具有表面效应的球形纳米电极颗粒中的反应-扩散-力学全耦合分析

表面效应在纳米电极颗粒中占有主导地位,论文首先建立了锂离子电池充放电过程中考虑表面效应的反应-扩散-力学全耦合模型;然后对比了有无表面效应对锂离子浓度、径向应力和环向应力的影响;最后探讨了反应系数和尺寸效应对浓度和扩散诱导应力的影响.数值结果表明表面效应随着充电时间的增加逐渐减小直至充电结束趋于稳定;表面压效应对本模型的浓度无影响但抑制了扩散诱导应力的增加;较慢的化学反应和较小的纳米电极颗粒尺寸可抑制电极应力的增加.     

锂离子薄膜电极充放电变形的原位实验观测方法

锂离子薄膜电极在充放电过程中的力学变形会严重影响锂离子电池的性能和使用寿命。本文提出一种原位观测锂离子薄膜电极充放电变形的实验方法,该方法通过设计一种新型的实验室模型电池,并采用基于位相增量叠加的相移电子散斑干涉方法测量变形,成功实现了对锂离子薄膜电极充放电变形的原位实验观测。实验结果表明,锂离子薄膜电极在充放电过程中会产生周期性的变形,该变形宏观上与电池的SOC(State of Charge,充电状态)相关,微观上则与锂离子在电极活性材料中的嵌入/脱出过程对应。该实验方法为深入研究锂离子薄膜电极变形对锂离子电池性能的影响提供了一种有力的实验手段。     

基于统一相场理论的锂电池电极颗粒断裂模拟研究

锂电池充放电过程中, 锂离子的脱出和嵌入会引发电极颗粒的不均匀体积变化和机械应力. 上述锂离子扩散过程诱发的应力与电极颗粒的尺寸大小、截面形状和冲放电速率有关, 可能会导致电极颗粒出现裂缝起裂、扩展甚至断裂等力学失效, 对锂离子电池的容量和循环寿命等性能产生不利影响. 为准确模拟并预测电极颗粒的力学失效过程, 在笔者前期提出的统一相场理论框架内进一步考虑化学扩散、力学变形和裂缝演化等耦合过程, 建立化学–力学耦合相场内聚裂缝模型, 发展相应的多场有限元数值实现算法, 并应用于二维柱状和三维球体锂电池电极颗粒的力学失效分析. 由于同时涵括了基于强度的起裂准则、基于能量的扩展准则以及基于变分原理的裂缝路径判据, 这一模型不仅适用于带初始缺陷电极颗粒的开裂行为模拟, 而且适用于无初始缺陷电极颗粒的损伤破坏全过程分析. 数值计算结果表明, 相场内聚裂缝模型能够模拟锂离子扩散引发的电极颗粒裂缝起裂、扩展、汇聚等复杂演化过程, 可为锂离子电池电极颗粒的力学失效预测和优化设计提供有益的参考.      

无限介质中单个纳米涂层夹杂反平面问题的两个模型

采用零厚度界面模型和界面层模型研究了无限介质中单个纳米涂层圆柱形夹杂的反平面问题，利用复变函数方法获得了两种模型夹杂、涂层和基体内应力场的封闭解析解．研究表明，当界面层模型中的界面相厚度趋于零时，界面层模型可以解析地退化为零厚度界面模型．数值算例分析了界面模量不同取值时应力场的分布和应力的尺度依赖性．本文结果丰富了对纳米夹杂力学行为的认识，并可为直接采用零厚度界面模型有困难的纳米夹杂问题的研究提供有价值的参考．     

高温超导带材超导涂层局部脱黏后的电磁力学行为分析

高温超导带材因其高载流z能力、低交流损耗等优点, 在超导领域得到了广泛的关注, 然而在带材的应用中出现的力学问题严重阻碍了其应用. 基于此, 本文分析了受外部磁场激励YBCO高温超导带材在超导层局部脱黏后的电磁力学响应. 基于超导临界态Bean模型和弹性力学平面应变方法, 给出了超导薄膜内正应力与基底界面处切应力相关联的控制方程, 基于数值方法研究了超导薄膜内的正应力及基底界面处的切应力随外部磁场的变化规律. 结果显示: 在脱黏区域附近, 超导薄膜内的正应力和基底$\!-\!$薄膜界面处的切应力急剧增大, 该正应力及切应力极易引起超导层的进一步脱黏. 同时, 剪切应力在结构边缘处出现极值. 基底材料的属性, 特别是杨氏模量对结构内的应力影响显著, 在软基底材料结构中, 超导薄膜内将出现较大的正应力, 而基底材料较硬时, 在基底$\!-\!$薄膜界面处将出现较大的剪切应力, 这些因素均会引起超导涂层结构的力学及电学性能的退化. 本文研究可望为超导带材的加工制备及脱黏的处理提供一定的理论指引.      

CTS试样I/II混合型断裂特性数值计算研究

采用CTS试样研究I/II混合型断裂特性计算裂纹前缘应力强度因子时可采用解析公式,一旦裂纹发生扩展,解析公式便不再适用。文中采用有限元法研究紧凑拉伸剪切（CTS）试样在I/II平面混合型加载下的裂纹扩展行为。采用ANSYS建立CTS试样I/II混合型测试系统有限元模型,为模拟真实受力状态,在CTS试样-销-扇型夹具以及扇型夹具-销-U型夹具之间分别建立接触对进行接触力学分析。通过与解析公式结果进行对比验证了该数值方法的可靠性。采用最大环向应力准则（MTS）,模拟了CTS试样不同加载角度下的裂纹扩展路径,获得了裂纹扩展路径中应力强度因子随裂纹长度的变化曲线,解释了裂纹扩展路径不与外载荷方向垂直的原因。结合文中计算结果,在CTS试样I/II混合型裂纹扩展速率实验测得裂纹长度与寿命的关系曲线a-N的基础上,便可得到材料I/II型混合型裂纹扩展速率曲线。     

CTS试样Ⅰ/Ⅱ混合型断裂特性数值计算研究

采用CTS试样研究Ⅰ/Ⅱ混合型断裂特性计算裂纹前缘应力强度因子时可采用解析公式,一旦裂纹发生扩展,解析公式便不再适用.文中采用有限元法研究紧凑拉伸剪切(CTS)试样在Ⅰ/Ⅱ平面混合型加载下的裂纹扩展行为.采用ANSYS建立CTS试样Ⅰ/Ⅱ混合型测试系统有限元模型,为模拟真实受力状态,在CTS试样-销-扇型夹具以及扇型夹具-销-U型夹具之间分别建立接触对进行接触力学分析.通过与解析公式结果进行对比验证了该数值方法的可靠性.采用最大环向应力准则(MTS),模拟了CTS试样不同加载角度下的裂纹扩展路径,获得了裂纹扩展路径中应力强度因子随裂纹长度的变化曲线,解释了裂纹扩展路径不与外载荷方向垂直的原因.结合文中计算结果,在CTS试样Ⅰ/Ⅱ混合型裂纹扩展速率实验测得裂纹长度与寿命的关系曲线a-N的基础上,便可得到材料Ⅰ/Ⅱ型混合型裂纹扩展速率曲线.     

网链缠结对凝胶薄膜起皱的影响

凝胶薄膜在变形时易发生屈曲、起皱等失稳现象,这在凝胶薄膜的应用中是非常重要的．近年来,针对凝胶薄膜的屈曲、起皱失稳行为,越来越多的科研人员尝试从力学角度进行分析．但是大多数的研究是基于Flory-Rehner弹性凝胶理论,未考虑凝胶网链缠结引起的物理交联对凝胶自由能的影响,模型精度不高．本文采用Edwards-Vilgis所提出的Slip-link模型对平面内起皱的凝胶薄膜进行分析,研究了不伸展参数、滑移参数对聚合物凝胶增量模量的影响以及不伸展参数、滑移参数、基底材料泊松比对凝胶薄膜起皱时的临界波长和临界应力的影响．结果表明：化学势在一定范围内变化时,随着化学势的增加,增量模量、临界波长、临界应力减小;不可伸长参数越大,增量模量、临界波长及临界应力越大;滑移参数越大,增量模量、临界波长及临界应力越小．     

纳米压痕法测磁控溅射铝薄膜屈服应力

为了在考虑残余应力下测量出磁控溅射铝薄膜的屈服应力,提出了一种实验测量方法,通过曲率测试法和球形压头纳米压痕法测出磁控溅射铝薄膜的屈服应力．建立球形压痕力学模型,并用ANSYS对球形压痕进行力学有限元仿真,利用直流磁控溅射技术在硅基上淀积一层1 μm厚的铝薄膜,首先通过曲率测试法测量膜内等双轴残余应力,再利用最小二乘曲线拟合法从薄膜/基底系统的球形压头纳米压痕实验数据中提取出铝薄膜的屈服应力,测得磁控溅射铝薄膜的屈服应力为371 MPa．该方法也可以用来研究其他材料的薄膜和小体积材料的力学特性．     

混凝土圆形骨料周边应力集中系数的解析法1）

由于骨料与砂浆材料力学特性的不同,混凝土内部存在应力集中现象.又由于混凝土内部骨料众多且分布复杂,采用细观力学方法分析混凝土各处应力会遇到计算量大、划分单元困难的难题.因此,针对二维模型推导出了计算混凝土圆形单骨料周边应力集中系数的解析解.根据此解析解,应用叠加方法可通过均匀介质模型近似计算非均匀的混凝土各处应力,使计算模型非常简单.通过对单骨料和四骨料模型进行计算,并与有限元计算结果比较证明本文所给解析方法能够满足精度要求.     

Modeling of progressive delamination in a thin film driven by diffusion-induced stresses

A semi-analytical method based on the cohesive model has been developed to investigate the progressive growth of interface delamination in an axisymmetric thin film electrode driven by diffusion-induced stresses under the assumption that the electrode remains elastic during the Li-ion diffusion process. The evolutions of the cohesive zone and debonding zone with respect to charging time have been predicted. The cohesive zone propagates in an accelerating manner and the debonding zone advances in a slowing down manner. The key parameters that control the interfacial stresses and delamination have been identified from the obtained governing equations. And according to the discussions on the key parameters, design insights into the geometry, charging velocity and material properties of the electrode have been provided.     

A computational model for the indentation and phase transformation of a martensitic thin film

We propose a computational model for a stress-induced martensitic phase transformation of a single-crystal thin film by indentation and its reverse transformation to austenite by heating. Our model utilizes a surface energy that allows sharp interfaces with finite energy and a penalty that forces the film to lie above the indenter and undergo a stress-induced austenite-to-martensite phase transformation. We introduce a method to nucleate the martensite-to-austenite phase transformation since in our model the film would otherwise remain in the martensitic phase in a local minimum of the energy.     

Buckling and postbuckling of a compressed thin film bonded on a soft elastic layer: a three-dimensional analysis

The wrinkling of a stiff thin film bonded on a soft elastic layer and subjected to an applied or residual compressive stress is investigated in the present paper. A three-dimensional theoretical model is presented to predict the buckling and postbuckling behavior of the film. We obtained the analytical solutions for the critical buckling condition and the postbuckling morphology of the film. The effects of the thicknesses and elastic properties of the film and the soft layer on the characteristic wrinkling wavelength are examined. It is found that the critical wrinkling condition of the thin film is sensitive to the compressibility and thickness of the soft layer, and its wrinkling amplitude depends on the magnitude of the applied or residual in-plane stress. The bonding condition between the soft layer and the rigid substrate has a considerable influence on the buckling of the thin film, and the relative sliding at the interface tends to destabilize the system.     

Surfactant spreading on a thin weakly viscoelastic film

A mathematical model is presented for surfactant-driven thin weakly viscoelastic film flows on a flat, impermeable plane. The Oldroyd-B constitutive relation is used to model the viscoelastic fluid. Lubrication theory and a perturbation expansion in powers of the Weissenberg number (We) are employed, which give rise to non-linear coupled evolution equations governing the transport of insoluble surfactant and thin liquid film thickness. Spreading on a Newtonian film is recovered to leading order and corrections to viscoelasticity are obtained at order We. These equations are solved numerically over a wide range of viscosity ratio (ratio of solvent viscosity to the sum of solvent and polymeric viscosities), pre-existing surfactant level and Peclet number (Pe). The effect of viscoelasticity on surfactant transport and fluid flow is investigated and the mechanisms underlying this effect are explored. Shear stress, streamwise normal stress and the temporal rate of change of extra shear stress generated from gradients in surfactant concentration dominate thin viscoelastic film flows whereas only shear stresses play a role in Newtonian thin film flows. Our results also reveal that, for weak viscoelasticity, the influence of viscosity ratio on the evolution of surfactant concentration and film thickness can be significant and varies considerably, depending on the concentration of pre-existing surfactant and surfactant surface diffusivity.     

Stochastic many-particle model for LFP electrodes

In the framework of non-equilibrium thermodynamics, we derive a new model for many-particle electrodes. The model is applied to \(\text {LiFePO}_{4}\) (LFP) electrodes consisting of many LFP particles of nanometer size. The phase transition from a lithium-poor to a lithium-rich phase within LFP electrodes is controlled by both different particle sizes and surface fluctuations leading to a system of stochastic differential equations. An explicit relation between battery voltage and current controlled by the thermodynamic state variables is derived. This voltage–current relation reveals that in thin LFP electrodes lithium intercalation from the particle surfaces into the LFP particles is the principal rate-limiting process. There are only two constant kinetic parameters in the model describing the intercalation rate and the fluctuation strength, respectively. The model correctly predicts several features of LFP electrodes, viz. the phase transition, the observed voltage plateaus, hysteresis and the rate-limiting capacity. Moreover we study the impact of both the particle size distribution and the active surface area on the voltage–charge characteristics of the electrode. Finally we carefully discuss the phase transition for varying charging/discharging rates.     

Model for charge/discharge-rate-dependent plastic flow in amorphous battery materials

Plastic flow is an important mechanism for relaxing stresses that develop due to swelling/shrinkage during charging/discharging of battery materials. Amorphous high-storage-capacity Li–Si has lower flow stresses than crystalline materials but there is evidence that the plastic flow stress depends on the conditions of charging and discharging, indicating important non-equilibrium aspects to the flow behavior. Here, a mechanistically-based constitutive model for rate-dependent plastic flow in amorphous materials, such as Li_xSi alloys, during charging and discharging is developed based on two physical concepts: (i) excess energy is stored in the material during electrochemical charging and discharging due to the inability of the amorphous material to fully relax during the charging/discharging process and (ii) this excess energy reduces the barriers for plastic flow processes and thus reduces the applied stresses necessary to cause plastic flow. The plastic flow stress is thus a competition between the time scales of charging/discharging and the time scales of glassy relaxation. The two concepts, as well as other aspects of the model, are validated using molecular simulations on a model Li–Si system. The model is applied to examine the plastic flow behavior of typical specimen geometries due to combined charging/discharging and stress history, and the results generally rationalize experimental observations.     

A 2D finite element based on a nonlocal constitutive model describing localization and propagation of phase transformation in shape memory alloy thin structures

Here, the effects of localization and propagation of martensitic phase transformation on the response of SMA thin structures subjected to thermo-mechanical loadings are investigated using nonlocal constitutive model in conjunction with finite element method. The governing equations are derived based on variational principle considering thermo-mechanical equilibrium and the spatial distribution of the nonlocal volume fraction of martensite during transformation. The nonlocal volume fraction of martensite is defined as a weighted average of the local volume fraction of martensite over a domain characterized by an internal length parameter. The local version of the thermo-mechanical behavior model derived from micromechanics considers the local volume fraction of martensite and the mean transformation strain. A 4-noded quadrilateral plane stress element with three degrees of freedom per node accounting for in-plane displacements and the nonlocal volume fraction of martensite is developed. Numerical simulations are conducted to bring out the influence of material and geometrical heterogeneities (perturbations/defects) on the localization and propagation of phase transformation in SMA thin structures. Also, a sensitivity analysis of the material response due to the localization and the other related model parameters is carried out. The detailed investigation done here clearly shows that the localization of phase transformation has significant effect on the response of shape memory alloys.     

Grain size effects in multiphase steels assisted by transformation-induced plasticity

The influence of the austenitic grain size on the overall stress–strain behavior in a multiphase carbon steel is analyzed through three-dimensional finite element simulations. A recently developed multiscale martensitic transformation model is combined with a plasticity model to simulate the transformation-induced plasticity effects of a grain of retained austenite embedded in a ferrite-based matrix. Grain size effects are included via a surface energy term in the Helmholtz energy. Tensile simulations for representative orientations of the grain of retained austenite show that the initial stability of the austenite increases as the grain size decreases. Consequently, the effective strength is initially higher for smaller grains. The influence of the grain size on the evolution of the transformation process strongly depends on the grain orientation. For “hard” orientations, the transformation rate is higher for larger grains. In addition, the phase transformation is partially suppressed as the grain size decreases. In contrast, for “soft” orientations, the transformation rate is lower for larger grains. The phase transformation is more homogeneous for smaller grains and, consequently, the effective transformation strain is larger. Nevertheless, in multiphase carbon steels with a relatively low percentage of retained austenite, the influence of the austenitic grain size on the overall constitutive response is smaller than the influence of the austenitic grain orientation.     

Simulation and measurement of 3D shear-driven thin liquid film flow in a duct

Three-dimensional flow behavior of thin liquid film that is shear-driven by turbulent air flow in a duct is measured and simulated. Its film thickness and width are reported as a function of air velocity, liquid flow rate, surface tension coefficient, and wall contact angle. The numerical component of this study is aimed at exploring and assessing the suitability of utilizing the FLUENT-CFD code and its existing components, i.e. Volume of Fluid model (VOF) along with selected turbulence model, for simulating the behavior of 3D shear-driven liquid film flow, through a comparison with measured results. The thickness and width of the shear-driven liquid film are measured using an interferometric technique that makes use of the phase shift between the reflections of incident light from the top and bottom surfaces of the thin liquid film. Such measurements are quite challenging due to the dynamic interfacial instabilities that develop in this flow. The results reveal that higher air flow velocity decreases the liquid film thickness but increases its width, while higher liquid flow rate increases both its thickness and width. Simulated results provide good estimates of the measured values, and reveal the need for considering a dynamic rather than a static wall contact angle in the model for improving the comparison with measured values.     

Wärmeübergang bei der Fallfilmverdampfung

At film evaporation in a vertical tube the heat transfer depends on the flow pattern of the falling film and the shear stress at film surface due to a significant flow in the gas phase. For heat transfer without superimposed gas flow equations exist which are checked experimentally. These equations have general validity for film evaporation and film condensation. By describing the influence of gas flow great differences occur between condensation and evaporation. The present work deals with a calculation method which was verified by condensation data. This method is compared and discussed with experimental results of film evaporation. It is shown that the presented method describing the shear stress influence is also applicable.