FCC铝纳米压痕的多尺度模拟

采用准连续介质方法模拟面心立方(FCC)铝单晶薄膜在纳米压痕下产生的变形过程.分别用四种不同的压头宽度,得出载荷-位移响应曲线和应变能变化曲线,发现压头宽度越大,晶体产生塑性变形的临界载荷越大;临界载荷的大小和采用能量理论预测的大小基本一致;模拟过程中,观察到位错成核现象,了解到载荷-位移响应曲线的突降是由位错成核现象所引起,四种情况中压头载荷的降幅大致相同;最后分析了模型在原子层次下的变形机理.     

单晶Ⅰ型弹塑性开裂取向效应的离散位错动力学-近场动力学研究

本文采用基于近场动力学框架的位错动力学叠加模型对FCC单晶在四种不同取向下的I型弹塑性开裂行为进行模拟研究.在模型中,无需预设裂纹扩展路径和内聚力区域,裂纹扩展路径由位错与裂纹的相互作用自动确定.数值计算了FCC单晶体在不同取向时的位错分布演化和裂纹扩展路径.分析表明取向会影响韧性和断裂行为,并证实了单晶体的单轴拉伸开裂行为遵循施密特因子关系,即位错更倾向于在施密特因子大的滑移面上形核并滑移.计算得到位错裂纹演化结果显示,不同取向时位错在滑移系上的分布和演化行为会导致不同晶体断裂模式.     

关联参照模型和位错发射过程的分子动力学模拟

提出关联参照模型和随位错位置变化的柔性位移边界条件．提供了一个在固定位移边界条件下位错穿越边界的方法．应用三维分子动力学方法研究了体心立方（ＢＣＣ）金属晶体钼裂尖发射位错的力学行为．     

纳米压痕中位错运动的原子模拟

利用分子动力学方法模拟研究了金刚石压头压入Ni薄膜(111)晶面的纳米压痕过程中薄膜进入初始塑性后的纳观机制,采用中心对称参数(CSP)研究不同压入深度时薄膜内部的位错的萌生和生长情况.结果表明:压痕力-压痕深度曲线的每一次的剧烈的振荡,都是一次能量释放的过程,在薄膜内部的位错生长也最剧烈.加载过程中,压入深度为0.66nm时出现位错(层错),压入深度为0.93nm时出现明显的位错形核,随着压入深度的增加,多个位错形核相互作用形成梯杆位错.压入深度为1.4nm时,梯杆位错旁出现了棱柱形不全位错环,随着压入深度的增加,棱柱形不全位错环沿着{111}滑移面运动.在最大压入深度处,薄膜塑性形变达到最大.     

纳米流控能量吸收耗散系统

基于纳米流控行为设计的新一代能量吸收耗散系统(nanofluidic energy absorption system,NEAS)将会比传统吸能材料具有更高的能量吸收密度,而且还可以重复使用,特别是在小体积应用环境下具有显著的优势.本文从实验和计算模拟两方面综述了目前关于NEAS能量吸收耗散行为的最新研究进展,其中实验研究主要包括准静态压缩和动态压缩测试,计算模拟研究主要是采用基于经验势的分子动力学模拟方法.通过准静态压缩实验,可以测量NEAS模型的载荷-位移关系曲线,从而获得NEAS模型的临界渗透压强,了解卸载后系统是否能够恢复到加载前的状态(即是否可以重复使用),并通过载荷-位移关系曲线下面积估算NEAS模型的吸能密度;通过动态压缩实验可以测量NEAS模型对脉冲载荷的缓冲保护作用,主要体现为降低脉冲载荷幅值和扩展脉冲宽度.计算模型研究可以明确给出NEAS对外载荷的微观响应,从而可以准确了解NEAS的能量吸收耗散机制以及吸能密度的主要影响因素.本研究可以帮助我们全面了解NEAS的研究进展,为NEAS的设计与优化提供重要指导.     

考虑应力梯度效应的金属微梁屈服模型研究

一系列微加载测试结果表明,金属微梁的弯曲强度会随着材料外部几何特征尺寸的减小而显著升高,呈现出明显的尺寸相关性.基于位错塞积模型,探讨了纯金属单晶微梁的初始屈服应力,并提出了描述其尺寸相关性行为的关键内禀特征长度.通过综合分析现有的微梁弯曲实验及其离散位错动力学数值模拟结果,并考虑到位错-自由表面交互作用的影响,提出了一种仅涉及位错源的位错塞积构型.在此构型下,对线性应力梯度作用下的位错塞积行为进行了连续性分析,并建立了一个由位错源主导的应力梯度屈服模型.该模型有效地解释了微梁初始屈服应力的尺寸相关性,并与实验结果一致.研究结果表明,针对外部几何特征尺寸在数微米及以下的纯金属单晶微梁,位错塞积行为是其尺寸相关性行为的主导机制,而且刻画这种行为需要两个内禀特征长度参数,即位错源长度和位错塞积长度.为解释非均匀加载条件下微尺度晶体材料屈服应力的尺寸相关性行为,特别是纯金属单晶微梁,提供了新的视角.     

Peierls框架与裂纹尖端位错行为

本文在Ｐｅｉｅｒｌｓ框架下对裂纹尖端位错成核与发射问题进行了严格的数学分析，在修正Ｒｉｃｅ设相的基础上，建立了一组新的控制方程，应力场与位错密度场分别表示成第一类与第二类切比雪夫多项式的级数，相应的张开位移与滑错位移以用三角级数表示。通过离散的方法，控制方程转化为一组非线性代数方程。用Ｎｅｗｔｏｎ－Ｒａｐｈｓｏｎ方法求解这组方程，得到远场为纯剪，纯拉及两者复合情况下的解答。计算结果清楚地揭示了裂纹     

面心立方铝剪切变形的准连续介质模拟

采用准连续介质多尺度方法模拟了纳米尺度单晶铝的剪切变形.分别采用三种不同晶体取向(分别为x[1-10],y[001],z[-1-10]; x[-1-12],y[111],z[-110]; x[-110],y[-1-12],z[111])和三种不同长宽比的几何模型(分别为1:1,2:1,4:1)进行模拟,得出各模型应力一应变响应曲线.加载过程中,对晶体内部变形比较剧烈的部分画出原子图,并从微观角度分析了产生剧烈变形的原因;讨论了三种晶体取向下的尺寸效应:单晶铝的剪切屈服应力随模型几何尺寸的增加而降低,并且随晶体取向的不同变化很大.最后,使用指数法则来描述模型的尺寸效应,提出了针对不同取向的指数法则参数,表明了晶体不同取向对剪切屈服应力的大小有影响.     

纳米流控能量吸收耗散系统

基于纳米流控行为设计的新一代能量吸收耗散系统(nanofluidic en-ergy absorption system,NEAS)将会比传统吸能材料具有更高的能量吸收密度,而且还可以重复使用,特别是在小体积应用环境下具有显著的优势.本文从实验和计算模拟两方面综述了目前关于NEAS能量吸收耗散行为的最新研究进展,其中实验研究主要包括准静态压缩和动态压缩测试,计算模拟研究主要是采用基于经验势的分于动力学模拟方法.通过准静态压缩实验,可以测量NEAS模型的载荷–位移关系曲线,从而获得NEAS模型的临界渗透压强,了解卸载后系统是否能够恢复到加载前的状态(即是否可以重复使用),井通过载荷–位移关系曲线下面积估算NEAS模型的吸能密度;通过动态压缩实验可以测量NEAS模型对脉冲载荷的缓冲保护作用,主要体现为降低脉冲载荷幅值和扩展脉冲宽度.计算模型研究可以明确给出NEAS对外载荷的微观响应,从而可以准确了解NEAS的能量吸收耗散机制以及吸能密度的主要影响因素.本研究可以帮助我们全面了解NEAS的研究进展,为NEAS的设计与优化提供重要指导.     

纳米硬度实验中的多位错生成分析

本文利用边界单元法及基于Peierls-Nabarro模型的位错理论，分析了理想纳米触头下多位错的生成，得到了滑移面上多位错的构形以及表面位移与载荷的关系曲线。根据得到的计算结果分析了薄膜厚度的影响，得到了与已有实验结果相同的结论。通过把表面看成一个包含在无穷大弹性体中的无穷大弹性体中无穷大裂纹来考虑表面的影响，从而可以直接采用已有的边界积分方程。该方法在连续介质力学的计算中引入了包含原子信息的层间势能函数，为分析多尺度的力学问题提供了有效的方法。     

QUASICONTINUUM SIMULATION OF NANOINDENTATION OF NICKEL FILM

A large-scale atom simulation of nanoindentation into a thin nickel film using thequasicontinuum method was performed. The initial stages of the plasticity deformation of nickelwere studied. Several useful results were obtained as follows: (1)The response of the load versusindentation depth—on the load versus indentation depth curve, besides the straight parts cor-responding to the elastic property of nickel, the sudden drop of the load occurred several times;(2) The phenomena of dislocation nucleation—the dislocation nucleation took place when theload descended, which makes it clear that dislocation nucleation causes the drop of the load;(3)The mechanism of the dislocation emission—the Peierls-Nabarro dislocation model and a pow-erful criterion were used to analyze the dislocation emission. And the computational value was ingood agreement with the predict value; (4) The density of geometrically necessary dislocations.A simple model was used to obtain the density of geometrically necessary dislocations beneaththe indenter. Furthermore, the influence of the boundary conditions on the simulation results wasdiscussed.     

A NUMERICAL STUDY OF INDENTATION WITH SMALL SPHERICAL INDENTERS

The finite element method for the conventional theory of mechanism-based strain gradient plasticity is used to study the indentation size effect. For small indenters （e.g., radii on the order of 10μm）, the maximum allowable geometrically necessary dislocation （GND） density is introduced to cap the GND density such that the latter does not become unrealistically high. The numerical results agree well with the indentation hardness data of iridium. The GND density is much larger than the density of statistically stored dislocations （SSD） underneath the indenter, but this trend reverses away from the indenter. As the indentation depth （or equivalently, contact radius） increases, the GND density decreases but the SSD density increases.     

Cylindrical nano-indentation on metal film/elastic substrate system with discrete dislocation plasticity analysis: A simple model for nano-indentation size effect

The cylindrical nano-indentation on metal film/elastic substrate is computationally studied using two-dimensional discrete dislocation plasticity combined with the commercial software ANSYS®, with a focus on the storage volume for geometrically necessary dislocations (GNDs) inside the films and the nano-indentation size effect (NISE). Our calculations show that almost all GNDs are stored in a rectangular area determined by the film thickness and the actual contact width. The variations of indentation contact width with indentation depth for various film thicknesses and indenter radii are fitted by an exponential relation, and then the GND density underneath the indenter is estimated. Based on the Taylor dislocation model and Tabor formula, a simple model for the dependence of the nano-indentation hardness of the film/substrate system on the indentation depth, the indenter radius and the film thickness is established, showing a good agreement with the present numerical results.     

The indenter tip radius effect in micro- and nanoindentation hardness experiments.

Nix and Gao established an important relation between the microindentation hardness and indentation depth. Such a relation has been verified by many microindentation experiments (indentation depths in the micrometer range), but it does not always hold in nanoindentation experiments (indentation depths approaching the nanometer range). Indenter tip radius effect has been proposed by Qu et al. and others as possibly the main factor that causes the deviation from Nix and Gao's relationship. We have developed an indentation model for micro- and nanoindentation, which accounts for two indenter shapes, a sharp, conical indenter and a conical indenter with a spherical tip. The analysis is based on the conventional theory of mechanism-based strain gradient plasticity established from the Taylor dislocation model to account for the effect of geometrically necessary dislocations. The comparison between numerical result and Feng and Nix's experimental data shows that the indenter tip radius effect indeed causes the deviation from Nix-Gao relation, but it seems not be the main factor. The project supported by the National Natural Science Foundation of China (10121202) and the Ministry of Education of China (20020003023)     

分子动力学方法在研究材料力学行为中的应用进展

报道近年来分子动力学方法应用于研究位错、裂纹、晶界及其相互作用方面的进展．主要包括:裂纹尖端的位错发射,位错发射的不稳定堆垛能,晶体与裂纹’几何关系对位错发射的影响,温度对位错发射的影响以及由裂纹尖端发射的位错列与不对称倾侧晶界的相互作用．报道主要以我们的工作为主,重点讨论裂纹尖端位错发射的研究结果      

High strain gradient plasticity associated with wedge indentation into face-centered cubic single crystals: Geometrically necessary dislocation densities

Experimental studies on indentation into face-centered cubic (FCC) single crystals such as copper and aluminum were performed to reveal the spatially resolved variation in crystal lattice rotation induced due to wedge indentation. The crystal lattice curvature tensors of the indented crystals were calculated from the in-plane lattice rotation results as measured by electron backscatter diffraction (EBSD). Nye's dislocation density tensors for plane strain deformation of both crystals were determined from the lattice curvature tensors. The least L²-norm solutions to the geometrically necessary dislocation densities for the case in which three effective in-plane slip systems were activated in the single crystals associated with the indentation were determined. Results show the formation of lattice rotation discontinuities along with a very high density of geometrically necessary dislocations.     

Continuum dynamics of the formation,migration and dissociation of self-locked dislocation structures on parallel slip planes

In continuum models of dislocations, proper formulations of short-range elastic interactions of dislocations are crucial for capturing various types of dislocation patterns formed in crystalline materials. In this article, the continuum dynamics of straight dislocations distributed on two parallel slip planes is modelled through upscaling the underlying discrete dislocation dynamics. Two continuum velocity field quantities are introduced to facilitate the discrete-to-continuum transition. The first one is the local migration velocity of dislocation ensembles which is found fully independent of the short-range dislocation correlations. The second one is the decoupling velocity of dislocation pairs controlled by a threshold stress value, which is proposed to be the effective flow stress for single slip systems. Compared to the almost ubiquitously adopted Taylor relationship, the derived flow stress formula exhibits two features that are more consistent with the underlying discrete dislocation dynamics: (i) the flow stress increases with the in-plane component of the dislocation density only up to a certain value, hence the derived formula admits a minimum inter-dislocation distance within slip planes; (ii) the flow stress smoothly transits to zero when all dislocations become geometrically necessary dislocations. A regime under which inhomogeneities in dislocation density grow is identified, and is further validated through comparison with discrete dislocation dynamical simulation results. Based on the findings in this article and in our previous works, a general strategy for incorporating short-range dislocation correlations into continuum models of dislocations is proposed.     

温度对金属材料钼位错发射的影响

应用关联参照模型、随位错位置变化的柔性位移边界条件和三维分子动力学方法研究了体心立方（ＢＣＣ）金属晶体钼在不同温度下裂尖发射位错的力学行为，随着温度的提高，不但发射位错的临界应力强度因子下降而且在同一应 度因子条件下，发射位错的数量出增加，位错速度和不全位错之间的扩展距离对温度不敏感，在位错发射过程中，发现了稳定的和不稳定的两个变形状态，在稳定的有状态，位错发射后，塞积在远离裂纹尖端处；必须增加外     

A model of size effects in nano-indentation

The indentation hardness-depth relation established by Nix and Gao [1998. Indentation size effects in crystalline materials: a law for strain gradient plasticity. J. Mech. Phys. Solids 46, 411-425] agrees well with the micro-indentation but not nano-indentation hardness data. We establish an analytic model for nano-indentation hardness based on the maximum allowable density of geometrically necessary dislocations. The model gives a simple relation between indentation hardness and depth, which degenerates to Nix and Gao [1998. Indentation size effects in crystalline materials: a law for strain gradient plasticity. J. Mech. Phys. Solids 46, 411-425] for micro-indentation. The model agrees well with both micro- and nano-indentation hardness data of MgO and iridium.     

A discrete dislocation analysis of bending

Bending of a strip in plane strain is analyzed using discrete dislocation plasticity where the dislocations are modeled as line defects in a linear elastic medium. At each stage of loading, superposition is used to represent the solution in terms of the infinite medium solution for the discrete dislocations and a complementary solution that enforces the boundary conditions, which is non-singular and obtained from a linear elastic, finite element solution. The lattice resistance to dislocation motion, dislocation nucleation and dislocation annihilation are incorporated into the formulation through a set of constitutive rules. Solutions for cases with multiple slip systems and with a single slip system are presented. The bending moment versus rotation relation and the evolution of the dislocation structure are outcomes of the boundary value problem solution. The effects of slip geometry, obstacles to dislocation motion and specimen size on the moment versus rotation response are considered. Also, the evolution of the dislocation structure is studied with emphasis on the role of geometrically necessary dislocations. The dislocation structure that develops leads to well-defined slip bands, with the slip band spacing scaling with the specimen height.