A multi-scale constitutive model for the sintering of an air-plasma-sprayed thermal barrier coating, and its response under hot isostatic pressing

A micromechanical model is developed for the sintering of an air-plasma-sprayed, thermal barrier coating, and is used to make predictions of microstructure evolution under free sintering and under hot isostatic pressing. It is assumed that the splats of the coating are separated by penny-shaped cracks; the faces of these cracks progressively sinter together at contacting asperities, initially by the mechanism of plastic yield and subsequently by interfacial diffusion. Diffusion is driven by the reduction in interfacial energy at the developing contacts of the cracks and also by the local contact stress at asperities. The contact stress arises from the remote applied stress and from mechanical wedging of the rough crack surfaces. Sintering of the cracks leads to an elevation in both the macroscopic Young's modulus and thermal conductivity of the coating, and thereby leads to a degradation in thermal performance and durability. An assessment is made of the relative roles of surface energy, applied stress and crack face roughness upon the sintering response and upon the evolution of the pertinent mechanical and physical properties. The evolution in microstructure is predicted for free sintering and for hot isostatic pressing in order to provide guidance for experimental validation of the micromechanical model.     

A discrete model for long time sintering

A discrete model for the sintering of polydisperse, inhomogeneous arrays of cylinders is presented with empirical contact force-laws, taking into account plastic deformations, cohesion, temperature dependence (melting), and long-time effects. Samples are prepared under constant isotropic load and are sintered for different sintering times. Increasing both external load and sintering time leads to a stronger, stiffer sample after cooling down. The material behavior is interpreted from both microscopic and macroscopic points of view.Among the interesting results is the observation that the coordination number, even though it has the tendency to increase, sometimes slightly decreases, whereas the density continuously increases during sintering—this is interpreted as an indicator of reorganization effects in the packing. Another result of this study is the finding that strongly attractive contacts occur during cool-down of the sample and leave a sintered block of material with almost equally strong attractive and repulsive contact forces.     

A dislocation density based material model to simulate the anisotropic creep behavior of single-phase and two-phase single crystals

The primary and secondary creep behavior of single crystals is observed by a material model using evolution equations for dislocation densities on individual slip systems. An interaction matrix defines the mutual influence of dislocation densities on different glide systems. Face-centered cubic (fcc), body-centered cubic (bcc) and hexagonal closed packed (hcp) lattice structures have been investigated. The material model is implemented in a finite element method to analyze the orientation dependent creep behavior of two-phase single crystals. Three finite element models are introduced to simulate creep of a γ′ strengthened nickel base superalloy in 〈1 0 0〉, 〈1 1 0〉 and 〈1 1 1〉 directions. This approach allows to examine the influence of crystal slip and cuboidal microstructure on the deformation process.     

Al2O3—40%TiO2和Cr2O3等离子喷涂层的摩擦磨损特性

研究了AC4C铸铝合金表面等离子喷涂Al2O3-40%TiO2和Cr2O3陶瓷粉末涂层的滑动摩擦磨损特性;采用划痕试验方法测定了涂层与基体之间的结合强度;用扫描电子显微镜观察分析了磨痕形貌和涂层显微组织特征.研究结果表明:Cr2O3涂层的摩擦学性能优于Al2O3-40%TiO2涂层;涂层的结合强度、硬度和表面空隙对磨损影响较大;Al2O3-40%TiO2涂层的磨损机理主要表现为塑性变形和层状剥离;而Cr2O3涂层则主要为磨粒磨损     

A theory for stress-driven interfacial damage upon cationic-selective oxidation of alloys

Imagine a void at an interface, separating an outwardly growing oxide and a substitutional solid solution of two metallic elements A and B. Assume the metal interface oxidizes, but the void-free surface does not. Interdiffusion inside the metal, and misfit dislocation activities at the oxidizing interface, both generate a stress-free strain rate field. The compositional and material constraints in the presence of a non-oxidizing void give rise to a multi-axial tensile stress field, while a viscoplastic strain field arises to relax stress. The tensile stress at the interface enforces a concave curvature near the void tip through the continuity condition of the chemical potential. Atoms interflow along the void surface under the combined action of curvature, stress and composition gradients. They enter the metal/oxide interface and flow under the action of local stress, curvature and composition fields. The void grows. The stress at the interface relaxes, and the interface recedes partially and non-uniformly. Interfacial voiding upon cationic-selective oxidation is a long-standing topic in the world of thermal barrier coating and interconnect systems. This paper develops governing equations, within the alloy, for stress generation upon composition evolution and induced plastic strain. Governing equations at the interface and the void surface are next formulated to describe a moving boundary problem that accounts for the simultaneous void extension and interface recession. These governing equations are boundary conditions for the bulk formulation.     

A method for the evaluation of design limits for structural materials in a cyclic state of creep

The purpose of the present paper is to demonstrate how the minimum theorems proposed in an accompanying paper (Ponter and Boulbibane, 2002) can be utilised in the prediction of the deformation and life assessment of structures subjected to cyclic mechanical and thermal loadings. The developed method, which is based upon bounding theorems and an associate programming method, the Linear Matching method, takes into account the changes in residual stress field occurring within a cycle. Although the solution provided a bound on the inelastic work, it also appears that generally the displacements predicted by this solution are smaller than those that would be predicted by the rapid cycle solution. By way of illustration a simple non-linear viscous model is adopted and a number of solutions are presented involving a Bree plate problem subjected to cyclic histories of load and temperature. An elastic follow-up factor is identified as a key design parameter for high temperature dwell periods.     

Interrelation of creep and relaxation for nonlinearly viscoelastic materials: application to ligament and metal

Creep and stress relaxation are known to be interrelated in linearly viscoelastic materials by an exact analytical expression. In this article, analytical interrelations are derived for nonlinearly viscoelastic materials which obey a single integral nonlinear superposition constitutive equation. The kernel is not assumed to be separable as a product of strain and time dependent parts. Superposition is fully taken into account within the single integral formulation used. Specific formulations based on power law time dependence and truncated expansions are developed. These are appropriate for weak stress and strain dependence. The interrelated constitutive formulation is applied to ligaments, in which stiffness increases with strain, stress relaxation proceeds faster than creep, and rate of creep is a function of stress and rate of relaxation is a function of strain. An interrelation was also constructed for a commercial die-cast aluminum alloy currently used in small engine applications.     

A methodology to model the complex morphology of rough interfaces

A methodology is proposed to model the complex morphology of rough interfaces using Fourier techniques and image analysis. It allows an optimal representation of a rough interface so as to enable a realistic calculation of the local stress and strain fields in the interface vicinity using finite element techniques. The methodology is illustrated through a sensitivity analysis carried out on a thermal barrier coating system. Typical bi-material interfaces with different levels of morphological complexity are described in 2D and 3D using both periodic (sinusoidal) and Fourier functions. The results are discussed in terms of their relative accuracy.     

Measuring device for precise evaluation of torsional creep and recovery data

An apparatus has been designed and built up to determine the shear creep compliance and viscosity with high accuracy in a wide range of temperature and time. The characteristic feature of this apparatus is the possibility to measure directly the recoverable compliance and to determine the steady state recoverable complianceJ _e . Disturbing instrumental forces are minimized by use of a magnetic bearing. The torque is applied inductively by a modified three phase asynchronous motor. The torsional angle is measured with a laser beam reflected from a mirror to an electro-optical measuring device. Sample thermostating is performed by radiation in a heating chamber, which allows observation of the specimen during measurement.First results of creep and creep recovery measurements are reported, which were carried out on a technical polystyrene above the glass rubbery transition.Dedicated to Prof. Dr. H. Janeschitz-Kriegl on the occasion of his 60th birthday.     

几种等离子喷涂陶瓷涂层之固体粒子冲蚀磨损的特性与数学模型

研究了几种等离子喷涂陶瓷（Ａｌ＿２Ｏ＿３、Ａｌ＿２Ｏ＿３－ＴｉＯ＿２、Ｃｒ＿２Ｏ＿３和ＺｒＯ＿２）涂层的固体粒子冲蚀磨损特性及其冲蚀磨损机理，同时根据冲蚀磨损表面形貌特征的扫描电子显微镜观察，并且从准静态压印断裂分析入手，提出了这类陶瓷涂层在固体粒子于较低速度和较小角度冲击下的冲蚀磨损数学模型（试验选用的粒子冲击速度有３０ｍ／ｓ和７０ｍ／ｓ的两种，冲击角度为３０°）．研究结果表明，固体粒子冲击压印断裂－层状剥落是这类陶瓷涂层的主要冲蚀磨损机理。根据所提出的模型得到涂层的体积冲蚀磨损率Ｅｖ与其硬度ＨＶ呈反比关系（即Ｅｖ∝ＨＶ－１），这与试验结果相符；由该模型推导出涂层的Ｅｖ之速度指数ｎ＝２．１，这与试验结果基本相符。按照这种模型，对于固体粒子以较低速度和较小角度冲击的情况，高硬度的陶瓷涂层具有较高的冲蚀磨损抗力；通过改善陶瓷涂层的断裂韧性，可以有效地提高其在正向冲击时的冲蚀磨损抗力。     

不同基体高铝青铜等离子喷焊层组织与摩擦磨损机理

采用等离子喷焊技术在不同基体上制备耐磨高铝青铜喷焊涂层,研究喷焊层与基体之间元素扩散对喷焊层组织的影响,并在室温条件下采用销-盘式摩擦磨损试验机考察喷焊层的摩擦磨损性能,进而分析喷焊层的磨损机理.结果表明:三种基体喷焊层在干摩擦条件下摩擦磨损机理存在明显差异,45钢基体喷焊层中团聚状k相易与对摩件发生黏着,脱落成为磨粒,导致严重的磨粒磨损,摩擦系数大;ZQAl9-4铝青铜基体喷焊层中脆性共晶组织(α+γ2)呈网状分布,断裂韧性对材料的磨损起支配作用,主要磨损机制为疲劳磨损与磨粒磨损;T3紫铜基体喷焊层中k相呈细小梅花状,均匀分布在固溶度较大的β'相中,涂层抵抗弹性变形能力提高,疲劳磨损机制得到抑制,摩擦系数小.     

A length-dependent model for the thermomechanical response of ceramics

We present a length-dependent model for the thermomechanical response of ceramics through a concurrent multiscale scheme that accounts for: (i) the locally varying values of the sub-grain thermal conductivity tensor due to the interaction of phonons with microstructural features such as grain boundaries, and (ii) a continuum model of thermal stresses that explicitly resolves the polycrystalline structure of the material. At the sub-grain level, we compute the values of the thermal conductivity tensor using the Boltzmann transport equation under the relaxation time approximation. At the continuum level, the polycrystalline structure of the specimen is resolved explicitly by a finite element mesh and the texture of the polycrystal is assumed to be given. At this level, we adopt a Fourier model of heat conduction which utilizes values of thermal conductivity obtained at the lower scale. The mechanical response of the grains is modeled as elastic and anisotropic. The capabilities of the model are demonstrated through a series of examples, which highlight the potential of our approach for designing materials with improved thermomechanical response.     

The accuracy of some formulae for the interconversion of creep and stress-relaxation data

The accuracy of the approximation formulaeJ (t) ~ 1/G (t) andd lnJ (t)/d lnt ~ —d lnG (t)/d lnt, which interconnect stress-relaxation modulusG (t) and creep complianceJ (t) and their double logarithmic rates are investigated. For glassy polymers, the errors in the first formula are less than 1–2%, and in the second, they are generally in the order of a few percent, too. Similar estimates can also be found for the real parts of the analogous complex functionsJ ^* () andG ^* ().     

A nonlinear atomization model for computation of drop size distributions and spray simulations

A model has been developed to provide a comprehensive simulation of a spray formed by a high‐speed liquid jet. The primary atomization process is simulated in a completely nonlinear fashion using the boundary element method under the assumption of axisymmetric, inviscid flow. The presence of the orifice boundary layer is simulated with a ring vortex whose strength and location are uniquely determined from boundary layer properties at the orifice exit plane. Droplet and axisymmetric ligament tracking models have been developed to provide more comprehensive spray simulations. The breakup of the axisymmetric ligaments shed from the parent surface is assessed both in a nonlinear fashion as well as using the linear stability analysis of Ponstein. Using this latter approach, drop size distributions have been generated from first principles and compared with the popular Rosin–Rammler model. Copyright © 2005 John Wiley & Sons, Ltd.     

A fuzzy model for the failure of composite structures

In this paper, the fuzzy theory is used to describe the uncertainty in failure definition of composite structures. The concept of structural failure level (SFL) is suggested and a method of evaluation is presented.     

A fractional non-linear creep model for coal considering damage effect and experimental validation

Accurate prediction of coal׳s creep behavior is of great significance to coalbed methane extraction. In this study, taking into account the visco-elastic–plastic characteristics and the damage effect, a fractional non-linear model is proposed to describe the creep behavior of coal. The constitutive and creep equations of the proposed fractional non-linear model are derived via the Boltzmann superposition principle and discrete inverse Laplace transform. Furthermore, uniaxial creep tests under different axial stress conditions were carried out to validate the proposed model. It is found that the present model can describe the experimental data from creep tests with better accuracy than classical models. Particularly, the present model can predict the accelerating creep deformation of coal which classical models fail to reproduce. Finally, the parametric sensitivity analysis is performed to investigate the effects of model parameters on the creep strain. It is verified that the introduction of fractional parameters and damage factor in the present model is essential to accurate prediction of the full creep stage of coal.     

等离子喷涂Al2O3/TiO2纳米复合涂层的制备、结构及摩擦学性能

采用喷雾干燥法对溶胶-凝胶法合成的系列A l2O3/TiO2纳米复合粉体进行造粒,使用等离子喷涂技术制备系列A l2O3/TiO2纳米复合涂层.对涂层结构和形貌分析表明所制备的A l2O3/TiO2纳米复合涂层形成了具有熔融区和半熔融区的双区形态的纳米复合结构.使用UMT-2MT试验机研究了复合涂层的摩擦磨损性能,结果表明复合涂层的磨损率随TiO2含量的增加表现出先降低而后增大的趋势,TiO2质量百分数为10%的纳米复合涂层的磨损率最低;而涂层的摩擦系数随TiO2含量的增加变化不大.复合涂层的磨损机制为裂纹扩展导致的磨损剥落.     

A chemo-thermo-mechanically coupled theory for elastic-viscoplastic deformation, diffusion, and volumetric swelling due to a chemical reaction

Thermal barrier coatings (TBCs) are applied to superalloy turbine blades to provide thermal insulation and oxidation protection. A TBC consists of an oxide/metal bilayer: the outer oxide layer (top-coat) imparts thermal insulation, while the metallic layer (bond-coat) affords oxidation protection through the formation of a thermally-grown-oxide (TGO) at elevated temperatures. The TGO layer possesses significantly different elastic, thermal expansion, and creep properties than the surrounding top-coat and bond-coat layers. An intrinsic mechanism which controls the long-term stability and mechanical integrity of a TBC is the volumetric change accompanying the oxide formation, and the attendant locally large stresses that can arise due to the geometrically uneven development of the TGO layer. In this paper we focus on modeling the response of the bond-coat material and its oxidation, and present a new continuum-level thermodynamically-consistent, large-deformation, fully three-dimensional theory which couples high-temperature elastic-viscoplastic deformation of the material with diffusion of oxygen, eventually leading to an oxidation reaction in which the reaction-product causes permanent swelling.The theory is chemo-thermo-mechanically coupled and complex, and at this point in time the list of material parameters appearing in the theory are not fully known. Once the material parameters in our theory are calibrated from suitable experiments, and the theory is numerically-implemented and validated, then the numerical simulation capability should provide an important ingredient for analyzing the evolution of the local stress and strain states which are important ingredients for the life-prediction and performance-improvement of TBCs.