腐蚀损伤模型研究进展

腐蚀会导致材料表面附近产生机械损伤，降低材料强度。腐蚀损伤演化过程的理解和模拟，对工程结构的剩余服役寿命预测、可靠性分析、以及材料耐腐蚀设计等至关重要。现有的腐蚀数学模型大多旨在描述单个或少数几个腐蚀点的界面演化过程。这些模型通常都基于扩散理论和电化学动力学定律，用于预测腐蚀点的几何形状演化和溶液中离子的浓度分布演化。本文简述了腐蚀的电化学动力学基础，为力学工作者参与腐蚀损伤研究提供了简要的背景知识介绍。对目前发展比较完善的点腐蚀模型进行了总结分类。重点介绍了近十年来几种主要的新型腐蚀模拟方法：元胞自动机法、相场模型和近场动力学模型。并分析了各方法的优缺点。提出了电偶腐蚀和应力腐蚀开裂模型分析中亟待解决的一些问题。最后，论文总结了腐蚀模拟在实际工程应用中的难点，展望了未来研究发展方向。     

陶瓷和金属微波烧结在线实验及微观机理分析

为研究陶瓷和金属微波烧结时的微观演化机理,从而为优化不同材料的烧结过程提供依据,本文采用同步辐射技术对陶瓷(SiC)和金属(Al)的微波烧结微结构演化过程进行实时、无损的观测,并结合有限元模拟分析两者的微结构演化特征及微观机理。通过滤波反投影等数字图像处理技术得到烧结过程中样品内部的二维、三维重建图像,清晰地观察到SiC和Al在颗粒表面和界面演化上存在差异。定量地统计了陶瓷和金属烧结颈相对尺寸与时间的双对数关系,并与陶瓷和金属双球模型的微波烧结模拟结果进行了对比。运用模拟分别对实验中的烧结颈和微观形貌演化进行分析,得出结论:陶瓷和金属微波烧结时的加热机制不同,分别为整体介质损耗加热和表面涡流损耗加热。陶瓷的整体加热将会在材料内部特别是界面产生较高的温度,而金属的表面加热使颗粒表面温度高于界面。由相应的加热机制产生的温度分布差异,将会对材料的物质扩散过程产生不同程度的影响,进而产生不同的微结构。     

金属铝微波烧结微结构演化的在线观测与相场模拟

材料内部微结构及其演化与材料宏观力学性能密切相关,而孔隙是微结构的一种重要形态。在金属粉末微波烧结过程中,由于烧结机理复杂,且受限于传统实验观测手段,目前对金属微波烧结孔隙演化机理的认识尚不清晰。本文采用SR-CT(Synchrotron Radiation Computed Tomography),同步辐射计算机断层扫描技术,对金属铝粉末微波烧结过程中的孔隙演化进行了在线观测,观测到呈条状的孔隙沿短轴闭合这一独特现象,与常规烧结中孔隙圆滑化和球化过程截然不同。基于这一现象,针对金属颗粒在微波电磁场作用下进行了受力分析,认为在微波电磁场中金属颗粒表面产生电子涡流,颗粒受到沿表面法线方向并指向孔隙内部的安培驱动力作用,促进了孔隙沿短轴方向的闭合,据此提出了条状孔隙演化的安培力驱动模型。将这一模型引入相场模拟,基于实验图像模拟孔隙的演化过程,得到了与实验一致的模拟结果,从而验证了安培力驱动模型的正确性。     

基于COMSOL的脆性材料相场断裂模型

相场法通过一系列微分方程描述材料断裂过程,避免了繁琐的裂纹面追踪,在模拟裂纹的萌生、扩展和分叉等方面具有优势。介绍了基于相场法的脆性材料断裂模型,给出了脆性材料断裂问题相场法控制方程的推导过程,提出了基于分步迭代法在COMSOL中实现脆性材料相场断裂模型的方法。再现了脆性材料单元模型和单边缺口平板受拉及受剪作用下的开裂过程,模拟的裂纹扩展路径与已有文献的结果相近,验证了程序的合理性。针对脆性材料相场断裂模型包含的诸多参数,采用Morris法对影响荷载-位移关系的脆性材料断裂模型参数进行了全局敏感性分析,结果表明,杨氏模量(E)、临界能量释放率(G_c)和位移增量(Δu_x)是影响模型荷载-位移关系输出结果的主要参数。基于COMSOL实现的相场断裂模型能够有效模拟脆性材料的裂纹萌生和扩展断裂过程,模型参数E,G_c和Δu_x对材料断裂性能的提升或模型参数反演效率的提高具有重要影响。     

混凝土单轴受拉的非局部本构模型

混凝土受拉本构行为存在很强的局部软化现象,使得单轴受拉试验无法给出应力-应变关系,而只能给出应力-位移关系。本文根据内变量理论和等效应变假设建立了基于真实应变的混凝土单轴受力本构方程,并根据Weibull分布可以描述混凝土等脆性材料断裂过程的试验现象,建立了关于弹性应变的损伤演化规律。然后,通过假设平均应变与真实弹性应变的函数关系,在应力-平均应变的本构关系中采用平均弹性应变以描述其非局部行为,而在材料的损伤演化规律中采用真实弹性应变以描述其局部行为,由此建立了单轴受拉荷载条件下的非局部本构模型。最后,对一个单调受拉试验和一个反复受拉试验的仿真结果表明所提出的非局部本构模型可以准确地模拟试验结果。     

基于相场模型的金属微波烧结演化机制分析及同步辐射断层扫描实验验证

为了探索不同种类金属材料的微波烧结机制,本文针对钛和铝两种具有不同电磁学特性的金属材料,分析了微波与金属微粒的相互作用。依据经典的麦克斯韦方程,金属表面产生电子涡流和趋肤效应。由P.Mishra和K.I.Rybakov等提出的金属在微波中的加热效率理论,推导出钛金属表面的热效应明显高于铝。因为电子涡流在磁场中产生指向颗粒内部的洛伦兹力这一微波非热效应,阻碍了内部物质向外的扩散,且铝的感应涡流大于钛,故其向心力更大。由于微波的热效应和非热效应导致物质扩散的驱动力不同,得出"钛的微波烧结速率明显大于铝"这一区别于常规烧结的结论。将获得的分析结果引入相场数值模拟,改变相场模型中控制演化过程中的表面和体扩散变量,获得不同的模拟结果,定量分析了烧结颈等微观结构参数随模拟时间的演化曲线。结合同步辐射断层扫描(SR-CT)技术获得的金属在微波烧结过程中的实验参数,与理论分析和模拟结果相吻合,从而验证了分析和模拟的正确性和可行性。上述结果可为研究金属在微波烧结过程中的演化机制提供支持。     

基于多尺度模型解释固体中的挠曲电效应

挠曲电效应是一种跨尺度的多场耦合现象。当前的宏观挠曲电理论均是基于应变梯度局部破坏晶体反演对称这一微观机理对该现象进行唯象描述。该宏观理论与基于晶格动力学及密度泛函理论的微观挠曲电理论模型之间存在较大差异。难以将两者结合用以跨尺度地研究材料中的挠曲电效应。针对该现状,本文基于前人提出的原子场理论,建立了一种新的多尺度挠曲电模型。并在该多尺度模型框架下解释了应变梯度诱发极化的微观机理。一方面,与基于连续介质力学的唯象理论不同,本文从材料微结构演化的角度推导了原子位移与极化的关系。另一方面,与通过晶格波假设原子位移的微观理论不同,本文得到的极化表达式更加真实和广义地解释了挠曲电效应。其能够适用于材料边界存在机械力作用,材料内部存在缺陷等复杂的情况。本文所建立的多尺度挠曲电模型能够为后续多尺度挠曲电效应的研究提供一些思路。     

固体炸药爆轰与惰性介质相互作用的一种扩散界面模型

提出一种保持热力学一致性的扩散界面模型，用来数值模拟固体炸药爆轰与惰性介质的相互作用问题。基于混合网格内各组分物质间可以达到力学平衡状态而不能达到热学平衡状态的假设，由混合网格能量守恒以及压力相等条件，推导出每种组分物质的体积分数演化方程。由此获得的扩散界面模型包括组分物质的质量守恒方程、混合物质的动量及总能量守恒方程，同时包括组分物质的体积分数演化方程和混合物质的压力演化方程。该扩散界面模型的主要特点是考虑了化学反应以及热学非平衡的影响。提出的扩散界面模型在物质界面附近不会出现物理量的非物理振荡现象、适用于任意表达形式的物质状态方程以及任意数目的惰性介质。     

瓷修复体界面断裂行为的模拟实验研究

本文利用云纹干涉法和云纹干涉－－有限元混合法，对瓷修复体的模拟双材料模型界面断裂问题进行了实验研究。用云纹干涉和数字错位云纹干涉法测量带边裂纹的双材料四点简支梁在剪切作用下界面表面的剪应变分布及界面两侧局部表面的位移场，实验表明，由于界面两两侧材料力学性质不同，表现出界面剪切断裂问题的非称性和裂尖附近复合型断裂的特点；用云纹干涉法和有限元法相结合的混合法对粘接界面角点应力奇异性进行研究，并对角点附近应力应变场作了分析，得到了应力奇异指数与边界楔角，载荷的关系，证明了用界面应力强度因子Kf来描述界面端部区域应力分布的公式，并得到了双材料界面端部区域的应力应变分布情况。本文的实验结果为进一步研究口腔金瓷修复体界面的优化设计提供了基础，同时也说明云纹干涉法对于双材料界面断裂行为的研究是有效的。     

基于一类非局部宏-微观损伤模型的混凝土典型试件力学行为模拟

混凝土是一类典型的准脆性材料, 其受力过程中的非线性分析与裂纹模拟依然是具有挑战性的问题. 经典的断裂力学与损伤力学分别从间断与连续的视角对裂纹拓扑进行了描述, 是早期人们研究固体破坏问题的有力工具. 21世纪以来, 相场理论和近场动力学在预测裂纹的萌生、扩展与非线性分析方面取得了重要的进展. 最近, 结合统一相场理论与近场动力学的基本思想, 发展了一类非局部宏-微观损伤模型. 该模型引入物质点偶的概念来刻画由于变形引起的微细观损伤, 对微细观损伤在作用域中进行加权平均得到定量描述物质不连续程度的拓扑损伤. 通过具有物理机制的能量退化函数, 将拓扑损伤嵌入到连续介质-损伤力学的框架中, 这使得该模型在进行非线性分析的同时可以自然地进行裂纹模拟, 而毋须预设初始裂纹与裂纹扩展路径. 本文考虑细观物理参数的空间变异性, 采用非局部宏-微观损伤模型进行混凝土试件受力全过程的精细化模拟. 通过一维建模标定模型细观参数, 并探讨了细观参数与混凝土材料细观物理-几何特性之间的内在关联, 在此基础上采用二维模型进行精细化分析. 进而, 考察了材料参数空间变异性对混凝土单轴受拉试件和带缺口三点弯曲试件力学行为的重要影响. 本文的研究工作为非局部宏-微观损伤模型细观参数的试验标定与复杂应力状态下混凝土等准脆性材料的非线性力学行为研究提供了有意义的参考.      

A nonlocal diffuse interface model for microstructure evolution of tin-lead solder

Microstructural length scales are relatively large in typical soldered connections. A microstructure which is continuously evolving is known to have a strong influence on damage initiation and propagation in solder materials. In order to make accurate lifetime predictions by numerical simulations, it is therefore necessary to take the microstructural evolution into account. In this work this is accomplished by using a diffuse interface model incorporating a strongly nonlocal variable. It is presented as an extension of the Cahn-Hilliard model, which is weakly nonlocal since it depends on higher order gradients which are by definition confined to the infinitesimal neighbourhood of the considered material point. Next to introducing a truly nonlocal measure in the free energy, this nonlocal formulation has the advantage that it is numerically more efficient. Additionally, the model is extended to include the elastically stored energy as a driving force for diffusion after which the entire system is solved using the finite element approach. The model results in a computational efficient algorithm which is capable of simulating the phase separation and coarsening of a solder material caused by combined thermal and mechanical loading.     

A nonlocal species concentration theory for diffusion and phase changes in electrode particles of lithium ion batteries

A nonlocal species concentration theory for diffusion and phase changes is introduced from a nonlocal free energy density. It can be applied, say, to electrode materials of lithium ion batteries. This theory incorporates two second-order partial differential equations involving second-order spatial derivatives of species concentration and an additional variable called nonlocal species concentration. Nonlocal species concentration theory can be interpreted as an extension of the Cahn–Hilliard theory. In principle, nonlocal effects beyond an infinitesimal neighborhood are taken into account. In this theory, the nonlocal free energy density is split into the penalty energy density and the variance energy density. The thickness of the interface between two phases in phase segregated states of a material is controlled by a normalized penalty energy coefficient and a characteristic interface length scale. We implemented the theory in COMSOL Multiphysics\(^{\circledR }\) for a spherically symmetric boundary value problem of lithium insertion into a \(\hbox {Li}_x\hbox {Mn}_2\hbox {O}_4\) cathode material particle of a lithium ion battery. The two above-mentioned material parameters controlling the interface are determined for \(\hbox {Li}_x\hbox {Mn}_2\hbox {O}_4\), and the interface evolution is studied. Comparison to the Cahn–Hilliard theory shows that nonlocal species concentration theory is superior when simulating problems where the dimensions of the microstructure such as phase boundaries are of the same order of magnitude as the problem size. This is typically the case in nanosized particles of phase-separating electrode materials. For example, the nonlocality of nonlocal species concentration theory turns out to make the interface of the local concentration field thinner than in Cahn–Hilliard theory.     

Nonlocal damage model using the phase field method: Theory and applications

A new nonlocal, gradient based damage model is proposed for isotropic elastic damage using the phase field method in order to show the evolution of damage in brittle materials. The general framework of the phase field model (PFM) is discussed and the order parameter is related to the damage variable in continuum damage mechanics (CDM). The time dependent Ginzburg–Landau equation which is also termed the Allen–Cahn equation is used to describe the damage evolution process. Specific length scale which addresses the interface region in which the process of changing undamaged solid to fully damaged material (microcracks) occurs is defined in order to capture the effect of the damaged localization zone. A new implicit damage variable is proposed through the phase field theory. Details of the different aspects and regularization capabilities are illustrated by means of numerical examples and the validity and usefulness of the phase field modeling approach is demonstrated.     

SIMULATIONS OF MECHANICAL BEHAVIOR OF POLYCRYSTALLINE COPPER WITH NANO-TWINS

Mechanical behavior and microstructure evolution of polycrystalline copper with nano-twins were investigated in the present work by finite element simulations. The fracture of grain boundaries are described by a cohesive interface constitutive model based on the strain gradient plasticity theory. A systematic study of the strength and ductility for different grain sizes and twin lamellae distributions is performed. The results show that the material strength and ductility strongly depend on the grain size and the distribution of twin lamellae microstructures in the polycrystalline copper.     

A consistent nonlocal scheme based on filters for the homogenization of heterogeneous linear materials with non-separated scales

In this work, the question of homogenizing linear elastic, heterogeneous materials with periodic microstructures in the case of non-separated scales is addressed. A framework if proposed, where the notion of mesoscopic strain and stress fields are defined by appropriate integral operators which act as low-pass filters on the fine scale fluctuations. The present theory extends the classical linear homogenization by substituting averaging operators by integral operators, and localization tensors by nonlocal operators involving appropriate Green functions. As a result, the obtained constitutive relationship at the mesoscale appears to be nonlocal. Compared to nonlocal elastic models introduced from a phenomenological point of view, the nonlocal behavior has been fully derived from the study of the microstructure. A discrete version of the theory is presented, where the mesoscopic strain field is approximated as a linear combination of basis functions. It allows computing the mesoscopic nonlocal operator by means of a finite number of transformation tensors, which can be computed numerically on the unit cell.     

Evolving Microstructure and Homogenization

In this article we formulate a mathematical model for the temporally evolving microstructure generated by phase changes and study the homogenization of this model. The investigations are partially formal, since we do not prove existence or convergence of solutions of the microstructure model to solutions of the homogenized problem. To model the microstructure, the sharp interface approach is used. The evolution of the interface is governed by an everywhere defined distribution partial differential equation for the characteristic function of one of the phases. This avoids the disadvantage commonly associated with this approach of an evolution equation only defined on the interface. To derive the homogenized problem, a family of solutions of the microstructure problem depending on the fast variable is introduced. The homogenized problem obtained contains a history functional, which is defined by the solution of an initial-boundary value problem in the representative volume element. In the special case of a temporally fixed microstructure the homogenized problem is reduced to an evolution equation to a monotone operator. Received March 15, 2000     

金属增材制造过程中材料微观组织演化的模拟研究

金属增材制造是集设计、制造一体化的一种新型金属构件制造技术, 在航天航空、交通运输、生物医疗等领域具有广阔的应用前景. 金属增材制造材料的力学性能与其材料微观组织密切相关. 因此, 发展金属增材制造过程中材料微观组织的模拟方法, 有助于指导和优化金属增材制造的工艺参数和流程, 从而制备出性能优异的金属材料. 本文发展了基于连续体假设的热传导模型与元胞自动机相结合的模拟方法, 并利用生死单元方法, 考虑晶粒的重熔和再生长过程, 解决了金属增材制造中多层粉末制造的数值模拟问题. 本文采用该方法模拟了镍基合金IN718、不锈钢316L和高熵合金FeCoCrNiMn的增材制造过程, 并获得了这些增材制造合金的典型材料微观组织, 其模拟结果与实验结果相吻合. 同时, 将该方法拓展到三维尺度的模拟, 研究了镍基合金IN718增材制造过程中三维晶粒的形核和生长. 最后, 对金属增材制造过程中材料微观组织演化的模拟研究中的主要问题进行了总结和展望.      

马氏体相变微结构演化过程的模拟与分析

实验中观察到形状记忆合金在应力诱发马氏体相变过程中,出现多界面的微结构,马氏体相会逐渐长大变粗,同时会出现由马氏体形核造成的应力突然降低.用多阱的弹性能函数来刻画此相变与微结构演化过程,发现相变时会出现多界面的微结构且伴随着马氏体相的形核至奥氏体相的消失过程,出现了界面数先增后减的变化,同时应力会出现跳跃而不连续.相对应的动力学模型的有限差分的计算结果同样显示形核时出现了多界面的微结构并伴随着应力的大幅振荡,随着载荷的增加界面位置随之移动,使得马氏体相区域逐渐长大.理论分析与数值模拟的结果较好地刻画了实验中观察到的马氏体相变过程中的形核,产生多界面,再到马氏体逐渐长大这一微结构的演化过程.     

Interface propagation and microstructure evolution in phase field models of stress-induced martensitic phase transformations

Analytical solutions for diffuse interface propagation are found for two recently developed Landau potentials that account for the phenomenology of stress-induced martensitic phase transformations. The solutions include the interface profile and velocity as a function of temperature and stress tensor. An instability in the interface propagation near lattice instability conditions is studied numerically. The effect of material inertia is approximately included. Two methods for introducing an athermal interface friction in phase field models are discussed. In the first method an analytic expression defines the location of the diffuse interface, and the rate of change of the order parameters is required to vanish if the driving force is below a threshold. As an alternative and more physical approach, we demonstrate that the introduction of spatially oscillatory stress fields due to crystal defects and the Peierls barrier, or to a jump in chemical energy, reproduces the effect of an athermal threshold. Finite element simulations of microstructure evolution with and without an athermal threshold are performed. In the presence of spatially oscillatory fields the evolution self-arrests in realistic stationary microstructures, thus the system does not converge to an unphysical single-phase final state, and rate-independent temperature- and stress-induced phase transformation hysteresis are exhibited.