A New View of Incipient Plastic Instability during Nanoindentation

Whether the dislocation nucleation or the sudden dislocation multiplication dominates the incipient plastic instability during the nanoindentation of initial defect-free single crystal still remains unclear. In this work, the dislocation mechanism corresponding to the incipient plastic instability is numerically investigated by coupling discrete dislocation dynamics with the finite element method. The coupling model naturally introduces the dislocation nucleation and accurately captures the heterogeneous stress field during nanoindentation. The simulation results show that the first dislocation nucleation induces the initial pop-in event when the indenter is small, while for larger indenters, the incipient plastic instability is ascribed to the cooperation between dislocation nucleation and multiplication. Interestingly, the local dislocation densities for both cases are almost the same when the sudden load drop occurs. Thus it is inferred that the adequate dislocations generated by either nucleation or multiplication, or both, are the requirement for the trigger of incipient plastic instability. A unified dislocation-based mechanism is proposed to interpret the precipitate incipient plastic instability.     

Dislocation structure and dynamics govern pop-in modes of nanoindentation on single-crystal metals

ABSTRACT

There are two types of pop-in mode that have been widely observed in nanoindentation experiments: the single pop-in, and the successive pop-in modes. Here we employ the molecular dynamics (MD) modelling to simulate nanoindentation for three face-centred cubic (FCC) metals, including Al, Cu and Ni, and two body-centred cubic (BCC) metals, such as Fe and Ta. We aim to examine the deformation mechanisms underlying these pop-in modes. Our simulation results indicate that the dislocation structures formed in single crystals during nanoindentation are mainly composed of half prismatic dislocation loops. These half prismatic dislocation loops in FCC metals are primarily constituted of extended dislocations. Lomer–Cottrell locks that result from the interactions between these extended dislocations can resist the slipping of half dislocation loops. These locks can build up the elastic energy that is needed to activate the nucleation of new half dislocation loops. A repetition of this sequence results in successive pop-in events in Al and other FCC metals. Conversely, the half prismatic dislocation loops that form in BCC metals after first pop-in are prone to slip into the bulk, which sustains plastic indentation process after first pop-in and prevents subsequent pop-ins. We thus conclude that pop-in modes are correlated with lattice structures during nanoindentation, regardless of their crystal orientations.     

Elastic and plastic effects on heterogeneous nucleation and nanowire formation

We investigate theoretically the effects of elastic and plastic deformations on heterogeneous nucleation and nanowire formation. In the first case, the influence of the confinement of the critical nucleus between two parallel misfitting substrates is investigated using scaling arguments. We present phase diagrams giving the nature of the nucleation regime as a function of the driving force and the degree of confinement. We complement this analytical study by amplitude equations simulations. In the second case, the influence of a screw dislocation inside a nanowire on the development of the morphological surface instability of the wire, related to the Rayleigh-Plateau instability, is examined. Here the screw dislocation provokes a torsion of the wire known as Eshelby twist. Numerical calculations using the finite element method and the amplitude equations are performed to support analytical investigations. It is shown that the screw dislocation promotes the Rayleigh-Plateau instability.     

Stiffness based technique to probe cyclic damage accumulation in micro-structurally graded bond coats via micro-beam bending tests

This paper highlights a novel technique to delineate the fatigue response of different regions within thin microstructurally graded platinum nickel aluminide bond coats. Notched clamped beam structures fabricated from distinct microstructural zones of these coatings are subjected to programmed cyclic bending using the nano-indentation system. A methodical approach is established herein to quantify the cyclic damage preceding crack pop-in by using the cyclic stiffness of the beam as an indicator to mark failure. Preliminary results from these tests show that there is a characteristic change in the stiffness of the beam before a crack pop-in event occurs and different regions within the coating show different stiffening characteristics. Factors affecting the measured stiffness such as offsets in the loading position and blunting of the notch tip have been estimated using the finite element method. A graded flow stress model has been proposed and implemented in FEM to quantify the local flow stress changes accompanying the measured rise in stiffness. Electron transparent foils lifted off from the notched region of the beam post-testing suggests that the cyclic stiffening of the beams occurs due to dislocation hardening in the plastically deformed region close to the notch tip. Toughening mechanisms active in the crack wake have thus been investigated and correlated to the measured cyclic stiffness.     

双模晶体相场研究形变诱导的多级微结构演化

本文采用双模晶体相场模型,计算了双模二维相图;模拟了形变诱导六角相向正方相转变过程的多级微结构演化,详细分析了位相差、形变方向对位错、晶界、晶体结构、新相形貌的影响规律.模拟结果表明:形变方向影响正方相晶核的形核位置和生长方向,拉伸时正方相优先在变形带上形核,垂直于形变方向长大,而压缩时正方相直接在位错和晶界的能量较高处形核,平行于形变方向长大;位相差对形变诱发晶界甄没过程有显著影响,体现在能量峰上为,小位相差晶界位错的攀滑移和甄没形成一个能量峰,大位相差晶界位错攀滑移和甄没因分阶段完成而不出现明显的能量峰;形变诱导相变过程中各种因素相互作用复杂,是相变与动态再结晶的复合转变.     

Identification of elastic-plastic and phase transition characteristics for relaxor ferroelectric PMN-PT anisotropic single crystals using nanoindentation technique

As one kind of important ferroelectric ceramics, relaxor ferroelectric PMN-PT single crystals have triggered a revolution in electromechanical devices owing to their giant piezoelectric properties and ultra-high electromechanical coupling factors. The present study focused on the mechanical responses of [100]- and [110]-oriented poled PMN-PT ferroelectric single crystals under an indenter loading. The hardness and Young’s modulus with different crystallographic orientations of the crystals were measured by using the continuous stiffness measurement (CSM) with nanoindentation technique. Using a spherical indenter pressured at different indentation depths, the typical quasi-static nanoindentation tests with displacement-controlled mode were performed on the PMN-PT single crystal samples. Load–displacement curves of indentations were recorded to reveal the yielding or inelasticity behaviour in [100]- and [110]-oriented PMN-PT through a pop-in event. It was further verified by the stress–strain curves evaluated from the corresponding load–displacement curves, to show the similar characteristic on the elastic–inelastic transition. When a Berkovich indenter was employed for mechanical response testing, another pop-in event was observed at a smaller indentation depth compared to the one for elastic–inelastic transition, which may indicate a pressure-induced phase transition from rhombohedral (R) to tetragonal (T) of the PMN-PT single crystals.     

Corroboration of a multiscale approach with all atom calculations in analysis of dislocation nucleation from surface steps

We present a comparative study of the influence of atomic-scale surface steps on dislocation nucleation at crystal surfaces based on an all atom method and a hierarchal multiscale approach. The multiscale approach is based on the variational boundary integral formulation of the Peiersl–Nabarro dislocation model in which interatomic layer potentials derived from atomic calculations of generalized stacking fault energy surfaces are incorporated. We have studied nucleation of screw dislocations in two bcc material systems, molybdenum and tantalum, subjected to simple shear stress. Compared to dislocation nucleation from perfectly flat surfaces, the presence of atomic scale surface steps rapidly reduces the critical stress for dislocation nucleation by almost an order of magnitude as the step height increases. In addition, they may influence the slip planes on which dislocation nucleation occurs. The results of the all atom method and the multiscale approach are in good agreement, even for steps with height of only a single atomic layer. Such corroboration supports the further use of the multiscale approach to study dislocation nucleation phenomena in more realistic geometries of technological importance, which are beyond the reach of all current atom simulations.     

Dislocation nucleation at amorphous intergrain boundaries in deformed nanoceramics

A theoretical model is proposed for lattice dislocation nucleation in deformed nanocrystalline ceramics with amorphous intergrain boundaries. According to the model, a lattice dislocation dipole nucleates at an amorphous intergrain boundary through a local plastic shear along the boundary cross section. The energy parameters of this nucleation process are calculated. It is demonstrated that the dislocation nucleation at amorphous intergrain boundaries is energetically favorable and can occur as an athermic process (without energy barrier) in the nanocrystalline phase of cubic silicon carbide 3C-SiC and in the TiN/a-Si₃N₄ nanocomposite over wide ranges of structural parameters and mechanical loads.     

Second-phase nucleation on an edge dislocation

A model for nucleation of second phase at or around a dislocation in a crystalline solid is considered. The model employs the Ginzburg–Landau theory of phase transitions comprising the sextic term in the order parameter (η⁶) in the Landau free energy. The ground state solution of the linearised time-independent Ginzburg–Landau equation is derived, through which the spatial variation of the order parameter is delineated. Moreover, a generic phase diagram indicating tricritical behaviour near and away from the dislocation is depicted. The relation between classical nucleation theory and the Ginzburg–Landau approach is discussed, for which the critical formation energy of the nucleus is related to the maximum of the Landau potential energy. A numerical example illustrating the application of the model to the case of nucleation of hydrides in zirconium alloys is provided.     

空位位错环的形成

本文研究了淬火面心立方金属内位错环和空洞的形核和长大问题。两种核都能形成,但是位错环的长大速度比空洞的长大速度大很多倍,故电子显微镜能看清的大缺陷都是位错环,而不是空洞。     

Homogeneous nucleation of glide dislocation loops in nanoceramics

A theoretical model is proposed for the homogeneous nucleation of glide dislocation loops in nanocrystalline ceramics under deformation at low and high temperatures. The nucleation of a dislocation loop in a crystalline grain is considered an ideal nanoscopic shear whose magnitude (the Burgers vector of the dislocation) increases gradually as the loop is nucleating. The characteristics of the homogeneous nucleation of glide dislocation loops in nanocrystalline ceramics based on cubic silicon carbide are calculated. It is shown that, in general, the homogeneous nucleation of a dislocation loop in nanocrystalline ceramics at high temperatures proceeds in two stages, namely, the athermal nucleation of a loop of a “noncrystallographic” partial dislocation and its thermally activated transformation into an ordinary partial lattice dislocation loop.     

Strain-rate-induced bcc-to-hcp phase transformation of Fe nanowires

Using molecular dynamics simulation method, the plastic deformation mechanism of Fe nanowires is studied by applying uniaxial tension along the [110] direction. The simulation result shows that the bcc-to-hcp martensitic phase transformation mechanism controls the plastic deformation of the nanowires at high strain rate or low temperature; however,the plastic deformation mechanism will transform into a dislocation nucleation mechanism at low strain rate and higher temperature. Furthermore, the underlying cause of why the bcc-to-hcp martensitic phase transition mechanism is related to high strain rate and low temperature is also carefully studied. Based on the present study, a strain rate-temperature plastic deformation map for Fe nanowires has been proposed.     

On the entropic nucleation barrier in a martensitic transformation

The nucleation of martensite in alloys is hindered by a free energy nucleation barrier, hence comprising contributions of the potential energy and the entropy. The leading effect is commonly attributed to the potential energy barrier due to strain fields. In this contribution, we investigate the nature of the entropic barrier by means of molecular dynamics (MD) simulations. We study a transformation process of an undercooled single crystal and examine two nucleation events observed under adiabatic conditions using vibrational mode analysis of the atomic trajectories. Our analysis shows that martensitic nucleations are indicated by transit from a state of uncorrelated into a state of correlated atomic motions. This correlation process is built up locally by a small group of atoms even before the product lattice can be recognized morphologically and it produces vibrational ‘soft’ modes along transformation paths. Phase space analyses unveil that the correlation process is characterized by narrow domains – ‘nucleation channels’ – the atomic trajectories have to pass, connecting the phase space domains of the parent and the product lattice. For a successful nucleation event, the nucleus atoms have to pass this channel collectively, which stochastically represents a rare event. Thermal fluctuations prevent finding the channel at elevated temperature and give rise for entropic stabilization of the parent phase. This ‘entropic nucleation barrier’ is reduced in the undercooled state but still effective, thus preventing the parent phase from collapsing into the product. The entropic barrier may be interpreted as the probability of a group of atoms to simultaneously pass the nucleation channel. Such group then represents a nucleus.     

高应变率压缩下纳米孔洞对金属铝塑性变形的影响研究

本文利用分子动力学模拟方法研究了含纳米孔洞金属铝在[110]晶向高应变率单轴压缩下弹塑性变形的微观过程. 对比单孔洞和完整单晶的模型, 讨论了多孔金属的应力应变关系及其位错发展规律. 研究结果表明, 对于多孔模型的位错积累过程, 位错密度随应变的增加可大致分为两个线性阶段. 由同一个孔洞生成的位错在相互靠近过程中, 其滑移速度越来越小; 随着位错继续滑移, 源自不同孔洞的位错之间开始交叉相互作用导致应变硬化. 达到流变峰应力之后又由于位错密度增殖速率升高发生软化. 当应变增加到11.8%时, 所有孔洞几乎完全坍缩, 并观察到在此过程中有棱位错生成.     

Plastic deformation transfer through the amorphous intercrystallite phase in nanoceramics

A three-dimensional model is proposed for plastic deformation transfer through the amorphous intercrystallite phase in mechanically loaded nanoceramics. In this model, glide dislocation loops are pressed against amorphous intercrystallite boundaries by the applied local shear stress and initiate in them local longitudinal plastic shears, which causes emission of new glide dislocation loops into neighboring grains. The energy characteristics of these processes and the critical applied stress required for barrierless nucleation of grainboundary and intragrain loops are calculated. As an example, a nanoceramic based on cubic silicon carbide is considered. It is shown that plastic deformation transfer through the amorphous intercrystallite phase in such nanoceramics is energetically favorable and can occur athermically over wide ranges of values of the applied stress and the structural characteristics of the material.     

体心立方金属钽Ⅱ型裂纹尖端缺陷萌生的多尺度分析

本文采用多尺度准连续介质法(quasi-continuum method, QC)模拟体心立方(body-centered-cubic, bcc)金属钽(Ta)Ⅱ型裂纹尖端位错的形核与发射过程,获得位错发射位置与应力强度因子关系曲线,分析裂纹尖端缺陷萌生过程,研究全位错分解以及扩展位错形成机理. 位错活动在不同阶段表现出不一致的特征,新位错的发射对于位错运动具有促进作用. 研究表明,裂纹扩展初始阶段首先萌生点缺陷,点缺陷随着加载强度增加会萌生新的点缺陷,点缺陷最终运动到边界,导致Ⅱ型断裂破坏. 在全位错发射之前有不全位错的形核与发射表明全位错的分解分步进行,从势能曲线上来看,也就是两个极小值点的形成机理不同. 关键词： 多尺度 准连续介质法 Ⅱ型裂纹 扩展位错     

Critical conditions for dislocation nucleation at surface steps

Dislocation nucleation at a surface step is analyzed based on a general variational boundary integral formulation of the Peierls–Nabarro dislocation model. By modelling the surface step as part of the surface of a three-dimensional crack, the free surface effect is taken into account by transferring the half space problem into an equivalent one in the infinite medium. The profiles of embryonic dislocations, corresponding to the relative displacements between the two adjacent atomic layers along the slip planes, are then rigorously solved through the variational boundary integral method. The critical conditions for dislocation nucleation are determined by solving the stress-dependent activation energies required to activate the embryonic dislocations from their stable to unstable saddle-point configurations. In particular, the effect of the step geometry, such as the height of the step, the dip angle of the slip plane and the inclined angle of the step surface on dislocation nucleation, is quantitatively ascertained. The results show that the atomic-scale surface step can rapidly reduce the critical stress required for dislocation nucleation from the surface by nearly an order of magnitude. The decrease in critical stress as a function of the height of the step is more significant for slip planes with smaller dip angles and surface steps with smaller inclined angles.     

On the nucleation of hadronic domains in the quark-hadron transition

We present numerical results on bubble profiles, nucleation rates and time evolution for a weakly first-order quark-hadron phase transition in different expansion scenarios. We confirm the standard picture of a cosmological first-order phase transition, in which the phase transition is entirely dominated by nucleation. We also show that, even for expansion rates much lower than those expected in heavy-ion collisions nucleation is very unlikely, indicating that the main phase conversion mechanism is spinodal decomposition.     

硅中位错增殖的实验观察

用化学侵蚀法研究了在机械应力和热应力作用下硅中位错的增殖和非均匀成核。结果表明,在使位错增殖和成核作用上,热应力同机械应力是等效的。硅中小角晶界中的位错,原生孤立位错都能成为位错源;晶体内部的缺陷及表面蚀斑处的应力集中能够引起位错成核;硅中螺型位错能够通过交叉滑移机制发生增殖。对新生位错环空间分布的研究表明,Frank-Read机制可能是位错增殖的主要形式。位错能否发生增殖,主要决定于位错源所受分切应力的数值、晶体温度、位错本身的结构特点以及钉扎情况等。     

A composite model of the plastic flow of amorphous covalent materials

A model based on the data available in the literature on the computer simulation of amorphous silicon has been proposed for describing the specific features of the plastic flow of amorphous covalent materials. The mechanism of plastic deformation involves homogeneous nucleation and growth of inclusions of a liquidlike phase under external shear stress. Such inclusions experience plastic shear, which is modeled by glide dislocation loops. The energy changes associated with the nucleation of these inclusions at room and increased temperatures have been calculated. The critical stress has been found, at which the barrierless nucleation of inclusions becomes possible. It has been shown that this stress decreases with an increase in temperature. According to the calculations, the heterogeneous (homogeneous) plastic flow of an amorphous material should be expected at relatively low (high) temperatures. Above the critical stress, the homogeneous flow is gradually replaced by the heterogeneous flow.