Polycrystalline Model Research Articles

Influence of prior dislocation structure on anisotropy of thermal creep of cold-worked Zr–2.5Nb tubes

Normally, creep anisotropy of hcp metals is thought to be controlled by the crystallographic texture. Here, we show that the creep anisotropy of cold-worked Zr–2.5Nb tubes is also very dependent on the anisotropic dislocation structures introduced by cold-work. The contribution of each slip system to the creep deformation of an individual grain orientation depends upon the activity of that slip system during prior cold-work. This conclusion is reached by comparing the self-consistant visco-plastic polycrystalline models with thermal creep tests performed on internally pressurized thin-wall capsules with different textures under a transverse stress of 300 MPa at 350 °C, where dislocation creep is the dominant operating mechanism. The non-uniform dislocation distributions prior to creep were derived by simulating the cold-work process of Zr–2.5Nb tubes from an Elasto-Plastic Self-Consistent (EPSC) model.

Polycrystalline Modeling of the Effect of Texture and Dislocation Microstructure on Anisotropic Thermal Creep of Pressurized Zr-2.5Nb Tubes

Abstract We have investigated the thermal creep of cold-worked Zr-2.5Nb tubes for a range of textures and stress states. The creep tests were performed on internally pressurized thin-wall standard (ratio of axial and transverse stress R≈0.5) and end-loaded (ratio of axial and transverse stress, 0.25<R<0.75) capsules 10 mm in diameter×40 mm long×0.5 mm wall-thickness at a stress of 300 MPa at 350°C where dislocation creep is the dominant operating mechanism. The tests showed an obvious correlation of anisotropic creep with the texture under different stress states. A self-consistent visco-plastic polycrystalline model based solely upon crystallographic texture showed a poor correlation with experimental results for radial basal textures, similar to that found previously for in-reactor creep. Hence texture alone is not sufficient to accurately predict the creep anisotropy. A modified self-consistent model is introduced to take into account different pre-existing anisotropic dislocation distributions (from cold-work) in different crystal orientations. Much better agreement with the experimental creep anisotropy was found, indicating that individual dislocation distributions in grains with different orientations are important in controlling the creep anisotropy. The predicted effect on creep anisotropy of introducing dislocation structures by a radically different strain path is very large.

Multiscale Analysis of Viscoplastic Behavior of Recrystallized Zircaloy-4 at 400°C

Abstract Zirconium alloys are used in the nuclear industry as cladding tubes to prevent the fissile material from leaking into the coolant as the first safety wall of nuclear fuel. More and more requirements on fuel performance lead to stronger mechanical solicitations and integrity of cladding tubes has to be guaranteed. In this framework, the polycrystalline models, which are based on plasticity mechanisms, have interesting advantages compared to phenomenological ones. Some previous studies have shown that a polycrystalline approach could be very useful to describe the mechanical behavior of zirconium alloys. This modelling strategy has been successfully applied to fresh material and also, more recently, to irradiated material. The micromechanical approach has been developed in the light of transmission electron microscopy (TEM) observations. These experiments have been achieved to identify the main deformation mechanisms, which occur in several grains of relaxed and crept Zircaloy-4 samples. The main purpose of this paper is to describe an improved micromechanical model able to reproduce both the anisotropic creep behavior and the elasto-plastic behavior of unirradiated recrystallized Zircaloy-4 at 400°C. Finally, the quantitative analyses, which have been carried out with TEM correspond well with the results provided by the micromechanical approach.

Basic Analysis of Microstructural Fracture Behavior in Structural Materials by Using FEM with Interface Element

A new finite element method with the interface element was developed for examining the microstructural fracture behavior, where the anisotropy of grain was modeled by the ordinary finite element while both the opening and shear deformations was demonstrated by the interface element. From the serial computations using two-dimensional virtual polycrystalline models obtained through Voronoi tessellations, it was found that the interaction between the interaction between opening and shear deformations would be a dominant factor of the fracture processes. Also, it can be concluded that this method would be a useful tool for examining microstructural fracture behavior. © 2011 Published by Elsevier Ltd. Selection and peer-review under responsibility of ICM11

Micromechanical modeling of the cyclic softening of EUROFER 97 steel

The quenched and tempered reduced-activation ferritic/martensitic steel EUROFER 97 is one of the candidates for structural components of fusion reactors. The cyclic behaviour of this steel during isothermal plastic strain-controlled tests is investigated at room temperature. Under Low-Cycle Fatigue (LCF) tests this steel shows, after the first few cycles, a pronounced cyclic softening accompanied by microstructural changes such as the decrease of the dislocation density inside the subgrain and the vanishing of low-angle boundaries. Based on the identified mechanisms of softening a mean-field polycrystalline model is proposed.

A quantitative and thermodynamically consistent phase-field interpolation function for multi-phase systems

The aimed properties of the interpolation functions used in quantitative phase-field models for two-phase systems do not extend to multi-phase systems. Therefore, a new type of interpolation functions is introduced that has a zero slope at the equilibrium values of the non-conserved field variables representing the different phases and allows for a thermodynamically consistent interpolation of the free energies. The interpolation functions are applicable for multi-phase-field and multi-order-parameter representations and can be combined with existing quantitative approaches for alloys. A model for polycrystalline, multi-component and multi-phase systems is formulated using the new interpolation functions that accounts in a straightforward way for composition-dependent expressions of the bulk Gibbs energies and diffusion mobilities, and interfacial free energies and mobilities. The numerical accuracy of the approach is analyzed for coarsening and diffusion-controlled parabolic growth in Cu–Sn systems as a function of R/ℓ, with R grain size and ℓ diffuse interface width.

Deformation of wrought uranium: Experiments and modeling

The room temperature deformation behavior of wrought polycrystalline uranium is studied using a combination of experimental techniques and polycrystal modeling. Electron backscatter diffraction is used to analyze the primary deformation twinning modes for wrought alpha-uranium. The {1 3 0}〈3 1 0〉 twinning mode is found to be the most prominent twinning mode, with minor contributions from the ‘{1 7 2}’〈3 1 2〉 and {1 1 2}‘〈3 7 2〉’ twin modes. Because of the large number of deformation modes, each with limited deformation systems, a polycrystalline model is employed to identify and quantify the activity of each mode. Model predictions of the deformation behavior and texture development agree reasonably well with experimental measures and provide reliable information about deformation systems.

Effects of temperature and tilt angle on the grain boundary structure in silicon oxide: Molecular dynamics study

Molecular Dynamic (MD) simulations on a crystalline and amorphous silicon oxide were performed by using modified-Born-Mayer-Huggins (modified-BMH) potential. Comparison of the lattice parameters and analyses of the RDF for five different bulk phases of silicon oxide showed that the modified-BMH potential was properly able to describe crystalline phases, as well as the amorphous phase. When a polycrystalline model system that was composed of two β-cristobalite grains with a tilt grain boundary was annealed, an amorphous-like grain boundary region formed. The thickness of the grain boundary region was practically identical, regardless of the annealing temperature within the MD calculation time, which showed a very early stage of grain boundary amorphization. The atomic distribution in the grain boundary region became more uniform as the annealing temperature increased due to the faster relaxation. On the other hand, the atomic configuration and the thickness of the grain boundary region hardly depended on the grain boundary tilt angle.

Influence of strain rate on P92 microstructural stability during fatigue tests at high temperature

9-12%Cr creep-resistant ferritic-martensitic steels are candidates for structural components of Generation IV nuclear power plants. However, they are sensitive to softening during fatigue and creep-fatigue loading. To better understand softening mechanisms in ASTM Grade 92, fatigue tests were carried out at 823 K at various strain amplitudes. Two different values of the strain rate (2 10−3 s−1 and 10−5 s−1) were used for one strain amplitude. The softening behavior is mainly due to microstructural evolution. Examination of fractured specimens (hardness tests, TEM) shows an influence of strain rate on both increase in subgrain size and decrease in free dislocation density during cycling. Study of the evolution of isotropic, kinematic and viscous contributions to stress during fatigue tests shows a decrease in the kinematic contribution during cycling. A simplified mean field polycrystalline model based on subgrain growth is proposed in order to account for this strain rate effect. Potential impact on further creep resistance behavior is discussed.

Anisotropic thermal creep of internally pressurized Zr–2.5Nb tubes

The anisotropy of creep of internally pressurized cold-worked Zr–2.5Nb tubes with different crystallographic textures is reported. The stress exponent n was determined to be about three at transverse stresses from 100 to 250 MPa with an activation energy of ∼99.54 kJ/mol in the temperature range 300–400 °C. The stress exponent increased to ∼6 for transverse stresses from 250 to 325 MPa. From this data an experimental regime of 350 °C and 300 MPa was established in which dislocation glide is the likely strain-producing mechanism. Creep tests were carried out under these conditions on internally pressurized Zr–2.5Nb tubes with 18 different textures. Creep strain and creep anisotropy (ratio of axial to transverse steady-state creep rate, ε ˙ A / ε ˙ T ) exhibited strong dependence on crystallographic textures of the Zr–2.5Nb tubes. It was found that the values of ( ε ˙ A / ε ˙ T ) increased as the difference between the resolved faction of basal plane normals in the transverse and radial directions ( f T − f R ) increases. The tubes with the strongest radial texture showed a negative axial creep strain and a negative creep rate ratio ( ε ˙ A / ε ˙ T ) and tubes with a strong transverse texture exhibited the positive values of steady-state creep rate ratio ( ε ˙ A / ε ˙ T ) and good creep resistance in the transverse direction. These behaviors are qualitatively similar to those observed during irradiation creep, and also to the predictions of polycrystalline models for creep in which glide is the strain-producing mechanism and prismatic slip is the dominant system. A detailed analysis of the results using polycrystalline models may assist in understanding the anisotropy of irradiation creep.

Study of internal strain evolution in Zircaloy-2 using polycrystalline models: Comparison between a rate-dependent and a rate-independent formulation

In the present paper, an elasto-viscoplastic model is proposed to describe the behavior of hexagonal close-packed materials where multiple deformation modes, including plastic slip and twinning, coexist. The model assists in interpreting the experimental lattice strains whose evolution is often complex because of the many deformation modes involved. The proposed rate-dependent model is compared with a previously developed rate-independent model by studying the development of internal strains in a moderately textured Zircaloy-2 slab. The comparison shows that most of the inflexions that are experimentally observed are well reproduced by the proposed model and the qualitative and quantitative agreement is generally better with the new rate-dependent formulation.

Polycrystalline modeling of the cyclic hardening/softening behavior of an austenitic–ferritic stainless steel

As other metallic materials, in low-cycle fatigue, duplex stainless steels (DSS) exhibit a cyclic hardening, followed by a cyclic softening, before stabilization of the stress. In order to simulate the cyclic hardening/softening curves in low-cycle fatigue of an austenitic–ferritic or duplex stainless steel (DSS), a new polycrystalline model is proposed. The polycrystalline model developed by Cailletaud (1992) and Pilvin (1990) and modified by Hoc and Forest (2001) was previously extended in Evrard et al. (2008) in order to take into account the bi-phased character of the DSS. This model correctly accounts for the cyclic hardening, but it is not able to simulate the cyclic softening, consequently, stresses at the stabilized state are overestimated. TEM observations of the dislocation structures built during a cyclic uniaxial tension/compression test show that, during the cyclic hardening, planar arrangements are observed in austenitic grains and no significant evolution is observed during the subsequent cyclic softening and stabilization stage. On the contrary, in ferritic grains, dislocations are homogeneously distributed during cyclic hardening, and the microstructure evolves during the subsequent cyclic softening and stabilization stage. Dislocation structures build progressively, consisting of hard zones or walls, separated by soft zones or channels. We propose to model the cyclic softening through dislocation structure evolution within ferritic grains. The single crystal law used by Hoc and Forest (2001) is modified in order to take into account the heterogeneous distribution of dislocations in the ferrite. Numerical simulations are compared with experimental data. A good agreement is observed between experimental and calculated hardening/softening curves and stabilized hysteresis loops.

Improvement of sol‐gel ZnO heterojunctions by hydrogen annealing

AbstractZnO films were formed quartz substrates and silicon (100) wafers by a sol‐gel technique, and they were crystallized (in air at 800 °C) and annealed in hydrogen (at 220 to 420 °C, for 10 to 120 min). Photoluminescence (PL) measurements of ZnO films on quartz substrates indicated that hydrogen annealing increased the near band edge (NBE) emission ten‐fold, but it only slightly decreased the deep level emission (DLE). Hall effect measurements showed an n‐type conduction of the films, with an electron concentration of about 1016 cm–3, Hall mobility of about 14 cm2/Vs, and resistivity of about 2 Ωcm. Before hydrogen annealing, n‐ZnO/p‐Si heterojunctions showed only ohmic behavio. After hydrogen annealing, however, the forward current was increased and the reverse current was decreased, and the final I‐V curve showed a typical rectifying characteristicc. These results can be explained by a conventional polycrystalline and grain boundary (GB) model with a potential barrier height near the GBs and defects in the grains. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A novel approach for anisotropic hardening modeling. Part II: Anisotropic hardening in proportional and non-proportional loadings, application to initially isotropic material

The modeling of anisotropic hardening, in particular for non-proportional loading paths, is a challenging task for advanced macroscopic models. The complex distortion of the yield locus is related to the activation and cross-hardening of different slip systems, depending on crystallographic orientations. These physical mechanisms can be taken into account in polycrystalline models but the computation times are enormous. The novel approach detailed in Part I ( Rousselier et al., 2009) consists in: (i) drastically reducing the number of crystallographic orientations to save the computation cost, (ii) applying a parameter calibration procedure to obtain a good agreement with the experimental database. This methodology is first applied here to the anisotropic hardening in the proportional loadings of the strongly anisotropic aluminum alloy of Part I. Very good modeling is achieved with only eight crystallographic orientations. Different levels of additional hardening in biaxial proportional loading as compared to uniaxial loading can be modeled with the same polycrystalline model. For this, only the parameter calibration has to be performed with different databases. The same methodology has also been applied for the modeling of isotropic behavior. The best compromise between model accuracy and numerical cost is obtained with fourteen orientations. The deviations from isotropy are acceptable in all loading directions. Different levels of hardening in orthogonal loading: simple shear followed by simple tension, are achieved without any modification of the model equations. Only the parameter calibration has to be performed with different hardening levels in the database. FE calculations of a deep drawing test have been performed. The CPU time of the polycrystalline model is only five times larger than that with the simple von Mises model. The CPU time with texture evolution is further increased by a factor of two. The effects of texture evolution in rolling of the initially isotropic fcc material have been investigated. The resulting texture and hardening are qualitatively good.

Modeling of work hardening behaviour of high Mn and low C polycristalline austenitic steel with twip effect

The steel of this work, 0.06C-25Mn-3Al-2Si-1Ni steel, presenting TWIP effect, was hot and cold rolled and then annealed at temperatures between 600 and 850ºC. The microstructure examination was focused in the recrystallization during annealing for different temperatures through optical and scanning electron microscopy. The volume fraction and recrystallized grain size measurements were performed. Tensile tests were conducted at room temperature. A polycrystalline model, based on micromechanics and working hardening theory, developed by Bouaziz et al., to predict the behavior of TWIP steels under different loading paths, was applied to the current steel. The results from the model are in good agreement with mechanical test and show a total elongation above 60%, uniform elongation up to 55% and a tensile strength greater than 600 MPa, which highlights the potential of this steel for its various applications, mainly automotive industry. The model parameters are discussed and their limitations are presented.

906 形状記憶合金における変形および形状回復の分子動力学解析(OS9-2 形状記憶材料の特性と応用)

Molecular dynamics simulations are carried out to clarify the mechanism of the deformation and shape- recovery in a shape memory alloys. An embedded-atom-method (EAM) potential for Ni-Al alloy are applied, and a series of thermo-mechanical condition, consisting of loading by an external shear force, unloading, heating and cooling processes, are imposed. Consequently, the shape memory behavior associated with deformation and phase transformation is successfully demonstrated. As an example of the simulation, a result obtained for a polycrystalline model is demonstrated in this paper, while various arrangement of crystal grains have been investigated. The resultant stress-strain curve showing a hysteresis loop is also exhibited, and the future study is noted as the concluding remarks.

A Polycrystalline Approach to the Cyclic Behaviour of f.c.c. Alloys – Intra‐Granular Heterogeneity

AbstractFor several decades, the plastic deformation mechanisms of f.c.c. metals under cyclic loading have received considerable attention. The extensive work on this subject has gradually lead to the identification of the physical processes to be included in a formal scheme of fatigue behavior. Accordingly, we propose a review of the physical mechanisms of plastic deformation in f.c.c. metals and alloys to define the state‐of‐the‐art and motivate future studies. The aim is to demonstrate the importance of a good knowledge of the heterogeneous nature of deformation at the intra‐granular scale in defining a physical model of cyclic behavior. A large characterization of the different stages associated with the evolution of heterogeneous dislocation structures during tensile and cyclic loadings is given for an austenitic stainless steel AISI 316L. A unified view of these various structures is proposed in the form of a modified Pedersen's map [εmax = f(εpcum), where εmax is the maximum plastic strain and εpcum the cumulative plastic strain] in the case of tensile loading and different kinds of cyclic loading: uni‐axial and multi‐axial tests under stress or strain amplitude control. The specificities of each domain defined in the map are discussed in terms of long‐range internal stresses in order to formalize, in a simple composite scheme, the intra‐granular stress–strain field. The importance of taking into account this scheme and the nature of the different dislocations populations in a polycrystalline model is illustrated.

Angular Distribution of Slip Steps by Three-Dimensional Polycrystalline Model for Stainless Steel

Localized deformation plays an important role in the initiation of irradiation-assisted stress corrosion cracking, and it can be characterized by the spacing and inclination of slip steps observed on the surface. In order to examine the contribution of mechanical factors (stress) to slipping, the angular distribution of slip steps was evaluated by using a three-dimensional polycrystalline model generated by Voronoi tessellation. An elastic finite element analysis was performed to derive the resolved shear stress (RSS) acting on each slip system. Random crystallographic orientations assigned to each grain caused the microstructural inhomogeneity of local stress due to anisotropic elastic properties. The angular distribution obtained was compared with the experimental results observed in irradiated and deformed stainless steel. It was shown that mechanical factors dominate the slipping behavior of the irradiated stainless steel and that not only RSS but also normal stress acting on the slip plane affects the crystallographic slip. The angular distribution was also evaluated from the maximum Schmid factor of individual grains, in which the inhomogeneous local stress was not taken into account. The angular distributions obtained using RSS and the Schmid factor were almost the same. This suggests that the inhomogeneity of local stress negligibly affects the angular distribution of slip steps, although the change in the local stress in the polycrystalline material is significant.

Three scale modeling of the behavior of a 16MND5-A508 bainitic steel: Stress distribution at low temperatures

An original approach is proposed to predict the behavior of the 16MND5 bainitic steel (similar to U.S. A508 cl.3) in the lower range of the ductile-to-brittle transition region and at lower temperatures [−196 °C; 20 °C], by developing a new polycrystalline modeling concurrently with X-ray diffraction (XRD) analysis. A two-level homogenization is used to take into account each kind of heterogeneity as well as the phase and grain interactions. A Mori–Tanaka formulation first enables to describe the elastoplastic behavior of a bainitic single crystal (modeled as a single crystal ferritic matrix reinforced by cementite inclusions), while the transition to polycrystal is achieved by a self-consistent approach. This model can simulate in particular the effects of temperature. It reproduces qualitatively the stress distribution in the material (stress states are lower in ferrite than in the bulk material due to cementite particles, the difference never exceeding 150 MPa), the intergranular strain heterogeneity (ripples observed on the ɛ ϕψ = f(sin 2 ψ) curve) and the pole figures determined by XRD on different scales. The proposed approach is validated here on the macroscopic, phase and intraphase scale.

A novel approach for modeling of anisotropic hardening and non proportional loading paths, application to finite element analysis of deep drawing

The modeling of deviations from isotropic hardening is still a difficult task for macroscopic models, in particular for non-proportional loading paths. The alternative polycrystalline models suffer from large CPU time in FE analyses. Due to a specific parameter calibration procedure, a "reduced texture" polycrystalline model with only 8 orientations is in excellent agreement with all experimental curves for a 2090-T3 aluminum sheet. In order to validate the methodology and to evaluate its performance, FE calculations of a deep drawing test have been performed. The CPU time based on the present study is only twice larger than the one with an advanced macroscopic model. The calculated cup heights with six ears are in good agreement with the experimental measurements.