain boundaries affects their cohesion, corrosion, and embrittlement and plays a critical role in heterogeneous nucleation. In order to quantitatively study segregation and low-dimensional phase separation at grain boundaries, here, we apply a density-based phase-field model. The current model describes the grain-boundary thermodynamic properties based on available bulk thermodynamic data, while the grain-boundary-density profile is obtained using atomistic simulations. To benchmark the performance of the model, Mn grain-boundary segregation in the Fe–Mn system is studied. 3D simulation results are compared against atom probe tomography measurements conducted for three alloy compositions. We show that a continuous increase in the alloy composition results in a discontinuous jump in the segregation isotherm. The jump corresponds to a spinodal Phase separation at grain boundary. For alloy compositions above the jump, we reveal an interfacial transient spinodal phase separation.
The transient spinodal phenomenon opens opportunities for knowledge-based microstructure design through the chemical manipulation of grain boundaries. The proposed density-based model provides a powerful tool to study thermodynamics and kinetics of segregation and phase changes at grain boundaries.
Systematic microstructure design requires reliable thermodynamic descriptions of each and all microstructure elements. While such descriptions are well established for most bulk phases, thermodynamic assessment of microstructure defects is challenging because of their individualistic nature. In this paper, a model is devised for assessing grain boundary thermodynamics based on available bulk thermodynamic data. We propose a continuous relative atomic density field and its spatial gradients to describe the grain boundary region with reference to the homogeneous bulk and derive the grain boundary Gibbs free energy functional. The grain boundary segregation isotherm and phase diagram are computed for a regular binary solid solution, and qualitatively benchmarked for the Pt–Au system. The relationships between the grain boundary's atomic density, excess free volume, and misorientation angle are discussed. Combining the current density-based model with available bulk thermodynamic databases enables constructing databases, phase diagrams, and segregation isotherms for grain boundaries, opening possibilities for studying and designing heterogeneous microstructures.
The underlying cause of mechanical anisotropy in additively manufactured (AM) parts is not yet fully understood and has been attributed to several different factors like microstructural defects, residual stresses, melt pool boundaries, crystallographic and morphological textures. To better understand the main contributing factor to the mechanical anisotropy of AM stainless steel 316L, bulk specimens were fabricated via laser powder bed fusion (LPBF). Tensile specimens were machined from these AM bulk materials for three different inclinations: 0◦, 45◦, and 90◦ relative to the build plate. Dynamic Young’s modulus measurements and tensile tests were used to determine the mechanical anisotropy. Some tensile specimens were also subjected to residual stress measurement via neutron diffraction, porosity determination with X-ray micro-computed tomography (μCT), and texture analysis with electron backscatter diffraction (EBSD). These investigations revealed that the specimens exhibited near full density and the detected defects were spherical. Furthermore, the residual stresses in the loading direction were between −74 ± 24 MPa and 137 ± 20 MPa, and the EBSD measurements showed a preferential ⟨110⟩ orientation parallel to the build direction. A crystal plasticity model was used to analyze the elastic anisotropy and the anisotropic yield behavior of the AM specimens, and it was able to capture and predict the experimental behavior accurately. Overall, it was shown that the mechanical anisotropy of the tested specimens was mainly influenced by the crystallographic texture.
Grain boundary energy effect on grain boundary segregation in an equiatomic high-entropy alloy
(2020)
Grain boundary (GB) Segregation has a substantial effect on the microstructure evolution and properties of polycrystalline alloys. The mechanism of nanoscale segregation at the various GBs in multicomponent alloys is of great challenge to reveal and remains elusive so far. To address this issue, we studied the GB segregation in a representative equiatomic FeMnNiCoCr high-entropy alloy (HEA) aged at 450 °C. By combining transmission Kikuchi diffraction, atom probe tomography analysis and a density-based thermodynamics modeling, we uncover the nanoscale segregation behavior at a series of well-characterized GBs of different characters. No segregation occurs at coherent twin boundaries; only slight nanoscale segregation of Ni takes place at the low-angle GBs and vicinal \Sigma 29b coincidence site lattice GBs. Ni and Mn show cosegregation of high levels at the general high-angle GBs with a strong depletion in Fe, Cr, and Co. Our density-based thermodynamic model reveals that the highly negative energy of mixing Ni and Mn is the main driving force for nanoscale cosegregation to the GBs. This is further assisted by the opposite segregation of Ni and Cr atoms with a positive enthalpy of mixing. It is also found that GBs of higher interfacial energy, possessing lower atomic densities (higher disorder and free volume), show higher segregation levels. By clarifying the origins of GB segregations in the FeMnNiCoCr HEA, the current work provides fundamental ideas on nanoscale segregation at crystal defects in multicomponent alloys.
Computational methods for lifetime prediction of metallic components under high-temperature fatigue
(2019)
The issue of service life prediction of hot metallic components subjected to cyclic loadings is addressed. Two classes of lifetime models are considered, namely, the incremental lifetime rules and the parametric models governed by the fracture mechanics concept. Examples of application to an austenitic cast iron are presented. In addition, computational techniques to accelerate the time integration of the incremental models throughout the fatigue loading history are discussed. They efficiently solve problems where a stabilized response of a component is not observed, for example due to the plastic strain which is no longer completely reversed and accumulates throughout the fatigue history. The performance of such an accelerated Integration technique is demonstrated for a finite element simulation of a viscoplastic solid under repeating loading–unloading cycles.
Due to their excellent creep resistance and good oxidation resistance, 9–12% Cr ferritic–martensitic stainless steels are widely used as high temperature construction materials in power plants. However, the mutual combination of different loadings (e.g., creep and fatigue), due to a “flexible” operation of power plants, may seriously reduce the lifetimes of the respective components. In the present study, low cycle fatigue (LCF) and relaxation fatigue (RF) tests performed on grade P92 helped to understand the behavior of ferritic–martensitic steels under a combined loading. The softening and lifetime behavior strongly depend on the temperature and total strain range. Especially at small strain amplitudes, the lifetime is seriously reduced when adding a hold time which indicates the importance of considering technically relevant small strains.
Modelling of environmentally assisted material degradation in the crack phase-field framework
(2019)
The simulation of crack propagation was conducted with a diffusive crack model in a variational framework. Moreover, the physically sound introduction of mass transport and coupling mechanisms due to environmentally assisted effects could be realised in this framework. The objective consists of the application of the phase-field Approach towards the simulation of environmentally assisted material degradation with the advantage of a non-required predefined crack path and a mesh-independent non-local formulation that facilitates the damage evolution with respect to material softening. The sharp crack is regularised by the introduction of a phase-field order parameter leading to a diffusive crack formulation.
Besides the equations originating from the linear momentum balance an additional evolution equation for the crack phase-field is introduced. Furthermore, mass transport is simulated by a Diffusion equation. The description delivered by the variational phase-field framework is able to simulate crack propagation according to published numerical test cases.
Additionally, the calculation of stress intensity factors is possible as well as crack resistance curves that describe stable crack propagation.
The sound numerical prediction of welding-induced thermal stresses, residual stresses, and distortions strongly depends on the accurate description of a welded material’s thermomechanical deformation behaviour. In this work, we provide experimental data on the viscoplastic deformation behaviour of a grade-s960ql steel up to a temperature of 1000 ◦C. In addition, a multi-phase viscoplastic material model is proposed, which accounts for the experimentally observed isothermal deformation behaviour of grade-s960ql steel base and austenitised material, as well as for athermal contributions that originate from solid-state phase transformations. The multi-phase viscoplastic and a classic rateindependent isotropic hardening material model were applied in the numerical simulations of both-ends-fixed bar Satoh tests and a single-pass gas metal arc weld. The influence of material modelling choices on the agreement between numerical simulation and experimental results is discussed, and recommendations for further work are given.
With the introduction of a mass transport mechanism the entire problem is subjected to a time frame that dictates the time-dependent action of soluted species on mechanical properties. A numerical framework within the phase-field approach is presented with an embrittlement-based coupling mechanism. The underlying functionals are expressed in terms of the displacement, mass concentration and crack phase-field. Within the phase-field approach the modelling of sharp crack discontinuities is replaced by a diffusive crack model facilitating crack initiation and complex crack topologies without the requirement of a predefined crack path. The isotropic hardening of the elasto-plastic deformation model and the local fracture criterion are affected by the species concentration. This allows for embrittlement and leads to an accelerated crack propagation. An extended mass transport equation for hydrogen embrittlement, accounting for mechanical stresses and deformations, is implemented. For stabilisation purposes a staggered scheme is applied to solve the system of partial differential equations by a multi-field finite-element method. A thermodynamically consistent coupling relation that accommodates the required mechanisms is presented.
Hydrogen is an attractive energy carrier that requires high effort for safe storage. For ensuring safety, storage cylinders must undergo a challenging approval process. Relevant standards and regulations for composite cylinders used for the transport of hydrogen and for its onboard storage are currently based on deterministic (e.g. ISO 11119-3) or to some respect semi-probabilistic criteria (UN GTR No. 13; with respect to burst strength).
This paper provides a systematic analysis of the load cycle properties resulting from these regulations and standards. Their characteristics are compared with the probabilistic approach of the Federal Institute for Materials Research and Testing BAM. The most important aspect of comparing different concepts is the rate for accepting designs with potentially unsafe or critical safety properties. This acceptance rate is analysed by operating Monte-Carlo simulations over the available range of production properties.
The creep behavior of single crystals of the nickel-based superalloy CMSX-4 was investigated at 1288 °C, which is the temperature of the hot isostatic pressing treatment applied to this superalloy in the industry. It was found that at this super-solvus temperature, where no gammaPrime-strengthening occurs, the superalloy is very soft and rapidly deforms under stresses between 4 and 16 MPa. The creep resistance was found to be very anisotropic, e.g., the creep rate of [001] crystals was about 11 times higher than that of a [111] crystal. The specimens of different orientations also showed a very different necking behavior. The reduction of the cross-sectional area psi of [001] crystals reached nearly 100 pct, while for a [111] crystal psi = 62 pct. The EBSD analysis of deformed specimens showed that despite such a large local strain the [001] crystals did not recrystallize, while a less deformed [111] crystal totally recrystallized within the necking zone. The recrystallization degree was found to be correlated with deformation behavior as well as with dwell time at high temperature. From the analysis of the obtained results (creep anisotropy, stress dependence of the creep rate, traces of shear deformation, and TEM observations), it was concluded that the main strain contribution resulted from <01-1>{111} octahedral slip.
A key limitation of the most constitutive models that reproduce a Degradation of quasi-brittle materials is that they generally do not address issues related to fatigue. One reason is the huge computational costs to resolve each load cycle on the structural level. The goal of this paper is the development of a temporal Integration scheme, which significantly increases the computational efficiency of the finite element method in comparison to conventional temporal integrations.
The essential constituent of the fatigue model is an implicit gradient-enhanced formulation of the damage rate. The evolution of the field variables is computed as amultiscale Fourier series in time.On a microchronological scale attributed to single cycles, the initial boundary value problem is approximated by linear BVPs with respect to the Fourier coefficients. Using the adaptive cycle jump concept, the obtained damage rates are transferred to a coarsermacrochronological scale associated with the duration of material deterioration. The performance of the developedmethod is hence improved due to an efficient numerical treatment of the microchronological problem in combination with the cycle jump technique on the macrochronological scale. Validation examples demonstrate the convergence of the obtained solutions to the reference simulations while significantly reducing the computational costs.
An improved diffusion model is proposed for pore annihilation during HIP of single-crystal nickel-base superalloys. The model assumes the pore dissolution by emission of vacancies and their sink to the low angle boundaries. Calculation, considering distribution of the pore sizes, predicts the kinetics of pore annihilation similar to the experimental one.