Effective Thermomechanical Properties Research Articles

Effective thermal and mechanical properties of short carbon fiber/natural rubber composites as a function of mechanical loading

Abstract Carbon fibers significantly improve thermal and mechanical properties of nanocomposites, and many researchers have focused their studies on determining the effective thermal and mechanical properties of these composites. Much effort has gone into determining how mechanical loading changes the effective properties of the nanocomposite, and studying its behavior under further mechanical loading. In the present study, a computer simulation of three different volume fractions of carbon fibers in natural rubber was subjected to eight loading scenarios, each, to study the effect of loading conditions on the effective thermomechanical properties of the nanocomposites. Results suggest that mechanical loading can improve the effective thermal conductivity and increase the elastic modulus of the nanocomposite.

Finite element modeling of effective thermomechanical properties of Al–B4C metal matrix composites

The present work aims to investigate the influences of thermal residual stresses and material properties on the thermomechanical deformation behavior of Al–B4C composites. Boron carbide-reinforced aluminum matrix composites having 4, 8, and 12 vol% boron carbide were fabricated using squeeze liquid stir casting method for experimental characterization of their microstructure, effective elastic moduli and effective CTEs at room temperature as well as elevated temperatures. Next, the thermomechanical behavior of fabricated composites was investigated using finite element modeling. The effects of thermal residual stresses on the effective material properties were examined by simulating the cooling process of MMCs from processing temperature to room temperature. The effective elastic moduli and the effective CTEs were predicted considering linear elastic as well as elastoplastic deformation of aluminum matrix, and the results obtained were compared with the experimental values. The effects of voids on effective material behavior are studied by simulating the void growth and nucleation using Gurson–Tvergaard–Needleman model.

Overall thermomechanical properties of layered materials for energy devices applications

This paper is concerned with the analysis of effective thermomechanical properties of multi-layered materials of interest for solid oxide fuel cells (SOFC) and lithium ions batteries fabrication. The recently developed asymptotic homogenization procedure is applied in order to express the overall thermoelastic constants of the first order equivalent continuum in terms of microfluctuations functions, and these functions are obtained by the solution of the corresponding recursive cell problems. The effects of thermal stresses on periodic multi-layered thermoelastic composite reproducing the characteristics of solid oxide fuel cells (SOFC-like) are studied assuming periodic body forces and heat sources, and the solution derived by means of the asymptotic homogenization approach is compared with the results obtained by finite elements analysis of the associate heterogeneous material.

Asymptotic expansion homogenisation and topology optimisation of cellular materials

Topology optimisation defines a set of tools associated to the modelling of an effective material domain within structural optimisation. Based on this type of optimisation, it is possible to obtain an optimal material distribution for several applications and requirements. Cellular materials are part of the most prominent materials today, both in terms of applications, and in terms of research and development. However, their potentially complex and heterogeneous structures carry some complexities, associated to the prediction of effective constitutive properties and to its design. Homogenisation procedures can provide answers for both cases. On the one hand, the asymptotic expansion homogenisation can be used to determine thermomechanical effective properties for these materials through the detailed modelling of representative unit-cells, in a flexible and accurate fashion, regardless of the type of constituent distribution. On the other hand, this homogenisation technique integrates a localisation procedure, able to obtain detailed information on the behaviour of the material within the unit-cell, giving way to local sensitivities that can be used to control optimisation procedures. This leads to a material topology optimisation approach, perfectly suited for the design of this type of material. Within this scope, this work focuses on the analysis of effective thermomechanical material properties of cellular materials designed with topology optimisation procedures.

Third-order thermo-mechanical properties for packs of Platonic solids using statistical micromechanics.

Obtaining an accurate higher order statistical description of heterogeneous materials and using this information to predict effective material behaviour with high fidelity has remained an outstanding problem for many years. In a recent letter, Gillman & Matouš (2014 Phys. Lett. A 378, 3070-3073. ()) accurately evaluated the three-point microstructural parameter that arises in third-order theories and predicted with high accuracy the effective thermal conductivity of highly packed material systems. Expanding this work here, we predict for the first time effective thermo-mechanical properties of granular Platonic solid packs using third-order statistical micromechanics. Systems of impenetrable and penetrable spheres are considered to verify adaptive methods for computing n-point probability functions directly from three-dimensional microstructures, and excellent agreement is shown with simulation. Moreover, a significant shape effect is discovered for the effective thermal conductivity of highly packed composites, whereas a moderate shape effect is exhibited for the elastic constants.

MODELING THE HYGRO-THERMO-MECHANICAL AGGLOMERATION RELATIONS OF CARBON-EPOXY HYBRID NANOCOMPOSITES

In the present work, the hygro-thermo-mechanical properties of hybrid nanocomposites are presented under the agglomeration effects of carbon nanotubes in the polymer matrix. In order to study the composite behaviors, the Voigt and Reuss homogenization method is adopted to present new relations for a hybrid nanocomposite that contains micro carbon fibers as inclusions along with the nanotubes. The experimental findings have shown that the nanotube agglomerations have a significant impact on the effective thermo-mechanical and moisture properties of nanocomposites. Experimental works also prove that nanotube agglomerations further degrade the electrical and vibration characteristics. Additionally, the existing fabrication methods have shown that extensive deagglomeration process has resulted in considerable damage to the nanotubes. Therefore, in order to overcome the above problems the hybrid nanocomposite concept has been proposed and the effective elastic, thermal, and moisture properties are derived in terms of the nanotube agglomeration. The effective hygro-thermo-mechanical properties of hybrid nanocomposites as a function of nanotube agglomeration volume fraction have been presented. The results prove that the effective properties of nanocomposites are reduced under nanotube agglomerations but enhanced when carbon fibers are used as inclusions. Consequently it is concluded that the nanocomposite properties can be improved by using carbon fibers as hybrid inclusions although nanotube agglomerations may be present.

THERMOELASTOPLASTIC AND VIBRATION CHARACTERISTICS OF COMPOSITES WITH INTERPHASES

ABSTRACTThis paper addresses the problem of predicting the behaviors of a compositematerial, which consists of a matrix and a spherical inclusion coated by a multilayeredinterphase, under thermal and/or mechanical loading variations and basedon the micromechanics principles. The multi-layered interphase, which in generalincludes different properties for each layer, is modeled by applying the multiinclusionmodel. The considered damage mode, which is represented by theprogressive debonding of the particle from the interphase, is assumed to becontrolled by a critical energy criterion and the Weibull’s distribution function. Theeffects of the interphase parameters such as its thickness and the properties of eachlayer on the effective thermomechanical properties and the vibration characteristicsof composites with multi-layered interphases are presented and discussed. Thenatural frequencies give information about the resonance avoidance whereas modeshapes give information about observability and controllability of different structures.Therefore, the natural frequencies and mode shapes as vibration characteristics areinvestigated based on Euler and Timoshenko theories.

Effective thermo-mechanical properties of aluminum–alumina composites using numerical approach

This study examines the effect of microstructural characteristics on the effective thermo-mechanical properties, i.e., elastic moduli, Poisson’s effect, and coefficient of thermal expansion (CTE), of ceramic particle-reinforced metal–matrix composites. Two-dimensional (2D) micro-structures for composites with 10% and 20% alumina volume contents dispersed in aluminum matrix are constructed from the micrograph images of the composite samples taken at various locations. A representative area element approximately of size 50μm×50μm is chosen to represent the microstructure of the composite. For each of the selected square regions, ceramic content and porosity are first determined in order to examine the validity of the represented microstructure. These microstructures are implemented in finite element (FE) in order to numerically characterize the effective thermo-mechanical properties of the composites. The alumina constituent is assumed to behave as linearly elastic solid, while the aluminum constituent is modeled as an elastic–plastic solid with material parameters varying with temperatures. The effect of loading directions, porosity, properties of the constituents, particle sizes, and thermal (residual) stresses developed during cooling from the sintering temperature to room temperature, on the overall thermo-mechanical properties of the composites are further discussed.

Prediction of effective properties for random heterogeneous materials with extrapolation

This work presents an efficient method to predict effective thermo-mechanical properties of random heterogeneous materials, with the purpose of reducing the cost of computation. The method is applied to morphologically realistic microstructures generated by a modified random morphology description functions algorithm. To achieve this purpose, firstly the convergence rates of the approximate effective material properties by homogenization with increasing cell domain size are numerically investigated, and it shows first-order accuracy of the approximate effective material properties. Secondly, Richardson extrapolation technique is introduced to obtain more accurate approximations of effective material properties by using some smaller cell domains, without the need for computations in larger cell domain. Numerical examples demonstrate that the method significantly saves computation time and computer memory while improving the accuracy of the effective material properties.

Effective thermoelastic properties of composites with periodicity in cylindrical coordinates

The aim of this work is to study composites that present cylindrical periodicity in the microstructure. The effective thermomechanical properties of these composites are identified using a modified version of the asymptotic expansion homogenization method, which accounts for unit cells with shell shape. The microscale response is also shown. Several numerical examples demonstrate the use of the proposed approach, which is validated by other micromechanics methods.

Status of ceramic breeder pebble bed thermo-mechanics R&D and impact on breeder material mechanical strength

Among the international fusion solid breeder blanket community, there exists steady progress on the experimental, phenomenological, and numerical characterizations of the pebble bed effective thermo physical and mechanical properties, and of thermomechanic state of the bed under prototypical operating conditions. This paper summarizes recent achievements in pebble bed thermomechanics that were carried out by members of the IEA Fusion Nuclear Technology Subtask I Solid Breeding Blanket. A major goal is on developing predictive capability while identifying a pre-conditioned equilibrium stress state that would warrant pebble bed integrity during operations. The paper reviews and synthesizes existing computational modeling approaches for pebble bed thermomechanics prediction, and differentiating points of convergence/divergence among existing approaches. The progress toward modeling benchmark is also discussed. These advancements have led to a framework to help navigate future research.

Fully coupled heat conduction and deformation analyses of nonlinear viscoelastic composites

This study presents an integrated micromechanical model-finite element framework for analyzing coupled heat conduction and deformations of particle-reinforced composite structures. A simplified micromechanical model consisting of four sub-cells, i.e., one particle and three matrix sub-cells is formulated to obtain the effective thermomechanical properties and micro–macro field variables due to coupled heat conduction and nonlinear thermoviscoelastic deformation of a particulate composite that takes into account the dissipation of energy from the viscoelastic constituents. A time integration algorithm for simultaneously solving the equations that govern heat conduction and thermoviscoelastic deformations of isotropic homogeneous materials is developed. The algorithm is then integrated to the proposed micromechanical model. A significant temperature generation due to the dissipation effect in the viscoelastic matrix was observed when the composite body is subjected to cyclic mechanical loadings. Heat conduction due to the dissipation of the energy cannot be ignored in predicting the factual temperature and deformation fields within the composite structure, subjected to cyclic loading for a long period. A higher creep resistant matrix material or adding elastic particles can lower the temperature generation. Our analyses suggest that using particulate composites and functionally graded materials can reduce the heat generation due to energy dissipation.

Numerical and Analytical Approaches for Calculating the Effective Thermo-Mechanical Properties of Three-Phase Composites

The aim of this article is to envisage the effective thermo-mechanical properties of three phase composites made up of coated unidirectional cylindrical fibers using homogenization techniques. The main focus is on square arrangements of cylindrical fibers in composite. The numerical approach is based on the micro-mechanical unit cell modeling technique using finite element method (FEM) with appropriate boundary conditions and it allows the extension to composites with arbitrary geometrical inclusion configurations, providing a powerful tool for fast calculation of their effective properties. The results obtained from the numerical technique are compared with those obtained by means of the analytical asymptotic homogenization method (AHM) for different fiber volume fractions. In order to analyze the interphase effect, the effective properties are compared with the results obtained from some theoretical approaches reported in the literature.

Prediction of effective thermo-mechanical properties of particulate composites

A micromechanics-based model is developed to predict the effective thermo-mechanical properties of energetic materials, which are composite materials made from agglomeration of particles of a range of sizes. A random packing algorithm is implemented to construct a representative volume element for the heterogeneous material based on the experimentally determined particle diameter distribution. The effective mechanical properties of the material are then evaluated through finite element modeling, while its thermal properties are determined through a finite volume approach. The model is first carefully validated against results from the literature and is then used to estimate the thermo-mechanical properties of particular energetic materials. Good agreement is found between experimental results and predictions. The stress-bridging phenomenon in the particulate materials is captured by the model. Thermodynamic averaging is shown to be a poor representation for the estimation of thermo-mechanical properties of these heterogeneous materials.

Modifying electric artworks to improve dimensional stability of microelectronic substrates

PurposeThe paper aims to deal with a tuning method to reduce warpage of microelectronic substrates.Design/methodology/approachThere are three major processes involved in this method: calculating effective thermomechanical properties of substrates with simple regular electric artworks using 3D finite element (FE) analyses; fitting simplified expressions to the results from the FE analyses; and developing 2D FE models of substrates with arbitrarily complicated artwork using the simplified expressions. These three processes were used to estimate the warpage. An optimization procedure through iterative searches was used to obtain optimized trace widths and/or spacing in order to reduce the warpage.FindingsUsing a printed circuit board design to prove our concept, it was found that the warpage could be significantly reduced by modifying trace widths and/or spacing of the printed circuit board.Originality/valueThe paper focuses on a tuning method to reduce warpage of microelectronic substrates.

Thermomechanical properties of strut-lattices

The quest for light and strong construction materials in transportation systems has inspired significant research interest in miniaturized strut-lattices. In such applications, it is possible for these structures to be subjected to extreme loading conditions involving both temperature and pressure. We evaluate the effective thermomechanical properties of periodic lattices using an energy-based homogenization method under the assumptions of small strut-level deformation. The effects of multi-phase strut constituents on the behavior of the overall lattice are assessed with the aid of various topologies. Some examples that highlight different ways in which one could engineer these materials to perform unique thermomechanical functions are presented. These examples include lattice structures with zero and negative effective thermal expansion coefficients. The role played by temperature on multi-axial yield modes is analyzed. Also investigated are the pressure-induced nodal forces in non-symmetrically joined struts within a pressurized lattice at non-ambient temperatures.

Multi-scale modeling of refractory woven fabric composites

Thermomechanical analysis of a refractory, woven fabric composite was conducted using a multi-scale analysis technique. The composite was made of carbons and ceramic materials. The fibers were made of carbons and the outer coating was made of a ceramic material. In order to reduce the thermal stress in the carbon fibers and the ceramic material caused by mismatch of coefficients of thermal expansion between the two materials, a graphitized carbon layer was introduced between the fiber and the ceramic coating. For the multi-scale analysis, a new analysis model was developed and used to bridge the micro-scale characteristics, i.e. the constituent material level such as carbon and ceramic materials, to the macro-scale behavior, i.e. the woven fabric composite level. Furthermore, finite element analyses were undertaken with discrete modeling of the representative fibers, coating, and the graphitized middle layers. Then, both multi-scale analytical and numerical results were compared. In this study, thermal stresses at the micro-level, i.e. in the fibers and coating materials, as well as effective thermomechanical properties of the refractory composites were computed using the multi-scale technique.

Prediction of microelectronic substrate warpage using homogenized finite element models

The focus of this study was to numerically predict effective thermo-mechanical properties and substrate warpage of high-density microelectronic substrates used in organic CPU packages. Microelectronic substrates are typically composed of several polymer, fiber-weave, and copper layers and are filled with a variety of complex features, such as electric traces, plated-through-holes, micro-vias, and adhesion holes. When subjected to temperature changes, these substrates may warp, driven by the mismatch in coefficients of thermal expansion (CTE) of the constituent materials. This study focused on predicting substrate warpage in an isothermal condition. The numerical approach consisted of three major tasks: estimating homogenized (effective) thermo-mechanical properties of the features; calculating effective properties of discretized layers using the effective properties of the features; and assembling the layers to create two-dimensional (2D) finite element (FE) plate models and to calculate warpage of the substrates. The effective properties of the features were extracted from three-dimensional (3D) unit cell FE models, and closed-form approximate expressions were developed using the numerical results, curve fitting, and some simple bounds. The numerical approach was applied to predict warpage of production substrates, analyzed, and validated against experimentally measured stiffness and CTEs. In this paper, the homogenization approach, numerical predictions, and experimental validation are discussed.

MICROMECHANICAL AND THERMOMECHANICAL STUDY OF A REFRACTORY FIBER/MATRIX/COATING SYSTEM

ABSTRACT Thermomechanical analysis of a refractory single-fiber system made of fiber/matrix/coating was conducted at the microlevel with progressive intralayer sliding failure in the matrix material. The effect of the matrix failure on reduction of coating thermal stress was studied using finite element analysis. The analysis included both transient thermal analysis and steady-state stress analysis in a staggered manner. To incorporate the effect of progressive matrix failure, introduction of an interface element and the matrix condensation technique were utilized. The interface element could effectively represent both reduction in stiffness and increase in thermal resistance for heat conduction as failure occurred in the material. The numerical example showed the effect of matrix failure as well as a series of parametric studies of the material properties on the change of thermal stress in the coating. Furthermore, the effective thermomechanical properties of the refractory fiber system were computed using the successive unit-cell approach. A parametric study of the effective thermomechanical properties was also presented.

A statistical micromechanics-based multi-scale framework for effective thermomechanical behaviours of particle reinforced composites

Particle-reinforced composite materials have been widely used as they can exhibit nearly isotropic material properties and are often easy to process. Some silicon carbide particle reinforced aluminium composites with high volume concentration of reinforcement exhibit excellent thermophysical properties and can be used in advanced electronic packaging. In this paper, a statistical micromechanics-based multi-scale material modelling framework is introduced to describe the macroscopic effective thermomechanical properties of the particle-reinforced composite. The formulation differs from most of the existing methods in that the interaction effects among the reinforcing particles are directly accounted for by considering pair-wise interaction and statistical information on particle distribution is included. The strain and stress concentration factor tensors that relate the local average strain and stress fields, respectively, to the corresponding global average fields are derived according to the theory of average fields. The effective coefficient of thermal expansion for the particle-reinforced composite material is derived. Comparisons of the prediction from the proposed framework to the results from other existing methods are presented. The results are expressed in analytical closed-form in terms of the thermal and mechanical properties of the two constituent phases and the volume fraction of particles. No parameter estimation or data fitting is required.