Composite materials whose phases have partially equal elastic moduli

Hill [J. Mech. Phys. Solids 11 (1963) 357, 12 (1964) 199] discovered that, regardless of its microstructure, a linearly elastic composite of two isotropic phases with identical shear moduli is isotropic and has the effective shear modulus equal to the phase ones. The present work generalizes this result to anisotropic phase composites by showing and exploiting the fact that uniform strain and stress fields exist in every composite whose phases have certain common elastic moduli. Precisely, a coordinate-free condition is given to characterize this specific class of elastic composites; an efficient algebraic method is elaborated to find the uniform strain and stress fields of such a composite and to obtain the structure of the effective elastic moduli in terms of the phase ones; sufficient microstructure-independent conditions are deduced for the orthogonal group symmetry of the effective elastic moduli. These results are applied to elastic composites consisting of isotropic, transversely isotropic and orthotropic phases.     

Optimal lower bounds on the local stress inside random thermoelastic composites

A methodology is presented for bounding all higher moments of the local hydrostatic stress field inside random two phase linear thermoelastic media undergoing macroscopic thermomechanical loading. The method also provides a lower bound on the maximum local stress. Explicit formulae for the optimal lower bounds are found that are expressed in terms of the applied macroscopic thermal and mechanical loading, coefficients of thermal expansion, elastic properties, and volume fractions. These bounds provide a means to measure load transfer across length scales relating the excursions of the local fields to the applied loads and the thermal stresses inside each phase. These bounds are shown to be the best possible in that they are attained by the Hashin–Shtrikman coated sphere assemblage.     

热载荷作用下嵌入SMA丝复合材料梁的横向自由振动

基于形状记忆合金Brinson一维热力学本构方程,采用复合材料细观力学分析方法,建立了热载荷作用下嵌入SMA丝复合材料梁的一维热弹性本构关系。其次利用Euler-Bernoulli梁的轴线可伸长几何非线性理论和自由振动理论,建立了嵌入SMA丝复合材料梁在均匀升温场内自由振动的动力学控制方程,导出了热过屈曲构形附近嵌入SMA丝复合材料梁微幅横向自由振动的模型。最后通过打靶法求解了两端固定约束条件下嵌入形状记忆合金丝复合材料梁在加热过程中的振动响应,获得了梁的前四阶固有频率在不同SMA相对体积含量时随温度变化的特征关系曲线。数值结果表明,SMA丝相变过程中的回复应力和弹性模量变化对梁在过屈曲前后的各阶固有频率均有影响,是实现梁自振频率主动控制的一种有效方法。     

On effective properties of composites with coated cylindrically orthotropic fibers

Composite systems consisting of a matrix phase and coated inclusions with curvilinear anisotropy are considered, and a concise framework is established for analysis of their effective thermomechanical behavior. An exact relation between the effective thermal stress tensor and the purely mechanical influence functions of such media is derived. The presented analysis includes as a special case some previous work by the authors on composites with coated and cylindrically orthotropic fibers, e.g., carbon fibers. Furthermore, it allows to prove analytically certain symmetry and consistency properties of the effective thermomechanical tensors of such systems as approximated by the Mori—Tanaka micromechanical model.     

Elastic–plastic thermomechanical response of composite co-axial cylinders

A new method is developed in this paper to deal with the thermomechanical response of continuous fiber-reinforced composites. Treating the matrix as an elastic-perfectly plastic solid, the analytical formulae of the deformations and stresses of the matrix are obtained from the plasticity theory, axisymmetric equilibrium equation, and stress–strain and strain–displacement relations. The fiber is taken to be an anisotropic, elastic material, and the formulae calculating its deformations and stresses are also presented. The boundary conditions and the consistence of deformations and stresses between the fiber and matrix, and between elastic and plastic regions of the matrix are employed to determine the unknown constants in the analytical formulae. With the developed method, the thermomechanical stress distributions in composites reinforced with circumferentially orthotropic, radially orthotropic and transversely isotropic fibers are investigated, and how the elastic-perfectly plastic property and different materials of the matrix affect the thermomechanical response of the composites is discussed. For the thermomechanical loads and composite systems given in this paper, the elastic-perfectly plastic property of the matrix can reduce the compressive stresses in the fiber, and the tensile circumferential and axial stresses in the matrix. A strong matrix can raise the compressive stresses in the fiber, and the tensile circumferential and axial stresses in the matrix.     

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.     

Finite element modeling of effective thermomechanical properties of Al–B<Subscript>4</Subscript>C 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.     

Synthesis of fly ash particle reinforced A356 Al composites and their characterization

A356 Al–fly ash particle composites were fabricated using stir-cast technique and hot extrusion. Composites containing 6 and 12 vol.% fly ash particles were processed. Narrow size range (53–106 μm) and wide size range (0.5–400 μm) fly ash particles were used. Hardness, tensile strength, compressive strength and damping characteristics of the unreinforced alloy and composites have been measured. Bulk hardness, matrix microhardness, 0.2% proof stress of A356 Al–fly ash composites are higher compared to that of the unreinforced alloy. Additions of fly ash lead to increase in hardness, elastic modulus and 0.2% proof stress. Composites reinforced with narrow size range fly ash particle exhibit superior mechanical properties compared to composites with wide size range particles. A356 Al–fly ash MMCs were found to exhibit improved damping capacity when compared to unreinforced alloy at ambient temperature.     

The dynamics of dislocation interaction with sessile self-interstitial atom (SIA) defect cluster atmospheres

The interaction dynamics between dislocations and radiation induced sessile self-interstitial atom (SIA) dislocation loops in FCC metals are investigated. As a result of dislocation line flexibility, its equilibrium configuration is found to be sensitive to the elastic field of nearby SIA dislocation loops. Dislocation line flexibility also influences the critical stress to free trapped dislocations from pinning atmospheres (i.e. the critical resolved shear stress (CRSS)). Calculated CRSS values differ by up to 100% from the estimates of Trinkaus et al. [J. Nucl. Mater. 249 (1997) 91; J. Nucl. Mater. 251 (1997) 172], which are based on cluster forces exerted on static rigid dislocations. The mechanism of dislocation unpinning from random cluster atmospheres is shown to be a consequence of morphological instabilities on the dislocation line. The initial location of the unlocking instability is always associated with regions of minimum line tension in the vicinity of the lowest cluster density. The growth of dislocation shape fluctuations leads to a sequence of unzipping events, freeing the dislocation from the elastic field of cluster atmospheres. The relative critical shear stress to unlock dislocations in FCC metals, (τ_C/μ), is found to be in the range: 0.001–0.002, for random atmosphere cluster densities of 10²⁴–10²⁵ m³, and in the range: 0.0014–0.003, for coherent cluster atmospheres of the same density range. These values are factors of 4–6 smaller than Kroupa's estimates. Implications of these results to the determination of the upper yield point of irradiated FCC metals are discussed.     

Thermomechanical behaviour of interfacial region in carbon fibre/epoxy composites

A study of the thermomechanical stability of the fibre-matrix interphase in carbon/epoxy composites has been carried out. The thermodynamic work of adhesion has been evaluated at room temperature by wetting measurements. The interfacial shear stress transfer level τ for sized and desized carbon fibre has been measured as a function of temperature by means of a single-fibre fragmentation test. As the test temperature increased τ values were found to decrease, with values being higher for the desized carbon fibre. The dependence of interfacial shear stress transfer on bulk matrix mechanical properties (modulus and shear strength) has also been discussed. Dynamic mechanical measurements performed on single-bundle composites confirmed the better thermomechanical stability of the desized fibre interphase.     

Developing a stochastic model to predict the strength and crack path of random composites

We characterize fracture and effective stress–strain graphs in 2D random composites subjected to a uniaxial in-plane uniform strain. The fibers are arranged randomly in the matrix. Both fibers and matrix are isotropic and elastic–brittle. We conduct this analysis numerically using a very fine two-dimensional triangular spring network and simulate the crack initiation and propagation by sequentially removing bonds which exceed a local fracture criterion. In particular, we focus on effect of geometric randomness on crack path of random composites. Based on that two stochastic micro-mechanic models are presented that can predict with confidence the failure probability of random matrix–inclusion composites.     

Lower bounds on the stress and strain fields inside random two-phase elastic media

Summary The heterogeneous media under consideration are isotropic composites consisting of two well-ordered elastic isotropic phases and subjected to uniform macroscopic loading. By extending a method due to Lipton [2], lower bounds on the stress and strain fields inside each phase are explicitly established in terms of the phase volume fractions and properties. These bounds on the second moments turn out to be optimal, since they are achieved by the relevant stress and strain fields inside the finite-rank laminates which, constructed by Francfort and Murat [6], attain the Hashin-Shtrikman lower and upper bounds on the elastic bulk and shear moduli.     

防热复合材料高温力学性能

通过对高温环境下防热材料内部热化学烧蚀机理的分析,利用Eshelby等效夹杂方法研究了组元材料烧蚀-相变特性和高温力学性能的变化规律。假设材料热化学反应后的热解(热氧化)生成相介质统计均匀分布,考虑了烧蚀反应产生的气孔与固体相介质之间的相互作用,预报了单向纤维增强复合材料微结构与宏观性能之间的变化关系,并进行了数值计算。研究结果表明:单向复合材料纵向杨氏模量随温度升高而衰减,并与加温速率有关,典型热防护材料的高温力学性能的理论预报与实验数据进行比较,结果吻合较好,说明理论模型正确,为防热复合材料热结构分析奠定了基础。      

Cold sheet rolling,the thermoviscoelastic problem,a numerical solution

The coupled system of equations governing the thermomechanical deformations of a viscoelastic sheet while it is being cold rolled is solved numerically. The pertinent energy equation is solved by the finite difference method and the mechanical problem is solved by the finite element method using uniform first order rectangular elements. The developed computer program enables one to compute the complete deformation and temperature fields in the sheet. Results presented graphically include the temperature distribution, the stress distribution at the middle surface, the contact pressure distribution and the asymmetric surface deformation of the sheet.     

Thermomechanically coupled micromechanical analysis of multiphase composites

One- and two-way thermomechanically coupled micromechanical analyses of multiphase composites are presented. In the first type of thermomechanical coupling, a constant temperature that affects the mechanical field only is prescribed at any point of the composite’s constituents. In the two-way thermomechanical coupling, on the other hand, a mutual interaction exists between the mechanical and temperature fields. It is shown that the macroscopic coupled energy equation that is established from a homogenization procedure cannot provide reliable information about the induced temperature that is caused by an applied far-field mechanical loading of the composite. The details of the induced temperature-field variations can be obtained, on the other hand, by the derived two-way thermomechanically coupled micromechanical analysis, thus enabling the identification of critical hot spots in the mechanically loaded composite. Results exhibit, in particular, the induced temperature field in metal-matrix and polymer-matrix composites.     

On the local elastic–plastic behaviour of the interface in titanium/silicon carbide composites

The purpose of this study is to conduct a high-resolution nonlinear finite element analysis of the elastic–plastic behaviour of titanium/silicon carbide composites subject to transverse loading. This class of metal matrix composites is designed for the next generation of supersonic jet engines and deserves careful assessment of its behaviour under thermo mechanical loads. Three aspects of the work are accordingly examined. The first is concerned with the development of a representative unit cell capable of accurately describing the local elastic–plastic behaviour of the interface in metal matrix composites under thermal and mechanical loads. The second is concerned with the determination of the influence of mismatch in the mechanical properties between the inhomogeneity and the matrix upon the induced stress fields and the plastic zone development and its growth. The third is concerned with unloading and the role played by the interface upon residual stresses. It is found that the maximum interfacial stress in the matrix appears in the case involving cooling from the relieving temperature with subsequent applied compressive loading. It is also found that the mismatch in mechanical properties between the matrix and the inhomogeneity introduces significant changes in the stress distribution in the matrix. Specifically, it is observed that the maximum radial and tangential stresses in the matrix take place at the interface. The plastic deformation of the matrix leads to a relaxation of these stresses and assists in developing a more uniform interfacial stress distribution. However, the matrix stresses and the resulting equivalent plastic strains still reach their maximum values at that interface. The results show similarities in the patterns of the interfacial stress distribution and plastic zone development for all ranges of fibre volume fractions and loading levels examined. However, they also show marked differences in both the magnitude and patterns of matrix stress distribution between the adjacent inhomogeneities as a result of interaction effects between the fibres.     

Particulate refinement and redistribution during the axisymmetric compression of an Al/SiCp metal matrix composite

Previous investigations have shown that the thermomechanical processing of Al/SiC_p metal matrix composites (MMC) can reduce the size of SiC particles and yield a more homogeneous spatial distribution of particles. Both of the above microstructural features are conducive to improvements in the ductility and fracture toughness of MMC. This research was designed to measure the effectiveness of thermomechanical processing on the microstructure of an MMC by monitoring the change in SiC particle size and spatial distribution during the course of deformation processing. The MMC used in this investigation was the Al alloy 2618 reinforced with 14 vol% SiC_p. Continuous and discontinuous axisymmetric compression tests were conducted, both at room and elevated temperatures. Optical and quantitative microstructural analysis was performed over many fields from each as-deformed specimen. This study finds that at elevated temperatures, a large number of fractured SiC particles corresponded with the macroscopic peak flow stress of the composite. Furthermore, the propensity for particulate fracture was most pronounced when specimens were deformed at room temperature, diminishing somewhat when specimens were deformed at elevated temperatures. However, deformation at elevated temperatures resulted in a more uniform spatial distribution of SiC particles within the matrix.     

A three-phase circular inhomogeneity with imperfect interface under thermomechanical loadings in plane elasticity

Summary The solution for a homogeneous circular inhomogeneity embedded in an infinite elastic matrix with a single interphase layer plays a fundamental role in many practical and theoretical applications. In particular, it serves as the basis for the solution of the generalized self-consistent method in the mechanics of composite materials. Thus, the study of three-phase problems is of great interest.A general method is presented for the rigorous solution of a three-phase circular inhomogeneity under thermomechanical loadings in plane elasticity. The bonding at the inhomogeneity-interphase interface is considered to be inperfect with the assumption that the interface imperfections are constant. On the remaining boundary, that being the interphase-matrix interface, the bonding is considered to be perfect. Although the problem of a three-phase circular inhomogeneity with imperfect bonding has previously been studied, it seems that the explicit expressions for the complete solutions cannot be located in the literature. In this paper, it is found that stress field within the inhomogeneity is determined by three, in general, complex coefficients while the stress field in the matrix is controlled by three other, in general, complex coefficients. The role of the interphase layer as well as the influence of the imperfect bonding condition, on the stress fields, is manifested by their effect on the six, in general, complex coefficients.The exact closed-form solutions are applied to the design of a three-phase circular inhomogeneity. In particular, for specific thermomechanical loadings, it is shown that a uniform stress state within the inhomogeneity can be achieved with the imperfect interface model provided the imperfect interface parameters are suitably chosen.     

Numerical aspects of finite element simulations of residual stresses in metal matrix composites

When a metal matrix composite (MMC) is cooled down from the fabrication or annealing temperature to room temperature, residual stresses are induced in the composite due to the mismatch of the thermal expansion coefficients of the matrix and reinforcement. A thermomechanical model describing these processes is presented considering that the reinforcement component has a thermo‐elastic behaviour and that the matrix material exhibits a thermo‐elastoviscoplastic behaviour. The model is implemented with a semi‐implicit forward gradient finite element method algorithm and the resulting code is used to perform numerical simulations and calculate thermally induced residual stress fields in MMCs. Several tests are performed on a continuously reinforced MMC and a short cylindrical particle MMC in order to optimize the algorithm and define its governing parameters. Good agreement was obtained with results from other authors. Copyright © 2001 John Wiley & Sons, Ltd.