An elastoplastic three-dimensional homogenization model for particle reinforced composites (original) (raw)
Related papers
Particle shape influence on elastic-plastic behaviour of particle-reinforced composites
Archives of materials science and engineering, 2014
Particle-reinforced composite materials very often provide unique and versatile properties. Modelling and prediction of effective heterogeneous material behaviour is a complex problem. However it is possible to estimate an influence of microstructure properties on effective macro material properties. Mentioned multi-scale approach can lead to better understanding of particle-reinforced composite behaviour. The paper is focused on prediction of an influence of particle shape on effective elastic properties, yield stress and stress distribution in particle-reinforced metal matrix composites. Design/methodology/approach: This research is based on usage of homogenization procedure connected with volume averaging of stress and strain values in RVE (Representative Volume Element). To create the RVE geometry Digimat-FE software is applied. Finite element method is applied to solve boundary value problem, in particular a commercial MSC.Marc software is used. Findings: Cylindrical particles provide the highest stiffness and yield stress while the lowest values of stiffness and yield stress are connected with spherical particles. On the other hand stress distribution in spherical particles is more uniform than in cylindrical and prismatic ones, which are more prone to an occurrence of stress concentration. Research limitations/implications: During this study simple, idealised geometries of the inclusions are considered, in particular sphere, prism and cylinder ones. Moreover, uniform size and uniform spatial distribution of the inclusions are taken into account. However in further work presented methodology can be applied to analysis of RVE that maps the real microstructure. Practical implications: Presented methodology can deal with an analysis of composite material with any inclusion shape. Predicting an effective composite material properties by analysis of material properties at microstructure level leads to better understanding and control of particle-reinforced composite materials behaviour. Originality/value: The paper in details presents in details an investigation of influence of inclusion shape on effective elastic-plastic material properties. In addition it describes the differences between stress distributions in composites with various inclusion shapes.
Prediction of Elastic Parameters of Particle Reinforced Composites Using Finite Element Simulations
Materials Research
The macroscopic properties of composite materials depend on the microscopic properties of the constituents and the geometric arrangement of their phases. Therefore, it is essential to predict heterogeneous materials' mechanical properties by simulating microstructural finite element models. The present article aims to analyze particle reinforced composites composed of spherical alumina inclusions surrounded by a glass matrix using a tridimensional representative volume element. Herein, microstructures are artificially created considering a regular or random arrangement of the inclusions. Two materials systems previously studied in the literature were analyzed. The discretization of the models was performed to have periodic mesh, thus enabling the use of periodic boundary conditions. A finite element model is created using Abaqus software. Numerical results show that the macroscopic properties can be estimated with high accuracy for the temperature where linear matrix behavior stands. The predictions were compared to experimental data from the literature. The models with a regular arrangement of inclusions show a difference inferior to 10%, while random arrangements show a difference inferior to 3.9%. The developed numerical algorithms can be modified to include new features, such as other dispersed phase arrangements or nonlinear material behavior.
Acta Materialia, 2009
We present an enhanced continuum model for the size-dependent strengthening and failure of particle-reinforced composites. The model accounts explicitly for the enhanced strength in a discretely defined "punched zone" around the particle in a metal matrix composite as a result of geometrically necessary dislocations developed through a mismatch in the coefficients of thermal expansion. We incorporate the punched zone explicitly through a unit-cell model within this work, but the approach can be used more generally to account for discrete particle distributions and particle shapes. Smaller particles lead to greater strengthening, and this size effect is larger for larger volume fractions. An equation for the coupling of the size-dependent increase of yield strength of metal matrix composites with the particle volume fraction is obtained. The results indicate that the punched zone effect may amplify the occurrence of a variety of failure modes such as matrix localization, particle fracture and/or particle-matrix interface failure; smaller particles perceive higher stresses. We account for interface failure through a cohesive approach, and show that the interface damage mechanism is also particle-sizedependent. Some implications are presented for microstructural design of metal matrix composites.
International Journal of Engineering Science, 2012
A systematic comparison of inhomogeneity shape effects on the linear elastic, thermoelastic and thermal conduction responses of particle reinforced composites is carried out. For this purpose, multi-particle unit cells that contain randomly positioned and, where applicable, oriented, identical particles having the shapes of spheres, regular octahedra, cubes or regular tetrahedra, respectively, and a volume fraction of 20% are employed. The macroscopic moduli and microscopic responses, such as phase averages, as well as phase-level standard deviations and distribution functions of the microfields are evaluated and compared to analytical estimates. The results indicate the presence of relatively small but consistent effects of the particle shape on the effective behavior of particulate composites. Effects on the microscopic stress and flux fields are predicted to be more pronounced.
A Micropolar Homogenization Approach for Random Particle-Based Composites
2016
This study presents a multiscale procedure for determining the size of the Representative Volume Element (RVE) and the homogenized moduli of particle-based composite materials, modeled as micropolar continua. The homogenization, consistent with a generalized Hill-Mandel condition, is adopted in conjunction with a statistical procedure, by which two hierarchies of scale-dependent bounds on classical and micropolar constitutive moduli are obtained using Dirichlet and Neumann BCs. Two different types of inclusion, either stiffer or softer than the matrix, are considered in the numerical applications. The results highlight the importance of accounting for micropolar bending deformation modes, spatial randomness of the medium, and presence of inclusions crossing the edges of the test window used in the homogenization. Sommario. Questo studio presenta una procedura multiscala per la determinazione della dimensione dell’Elemento di Volume Rappresentativo e dei moduli omogeneizzati di mater...
Materials Science and Engineering: A, 1999
In this first of a two part sequence of papers, 3-D microstructures of Si particle reinforced aluminum matrix composites are computationally constructed by assembling digitally acquired micrographs obtained by serial sectioning. The material samples considered vary in volume fraction and in particle size. Furthermore, equivalent microstructures with actual particles replaced by ellipses (in 2-D) or ellipsoids (in 3-D) are computationally simulated for efficiency. The equivalent microstructures are tessellated by a particle surface based algorithm into a mesh of Voronoi cells. Various 3-D characterization functions are developed to identify particle size, shape, orientation and spatial distribution in the actual materials and to compare with 2-D micrographs. Through this analysis, differences between 2-and 3-D characterization are established. Results indicate that it may not be sufficient to use 2-D section information for characterizing detailed microstructural features like particle shapes, orientations and near-neighbor distances. The second part of this sequence of papers will describe the important relationship of these features to damage evolution in these same materials. This sequence of papers is perhaps one of the first on 3-D physical characterization of the phase and damage structure for this class of materials.
A three-dimensional realistic microstructure model of particle-reinforced metal matrix composites
Modelling and Simulation in Materials Science and Engineering, 2014
A new and robust methodology is presented for the complete computer simulation of large three-dimensional (3D) microstructures of particlereinforced metal matrix composites (PRMMCs), by integrating the boundary representation scheme, the random cutting algorithm and the random sequential adsorption algorithm. The methodology allows large realistic 3D microstructure models to be generated that can be used for multi-scale investigation of PRMMC structure and design. The effect of the simulation parameters on the simulated microstructure is investigated by applying a quantitative metallographic analysis of the distribution functions of aspect ratio, diameter and the area of reinforcements. Simulated large realistic homogenous 3D microstructures of PRMMC are in close agreement with the experimental microstructures.
European Journal of Mechanics - A/Solids, 2012
In many applications elastoplastic composites are used in limited amounts, therefore it is important to have estimates of the size of their representative volume element both for modeling and experimental purposes. In this work the tensile response of particle reinforced random composites is simulated by microstructural finite element models. Several microstructural realizations are considered for each composition and volume, and the scatter in the response is used as representativeness metric. The microstructural morphology is characterized using methods and statistical descriptors that can be employed with micrographs of real materials. Numerical results show that the representative volume element dimensions can be estimated by verifying either the consistency of the stressestrain curve for single microstructural realizations and increasing material volume sizes or the convergence of the response of several microstructural realizations at the same material volume size. The analysis of the stressestrain state at the microstructural level shows that the plastic strain and the hydrostatic pressure in the matrix material depend hyperbolically on the interparticle distance. Microstructural analyses show that the matrix coarseness is correlated to the scatter in the mechanical response and therefore can be used to have approximate estimates of the representative volume element size.