Coupled heat conduction and thermal stress analyses in particulate composites

This study introduces two micromechanical modeling approaches to analyze spatial variations of temperatures, stresses and displacements in particulate composites during transient heat conduction. In the first approach, a simple micromechanical model based on a first order homogenization scheme is adopted to obtain effective mechanical and thermal properties, i.e., coefficient of linear thermal expansion, thermal conductivity, and elastic constants, of a particulate composite. These effective properties are evaluated at each material (integration) point in three dimensional (3D) finite element (FE) models that represent homogenized composite media. The second approach treats a heterogeneous composite explicitly. Heterogeneous composites that consist of solid spherical particles randomly distributed in homogeneous matrix are generated using 3D continuum elements in an FE framework. For each volume fraction (VF) of particles, the FE models of heterogeneous composites with different particle sizes and arrangements are generated such that these models represent realistic volume elements “cut out” from a particulate composite. An extended definition of a RVE for heterogeneous composite is introduced, i.e., the number of heterogeneities in a fixed volume that yield the same expected effective response for the quantity of interest when subjected to similar loading and boundary conditions. Thermal and mechanical properties of both particle and matrix constituents are temperature dependent. The effects of particle distributions and sizes on the variations of temperature, stress and displacement fields are examined. The predictions of field variables from the homogenized micromechanical model are compared with those of the heterogeneous composites. Both displacement and temperature fields are found to be in good agreement. The micromechanical model that provides homogenized responses gives average values of the field variables. Thus, it cannot capture the discontinuities of the thermal stresses at the particle-matrix interface regions and local variations of the field variables within particle and matrix regions.     

A multi-scale model for coupled heat conduction and deformations of viscoelastic functionally graded materials

An integrated micromechanical-structural framework is presented to analyze coupled heat conduction and deformations of functionally graded materials (FGM) having temperature and stress dependent viscoelastic constituents. A through-thickness continuous variation of the thermal and mechanical properties of the FGM is approximated as an assembly of homogeneous layers. Average thermo-mechanical properties in each homogeneous medium are computed using a simplified micromechanical model for particle reinforced composites. This micromechanical model consists of two isotropic constituents. The mechanical properties of each constituent are time–stress–temperature dependent. The thermal properties (coefficient of thermal expansion and thermal conductivity) of each constituent are allowed to vary with temperature. Sequentially coupled heat transfer and displacement analyses are performed, which allow analyzing stress/strain behaviors of FGM having time and temperature dependent material properties. The thermo-mechanical responses of the homogenized FGM obtained from micromechanical model are compared with experimental data and the results obtained from finite element (FE) analysis of FGMs having microstructural details. The present micromechanical-modeling approach is computationally efficient and shows good agreement with experiments in predicting time-dependent responses of FGMs. Our analysis forecasts a better design for creep resistant materials using particulate FGM composites.     

A two-scale homogenization framework for nonlinear effective thermal conductivity of laminated composites

In this study, we formulate the effective temperature-dependent thermal conductivity of laminated composites. The studied laminated composites consist of laminas (plies) made of unidirectional fiber-reinforced matrix with various fiber orientations. The effective thermal conductivity is obtained through a two-scale homogenization scheme. A simplified micromechanical model of a unidirectional fiber-reinforced lamina is formulated at the lower scale. Thermal conductivities of fiber and matrix constituents are allowed to change with temperature. The upper scale uses a sublaminate model to homogenize temperature-dependent thermal conductivities of only a representative lamina stacking sequence in laminated composites. The effective thermal conductivity of each lamina, in the sublaminate model, is obtained using the simplified micromechanical model. The thermal conductivities from the micromechanical and sublaminate models represent average nonlinear properties of fictitiously homogeneous composite media. Interface conditions between fiber and matrix constituents and within laminas are assumed to be perfect. Experimental data available in the literature are used to verify the proposed multi-scale framework. We then analyze transient heat conduction in the homogenized composites. Temperature profiles, during transient heat conduction, in the homogenized composites are compared to the ones in heterogeneous composites. The heterogeneous composites, having different fiber arrangements and sizes, are modeled using finite element (FE) method.     

Responses of viscoelastic polymer composites with temperature and time dependent constituents

This study formulates a concurrent micromechanical model for predicting effective responses of fiber reinforced polymer (FRP) composites, whose constituents exhibit thermo-viscoelastic behaviors. The studied FRP composite consists of orthotropic unidirectional fiber and isotropic matrix. The viscoelastic material properties for the fiber and matrix constituents are allowed to change with the temperature field. The composite microstructures are idealized with periodically distributed square fibers in a matrix medium. A unit-cell model, consisting of four fiber and matrix subcells, is generated to obtain effective nonlinear thermo-viscoelastic responses of the composites. A time-integration algorithm is formulated to link two different thermo-viscoelastic constitutive material models at the lowest level (homogeneous fiber and matrix constituents) to the effective material responses at the macro level, and to transfer external mechanical and thermal stimuli to the constituents. This forms a concurrent micromechanical model, which is needed as the material properties of the constituents depend on the temperature field. Consistent tangent stiffness matrices are formulated at the fiber and matrix constituents and also at the effective composite level to improve prediction accuracy. The thermo-viscoelastic responses obtained from the concurrent micromodel are verified with available experimental data. Detailed finite element (FE) models of the FRP microstructures are also generated using 3D continuum elements for several fiber volume fractions. Thermo-viscoelastic responses of the concurrent micromodel are also compared to the ones of the detailed FRP microstructures.     

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.     

Thermoelastic properties and conductivity of composites reinforced by spherically anisotropic particles

The present paper is concerned with the overall thermoelastic properties and conductivity of composites reinforced by spherically anisotropic particles. Based on the concept of the replacement particle an equivalent bulk modulus, thermal expansion coefficient and thermal conductivity are derived for the spherically anisotropic particle. Such equivalent properties can be employed in the micromechanical models to predict the overall behavior of the composite. In addition to these, the shear loading is considered. The effective shear modulus is evaluated on the basis of Mori and Tanaka's approximations and the dilute phase concentration factors are derived from exact solutions of an auxiliary boundary value problem.     

Time-dependent response of active composites with thermal, electrical, and mechanical coupling effect

The mechanical and physical properties of materials change with time. This change can be due to the dissipative characteristic of materials like in viscoelastic bodies and/or due to hostile environmental conditions and electromagnetic fields. We study time-dependent response of active fiber reinforced polymer composites, where the polymer constituent undergoes different viscoelastic deformations at different temperatures, and the electro-mechanical and piezoelectric properties of the active fiber vary with temperatures. A micromechanical model is formulated for predicting effective time-dependent response in active fiber composites with thermal, electrical, and mechanical coupling effects. In this micromechanical model limited information on the local field variables in the fiber and matrix constituents can be incorporated in predicting overall performance of active composites. We compare the time-dependent response of active composites determined from the micromechanical model with those obtained by analyzing the composites with microstructural details. Finite element (FE) is used to analyze the composite with microstructural details which allows quantifying variations of field variables in the constituents of the active composites.     

Bounds on the effective thermal conductivity of composites with imperfect interface

A new model is developed to bound the effective thermal conductivity of composites with thermal contact resistance between spherical inclusions and matrix. To construct the trial temperature and heat flux fields which satisfy the necessary interface conditions, the transition layer for each spherical inclusion is introduced. For the upper bound, the trial temperature field needs to satisfy the thermal contact resistance conditions between spherical inclusions and transition layers and the continuous interface conditions between transition layers and remnant matrix. For the lower bound, the trial heat flux field needs to satisfy the continuous interface conditions between different regions. It should be pointed out that the continuous interface conditions mentioned above are absolutely necessary for the application of variational principles, and the thermal contact resistance conditions between spherical inclusions and transition layers are suggested by the author. According to the principles of minimum potential energy and minimum complementary energy, the bounds of the effective thermal conductivity of composites with imperfect interfaces are rigorously derived. The effects of the size and distribution of spherical inclusions on the bounds of the effective thermal conductivity of composites are analyzed. It should be shown that the present method is simple and does not need to calculate the complex integrals of multi-point correlation functions. Meanwhile, the present method provides an entirely different way to bound the effective thermal conductivity of composites with imperfect interface, which can be developed to obtain a series of bounds by taking different trial temperature and heat flux fields. In addition, the present upper and lower bounds are finite when the thermal conductivity of spherical inclusions tends to ∞ and 0, respectively.     

Numerical Investigation of Thermal and Thermo-mechanical Effective Properties for Short Fibre Reinforced Composite

This study aims to investigate the thermal conductivity and the linear coefficient of thermal expansion for short fibre reinforced composites. The study combines numerical and statistical analyses in order to primarily examine the representative size and the effective properties of the volume element. Effects of various micromechanical parameters, such as fibre’s aspect ratio and fibre’s orientation, on the minimum representative size are discussed. The numerically acquired effective properties, obtained for the representative size, are presented and compared with analytical models.     

Void formation in metal matrix composites by solidification and shrinkage of an AlSi7 matrix between densely packed particles

Particle reinforced metals are developed as heat sink materials for advanced thermal management applications. Metal matrix composites combine the high thermal conductivity of a metal with a low coefficient of thermal expansion of ceramic reinforcements. SiC and carbon diamond particle reinforced aluminum offer suitable thermal properties for heat sink applications. These composites are produced by liquid metal infiltration of a densely packed particle preform. Wettability, interface bonding strength and thermal mismatch are critical for void formation which leads to thermal fatigue damage under operation. The evolution of voids in AlSiC and AlCD has been studied by in-situ high resolution synchrotron tomography during matrix solidification. Large irregularly shaped matrix voids form during eutectic solidification. These voids help alleviate thermal expansion mismatch stresses by visco-plastic matrix deformation during cooling to RT after solidification, if sufficient interface bonding strength is assumed.     

A homogenization technique for heat transfer in periodic granular materials

A homogenization technique is proposed to simulate the thermal conduction of periodic granular materials in vacuum. The effective thermal conductivity (ETC) and effective volumetric heat capacity (EVHC) can be obtained from the granular represent volume element (RVE) via average techniques: average heat flux and average temperature gradient can be formulated by the positions and heat flows of particles on the boundaries of the RVE as well as of the contact pairs within the RVE. With the thermal boundary condition imposed on the border region around the granular RVE, the ETC of the granular RVE can be computed from the average heat flux and average temperature gradient obtained from thermal discrete element method (DEM) simulations. The simulation results indicate that the ETC of the granular assembly consisting of simple-cubic arranged spheres coincides with the theoretical prediction. The homogenization technique is performed to obtain the ETC of the RVE consisting of random packed particles and the results exhibit the anisotropy of the thermal conduction properties of the RVE. Both the ETC and EVHC obtained are then employed to simulate the thermal conduction procedure in periodic granular materials with finite element analyses, which give the similar results of temperature profile and conduction properties as the DEM simulations.     

Internal stresses and voids in SiC particle reinforced aluminum composites for heat sink applications

Metal-matrix composites (MMC) are being developed for power electronic IGBT modules, where the heat generated by the high power densities has to be dissipated from the chips into a heat sink. As a means of increasing long term stability a base plate material is needed with a good thermal conductivity (TC) combined with a low coefficient of thermal expansion (CTE) matching the ceramic insulator. SiC particle reinforced aluminum (AlSiC) offers the high TC of a metal with the low CTE of a ceramic. Internal stresses are generated at the matrix-particle interfaces due to the CTE mismatch between the constituents of the MMC during changing temperatures. Neutron and synchrotron diffraction was performed to evaluate the micro stresses during thermal cycling. The changes in void volume fraction, caused by plastic matrix deformation, are visualized by synchrotron tomography. The silicon content in the matrix connecting the particles to a network of hybrid reinforcement contributes essentially to the long term stability by an interpenetrating composite architecture.     

Investigation of thermal properties of Al–Si matrix reinforced fine SiCp composites

Abstract

The characterisation of thermal expansion coefficient and thermal conductivity of Al–Si matrix alloy and Al–Si alloy reinforced with fine SiC_p (5 and 20 wt-%) composites fabricated by stir casting process are investigated. The results show that with increasing temperature up to 350°C, thermal expansion of composites increases and slowly reduces when the temperature reaches to 500°C. The values of both thermal expansion and conductivity of composites are less than those for Al–Si matrix. Microstructure and particles/matrix interface properties play an important role in the thermal properties of composites. Thermal properties of composites are strongly dependent on the weight percentage of SiC_p.     

Interfaces in discontinuously reinforced metal matrix composites: An overview

The fundamental and engineering aspects pertaining to the matrix-reinforcement interfaces in discontinuously reinforced metal matrix composites are presented in this overview. The interfaces play a key role in determining mechanical properties, namely Young’s modulus, yield strength, elongation, creep and fracture behaviour, as well as physical properties like coefficient of thermal expansion, thermal conductivity and damping characteristics of metal matrix composites; these are discussed in detail. The ratio of the experimental value of the Young’s modulus to that predicted from the rule of mixtures has been used as a measure of interfacial bond strength. Various issues such as the nature of the interfacial bond, chemical reaction at the interfaces, and effect of alloying and processing on the structure of the interfaces and the properties of the composite are examined. In order to exploit the full potential of reinforcing the metallic matrix, the suggested strategies include creation of metallic bonding at the interface, use ofin situ processing, choice of right type of alloying elements, and heat treatments and engineering of interfaces.     

Thermoelastic Characterization and Evaluation of Residual Stresses in Bi-Directional Fibrous Composites

The thermoelastic behavior of bi-directional fibrous composites will be studied through the use of a finite element-based micromechanical model. The model is used to study the effect of the crossing angle of the fibers on the composite’s coefficient of thermal expansion (CTE) and the residual thermal stresses that develop after a temperature change. The effect of the fiber volume fraction (V _f ) on the same results is also studied. For anisotropic materials, one can see that in addition to normal strains, shear strains will also be developed due to temperature change. This method will lend itself to evaluate the coefficients of thermal expansions not only due to normal expansion, but also due to shear expansion for composites with no principal directions. In this micromechanical model, parallelepiped unit cells incorporating the fibers at different cross angles are created to represent the periodic microstructure of the angular bi-directional composite. The volume averaged stresses per unit temperature of the individual constituents are used to study the residual thermal stresses that develop. Two different sets of materials are used to test this model. Results show that when the fiber’s cross angle is not 0^o or 90^o, shear strains are created. Also, residual stresses in the unit cell are functions of the cross angle between the fibers.     

Thermal and electrical properties of FeNi/Cu composites

Abstract

Powder metallurgy FeNi/Cu composites with low thermal expansivity and high electrical (thermal) conductivity were fabricated. The effects of Cu content, FeNi particle size, sintering temperature, and rolling reduction on the coefficient of thermal expansion (CTE) and electrical (thermal) resistivity were investigated. The results show that the CTE and electrical resistivity were affected by the volume fraction of the components, the particular properties of the FeNi alloy, diffusion between the FeNi particles and the Cu particles, and the distribution of the Cu particles and the FeNi particles. The experiments indicated that the FeNi/Cu composites could be used as heat sinks in welding type bolt silicon rectifier tubes.     

镁基复合材料热膨胀的研究进展和前景展望

简要介绍了镁合金及镁基复合材料热膨胀的研究进展,叙述了温度、增强体体积分数、增强体颗粒尺寸、增强体颗粒形状、增强体种类和热处理及其他对镁基复合材料热膨胀的影响。简要介绍了热膨胀的理论预测模型,并对今后的发展做了展望。     

基于耦合法的二维三轴编织复合材料热学性能预测及验证

为了改善传统方法建模划分网格繁杂和计算效率低的缺点,利用耦合建模法创建二维三轴编织复合材料的单胞模型,用耦合的思维将增强相单元网格与整体区域单元网格进行耦合处理,协调两者之间的位移场自由度和温度场自由度,通过匹配材料的热学性能,施加温度周期性边界条件,获得单胞模型的等效传热系数和等效热膨胀系数,基于该方法预测并分析编织角和纤维体积含量对各个方向的热传导系数和热膨胀系数的影响程度和规律。     

Experimental description of thermomechanical properties of carbon fiber-reinforced TiC matrix composites

Titanium carbide ceramic is a good potential material used in high temperature environment for its good strength, erosion resistance and thermal stability. Unfortunately, the low thermal shock resistance and low fracture toughness are the well-known impediments to its application as high temperature structure components. In order to extend the application of TiC ceramics at high temperature, 20 vol.% short carbon fiber was added into TiC matrix to improve the thermomechanical properties. With the incorporation of carbon fiber, the thermal expansion coefficient of TiC composites was decreased and the thermal conductivity was increased slightly below 900 °C. The flexural strength was improved from 471 MPa for monolithic TiC to 593 MPa for TiC composites, and the strengthening effect of carbon fiber became more prominent at high temperatures. The addition of fiber decreased the elastic modulus of TiC composite. The elastic modulus of the composite decreased with increasing temperature. The improvement of high temperature strength and thermal conductivity and the decrease of thermal expansion will benefit the application of TiC composites in high temperature environment where the temperature usually varies.     

Pressure infiltration casting process and thermophysical properties of high volume fraction SiCp/Al metal matrix composites

Abstract

SiC_p/Al composites containing high volume fraction SiC particles were fabricated using a pressure infiltration casting process, and their thermophysical properties, such as thermal conductivity and coefficient of thermal expansion (CTE), were characterised. High volume fraction SiC particulate preforms containing 50–70 vol.-%SiC particles were fabricated by ball milling and a pressing process, controlling the size of SiC particles and contents of an inorganic binder. 50–70 vol.-%SiC_p/Al composites were fabricated by high pressure infiltration casting an Al melt into the SiC particulate preforms. Complete infiltration of the Al melt into SiC preform was successfully achieved through the optimisation of process parameters, such as temperature of Al melt, preheat temperature of preform, and infiltration pressure and infiltration time after pouring. Microstructures of 50–70 vol.-%SiC_p/Al composites showed that pores resided preferentially at interfaces between the SiC particles and Al matrix with increasing volume fraction of SiC particles. The measured coefficients of thermal expansion of SiC_p/Al composites were in good agreement with the estimated values based on Turner's model. The measured thermal conductivity of SiC_p/Al composites agreed well with estimated values based on the 'rule of mixture' up to 70 vol.-% of SiC particles, while they were lower than the estimated values above 70 vol.-% of SiC particles, mainly due to the residual pores at SiC/Al interfaces. The high volume fraction SiC_p/Al composite is a good candidate material to substitute for conventional thermal management materials in advanced electronic packages due to their tailorable thermophysical properties.