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Stress evolution in thermal barrier coatings for rocket engine applications 火箭发动机用热障涂层的应力演化
IF 4.03 Pub Date : 2015-09-05 DOI: 10.1186/s40759-015-0005-2
Martin Bäker, Torben Fiedler, Joachim Rösler

Thermal barrier coatings are a promising concept to improve the lifetime of the copper liner of a rocket engine. Due to the high heat fluxes and the large thermal conductivity of copper, coatings have to be designed especially for this application.

In this paper, we perform fully thermo-mechanically coupled finite element analyses of a small section of a combustion chamber with a coating system comprising a NiCuCrAl bond coat and a NiCrAlY top coat.

Heat fluxes are calculated to determine reasonable coating thickness values. Elastic and plastic deformation in the materials is considered to study the stress evolution. A crack model serves to estimate the possibility of vertical cracks propagating through the coating system.

Several design guidelines are developed from these results that will aid future development of thermal barrier coatings.

热障涂层是一个很有前途的概念,可以提高火箭发动机铜衬里的使用寿命。由于铜的高热流通量和大导热性,必须专门为这种应用设计涂层。在本文中,我们对燃烧室的一小部分进行了完全热-机械耦合有限元分析,该燃烧室的涂层系统包括NiCuCrAl结合涂层和NiCrAlY面涂层。计算热通量以确定合理的涂层厚度值。考虑材料的弹塑性变形来研究应力演化。裂纹模型用于估计垂直裂纹在涂层系统中传播的可能性。从这些结果中制定了一些设计准则,这些准则将有助于热障涂层的未来发展。
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引用次数: 16
Strain gradient elasticity with geometric nonlinearities and its computational evaluation 几何非线性应变梯度弹性及其计算评价
IF 4.03 Pub Date : 2015-07-08 DOI: 10.1186/s40759-015-0004-3
B Emek Abali, Wolfgang H Müller, Victor A Eremeyev

The theory of linear elasticity is insufficient at small length scales, e.g., when dealing with micro-devices. In particular, it cannot predict the “size effect” observed at the micro- and nanometer scales. In order to design at such small scales an improvement of the theory of elasticity is necessary, which is referred to as strain gradient elasticity.

There are various approaches in literature, especially for small deformations. In order to include geometric nonlinearities we start by discussing the necessary balance equations. Then we present a generic approach for obtaining adequate constitutive equations. By combining balance equations and constitutive relations nonlinear field equations result. We apply a variational formulation to the nonlinear field equations in order to find a weak form, which can be solved numerically by using open-source codes.

By using balances of linear and angular momentum we obtain the so-called stress and couple stress as tensors of rank two and three, respectively. Since dealing with tensors an adequate representation theorem can be applied. We propose for an isotropic material a stress with two and a couple stress with three material parameters. For understanding their impact during deformation the numerical solution procedure is performed. By successfully simulating the size effect known from experiments, we verify the proposed theory and its numerical implementation.

Based on representation theorems a self consistent strain gradient theory is presented, discussed, and implemented into a computational reality.

线弹性理论在小长度尺度下是不够的,例如在处理微型装置时。特别是,它不能预测在微观和纳米尺度上观察到的“尺寸效应”。为了在如此小的尺度上进行设计,有必要改进弹性理论,这被称为应变梯度弹性。文献中有各种各样的方法,特别是对于小的变形。为了包含几何非线性,我们首先讨论必要的平衡方程。然后,我们提出了一种获得充分本构方程的一般方法。将平衡方程与本构关系相结合,得到非线性场方程。我们将变分公式应用于非线性场方程,以找到一种可以用开源代码进行数值求解的弱形式。通过使用线动量和角动量的平衡,我们得到了所谓的应力和耦合应力,分别作为第2级和第3级张量。由于是处理张量,所以可以应用一个充分的表示定理。对于各向同性材料,我们提出了两个应力和三个材料参数的一对应力。为了理解它们在变形过程中的影响,执行了数值求解程序。通过成功地模拟实验中已知的尺寸效应,我们验证了所提出的理论及其数值实现。基于表示定理,提出、讨论了自洽应变梯度理论,并将其实现为计算现实。
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引用次数: 63
A study of balloon type, system constraint and artery constitutive model used in finite element simulation of stent deployment 支架展开有限元模拟中球囊型、系统约束及动脉本构模型的研究
IF 4.03 Pub Date : 2015-05-05 DOI: 10.1186/s40759-014-0002-x
A Schiavone, L G Zhao

Finite element is an effective tool to simulate stent expansion inside stenotic arteries, which provides an insightful understanding of the biomechanical behaviour of the whole stent-artery system during the procedure. The choice of balloon type, system constraint and artery constitutive model plays an important role in finite element simulation of stent deployment.

Commercial finite element package ABAQUS was used to model the expansion of Xience stent inside a diseased artery with 40% stenosis. The arterial wall, consisting of intima, media and adventitia layers, and the stenotic plaque were described by different hyperelastic models. Both folded and rubber balloons were considered and inflated with a linearly increasing pressure of 1.4 MPa. Simulations were also carried out by considering free, partially and fully constrained arteries.

Folded balloon produces sustained stent expansion under a lower pressure when compared to rubber balloon, leading to increased stress level and enhanced final expansion for the system. Fully constrained artery reduces the stent expansion when compared to free and partially constrained arteries, due to the increased recoiling effect. Stress in the artery-plaque system has higher magnitude for stent expansion in a free artery due to more severe stretch. Calcified plaque limits stent expansion considerably when compared to hypocellular plaque. The negligence of the second stretch invariant in the strain energy potential leads to the disappearance of saturation behaviour during stent expansion. The use of anisotropic artery model reduces the system expansion at peak pressure when compared to the isotropic model, but with an increased final diameter due to reduced recoiling effect. The stress distribution in the artery-plaque system is also different for different combinations of artery and plaque constitutive models.

Folded balloon should be used in the simulation of stent deployment, with the artery partially constrained using spring elements with a proper stiffness constant. The blood vessel should be modelled as a three-layer structure using a hyperelastic potential that considers both the first and second stretch invariants as well as the anisotropy. The composition of the plaque also has to be considered due to its major effect on stent deployment.

有限元是模拟狭窄动脉内支架扩张的有效工具,它提供了对整个支架-动脉系统在手术过程中的生物力学行为的深刻理解。球囊类型、系统约束和动脉本构模型的选择在支架展开有限元模拟中起着重要作用。采用商业有限元软件ABAQUS对狭窄40%的病变动脉内Xience支架的扩张进行建模。用不同的超弹性模型描述由内膜、中膜和外膜层组成的动脉壁和狭窄斑块。考虑折叠气球和橡胶气球,并以1.4 MPa线性增加的压力进行充气。模拟还考虑了自由、部分和完全受限的动脉。与橡胶球囊相比,折叠球囊在较低的压力下产生持续的支架膨胀,从而增加了应力水平,增强了系统的最终膨胀。与自由和部分受限的动脉相比,完全受限的动脉由于后坐力的增加而减少了支架的扩张。动脉-斑块系统中的应力在游离动脉中由于更严重的拉伸而具有更高的强度。与低细胞斑块相比,钙化斑块限制了支架扩张。应变能势中第二个拉伸不变量的忽略导致支架膨胀过程中饱和行为的消失。与各向异性动脉模型相比,各向异性动脉模型的使用减少了系统在峰值压力下的膨胀,但由于减少了后坐力效应,最终直径增加。不同的动脉和斑块本构模型组合,动脉-斑块系统的应力分布也不同。在模拟支架部署时应使用折叠球囊,使用具有适当刚度常数的弹簧元件对动脉进行部分约束。血管应该建模为一个三层结构,使用超弹性势,同时考虑第一和第二拉伸不变量以及各向异性。斑块的组成也必须考虑,因为它对支架部署有重要影响。
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引用次数: 49
Fatigue crack growth in a nickel-based superalloy at elevated temperature - experimental studies, viscoplasticity modelling and XFEM predictions 高温镍基高温合金疲劳裂纹扩展的实验研究、粘塑性模型和XFEM预测
IF 4.03 Pub Date : 2015-05-05 DOI: 10.1186/s40759-015-0003-4
Farukh Farukh, Liguo Zhao, Rong Jiang, Philippa Reed, Daniela Proprentner, Barbara Shollock

Nickel-based superalloys are typically used as blades and discs in the hot section of gas turbine engines, which are subjected to cyclic loading at high temperature during service. Understanding fatigue crack deformation and growth in these alloys at high temperature is crucial for ensuring structural integrity of gas turbines.

Experimental studies of crack growth were carried out for a three-point bending specimen subjected to fatigue at 725°C. In order to remove the influence of oxidation which can be considerable at elevated temperature, crack growth was particularly tested in a vacuum environment with a focus on dwell effects. For simulation, the material behaviour was described by a cyclic viscoplastic model with nonlinear kinematic and isotropic hardening rules, calibrated against test data. In combination with the extended finite element method (XFEM), the viscoplasticity model was further applied to predict crack growth under dwell fatigue. The crack was assumed to grow when the accumulated plastic strain ahead of the crack tip reached a critical value which was back calculated from crack growth test data in vacuum.

Computational analyses of a stationary crack showed the progressive accumulation of strain near the crack tip under fatigue, which justified the strain accumulation criterion used in XFEM prediction of fatigue crack growth. During simulation, the crack length was recorded against the number of loading cycles, and the results were in good agreement with the experimental data. It was also shown, both experimentally and numerically, that an increase of dwell period leads to an increase of crack growth rate due to the increased creep deformation near the crack tip, but this effect is marginal when compared to the dwell effects under fatigue-oxidation conditions.

The strain accumulation criterion was successful in predicting both the path and the rate of crack growth under dwell fatigue. This work proved the capability of XFEM, in conjunction with advanced cyclic viscoplasticity model, for predicting crack growth in nickel alloys at elevated temperature, which has significant implication to gas turbine industries in terms of “damage tolerance” assessment of critical turbine discs and blades.

镍基高温合金通常用作燃气涡轮发动机热部件的叶片和盘,这些部件在使用过程中要承受高温循环载荷。了解这些合金在高温下的疲劳裂纹变形和扩展对确保燃气轮机结构的完整性至关重要。在725℃的疲劳条件下,对三点弯曲试样进行了裂纹扩展实验研究。为了消除氧化的影响(氧化在高温下可能是相当大的),在真空环境中特别测试了裂纹扩展,重点是驻留效应。为了进行模拟,材料的行为由一个具有非线性运动和各向同性硬化规则的循环粘塑性模型来描述,并根据测试数据进行校准。结合扩展有限元法(XFEM),将粘塑性模型进一步应用于长居疲劳裂纹扩展预测。当裂纹尖端前方的累积塑性应变达到临界值时,假定裂纹开始扩展,该临界值由真空条件下裂纹扩展试验数据反演得到。对静止裂纹的计算分析表明,在疲劳作用下,裂纹尖端附近的应变逐渐累积,证明了XFEM预测疲劳裂纹扩展的应变累积准则是正确的。在模拟过程中,记录了裂纹长度与加载循环次数的关系,结果与实验数据吻合较好。实验和数值结果还表明,裂纹尖端附近蠕变变形的增加导致裂纹扩展速率的增加,但与疲劳氧化条件下的蠕变效应相比,这种影响是微不足道的。应变累积准则可以成功地预测裂纹在疲劳状态下的扩展路径和扩展速率。这项工作证明了XFEM结合先进的循环粘塑性模型预测高温下镍合金裂纹扩展的能力,这对燃气轮机工业在关键涡轮盘和叶片的“损伤容限”评估方面具有重要意义。
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引用次数: 19
Validated predictive computational methods for surface charge in heterogeneous functional materials: HeteroFoaM™ 非均质功能材料表面电荷的验证预测计算方法:HeteroFoaM™
IF 4.03 Pub Date : 2015-05-05 DOI: 10.1186/s40759-014-0001-y
Kenneth L Reifsnider, Dan G Cacuci, Jeffrey Baker, Jon Michael Adkins, Fazle Rabbi

Essentially all heterogeneous materials are dielectric, i.e., they are imperfect conductors that generally display internal charge displacements that create dissipation and local charge accumulation at interfaces. Over the last few years, the authors have focused on the development of an understanding of such behaviour in heterogeneous functional materials for energy conversion and storage, called HeteroFoaM (www.HeteroFoaM.com). Using paradigm problems, this work will indicate major directions for developing generally applicable methods for the multiphysics, multi-scale design of heterogeneous functional materials.

The present paper outlines the foundation for developing validated predictive computational methods that can be used in the design of multi-phase heterogeneous functional materials, or HeteroFoaM, as a genre of materials. Such methods will be capable of designing not only the constituent materials and their interactions, but also the morphology of the shape, size, surfaces and interfaces that define the heterogeneity and the resulting functional response of the material system.

Relationships to applications which drive this development are identified. A paradigm problem based on dielectric response is formulated and discussed in context.

We report an approach that defines a methodology for designing not only the constituent material properties and their interactions in a heterogeneous dielectric material system, but also the morphology of the shape, size, surface, and interfaces that defines the heterogeneity and the resulting functional response of that system.

基本上所有的非均质材料都是介电的,也就是说,它们是不完美的导体,通常会显示内部电荷位移,从而在界面处产生耗散和局部电荷积累。在过去的几年里,作者专注于对能量转换和存储的异质功能材料的这种行为的理解的发展,称为HeteroFoaM (www.HeteroFoaM.com)。利用范式问题,这项工作将为开发多物理场、多尺度异质功能材料设计的普遍适用方法指明主要方向。本文概述了开发可用于多相异质功能材料(HeteroFoaM)设计的有效预测计算方法的基础。这些方法不仅能够设计组成材料及其相互作用,而且能够设计形状、大小、表面和界面的形态,这些形态定义了材料系统的异质性和由此产生的功能响应。确定与驱动此开发的应用程序的关系。本文提出并讨论了一个基于介电响应的范式问题。我们报告了一种方法,该方法定义了一种方法,不仅可以设计非均质介电材料系统中的组成材料特性及其相互作用,还可以设计形状、尺寸、表面和界面的形态,这些形态定义了该系统的非均质性和由此产生的功能响应。
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引用次数: 3
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Mechanics of Advanced Materials and Modern Processes
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