COMPUTATIONAL HOMOGENIZATION OF POLYCRYSTALLINE MATERIALS WITH PORES: A THREE-DIMENSIONAL GRAIN BOUNDARY FORMULATION

2012 ◽  
Vol 04 (03) ◽  
pp. 1250012 ◽  
Author(s):  
F. TRENTACOSTE ◽  
I. BENEDETTI ◽  
M. H. ALIABADI
Keyword(s):  
Grain Boundary ◽  
Mechanical Model ◽  
Volume Fraction ◽  
Effective Properties ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Elastic Problem ◽  
Polycrystalline Materials ◽  
Effective Material Properties ◽  
Boundary Integral Representation

In this study, the influence of porosity on the elastic effective properties of polycrystalline materials is investigated using a 3D grain boundary micro mechanical model. The volume fraction of pores, their size and distribution can be varied to better simulate the response of real porous materials. The formulation is built on a boundary integral representation of the elastic problem for the grains, which are modeled as 3D linearly elastic orthotropic domains with arbitrary spatial orientation. The artificial polycrystalline morphology is represented using 3D Voronoi Tessellations. The formulation is expressed in terms of intergranular fields, namely displacements and tractions that play an important role in polycrystalline micromechanics. The continuity of the aggregate is enforced through suitable intergranular conditions. The effective material properties are obtained through material homogenization, computing the volume averages of micro-strains and stresses and taking the ensemble average over a certain number of microstructural samples. The obtained results show the capability of the model to assess the macroscopic effects of porosity.

A Novel Micro-Mechanical Model for Polycrystalline Inter-Granular and Trans-Granular Fracture

2017 ◽  
Vol 754 ◽  
pp. 177-180
Author(s):  
Vincenzo Gulizzi ◽  
Chris H. Rycroft ◽  
Ivano Benedetti
Keyword(s):  
Grain Boundary ◽  
Grain Boundaries ◽  
Integral Equations ◽  
Crystallographic Orientation ◽  
Mechanical Model ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Polycrystalline Materials ◽  
Fracture Mechanisms ◽  
Cohesive Laws

In this work, a novel grain boundary formulation for inter-and trans-granular cracking of polycrystalline materials is presented. The formulation is based on the use of boundary integral equations for anisotropic solids and has the advantage of expressing the considered problem in terms of grain boundary variables only. Inter-granular cracking occurs at the grain boundaries whereas trans-granular cracking is assumed to take place along specific cleavage planes, whose orientation depends on the crystallographic orientation of the grains. The evolution of inter-and trans-granular cracks is then governed by suitably defined cohesive laws, whose parameters characterize the behavior of the two fracture mechanisms. The results show that the model is able to capture the competition between inter-and trans-granular cracking.

Effective Thermal Conductivity of Lithium Ion Battery Electrodes Employing Fully Resolved Simulations for Use in Volume Averaged Models

2013 ◽  
Author(s):  
Ajay Vadakkepatt ◽  
Bradley L. Trembacki ◽  
Sanjay R. Mathur ◽  
Jayathi Y. Murthy
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Volume Fraction ◽  
Effective Properties ◽  
Three Dimensional ◽  
Lithium Ion ◽  
Volume Averaging ◽  
Porous Electrodes ◽  
Multiphase Materials ◽  
Averaged Models

Simulations of lithium ion batteries on a cell level are usually performed with volume averaging methods that employ effective transport properties. Bruggeman’s model, which is widely used to determine these effective properties, is solely based on the volume fraction of these porous electrodes. However, other factors like the topology and microstructure of electrodes also play a crucial role in determining effective properties. In this paper, a general derivation of the effective thermal conductivity of multiphase materials, which can be correlated with these factors, is derived using the volume averaging technique. For demonstration, three-dimensional microstructures of various porous materials are reconstructed from scanned images. These images are used to generate fully-resolved finite volume meshes representing the various constituents. The resulting mesh is then employed for numerical analysis of thermal transport, results from which are used for correlating the effective thermal conductivity with various parameters describing the microstructure. It is shown that commonly used power law exponents in the Bruggeman model for effective thermal conductivity must be recalibrated to fit the effective thermal conductivity computed from these detailed simulations.

scholarly journals A three-dimensional study of coupled grain boundary motion with junctions

2015 ◽  
Vol 471 (2178) ◽  
pp. 20150127 ◽  
Author(s):  
Anup Basak ◽  
Anurag Gupta
Keyword(s):  
Grain Boundary ◽  
Three Dimensional ◽  
Continuum Theory ◽  
Coupling Factor ◽  
Polycrystalline Materials ◽  
Triple Junctions ◽  
Kinetic Coefficients ◽  
And Migration ◽  
Grain Boundary Motion

A novel continuum theory of incoherent interfaces with triple junctions is applied to study coupled grain boundary (GB) motion in three-dimensional polycrystalline materials. The kinetic relations for grain dynamics, relative sliding and migration of the boundary and junction evolution are developed. In doing so, a vectorial form of the geometrical coupling factor, which relates the tangential motion at the GB to the migration, is also obtained. Diffusion along the GBs and the junctions is allowed so as to prevent nucleation of voids and overlapping of material near the GBs. The coupled dynamics has been studied in detail for two bicrystalline and one tricrystalline arrangements. The first bicrystal consists of two cubic grains separated by a planar GB, whereas the second is composed of a spherical grain embedded inside a larger grain. The tricrystal has an arbitrary-shaped grain embedded inside a much larger bicrystal made of two cubic grains. In all these cases, analytical solutions are obtained wherever possible while emphasizing the role of various kinetic coefficients during the coupled motion.

A Micro-Mechanical Model for Grain-Boundary Cavitation in Polycrystalline Materials

2015 ◽  
Vol 665 ◽  
pp. 65-68
Author(s):  
Vincenzo Gulizzi ◽  
Alberto Milazzo ◽  
Ivano Benedetti
Keyword(s):  
Grain Boundary ◽  
Mechanical Model ◽  
Evolution Equations ◽  
Scale Model ◽  
Polycrystalline Materials ◽  
Statistical Features ◽  
Voronoi Tessellations ◽  
Numerical Tests ◽  
Cohesive Laws ◽  
Polycrystalline Aggregates

In this work, the grain-boundary cavitation in polycrystalline aggregates is investigated by means of a grain-scale model. Polycrystalline aggregates are generated using Voronoi tessellations, which have been extensively shown to retain the statistical features of real microstructures. Nucleation, thickening and sliding of cavities at grain boundaries are represented by specific cohesive laws embodying the damage parameters, whose time evolution equations are coupled to the mechanical model. The formulation is presented within the framework of a grain-boundary formulation, which only requires the discretization of the grain surfaces. Some numerical tests are presented to demonstrate the feasibility of the method.

scholarly journals BEM Solutions of Frequency Domain Gradient Elastodynamic 3-D Porblems

2007 ◽  
Vol 1 (2) ◽  
Author(s):  
D. Polyzos ◽  
K. G. Tsepoura ◽  
D. E. Beskos
Keyword(s):  
Integral Representation ◽  
Frequency Domain ◽  
Three Dimensional ◽  
Normal Derivative ◽  
Solution Procedure ◽  
Boundary Integral ◽  
Material Behavior ◽  
Linear Elastic ◽  
Microstructural Effects ◽  
Boundary Integral Representation

A boundary element methodology is presented for the frequency domain elastodynamic analysis of three-dimensional solids characterized by a linear elastic material behavior coupled with microstructural effects taken into account with the aid of the simple gradient elastic theory of Aifantis. A variational statement is established to determine all possible classical and non-classical (due to gradient terms) boundary conditions of the general boundary value problem. The gradient frequency domain elastodynamic fundamental solution is explicitly derived and used to construct the boundary integral representation of the solution with the aid of a reciprocal integral identity. In addition to a boundary integral representation for the displacement, a boundary integral representation for its normal derivative is also necessary for the complete formulation of a well posed problem. All the kernels in the integral equations are explicitly provided. Surface quadratic quadrilateral boundary elements are employed and the discretization is restricted only to the boundary. The solution procedure is described in detail. A numerical example serves to illustrate the method and demonstrate its accuracy. The present version of the method does not provide explicit expressions for the computation of interior stresses.

Determination of Mechanical and Electrical Damages of Piezoelectric Material with Periodically Distributed Microvoids

2007 ◽  
Vol 23 (3) ◽  
pp. 239-244 ◽  
Author(s):  
X. H. Yang ◽  
G. W. Zeng ◽  
C. Y. Chen
Keyword(s):  
Volume Fraction ◽  
Effective Properties ◽  
Three Dimensional ◽  
Electromechanical Properties ◽  
Dimensional Finite Element ◽  
Microstructure Parameters ◽  
Three Dimensional Finite Element ◽  
The Continuum ◽  
Mechanical And Electrical Damages

AbstractThis paper emphasizes on determining the mechanical and electrical damages of piezoelectric ceramics with periodically distributed ellipsoidal or spherical microvoids. Based on the unit cell method, detailed three-dimensional finite element analyses are carried out to acquire the effective electromechanical properties of voided PZT-7A materials, and then the mechanical and electrical damages are determined through the relations between the damage variables and the effective properties in the continuum piezoelectric damage constitutive theory. The quantitative connections between the damages and microstructure parameters, including the microvoid volume fraction and the microvoid aspect ratio, are analyzed in detail. Some interesting conclusions are obtained.

scholarly journals INVESTIGATION OF THERMAL PERFORMANCE OF AIR TO WATER HEAT EXCHANGER USING NANO-FLUIDS

2011 ◽  
Vol 12 (3) ◽  
Author(s):  
Nawaf Hazim Saeid
Keyword(s):  
Heat Exchanger ◽  
Volume Fraction ◽  
Effective Properties ◽  
Three Dimensional ◽  
Cross Flow ◽  
Nano Particles ◽  
Enhancement Of Heat Transfer ◽  
Nano Powder ◽  
Flow Heat ◽  
Nano Fluids

In the present study the three-dimensional numerical simulation is selected as a tool to investigate the effectiveness of a cross flow heat exchanger. Water is selected to be mixed with nano-particles and flow inside a circular pipe while a pure air is flowing across it. Numerical simulations is carried out under laminar flow for both water and air sides. The thickness of the pipe is neglected in the present preliminary study. From the physics of the problem, the governing parameters can be determined as: the Reynolds, the type and the volume fraction of the nono-fluid. The effect of these governing parameters is studied and the results are presented. The results show significant enhancement of heat transfer with introduction of nano-particles, such as titanium-oxide (TiO2) nano-powder, compared to the pure base fluid. The accuracy of the results presented in the present study depends on the accuracy of the effective properties of the nano-fluids, which are taken from the open literature. ABSTRAK: Dalam kajian ini, simulasi tiga dimensi berangka digunakan untuk mengkaji keberkesanan penukar haba aliran silang.  Air dipilih untuk dicampurkan dengan zarah bersaiz nano dan dialirkan di dalam paip berbentuk bulat, sementara udara tulen mengalir melaluinya.  Simulasi berangka dijalankan di bawah aliran lamina untuk kedua-dua belah air dan udara. Ketebalan paip diabaikan di dalam kajian permulaan ini.  Dari sudut permasalahan fizik, parameter pengawal imbang boleh ditentukan sebagai: nombor Reynolds, jenis dan isipadu pecahan bendalir nano. Kesan parameter pengawal imbang ini dikaji dan keputusannya dibentangkan.  Keputusan menunjukkan peningkatan pemindahan haba yang ketara dengan penggunaan zarah bersaiz nano seperti serbuk titanium oksida (TiO2), berbanding dengan bendalir tulen.  Ketepatan keputusan kajian ini bergantung kepada ketepatan sifat-sifat efektif bendalir nano yang dirujuk daripada sumber maklumat terdahulu.

Boundary Element Crystal Plasticity Method

2017 ◽  
Vol 08 (03n04) ◽  
pp. 1740003
Author(s):  
Ivano Benedetti ◽  
Vincenzo Gulizzi ◽  
Vincenzo Mallardo
Keyword(s):  
Grain Boundary ◽  
Boundary Element ◽  
Crystal Plasticity ◽  
Boundary Integral Equations ◽  
Voronoi Tessellation ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Integral Approach ◽  
Rate Dependent ◽  
Individual Grains

A three-dimensional (3D) boundary element method for small strains crystal plasticity is described. The method, developed for polycrystalline aggregates, makes use of a set of boundary integral equations for modeling the individual grains, which are represented as anisotropic elasto-plastic domains. Crystal plasticity is modeled using an initial strains boundary integral approach. The integration of strongly singular volume integrals in the anisotropic elasto-plastic grain-boundary equations are discussed. Voronoi-tessellation micro-morphologies are discretized using nonstructured boundary and volume meshes. A grain-boundary incremental/iterative algorithm, with rate-dependent flow and hardening rules, is developed and discussed. The method has been assessed through several numerical simulations, which confirm robustness and accuracy.

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