Model Of Polycrystalline Material Research Articles

Influence of textural variability on plastic response of porous crystal embedded in polycrystalline aggregate: A crystal plasticity study

Damage evolution in polycrystalline aggregates is complicated by the intricate interplay of crystallographic orientation of the porous grain and the surrounding anisotropic matrix. Therefore, formulation of design rules and damage models for polycrystalline materials proves daunting due to relative lack of thorough understanding of the underlying heterogeneity at the mesoscale. This work explores the orientation dependent void growth in a porous crystal embedded in an anisotropic polycrystalline matrix with different initial textures. Polycrystalline face-centered cubic based aggregate is simulated within the framework of crystal plasticity finite element method. Porosity is first modeled in the form of a single pre-existing spherical void in the central grain of the randomly oriented polycrystal. One-hundred crystallographic orientations of the central grain in three-dimensional Euler space are analyzed to reveal the orientation dependent trends of the porous grain. To account for textural variability, the analysis is repeated for polycrystals exhibiting preferred textures like Cube, Brass, Copper and Goss. In this manner, interesting orientation dependent trends in basic tenets of void growth like yield strength, coalescence strain and porosity evolution are unraveled across various polycrystalline textures. To account for spatial heterogeneity as well, porosity in the central grain is then re-distributed and the aforementioned analysis is repeated for all the crystallographic orientations of the central grain embedded in polycrystals with different textures. Owing to the large amount of data thus generated, statistical analysis is invoked to identify stimulating trends and key statistical variables governing the strength and toughness. Consequently, a statistical void growth model is also presented by assessing the CP simulation results and identifying suitable distribution function governing the growth of voids in polycrystals. The modeling framework is expected to inform porous plasticity models aimed at capturing damage evolution in porous grains embedded in polycrystalline materials exhibiting topological and crystallographic anisotropy.

Phase-field modeling of anisotropic crack propagation based on higher-order nonlocal operator theory

This paper presents a novel higher-order nonlocal operator theory for the phase-field modeling of brittle fracture in anisotropic materials. Incorporating higher order nonlocal operators can enhance the accuracy of the phase-field model by effectively capturing long-range interactions that hold significance in numerous materials. The reproducing kernel particle method is employed to derive a nonlocal differential operator to enhance computational stability and accuracy. Moreover, the proposed method eliminates the need for direct computation of derivatives of the modified kernel function, which avoids the calculation of moment matrix derivatives and improves computational efficiency. The phase-field modeling of polycrystalline materials, considering the anisotropic fracture resistance of each grain, is implemented using this numerical framework. The present method is able to capture different scenarios intergranular and transgranular crack propagation patterns in polycrystalline materials. The proposed method involves a detailed representation of the complex process of crack initiation and propagation in 2D and 3D models of polycrystalline materials.

The Influence of Materials Structure on the Main Features of the Fracture Process in Rocks: Discrete Elements Method and Laboratory Experiment

A computer model of fracture of the heterogeneous materials (including rocks) based on the Discrete Element Method (DEM) is proposed. We used the bonded particle model (BPM), various modifications of which are widely used in the study the fracture process. The material is modeled by a set of spherical particles (simulating polycrystalline grains) connected by bonds placed at the points of particle contacts (simulating grain boundaries). In BPM model, the initiation of cracks was determined by the bonds breakage, and their propagation is provided by the coalescence of many broken bonds. Computer experiments were carried out for the materials with different features (various grain mechanical properties and sizes, various mechanical properties of the grain boundaries), in order to find out the influence of these parameters on local stresses and the defect formation. Calculations were held in the MUSEN software. Cylindrical samples were filled with spherical particles of the same or different radii. The parameters of materials for grains and bonds (grain boundaries) were taken corresponding to granite, quartz, orthoclase, oligoclase, and glass. The sample was placed in a virtual press, in which the lower plate was stationary, and the upper plate moved towards the lower one at a constant velocity until the sample was destroyed. The calculation of the maximum local stresses showed that the homogeneity of material leads to greater space heterogeneity of local stresses and vice versa, heterogeneity contributes to their greater uniformity. Comparison with the results of laboratory experiments on rock deformation showed that the proposed model of polycrystalline materials realistically describes some features of their destruction when the main processes occur along the grain boundaries. These features include the brittle nature of homogeneous materials fracture and the presence of nonlinear elasticity (plasticity) for ones that were more heterogeneous. For heterogeneous materials, the model demonstrates a two-stage character of fracture process, when at the first stage the accumulation of defects occurs uniformly over the sample, and at the second stage – the formation and growth of the fracture site.

Generating polycrystalline microstructures with prescribed tensorial texture coefficients

This work is concerned with synthetic microstructure models of polycrystalline materials. Once a representation of the microstructure is generated, the individual grains need to be furnished with suitable crystal orientations, matching a specific crystal orientation distribution. We introduce a novel method for this task, which permits to prescribe the orientations based on tensorial Fourier coefficients. This compact representation gives rise to the texture coefficient optimization for prescribing orientations method, enabling the determination of representative orientations for digital polycrystalline microstructures. We compare the proposed method to established and dedicated algorithms in terms of the linear elastic as well as the non-linear plastic behavior of a polycrystalline material.

Void growth based inter-granular ductile fracture in strain gradient polycrystalline plasticity

The precipitation hardened, high strength aerospace alloys (e.g. Al 7000 alloy series) suffer from loss of fracture toughness due to the heat treatment leading to intergranular ductile fracture. Depending on the quenching and aging processes, large precipitates at the grain boundaries with wide precipitate free zones might develop. Therefore the grain boundaries constitute a potential location for micro void formation and evolution under the effect of external loads. This is a common problem of such materials where there is considerable ductile intergranular fracture, which is normally attributed to the embrittlement effects of the environment in other type of alloys. In this context, for the modeling of such a degradation process, the current paper develops a physics based intergranular cracking model of polycrystalline materials where a strain gradient crystal plasticity model is combined with cohesive zone elements whose traction separation relation is based on the evolution of micro-voids at the grain boundaries. The framework successfully predicts the intergranular crack formation and propagation, taking into account different microstructural features, such as porosity, pore shape, grain orientation distribution, and grain boundary conditions.

Integrated Physical-Constitutive Computational Framework for Plastic Deformation Modeling

An integrated framework for deformation modeling has been developed, which combines a physical state parameter-based formulation for microstructure evolution during plastic deformation processes with constitutive creep models of polycrystalline materials. The implementations of power law, Coble, Nabarro–Herring and Harper–Dorn creep and grain boundary sliding are described and their contributions to the entire stress response at a virtual applied strain rate are discussed. The present framework simultaneously allows calculating the plastic deformation under prescribed strain rate or constant stress, as well as stress relaxation after preceding stress or strain loading. The framework is successfully applied for the construction of deformation mechanism maps.

A pseudorandom based crystal plasticity finite element method for grain scale polycrystalline material modeling

Recently, the grain scale modeling has gained much attention in the area of properties characterization, processing and application for polycrystalline materials at micro-nanometer level. In order to develop the high-quality grain scale representative volume element (RVE) models for polycrystalline materials, this paper proposes a pseudorandom based crystal plasticity finite element (CPFE) modeling method, which can take full advantage of true grain scale information and generate pseudorandom grains. Further, the uniaxial tension experiments, EBSD copying modeling method and Voronoi modeling method, were used to validate the proposed pseudorandom based CPFE modeling method. Results show that the Pseudorandom model is better than existing advanced grain scale RVE models in terms of simulation efficiency, representativeness, strain rate stability, mesh density stability and truth proximity. In the end, this research provides a better grain scale RVE modeling method and can promote the progress of material characterization, processing and application for polycrystalline materials at micro-nanometer scale.

A Crystal-Plasticity Cyclic Constitutive Model for the Ratchetting of Polycrystalline Material Considering Dislocation Substructures

A crystal-plasticity cyclic constitutive model of polycrystalline material considering intra-granular heterogeneous dislocation substructures, in terms of three dislocation categories: mobile dislocations, immobile dislocations in the cell interiors and in the cell walls, is proposed based on the existing microscopic and macroscopic experimental results. The multiplication, annihilation, rearrangement and immobilization of dislocations on each slip system are taken as the basic evolutionary mechanism of the three dislocation categories, and the cross-slip of screw dislocations is viewed as the dynamic recovery mechanism at room temperature. The slip resistance associated with the isotropic hardening rule results from the interactions of dislocations on the slip systems. Meanwhile, a modified nonlinear kinematic hardening rule and a rate-dependent flow rule at the slip system level are employed to improve the predictive capability of the model for ratchetting deformation. The predictive ability of the developed model to uniaxial and multiaxial ratchetting in macroscopic scale is verified by comparing with the experimental results of polycrystalline 316L stainless steel. The ratchetting in intra-granular scale which is obviously dependent on the crystallographic orientation and stress levels can be reasonably predicted by the proposed model.

Application of Ultrasonic Inspection for Microstructure Analysis of Stainless Steel Grade 304L

Ultrasonic inspection is one of the most widely used non-destructive testing methods for inspection of fabricated structures and components. During ultrasonic inspection, mechanical waves in form of ultrasound are transmitted and propagate through volume of parts or components and reflect when the waves meet with the existing interface such as flaws in the welds. In addition to detection of flaws or defects within the structures, ultrasonic inspection is also used for determination of component thickness as well as characterization of microstructure of different materials. As the ultrasound is transmitted through media, the loss of ultrasound amplitude is referred to as acoustic attenuation. This attenuation effects greatly result from heterogeneity, anisotropy, and different grain sizes of crystalline media the ultrasound goes through. In order to develop the ultrasonic backscattering models for polycrystalline materials, experimental results of the correlation between the changes in attenuation coefficient and the actual microstructure of polycrystalline materials are necessary. This research article presents the preliminary results of this correlation study in stainless steel 304L specimens in as-received conditions compared with different annealed and heat-treated conditions. Such correlations of attenuation coefficient, hardness, and grain size will be used as baseline for future additional characterization technique such as electron backscattered diffraction to better understand the attenuation effects for textured polycrystalline materials.

Multiscale finite element based trans-scale calculation method for polycrystalline materials

In the present paper a multiscale finite element based trans-scale calculation method for polycrystalline materials is proposed to investigate the interaction between mechanical properties at macro and meso scale. The model analyzes the interaction between macro-scale factors such as structure and loads, and meso-scale factors such as geometry, distribution and orientation of polycrystal. Multiscale finite element was created by user subroutines of the ABAQUS. Also Voronoi diagram based polycrystalline finite element was realized by MATLAB. The polycrystalline finite element and the conventional finite element were connected using the multiscale finite element. The mesh independency and convergence of the model were investigated with perforated plate, and the correctness and feasibility of the model were verified with a laser repaired compact tensile specimen. The number of degrees of freedom of multiscale finite element based trans-scale calculation model for polycrystalline materials is much smaller than that of the model with the fine-scale elements, but the reduction in calculation accuracy is negligible. The model can be used to study the mechanical behavior of heterogenous materials simultaneously by combining meso-scale and macro-scale with a smaller amount of computation.

Niobium and zinc doped titanium-tin-oxide solid-solution ceramics: Synthesis, structure and electrical characterization

This paper describes the processing, microstructure, optical and electrical properties of the nanocrystalline (NC) niobium and zinc doped titanium-tin-oxide (TTO:NZ) based ceramics. Variety of techniques was employed (X-ray diffraction, scanning electron microscopy, energy dispersive, Raman and impedance spectroscopy) in the characterization of the obtained TTO:NZ, which confirmed the formation of NC solid-solution matrix with Ti0.8Sn0.2O2 composition. A specific highly dense (approximately 97% of the theoretical density was reached) varistor like microstructure (matrix metal-oxide grains surrounded by the grain-boundary regions) and accordingly resembling electrical properties (breakdown electric field of approximately 130 V/mm and nonlinearity coefficient of α ≈ 6.5) were achieved through double cation doping and elected condition of the mechanochemical solid-state synthesis. Impedance response analysis of TTO:NZ ceramics by means of an equivalent electrical circuit based on the brick-layer model for polycrystalline materials revealed the presence of two temperature dependent electrical relaxation phenomena of the non-Debye type as well as the negative temperature coefficient of resistance behavior.

On the symmetry identification for the multi-level models of polycrystalline materials

An approach to identify the elastic symmetry of anisotropic materials is considered and applied together with the multi-level constitutive models of polycrystals. By using the two-level model of elasto-visco-plasticity, the changes in the symmetry of the elasticity tensor for the representative volume element of a polycrystalline copper during inelastic deformation are studied. The two-link strain trajectories of the “simple shear – simple shear” type are analyzed and the problem of the compatibility of the properties under investigation with any symmetry classes is formulated and solved at various deformation stages.

Multilevel model of polycrystalline materials: grain boundary sliding description

Material behavior description in a wide range of thermomechanical effects is one of the topical areas in mathematical modeling. Inclusion of grain boundary sliding as an important mechanism of polycrystalline material deformation at elevated temperatures and predominant deformation mechanism of metals and alloys in structural superplasticity allows to simulate various deformation regimes and their transitions (including superplasticity regime with switch-on and switch-off regimes). The paper is devoted to description of grain boundary sliding in structure of two-level model, based on crystal plasticity, and relations for determination the contribution of this mechanism to inelastic deformation. Some results are presented concerning computational experiments of polycrystalline representative volume deformation using developed model.

A 3D finite element modelling of crystalline anisotropy in rolling contact fatigue

Rolling contact fatigue (RCF) is one of the primary modes of failure in bearings and in this study it is hypothesized and demonstrated that RCF is strongly influenced by inhomogeneity in polycrystalline material microstructure. This paper presents a three-dimensional modeling approach to include the effects of microstructure topology and material anisotropy in a polycrystalline microstructural bearing steel subject to RCF loading. A randomly generated 3D Voronoi tessellation is used to represent the microstructural topology of the material. A cubic material definition with random spatial orientation is specified for the material grains to simulate the polycrystalline anisotropy. The size of the RVE was chosen such that it represented the macroscopic linear elastic material properties of a polycrystalline aggregate. The semi-infinite domain is then subjected to a moving Hertzian pressure to simulate a load cycle. Due to inhomogeneity in the polycrystalline material local stress risers occur at the grain boundaries, however, in general, the locations of the maximum shear stresses compare well to the experimental RCF results readily available in literature. Elemental shear stresses averaging scheme was employed to illustrate that the finite element model is mesh independent. The estimated fatigue life scatter obtained from the inhomogeneous polycrystalline material model corroborates well with the fatigue life scatter obtained from the RCF experiments.

Fully scalable implementation of a volume coupling scheme for the modeling of multiscale materials

We present in this paper a new implementation of a multi-scale, multi-model coupling algorithm, with a proposed parallelization scheme for the construction of the coupling terms between the models. This allows one to study such problems with a fully scalable algorithm on large computer clusters, even when the models and/or the coupling have a high number of degrees of freedom. As an application example, we will consider a system composed by an homogeneous, macroscopic Elastic model and an anisotropic polycrystalline material model, with a volume coupling based on the Arlequin framework.

Diffuse-interface polycrystal plasticity: expressing grain boundaries as geometrically necessary dislocations

The standard way of modeling plasticity in polycrystals is by using the crystal plasticity model for single crystals in each grain, and imposing suitable traction and slip boundary conditions across grain boundaries. In this fashion, the system is modeled as a collection of boundary-value problems with matching boundary conditions. In this paper, we develop a diffuse-interface crystal plasticity model for polycrystalline materials that results in a single boundary-value problem with a single crystal as the reference configuration. Using a multiplicative decomposition of the deformation gradient into lattice and plastic parts, i.e. F(X,t)=FL(X,t)FP(X,t), an initial stress-free polycrystal is constructed by imposing FL to be a piecewise constant rotation field R0(X), and FP=R0(X)T, thereby having F(X,0)=I, and zero elastic strain. This model serves as a precursor to higher order crystal plasticity models with grain boundary energy and evolution.

Structural, optical, and electrical properties of Cu2SnS3 thin films produced by sol gel method

The structural, optical, and electrical properties of p-type Cu2SnS3 thin films produced by the deposition of a dimethylsulfoxide-based sol gel solution using the centrifugation on substrates with subsequent heat treatment of the layers formed have been studied. The conditions of formation of the films using low-temperature short-time treatments in open atmosphere and a final annealing in a low vacuum (0.1 Pa) have been analyzed. The crystallite sizes D ~ 42 nm in the polycrystalline films have been found using X-ray phase analysis. Their compositions have been confirmed using the Raman spectra and the energy-dispersive X-ray analysis. The optical forbidden band width of direct allowed (E g d ~ 1.25 eV) and direct forbidden (E g df ≈ 0.95 eV) optical transitions have been determined as a result of the light transmission and absorption. Based on the study of the electrical properties using a model of polycrystalline materials, the validity of the produced films with resistivity ρ ≈ 0.21 Ω cm, the hole concentration p 0 ≈ 1.75 × 1019 cm–3, and the effective mobility μ p ≈ 1.67 cm2/(V s) for manufacturing solar cells.

Shear anisotropy: Tuning high temperature metal hexaborides from soft to extremely hard

Easy machining into sharp lending edge, nose tip and complex shape components plays a pivotal role in the application of ultrahigh temperature ceramics in hypersonic vehicles, wherein low and controllable hardness is a necessary parameter to ensure the easy machinability. However, the mechanism that driving the hardness of metal hexaborides is not clear. Here, using a combination of the empirical hardness model for polycrystalline materials and density functional theory investigation, the hardness dependence on shear anisotropic factors of high temperature metal hexaborides has been established. It has come to light that through controlling the shear anisotropic factors the hardness of polycrystalline metal hexaborides can be tailored from soft and ductile to extremely hard and brittle, which is underpinned by the degree of chemical bonding anisotropy, i.e., the difference of B-B bond within the B6 octahedron and that connecting the B6 octahedra.

Optical properties and mechanisms of current flow in Cu2ZnSnS4 films prepared by spray pyrolysis

Thin films Cu2ZnSnS4 (up to 0.9 μm thick) with p-type conductivity and band gap Eg = 1.54 eV have been prepared by the spray pyrolysis of 0.1 M aqueous solutions of the salts CuCl2 · 2H2O, ZnCl2 · 2H2O, SnCl4 · 5H2O, and (NH2)2CS at a temperature TS = 290°C. The electrophysical properties of the films have been analyzed using the model for polycrystalline materials with electrically active grain boundaries. The energy and geometric parameters of the grain boundaries have been determined as follows: the height of the barriers is Eb ≈ 0.045–0.048 eV, and the thickness of the depletion region is δ ≈ 3.25 nm. The effective concentrations of charge carriers p0 = 3.16 × 1018 cm–3 and their mobilities in crystallites μp = 85 cm2/(V s) have been found using the technique for determining the kinetic parameters from the absorption spectra of thin films at a photon energy hν ≈ Eg. The density of states at grain boundaries Nt = 9.57 × 1011 cm–2 has been estimated.

Magnetic hysteresis at the domain scale of a multi-scale material model for magneto-elastic behaviour

This paper proposes a multi-scale energy-based material model for poly-crystalline materials. Describing the behaviour of poly-crystalline materials at three spatial scales of dominating physical mechanisms allows accounting for the heterogeneity and multi-axiality of the material behaviour. The three spatial scales are the poly-crystalline, grain and domain scale. Together with appropriate scale transitions rules and models for local magnetic behaviour at each scale, the model is able to describe the magneto-elastic behaviour (magnetostriction and hysteresis) at the macroscale, although the data input is merely based on a set of physical constants. Introducing a new energy density function that describes the demagnetisation field, the anhysteretic multi-scale energy-based material model is extended to the hysteretic case. The hysteresis behaviour is included at the domain scale according to the micro-magnetic domain theory while preserving a valid description for the magneto-elastic coupling. The model is verified using existing measurement data for different mechanical stress levels.