Anisotropic Moduli Research Articles

A potential mechanism for abnormal grain growth in Ni thin films on c-sapphire

Normal grain growth (NGG) of a (111) textured Ni film on c-sapphire and abnormal grain growth (AGG) of (100) grains at the expense of this (111) texture has been studied as a function of temperature with and without a capping layer. The grain boundaries (GBs) in the Ni film are controlled by the preferred orientation relationships (ORs) adopted by the Ni grains on the sapphire substrate. The 2 variants of a single OR, Ni(111)<11¯0>//Al2O3(0001)<11¯00>, form a (111) mazed bicrystal with Σ3 GBs. The (100) grains have a single OR, Ni(100)<010>//Al2O3(0001)<11¯00> with 3 variants; their GBs within the (111) grains have the (111)<11¯0>//(100)<010> misorientation.(100) AGG within the (111) mazed bicrystal of the 100 nm Ni film takes place above 1023 K. The orientation transition is driven by the biaxial elastic modulus anisotropy which favors the growth of (100) grains over (111) grains, as this reduces the elastic strain energy induced by the thermal mismatch between Ni and sapphire. (100) AGG is suppressed and the NGG of the (111) texture is slowed down when the film is covered by a 10 nm amorphous alumina layer aimed at inhibiting surface diffusion. Thus, it is proposed that as long as the surface can act as a sink for the point defects diffusing along the GBs, the movement of the GBs is correlated to the diffusivity of atoms and vacancies, which is a function of their misorientation and crystallographic GB structure.

Insights on the mechanical properties and failure mechanisms of calcium silicate hydrates based on deep-learning potential molecular dynamics

The molecular-scale mechanical properties of calcium silicate hydrates are crucial to the macro performance of cementitious materials, while achieving coincidence between accuracy and efficiency in computational simulations still remains a challenge. This study utilizes a deep-learning potential, specifically developed for calcium silicate hydrates based on artificial neural network, to achieve molecular dynamics simulations with accuracy comparable to first-principle methods. With this potential, the elastic properties and uniaxial mechanical behaviors are explored, wherein the anisotropy and impact mechanism of calcium ratios are analyzed. The results add to evidence that the deep-learning potential possess a higher accuracy than common force fields. The anisotropy of elastic modulus is mainly attributed to different atomic interactions in various directions, while the anisotropy of strength is additionally affected by the form of failure. This study may advance the accurate molecular-scale simulation and deepen the understanding of the strength source and cohesion mechanism of cement-based materials.

Planar structured materials with extreme elastic anisotropy

Designing anisotropic structured materials by reducing symmetry results in unique behaviors, such as shearing under uniaxial compression. While rank-deficient materials such as hierarchical laminates have been shown to exhibit extreme elastic anisotropy, there is limited knowledge about the fully anisotropic elasticity tensors achievable with single-scale fabrication techniques. No established upper and lower bounds on anisotropic moduli exist. In this paper, we estimate the range of anisotropic stiffness tensors achieved by single-scale two-dimensional structured materials. We first develop a database of periodic anisotropic single-scale unit cell geometries using linear combinations of periodic cosine functions. The database covers a wide range of anisotropic elasticity tensors, which are then compared with the elasticity tensors of hierarchical laminates. We identify the regions in the property space where hierarchical design is necessary to achieve extremal properties. We demonstrate a method to construct various 2D functionally graded structures using this cosine function representation. These graded structures seamlessly interpolate between unit cells with distinct patterns, allowing for independent control of several functional gradients, such as porosity, anisotropic moduli, and symmetry. When designed with unit cells positioned at extreme parts of the property space, these graded structures exhibit unique mechanical behaviors such as selective strain energy localization, compressive strains under tension, and localized rotations.

A single-phase Nb25Ti35V5Zr35 refractory high-entropy alloy with excellent strength-ductility synergy

Refractory high entropy alloys (RHEAs) are promising candidates for high-temperature structural materials due to their excellent high-temperature performance. However, the room-temperature brittleness of most alloys results in poor plastic formability, thereby limiting their engineering applications. In this study, Nb25Ti35V5Zr35 alloy with cold-rollability was developed, and its phase stability, tensile mechanical properties, elastic properties, strengthening mechanism, and deformation mechanism were investigated by combining experiments, CALPHAD, DFT and molecular statics (MS) methods. The results demonstrate that Nb25Ti35V5Zr35 alloy possesses good phase stability, with both the as-cast and annealed states maintaining a single-phase BCC structure without undergoing phase transformation. The tensile yield strength of the alloy reaches its peak at 1152 MPa in the cold-rolled condition, while its annealed state exhibits an optimal balance of strength and plasticity, with a yield strength of 836 MPa and an elongation of 22.45 %, respectively. Solid solution strengthening is the primary source of its high strength, with V and Zr playing key roles in this strengthening mechanism. Dislocation slip plays a dominant role in plastic deformation. Additionally, compared to traditional BCC alloys, the significance of edge dislocations in the deformation process is notably enhanced, with the {112} plane serving as the preferred slip plane for dislocations. DFT results indicate that the alloy exhibits significant anisotropy in both Young's modulus and shear modulus. This work contributes to understanding the material properties of the Nb25Ti35V5Zr35 alloy and provides a reference for the design of new ductile RHEAs.

Studying hcp-bcc transition of Be via anisotropy of modulus and sound velocity

Abstract Based on ab initio calculations, we utilize the mean-field potential approach with the quantum modification in conjunction with stress-strain relation to investigate the elastic anisotropies and sound velocities of hcp and bcc Be at high-temperature (0-6000 K) and high-pressure (0-500 GPa) conditions. We propose the general defintion of anisotropy for elastic moduli and sond velocities. Results suggest that the elastic anisotropy of Be is more significantly influenced by pressure than by temperature. The pressure induced increase of c/a ratio makes the anisotropy of hcp Be significantly strengthen. Whereas the hcp Be still exhibits smaller anisotropy than bcc Be in terms of elastic moduli and sound velocities. We suggest that measuring the anisotropy in shear sound velocity may be an approach to distinguishing the hcp-bcc phase transition under extreme conditions.

Maximum shear modulus anisotropy of rooted soils

The maximum shear modulus (G0(ij)) of rooted soils is crucial for assessing the deformation and liquefaction potential of vegetated infrastructures under seismic loading conditions. However, no data or theory is available to account for the anisotropy of G0(ij) of rooted soils. This study presents a new model that can predict G0(ij) anisotropy of rooted soils by incorporating the projection of the stress tensor on two independent tensors that describe soil fabric and root network. Bender element tests were conducted on bare and vegetated specimens under isotropic and anisotropic loading conditions. The presence of roots in the soil increased G0(VH) at all confining pressures (p′), as well as G0(HH) and G0(HV) at low p′. However, the trend was reversed at higher p′ because the roots reduced the effects of confinement on G0(ij) by replacing stronger soil–soil interfaces with weaker soil–root interfaces. Roots made the soil fabric and G0(ij) more anisotropic. The proposed model can effectively predict the observed anisotropy of G0(ij) under isotropic and anisotropic loading conditions. The new model also offers a new method for determining the fabric anisotropy of sand based on the anisotropy of shear modulus.

Design and physical property study of seven novel carbon allotropes by Random methods combined group and Graph theories

Carbon materials are important semiconductor materials. For enriching the structure of carbon materials, the eight novel carbons with R-3m phase are predicted by using Random methods based on Group and Graph theories. Among these allotropes, one (R-3m/C−8(-|-)) was excluded through stability criterion, and the others new carbon structures meet all stability conditions, including thermal stability, dynamical stability, mechanical stability, and thermodynamic stability. According to two empirical hardness model criteria, all the hardness of seven novel carbon allotropes are above 50 GPa. Particularly, R-3m/C, R-3m/C−2(-|-), R-3m/C−3(-|-), R-3m/C−6(-|-), and/R−3(-|-)m/C−7(-|-) belong to superhard materials. Electronic band structures of these materials are demonstrated by HSE06 hybrid functional, where R-3m/C, R-3m/C−2(-|-), R-3m/C−3(-|-), R-3m/C−4(-|-), R-3m/C−6(-|-), and/R−3(-|-)m/C−7(-|-) are wide band gap semiconductors, while R-3m/C, R-3m/C−2(-|-) are quasi-direct band gap structures. The R-3m/C−4(-|-) exhibits the greatest elastic anisotropy in elastic modulus. There materials with different crystalline phase structures are characterized by using X-ray diffraction spectroscopy. Here, the predicted new allotropes with excellent physical properties provide theoretical guidance for further development and expansion of carbon material applications.

Ultrastrong and ductile FeNi-based alloys through Pd-containing multicomponent L12-type precipitates

Precipitation strengthening stands as a paramount strategy for enhancing the mechanical properties of FeNi-based alloys. Conventional precipitates used for strengthening typically contain only two major constituent elements selected from Ni, Al, and Ti. However, knowledge about the intrinsic properties and strengthening mechanisms of multicomponent precipitates remains limited. Here, we propose introducing novel multicomponent L12-type precipitates containing palladium (Pd) to strengthen FeNi-based alloys. The strengthened FeNi alloy achieves an eightfold increase in strength compared to the FeNi matrix while maintaining good ductility. Using meticulous micro-characterization and energy-dispersive X-ray spectroscopy (EDS) techniques, in conjunction with first-principles calculations, this study investigated the effects of Pd addition on the thermodynamic stability, morphology, coherency, and strengthening mechanisms of the precipitates. Results indicate that the addition of Pd induces the nucleation of L12-type precipitates, increases their ductility, and eliminates anisotropy in the shear modulus of the precipitates. Excessive Pd content can alter the shape of precipitates from spherical to acicular due to increased interfacial mismatch between the precipitates and the FeNi matrix. These insights shed light on the impact of Pd addition on the intrinsic properties of L12-type precipitates, offering a promising pathway for the design of advanced FeNi-based alloys with optimized mechanical performance.

Enhancing the stability of Li-Rich Mn-based oxide cathodes through surface high-entropy strategy

Li-rich Mn-based layered oxides (LMR) hold promise as cathode materials for lithium-ion batteries (LIBs) due to their high reversible capacity. However, issues such as oxygen release and structural degradation associated with oxygen redox cause voltage decay and capacity decline during cycling. In this study, a monodisperse Li1.2Ni0.13Co0.13Mn0.54O2 cathode material with surface high-entropy architecture (MZCN-LMR) was synthesized to enhance the overlap between the non-bonding orbitals of oxygen (|O2p) and the (TM-O)* occupied band. This enhancement enables regulation of the depth of oxygen oxidation, improving reversible oxygen redox and creating highly flexible structures, with mitigated anisotropic modulus and lattice strain evolution during (de)intercalation. Consequently, the developed MZCN-LMR cathode exhibits impressive capacity retention of 80.5 % after 400 cycles and minimal voltage decay of 0.7 mV per cycle with the voltage range of 2.1–4.6 V. This surface high-entropy strategy offers a universal approach to enhancing the redox stability of anions, contributing to the application of LMR.

Regulating the mechanical anisotropy of Mo2AC MAX phases through interlayer control

The structural editing protocol for layered carbides (MAX phases) has been proven to be an effective means of expanding the MAX family. Therefore, this study employs first-principles calculations to manipulate the mechanical anisotropy of Mo2AC MAX phase by regulating the interlayer (A = Fe, Co, Ni, Cu, Zn, Ga, Ge, As, Se). By manipulating the A layer, the anisotropy of Young's modulus can alternate among spindle, funnel, and shuttle shapes, while the shear modulus can similarly transition among these forms. This method can adjust anisotropy indices AU from 0.13 to as high as 3.4 and Ashear from 1.15 % to 25.37 %. Besides, electronic calculations indicate that the interlayers of Mo2AC (A = metal) possess a large number of free electrons along the XY plane, while the electrons in Mo2AsC and Mo2SeC are distributed along the Z-axis. Consequently, Mo2AsC and Mo2SeC exhibit good ductility and are suitable for mechanical processing. This work lays a solid foundation for the manipulation of mechanical anisotropy in practical engineering applications through the regulation of the interlayer in the Mo2AC MAX phase.

Electronic structures, elastic and anisotropic properties of TiAl3 intermetallics doped with Nb

The elastic and anisotropic properties of TiAl3 intermetallics doped with Nb are investigated systematically based on the electronic structures calculation. It shows that the Nb atoms are preferentially to substitute Ti sites forming a stable crystal structure. The DOS of Nb–doped TiAl3 suggests that there is a pseudogap in (Ti18–x + Nbx)Al54. It reinforces atomic covalent bonds while the metallic bond in Ti18(Al54–x + Nbx) is increased. The predicted elastic properties of Nb–doped TiAl3 implies that its strength can be reinforced when the Ti sites substituted by Nb whereas the ductility of the doped intermetallics can be ameliorated when Al sites substituted by Nb. The anisotropy of Young's modulus and shear modulus indicate the uniform deformation ability of (Ti18–x + Nbx)Al54 is better than that of Ti18(Al54–x + Nbx). Poisson's ratio of Ti18Al54 and Ti18(Al51+Nb3) suggest an auxetic feature may be existed when a tensile stress is applied on a specific direction.

Insight into the Physical Properties of the Chalcogenide XZrS3 (X = Ca, Ba) Perovskites: A First-Principles Computation

This study investigates the structural, mechanical, optical, thermal, and electronic properties of the ionic semiconducting materials XZrS3 (X = Ca, Ba) within the framework of density functional theory (DFT). Here, the elastic constants, modulus (bulk, shear, Young's), ratios (Pugh, Poisson) and elastic anisotropy for XZrS3 (X = Ca, Ba) are studied. Furthermore, the electronic, optical, and thermal properties for XZrS3 (X = Ca, Ba) are regenerated and designed using the values obtained with Cambridge Serial Total Energy Package (CASTEP) software. The calculated lattice parameters show excellent agreement with theoretical and experimental values. The elastic stiffness constants confirm the mechanical stability of both compounds. Although XZrS3 (X = Ca, Ba) is elastically anisotropic, it has little optical anisotropy. The electronic band structures of the material exhibit direct-bandgap semiconducting behavior, with values of 1.3 eV (CaZrS3) and 1.1 eV (BaZrS3) using the generalized gradient approximation (GGA), respectively, which is ideal for solar cell (0.9–1.56 eV) and optoelectronic device applications. Bandgap values of 1.9 eV and 1.6 eV are found for CaZrS3 and BaZrS3, respectively, using the Heyd–Scuseria–Ernzerhof HSE06 functional, which is consistent with previous theoretical and experimental bandgap results. The optical properties including dielectric function, refractive index, absorption coefficient, reflectivity, and loss function are characterized using the GGA of Perdew–Burke–Ernzerhof (GGA-PBE) and HSE06 methods and are discussed in detail. Because of the relatively low Debye temperature (D), thermal conductivity of the lattice (kph), and minimum thermal conductivity (Kmin), the studied materials can be used as thermal barrier coating (TBC) materials. The capacity of heat, Debye temperature, and thermal coefficient of expansion are all computed.

First-principles study of binary and ternary phases in Mg-Gd-Ni alloys

Given the high demand for magnesium alloys across industries, it's crucial to enhance their performance by developing alloys with superior characteristics. The performance of magnesium alloys is closely related to the properties of the precipitated phase. However, there has been insufficient exploration of the mechanical properties of precipitated phases in Mg-Gd-Ni alloys. Hence, this paper calculates the formation energy, electronic structure, elastic modulus, and elastic anisotropy of the precipitated phase in Mg-Gd-Ni alloys using first principles. Calculations of formation energies and elastic constants demonstrate that MgGdNi4, Mg2Ni, 18R-LPSO, Mg2Gd, and 14H-LPSO possess commendable thermodynamic and mechanical stability. Elastic modulus calculations reveal a significant increase in the elastic modulus of magnesium, especially the bulk modulus, upon the addition of Gd and Ni elements, increasing from 34.5 GPa to a peak of 84.9 GPa. Furthermore, the strength increments of the corresponding precipitated alloys, calculated based on the elastic modulus, underscore MgGdNi4 as exhibiting the most significant strength increment. The elastic anisotropy of each second phase is evaluated using the elastic anisotropy factor, the three-dimensional surface, and the projection onto each two-dimensional plane. The order of elastic modulus anisotropy for shear and Young's modulus is MgGdNi4 > Mg2Ni > 18R-LPSO > Mg2Gd > 14H-LPSO. This study provides valuable data for regulating properties in magnesium alloys.

Investigation of anisotropic shrinkage in liquid silicone rubber injection molding: Process variables

AbstractInjection molded liquid silicone rubber (LSR) devices are used in high performance applications for the medical, transportation, and energy industries. Anisotropic shrinkage in LSR injection molding has been observed in practice but is generally not well understood. This research focused on anisotropic shrinkage based on flow and cross‐flow orientation. LSR parts were molded at varying thicknesses, shear rates, fill times, and cure temperatures. Simulations accurately predicted the fill pattern and were used to predict the cure rate of the samples. LSR molding showed a significant range of linear shrinkage ratios between the flow versus crossflow directions shrinkage from above 1.30 to below 0.92. The underlying driver of anisotropic behavior is believed to be reaching a sufficient average cure through the cross section combined with flow‐induced orientation. Shrinkage anisotropy was found to generally increase with increasing shear rate in regions where curing was significant. Additionally, dynamic mechanical analysis showed a connection between the polymer network using the modulus and anisotropic linear shrinkage.Highlights Liquid silicone rubber injection molding experienced anisotropic shrinkage. Shrinkage was greater in the flow direction than in the crossflow direction. Shear flow caused orientation and strain of silicone polymer chains in cavity. Reaching cure threshold during flow caused increased shrinkage anisotropy. Shrinkage anisotropic showed due to network structure with anisotropic moduli.

Study of the novel boron nitride polymorphs: First- principles calculations and machine learning

This study explores two new boron nitride polymorphs, namely C2221 BN and I-4 BN, characterized by sp2 hybridization. The investigation is conducted through first-principles calculations, including assessments of their structural properties, stability, elastic properties, anisotropy, and electronic properties. The newly discovered boron nitride polymorphs exhibit mechanical stability, dynamic stability, and thermodynamic stability, as ascertained by analyzing their elastic constants, phonon spectra, and associated enthalpies. The B/G values for both C2221 BN and I-4 BN far exceed the threshold of 1.75, thus confirming that they are ductile materials. The BN polymorphs investigated in this work exhibit different degrees of anisotropy in Young's modulus, shear modulus, and Poisson's ratio. Meanwhile, two different datasets were trained using four machine learning algorithms, and the random forest model with the m2ax dataset showed a high fitting degree, small error, and good stability. Then, the machine learning model, which has undergone training, is used to predict the elastic modulus of boron nitride polymorphs. Upon comparing the computed GGA values with the experimental values of c-BN, it is evident that the random forest model outperforms in accurately predicting the elastic modulus of boron nitride polymorphs.

Simulation and optimization of unstable dynamic propagation of multiple fractures in the shale formation

Multi-cluster hydraulic fracturing of horizontal wells is a well-adopted technique with high efficiency to increase the production of tight and shale formations. However, the stress shadows among clusters pose challenges to the synchronous propagation of hydraulic fractures during multi-cluster fracturing. In order to explore the fracture propagation mechanism and characteristics under the influence of stress shadow in low-spacing staged multi-cluster fracturing, a three-dimensional hydraulic fracturing model was generated using a lattice-based method. This model considered the impact of geological and engineering parameters on the propagation behavior of multiple fractures in shale formation. A variable pumping approach is adopted, where the fracturing fluid is initially injected at a high rate and then transitioned to a lower rate. Afterward, a method was proposed to quantitatively assess the extent of fracturing in a specific area (i.e., the stimulated area), considering the impact of stress shadow within a single stage. The simulation results demonstrated significant differences in the fracture stimulation area due to the influence of each parameter in the case of uncontrollable geological factors and controllable engineering factors. An increase in both Young’s modulus and stress anisotropy of the reservoir results led to a corresponding increase in the total fracture stimulation area. As the principal stress orientation increased, the fracture stimulation area gradually decreased. In terms of operational parameters, the stimulated area of hydraulic fractures gradually decreased as the fracture spacing increased. With increasing injection rate, the stimulated area initially expanded and then decreased, peaking at an injection rate of 0.04 m3/s. These findings can provide valuable insights into the propagation behavior of multi-cluster hydraulic fractures under uncertain parameters, with significant implications for future engineering applications.

Текстура рекристалізації та анізотропії пружних властивостей листів сталі DC04

We studied steel sheets DC04 (0.06% C, up to 0.35% Mn, up to 0.40% Si, ~ 0.025% S and P) with a thickness of 0.95 mm as delivered. Sheets of A4 size were annealed in a laboratory oven (6000C in an argon atmosphere, hold for 1 hour). The structure of DC04 steel sheets after recrystallization annealing was studied. The microstructure of the steel sheets under study is presented from the side of the rolling plane and in the section of the sheet perpendicular to the direction. In the plane of the sheets, the grains are elongated; in the cross section, the grains are approximately equiaxed. Pole figures (PF) were constructed based on the results of electron backscatter diffraction (EBSD) on a LEO 1455 VP electron microscope at an accelerating voltage of 20 kV from the plane of the sheets and from the section of the sheet perpendicular to the rolling direction. To improve statistics, PF were constructed by averaging reflex stereographic projections from 20 different representative volumes of material relative to the rolling direction and transverse direction. The texture and anisotropy of Young's modulus in the plane and cross section of steel sheets DC04 after recrystallization annealing was studied using EBSD method. A connection has been obtained between ideal orientations that describe the texture in two mutually perpendicular planes and the corresponding integral characteristics of texture (ICT). Rectangular samples with a length of 100 and a width of 10 mm at different angles to the rolling direction every 150 to measure Young's modulus. Samples were processed in a bag to ensure uniform dimensions. Young's modulus was determined by the dynamic method from the frequency of natural transverse vibrations. Three batches of samples were used to construct Young's modulus anisotropy curves. The anisotropy of the Young's modulus in the plane of steel sheets, calculated from the ICT based on the results of EBSD data, is in good agreement with the results of direct measurements. The value of Young's modulus in the direction normal to the plane of the sheet and in the section plane in the direction normal to the plane of the sheet, calculated from the ICT and the values of the compliance constants of iron, coincide. Keywords: texture, pole figure, anisotropy, integral characteristics of texture, Young's modulus.

Cage-C22 and Cage-C28: Two novel superhard orthorhombic carbon allotropes

In this work, two novel three-dimensional Cage carbon allotropes with all-sp3 and mixed sp2-sp3 hybridized networks, namely, Cage-C22 and Cage-C28 are theoretically predicted by the analysis executed using based on the density functional theory. Cage carbon superhard crystals possess Pmmm (47) symmetry (space group no. 25) which are orthorhombic crystals. The electronic properties, mechanical properties (hardness, elastic anisotropy, elastic modulus, and directional dependence of Young's modulus in GPa), and structural properties for both the carbon phases are systematically investigated and analyzed. The calculated phonon dispersions and elastic coefficients Cij show that Cage carbon allotropes are dynamically and mechanically stable at ambient conditions (0 GPa). To study the mechanical properties of these structures, the (Young's, shear, bulk) modulus were obtained by using the Voigt-Reuss-Hill approximation. The ratios of Emax/Emin as significant ratios of mechanical anisotropy in Young's modulus are greater than that of diamond (1.10) which means that Cage structures show elastic anisotropy. Furthermore, the electronic properties of these two new structures show that Cage-C22 crystal is a direct semiconductor and its gap energy is about 1.5 eV at Z point, while Cage-C28 is a metal because it has zero band gap between valence bands (VB) and conduction bands (CB). The calculated X-ray spectrum patterns show noncrystalline behavior which is derived from its structural complexity, and bond angles and bond lengths are also effective in this matter. The calculated results indicate that these two 3D superhard structures have the required potential for the use of cathode materials in capacitors, electrical and mechanical applications.

Morphology and Compressive Properties of Extruded Polyethylene Terephthalate Foam.

The cell structure and compressive properties of extruded polyethylene terephthalate (PET) foam with different densities were studied. The die of the PET foaming extruder is a special multi-hole breaker plate, which results in a honeycomb-shaped foam block. The SEM analysis showed that the aspect ratio and cell wall thickness of the strand border is greater than that of the strand body. The cells are elongated and stronger in the extruding direction, and the foam anisotropy of the structure and compressive properties decrease with increasing density. The compression results show typical stress-strain curves even though the extruded PET foam is composed of multiple foamed strands. The compression properties of PET foam vary in each of the three directions, with the best performing direction (i.e., extrusion direction) showing stretch-dominated structures, while the other two directions show bending-dominated structures. Foam mechanics models based on both rectangular and elongated Kelvin cell geometries were considered to predict the compressive properties of PET foams in terms of relative density, structure anisotropy, and the properties of the raw polymer. The results show that the modulus and strength anisotropy of PET foam can be reasonably predicted by the rectangular cell model, but more accurate predictions were obtained with an appropriately assumed elongated Kelvin model.

Phase field simulation of intra/intergranular pore morphology evolution of neutron-irradiated austenitic stainless steel

Intergranular or intragranular anisotropic pores can be easily observed in the FCC structure of nuclear reactor core structural materials, such as austenitic stainless steel or nickel-based alloys. Austenitic stainless steel contains a certain amount of nickel(Ni), Ni undergo transmutation reaction under neutron irradiation to produce helium. Helium combines with vacancy and continuously absorbs more helium and vacancy, evolving into underpressure pores filled with a small amount of helium. The morphology of pores is influenced by both the surface anisotropy of the crystal and grain boundary characteristic because pores nucleation predominantly occurs at grain boundaries. The swelling effect caused by pores and the embrittlement effect of high temperature helium are related to the morphology, size and distribution of pores. The phase field method can couple multiple physical fields and accurately describe the effects of material microscopic defects on pores. In this study, we use establish a free energy functional coupling between crystal plane anisotropy and pore-grain boundary interactions, using phase field methods to simulate pores’ evolution and morphology. Our results demonstrate that helium gas induces pore nucleation, with higher concentrations leading to shorter incubation period, faster nucleation rate, and greater growth rate. Grain boundaries act as heterogeneous nucleation sites for helium pores, leading to the formation of pores along these boundaries and high-density diffusion pores within grains. The intragranular pores exhibit anisotropic characteristics regulated by interfacial energy's anisotropic modulus, the strength of the anisotropy, and crystal orientation. The high-density intergranular pores interact significantly and are influenced by grain boundaries, while the anisotropic morphology is negligible. Additionally, it has been observed that the pores located at the middle of grain boundaries tend to exhibit an elliptical shape. The stress inside the pores that contain a small amount of helium gas is negative, which is lower than the value in the matrix. The findings presented herein align well with experimental results and have implications for life prediction models for service components as well as core material design.