Asymptotic homogenization algorithm for reinforced metal-matrix elasto-plastic composites

The theory of the two-scale convergence was applied to homogenization of initial flow stresses and hardening constants in some exponential hardening laws for elasto-plastic composites with a periodic microstructure. The theory is based on the fact that both the elastic and the plastic part of the stress field two-scale converge to a limit, which can be factorized by parts, one of which depends only on the macroscopic, and the other one – only on the microscopic characteristics. The first factor is represented in terms of the homogenized stress tensor and the second factor – in terms of stress concentration tensor, that relates to the micro-geometry and elastic or plastic micro-properties of composite components. The theory was applied to a composite, that consists of the metallic elasto-plastic matrix with Ludwik and Hocket–Sherby hardening law and pure elastic silica inclusions. Results were compared with those of averaging based on the self-consistent methods.     

Verschleiß von TaC- und TiC-Laserdispersionsschichten durch weiche und harte Abrasivstoffe

Wear of TaC and TiC steel composite hardfacings by soft and hard abrasives TiC and TaC steel composite layers were produced on a die steel 90MnCrV8 (0.9% C) by using a CO₂-laser. The hard particles of it median size of 3 μm and 30 μm, respectively, and a volume fraction of about 50% were homogeneously distributed in the steel matrix. Hardness of the martensitie matrix was variied by heat treatments. Wear resistance of the hardfacings against flint and SiC with varying mesh sizes were measured using an abrasive wear tester at laboratory atmosphere. Abrasive wear resistance was increased by more than one magnitude of order by embedding the hard phases in the steel surface. The results showed the effects of type and size of the hard phase, hardness of the steel matrix and also of the type and mesh size of abrasive grits on wear resistance. Experimental results arc discussed as a function of those parameters and theoretical models arc developed.     

Multi-scale computational method for elastic bodies with global and local heterogeneity

A multi-scale computational method using the homogenization theory and the finite element mesh superposition technique is presented for the stress analysis of composite materials and structures from both micro- and macroscopic standpoints. The proposed method is based on the continuum mechanics, and the micro–macro coupling effects are considered for a variety of composites with very complex microstructures. To bridge the gap of the length scale between the microscale and the macroscale, the homogenized material model is basically used. The classical homogenized model can be applied to the case that the microstructures are periodically arrayed in the structure and that the macroscopic strain field is uniform within the microscopic unit cell domain. When these two conditions are satisfied, the homogenization theory provides the most reliable homogenized properties rigorously to the continuum mechanics. This theory can also calculate the microscopic stresses as well as the macroscopic stresses, which is the most attractive advantage of this theory over other homogenizing techniques such as the rule of mixture. The most notable feature of this paper is to utilize the finite element mesh superposition technique along with the homogenization theory in order to analyze cases where non-periodic local heterogeneity exists and the macroscopic field is non-uniform. The accuracy of the analysis using the finite element mesh superposition technique is verified through a simple example. Then, two numerical examples of knitted fabric composite materials and particulate reinforced composite material are shown. In the latter example, a shell-solid connection is also adopted for the cost-effective multi-scale modeling and analysis. This revised version was published online in June 2006 with corrections to the Cover Date.     

Overlapping tracks processed by TIG melting TiC preplaced powder on low alloy steel surfaces

An overlapping composite track coating was produced on a steel surface by preplacing a 0·5 mm thick layer of TiC powder and then melting using a tungsten inert gas torch of constant energy input. The influence of the overlapping operation on preheating of the substrate, the dissolution of TiC particulates and the subsequent depth and hardness of the composite layer was analysed. The melt microstructure consisted of both undissolved and partially dissolved TiC particulates, together with a variety of morphologies and sizes of TiC particles precipitated during solidification. Preheating, resulting from the overlapping operation, occurred, producing additional melting of the TiC particulates and deeper melt depths but with a reduced volume fraction of TiC precipitates in the subsequent tracks. A maximum hardness of over 800 HV was developed in the composite layer. The high hardness was unevenly distributed in tracks melted at the initial and final stages, while it varied across the melt depths in other tracks.     

Geometry effects of substrate and coating layers on the thermal stress response of FGM structure

Summary Due to transient temperature change, the plane strain elastic-plastic problem for a functionally graded material (FGM) bonded to a homogeneous coating layer and a metal substrate is considered by the use of the finite element method (FEM). The substrate and the coating are assumed to be aluminum and partially stabilized zirconia, respectively. The FGM layer is a particulate composite of aluminum and partially stabilized zirconia with volume fractions continuously varying through the thickness. Generally in high temperature applications, the FGM system is sandwiched between a substrate layer and a coating layer. The coating layer increases the protection from heat but decreases the thermal shock resistance while the substrate layer increases the rigidity of the structure and decreases strength-related properties at high temperature. In order to compromise the thickness of both the coating and substrate layers, different values of the substrate and coating thickness are studied in order to evaluate their effects on the thermal stress response of the FGM structure. Since the main objective of the FGMs is using them in different applications with severe thermal loading conditions, the thermal stresses may be so high that some reinforcements may be fractured and/or debonded from the matrix giving a weakening effect instead of a reinforcing one. Hence, the behaviors of the reinforcements and the matrix are essential to be studied. In this regard, microscopic constitutive equations along with the temperature-dependent properties of the constituent materials are considered to enable us obtaining more realistic results of thermal stresses. Since the FGM structures are fabricated at high temperatures, thermal residual stresses are produced. In order to find out the importance of the consideration of the residual stresses arising from the fabrication process, the FGM structure with stress-free conditions is heated to the operating temperature, and its thermal stress response is compared with that one where the residual stresses are taken into account. Also, several functional forms of gradation of the constituents in the FGM layer are examined to reach the optimum profile giving the minimum stress level for the FGM structure under thermo-elasto-plastic behavior.     

Strain energy-based homogenization of nonlinear elastic particulate composites

The macroscopic constitutive law for a heterogeneous solid containing two dissimilar nonlinear elastic phases undergoing finite deformation is obtained. Attention is restricted to the case of spherical symmetry such that only the materials consisting of an irregular suspension of perfectly spherical particles experiencing all-round uniform loading are considered which leads to a one-dimensional modeling. For the homogenization procedure, a strain-energy based scheme which utilizes Hashin’s composite sphere is employed to obtain the macroscopic stress-deformation relation added by the initial volume fraction of the particles. As applications of the procedure, the closed-form macroscopic stress expression for a generalized Carroll composite material is derived. Then, by choosing carbon black-filled rubbers, unknown bulk modulus of the carbon black particles is calculated. Finally, the particle-reinforced flexible polyurethane foam is studied using the Ritz method. It is shown that the analytical outcome for composites filled by compressible inclusions is applicable for porous materials with the same matrix.     

Lower strain and stress bounds for elastic random composites consisting of two isotropic phases and exhibiting cubic symmetry

This work is concerned with a composite consisting of two linearly elastic isotropic phases which are distributed at the microscopic scale in such a way that the composite exhibits cubic symmetry at the macroscopic scale. Lower bounds on the second-order and higher order moments of the phase stress and strain fields of such a composite undergoing uniform macroscopic loading are provided in terms of the phase volume fractions and moduli. The lower bounds on the phase second-order strain and stress moments are proved to be optimal by showing that the stress and the strain fields inside appropriate finite-rank laminates achieve them.     

On the sintering with rigid inclusions

The sintering of porous matrices containing rigid, i.e. non-densifying, inclusions is discussed on the basis of the composite sphere model of Scherer. Recognizing that internal stresses are generated by the presence of the non-densifying inclusions, a new equation for the densification rate of the composite is proposed. It takes into account three contributions: (i) the free densification strain rate, which is independent of the stresses present, (ii) the strain rate due to the microscopic effect of the stresses on the sintering mechanism and (iii) the macroscopic deformation strain rate induced by the stresses. This result indicates that the presence of rigid inclusions may generate higher internal stresses in the densify ing compact than those calculated by the original Scherer's approach.     

Interfacial Microstructure between WC-Based Cermet and Cu Alloy

A WC-TiC-Co/CuZnNi composite layer was produced on 1045 steel substrate by means of inside-furnace brazing technique. The microstructure, phase constituent and interfacial diffusion behavior between cermet and CuZnNi alloy were investigated by means of scanning electron microscopy (SEM), transmission electron microscope (TEM), electron probe microanalyzer (EPMA) and X-ray diffraction. The results showed that microstructure of matrix was α and β phases. Cermet particies were surrounded by the α+β phases in the composite layer and their sizes were almost similar to those in original state. The interfacial zone was formed by the mutual diffusion of elements under the condition of high temperature. The interface consists of WC, TiC, CuZn, and CuNi phases, and there are no microcracks and inclusions near the interface.     

Thermomechanical analysis of residual stresses in brazed diamond metal joints using Raman spectroscopy and finite element simulation

Thermal residual stresses are one of the crucial parameters in engineered grinding tool (EGT) life and its consistency. Predicting failure of brazed diamond metal joints in EGTs is related to analyzing the thermal residual stresses during the cooling process. Thus thermal residual stresses have been simulated in a model with realistic materials properties, for instance isotropic hardening and a hyperbolic-sine creep law for SS316L and the silver–copper–titanium active filler alloy, named Cusil ABA™. Also, special modeling techniques such as tie constraint and sub-modeling have been used to model an intermetallic layer titanium-carbide (TiC) with dimensions in nanometers, where the rest of the model’s dimensions are in millimeters. To verify the simulated stress state of the diamond, Raman-active optical phonon modes at three different paths in the diamond were measured. As the experiments with Raman spectroscopy (RS) do not deliver stress components, the solution is to directly compute the peak shift of Raman spectrum. The splitting in phonon frequencies and the mixing of phonon modes contain information about the thermal residual stresses in the diamond. Finally the shift in the phonon frequencies was calculated from the different numerical residual elastic strain components and compared to the experimental results.     

Thermo-elasto-plastic stresses in functionally graded materials subjected to thermal loading taking residual stresses of the fabrication process into consideration

Functionally graded materials (FGMs) have recently been received with considerable interest, primarily as high temperature resistant materials for space vehicles subjected to high temperature environment. FGMs are one of the composite materials and consist of continuous change of composition of different material components from one surface to the other. FGMs usually fabricated at high temperature at which the FGMs have stress free condition. After the FGMs cooled from the fabrication temperature to the room temperature residual thermal stresses produced. In this paper, elasto-plastic thermal stresses in a rectangular plate (FGP) of a particle reinforced composite FGM are treated by finite element method due to the microscopic combination law when the FGP is subjected to three kinds of temperature conditions, first is cooling from the fabricated temperature to the room temperature, second is heating and last is heating after cooling from the fabricated temperature. In the analysis, the thermal stress constitutive equation of a particle-reinforced composite taking temperature change and damage process into consideration is used. The effects of the particle volume fraction and the three kinds of temperature conditions on the stresses in the matrix, stresses in the particle and macroscopic stress are discussed.     

Raman spectroscopy characterization of diamond films on steel substrates with titanium carbide arc-plated interlayer

Diamond chemical vapour deposition (CVD) on steel represents a difficult task. The major problem is represented by large diffusion of carbon into steel at CVD temperatures. This leads to very low diamond nucleation and degradation of steel microstructure and properties. Recent work [R. Polini, F. Pighetti Mantini, M. Braic, M. Amar, W. Ahmed, H. Taylor, Thin Solid Films 494 (2006) 116] demonstrated that well-adherent diamond films can be grown on high-speed steels by using a TiC interlayer deposited by the PVD-arc technique. The resulting multilayer (TiC/diamond) coating had a rough surface morphology due to the presence of droplets formed at the substrate surface during the reactive evaporation of TiC. In this work, we first present an extensive Raman investigation of 2 μm, 4 μm and 6 μm thick diamond films deposited by hot filament CVD on TiC interlayers obtained by the PVD-arc technique. The stress state of the diamond was dependent on both the films thickness and the spatial position of the coating on the substrate. In fact, on the top of TiC droplets, the stress state of the diamond was much lower than that of diamond in flatter substrate areas. These results showed that diamond films deposited on rough TiC interlayers exhibited a wide distribution of stress values and that very large compressive stress exists in the diamond film grown on flat regions of steel substrates with a TiC interlayer. Diamond films could accommodate stresses as large as 10 GPa without delamination.     

Stress analysis of steel beams strengthened with a bonded hygrothermal aged composite plate

In this paper, the problem of interfacial stresses in steel beams strengthened with bonded hygrothermal aged composite laminates is analyzed using linear elastic theory. The analysis is based on the deformation compatibility approach developed by Tounsi (Int. J. Solids Struct. 43:4154–4174, 2006) where both the shear and normal stresses are assumed to be invariant across the adhesive layer thickness. The adopted model takes into account the adherend shear deformations by assuming a linear shear stress through the depth of the steel beam. This solution is intended for application to beams made of all kinds of materials bonded with a thin composite plate. For steel I-beam section, a geometrical coefficient ξ is determined to show the effect of the adherend shear deformations. This research is helpful for the understanding on mechanical behaviour of the interface and design of such structures.     

Mechanical analysis of 3-D braided composites by the finite multiphase element method

A finite multiphase element method (FMEM), in which the element comprises more than one kind of material, has been proposed to predict the effective elastic properties of 3-D braided composites. This method is based on the variational principle and our previous geometric model that assumes the existence of different types of unit cells in the three regions in a 3-D braided composite, i.e. the interior, surface and corner. The numerical procedure involved two steps. First, a fine local mesh at the unit cell level is used to analyze the stress/strain of each unit cell. Then, a relatively coarse global mesh is used to obtain the overall responses of the composite at macroscopic level. By using the stress volume averaging method, the effective elastic properties of the composite can be calculated under the prescribed uniform strain boundary conditions. Finally, the predicted stress/strain curves are compared with experimental results, demonstrating the applicability of the FME method.     

激光熔覆原位自生TiC颗粒增强镍基复合涂层的组织与耐磨性

采用预置粉末法在45钢表面进行激光熔覆镍基Ni60A+x%(SiC+Ti)(质量分数,下同)复合粉末涂层的实验研究。使用往复式磨损试验机对不同涂层材料的熔覆层进行干摩擦磨损实验,利用金相显微镜、扫描电镜(SEM)观察和分析熔覆层的显微组织与磨损形貌。结果表明:复合粉末通过原位反应生成弥散分布的TiC颗粒增强复合涂层,随着(SiC+Ti)含量的增加,颗粒状TiC的尺寸和数目逐渐增加;复合粉(SiC+Ti)含量达到60%时,微观组织有气孔和夹杂缺陷;复合粉(SiC+Ti)含量为48%时,熔覆层耐磨性最佳;复合涂层的磨损主要为磨粒磨损,机理为微观切削和挤压剥落。     

Connecting the macro- and microstrain responses in technical porous ceramics: modeling and experimental validations

The relation between the macroscopic and the microscopic (lattice) strain response to external uniaxial stress has been investigated for porous ceramics. Analytical and finite element modeling (FEM) have been performed and neutron diffraction data on porous sintered alumina and extruded honeycomb SiC have been used to validate the theoretical approach. By FEM simulations, it is shown that in spite of the complex pore microstructure, shear stresses are small during uniaxial compression. Analytical modeling shows that while the average microscopic stress depends on the applied macroscopic stress only through the porosity p, the average microscopic strain depends on the macroscopic stress through the pore morphology factor m, as well. Novel relationships are proposed to describe this dependence. Analytical calculations and numerical modeling perfectly agree with each other, and both show good consistency with experiments. As predicted, it has been observed that the microscopic (diffraction) Young’s modulus does not depend on the pore morphology factor, and follows the rule-of-mixtures, while the microscopic Poisson’s ratio does not even depend on porosity, but is equal to the value for the dense material property. A practical implication of these findings is that it is not possible to attach a pore morphology factor to a material, unless the processing conditions are tailored to vary p without varying m. In fact, the different values of m found for the different porosities explain why many models can be used to rationalize the experimental data. With the proposed method, the factor m can be independently evaluated by the use of macro- and micro-elastic properties of the porous body. Analogously, the macroscopic elastic properties of the dense material can be obtained by macroscopic and microscopic values measured on the correspondent porous material.     

树脂基纤维复合材料的热残余应力数值分析

以环氧树脂R368-1/硼纤维复合材料为研究对象,采用柱体单胞结构,建立了三维有限元分析模型。考虑试样加工制备过程和常温使用时的温度差,对残余应力分布特点和应力水平进行了讨论,给出了应力分布云图和应力沿径向的分布规律。进一步考察了纤维体积分数、温度差和附加界面层对残余应力分布的影响,结果表明,基体主要受拉伸应力作用,纤维主要受压缩应力作用,纤维体积分数增加和附加界面层有助于改善复合材料中残余应力的分布,试样制备温度的升高对纤维中应力的增加具有较大影响。     

中锰钢表面堆焊TiC的组织与性能

中锰钢预热系数小,膨胀系数高且具有良好的耐磨特性,在工业领域应用广泛。但因其运行环境恶劣,常受到外界压力的持续冲击,加之铸造过程中表面形成气孔、夹杂等缺陷使得中锰钢常因疲劳而破裂损坏。为了解决这一问题,运用表面改性技术,使用自蔓延特种陶瓷焊条对坦克装甲履带中锰钢表面进行焊接,在中锰钢的表面熔入大量的 TiC 颗粒。实验结果表明：熔有陶瓷相的中锰钢的表面组织更加均匀,气孔明显减少,并且 TiC 陶瓷相均匀分布在中锰钢中,与中锰钢组织结合良好,无明显裂纹出现。实验证明 TiC 陶瓷相的加入可有效地提高中锰钢的硬度和耐磨性能。     

Elastic analysis of a half-plane with multiple inclusions using volume integral equation method

A volume integral equation method (VIEM) is used to calculate the elastostatic field in an isotropic elastic half-plane containing circular inclusions subject to remote loading parallel to the traction-free boundary. The material of the inclusions may be either isotropic or anisotropic and they are assumed to be distributed in square or hexagonal array. A detailed analysis of the stress field at the interface between the matrix and one of the inclusions is carried out for different distances between the inclusion and the surface of the half-plane. The results of the calculations are compared with available results. The VIEM is shown to be very accurate and effective for investigating the local stresses in the presence of multiple inclusions. The method can be applied to multiple inclusions of arbitrary geometry and elastic properties embedded in extended isotropic elastic media.     

Interfacial phenomenology of SiC fibre reinforced Li2O·Al2O3·6SiO2 glass-ceramic composites

The microstructures of SiC fibre-reinforced Li₂O·Al₂O₃·6SiO₂ glass-ceramic composites with Ta₂O₅, Nb₂O₅, TiO₂ and ZrO₂ dopants were investigated. An amorphous carbon-rich layer, from 100–170 nm thick, was observed in the interfacial region between fibre and matrix. A second interfacial layer of TaC, NbC, or TiC precipitates, appeared adjacent to the C-rich layer. Low bond strength between these two interfacial layers resulted in low interfacial shear strength, and this in turn led to an increase in toughness of the composites containing 4 mol% Ta₂O₅ or Nb₂O₅ dopant. 2 mol% Ta₂O₅ dopant in this composite acted as a nucleating agent for the matrix but was not adequate to form an appreciable volume of TaC particles in the interfacial region, hence a flexural strength decrease was observed. The composite containing TiO₂ dopant exhibited low flexural strength and fracture toughness resulting from the formation of a TiC layer which had a larger coherent bond strength with the interfacial C-rich layer, and attacked the structural integrity of the fibres.