Discrete dislocation simulation of nanoindentation: the influence of obstacles and a limited number of dislocation sources

Nanoindentation is simulated on the computer by means of a 2D discrete dislocation model under the conditions of a constrained geometry. First, an indentation test near a grain boundary is investigated by the arrangement of only one boundary and second, an indentation test into the center of the surface of a small grain (lamella) is mimicked by the arrangement of two boundaries. The effect of a limited number of dislocation sources is studied by the simulations of an indentation test in a plastically deformable film on an ideal elastic substrate and by such tests on an ideal elastic film on a plastically deformable substrate. The discrete nature of plasticity is shown to have a significant influence on the mechanical material behavior in all our investigations.     

Reference motion in deformable bodies under rigid body motion and vibration. Part II: evaluation of the coefficient of restitution for impacts

The dynamic analysis of rigid body impacts is usually performed by using the coefficient of restitution as a measure of the mechanical energy lost in the process. The coefficient of restitution provides an algebraic equation that allows impulse-momentum balance equations to be solved. This paper reports a method for calculating the kinematic coefficient of restitution for the impact of deformable bodies by using a numerical simulation procedure. Calculations were done within the framework of the floating reference frame approach. As shown here for the first time, discriminating between reference velocities and rigid body equivalent velocities is essential with a view to accurately calculating the kinematic coefficient of restitution. Thus, the velocities at which the contact points approach and depart must be calculated as rigid body equivalent velocities. If references velocities are used instead, the resulting coefficient of restitution lacks physical significance. The proposed method is illustrated with two applications, namely: an axial impact of a rigid body on a deformable rod and a transverse impact of a beam on a fixed stop.     

Plastic shear response of a single asperity: a discrete dislocation plasticity analysis

We investigate the plastic shear response during static friction of an asperity protruding from a large FCC single crystal. The asperity is in perfectly adhesive contact with a rigid platen and is sheared by tangentially moving the platen. Using discrete dislocation plasticity simulations, we elucidate the plastic shear behaviour of single asperities of various size and shape, in search for the length scale that controls the plastic behaviour. Since plasticity can occur also in the crystal, identification of the length scale that controls a possible size-dependent plastic behaviour is far from being trivial. It is found that scaling down the dimensions of an asperity results in a higher contact shear strength. The contact area is dominant in controlling the plastic shear response, because it determines the size of the zone, in and below the asperity, where dislocation nucleation can occur. For a specific contact area, there is still a dependence on asperity volume and shape, but this is weaker than the dependence on contact area alone.     

Reference motion in deformable bodies under rigid body motion and vibration. Part I: theory

This paper examines the motions of reference systems linked to deformable bodies under simultaneously vibration and large translations and rotations. These motions depend on the particular type of linkage between the moving reference system and the deformable body, which is defined by the so-called reference conditions. When using the Rayleigh-Ritz method, the reference conditions also dictate the boundary conditions to be fulfilled by the shape functions used to describe the body's elasticity. This paper analyses three different types of reference conditions, namely: free linkage, rigid linkage and two-point linkage. It is shown that, moving reference frames only evolve at a constant velocity in the absence of external forces when the free linkage is used. The reference velocities for systems with a free linkage are designated rigid body equivalent velocities for the deformable body here. Such velocities can also be calculated under other types of reference conditions and are usually functions of the elastic and reference co-ordinates, and also of their derivatives. Rigid body equivalent velocities are useful for purposes such as estimating the trajectory of deformable bodies moving freely in space without the need to examine the deformations they undergo. Also, their calculation is required with a view to determining the kinematic restitution coefficient for deformable body collisions, which is dealt within Part II of this series.     

Contact mechanics analysis of oscillatory sliding of a rigid fractal surface against an elastic–plastic half-space

Oscillatory sliding contact between a rigid rough surface and an elastic–plastic half-space is examined in the context of numerical simulations. Stick-slip at asperity contacts is included in the analysis in the form of a modified Mindlin theory. Two friction force components are considered – adhesion (depending on the real area of contact, shear strength and interfacial adhesive strength) and plowing (accounting for the deformation resistance of the plastically deformed half-space). Multi-scale surface roughness is described by fractal geometry, whereas the interfacial adhesive strength is represented by a floating parameter that varies between zero (adhesionless surfaces) and one (perfectly adhered surfaces). The effects of surface roughness, apparent contact pressure, oscillation amplitude, elastic–plastic properties of the half-space and interfacial adhesion on contact deformation are interpreted in the light of numerical results of the energy dissipation, maximum tangential (friction) force and slip index. A non-monotonic trend of the energy dissipation and maximum tangential force is observed with increasing surface roughness, which is explained in terms of the evolution of the elastic and plastic fractions of truncated asperity contact areas. The decrease of energy dissipation with increasing apparent contact pressure is attributed to the increase of the elastic contact area fraction and the decrease of the slip index. For a half-space with fixed yield strength, a lower elastic modulus produces a higher tangential force, whereas a higher elastic modulus yields a higher slip index. These two competing effects lead to a non-monotonic dependence of the energy dissipation on the elastic modulus-to-yield strength ratio of the half-space. The effect of interfacial adhesion on the oscillatory contact behaviour is more pronounced for smoother surfaces because the majority of asperity contacts deform elastically and adhesion is the dominant friction mechanism. For rough surfaces, higher interfacial adhesion yields less energy dissipation because more asperity contacts exhibit partial slip.     

Dislocation Plasticity Effects on Interfacial Fracture

Analyses are reviewed where plastic flow in the vicinity of an interfacial crack is represented in terms of the nucleation and glide of discrete dislocations. Attention is confined to cracks along a metal-ceramic interface, with the ceramic idealized as being rigid. Both monotonic and fatigue loading are considered. The main focus is on the stress and deformation fields near the crack tip predicted by discrete dislocation plasticity, in comparison with those obtained from conventional continuum plasticity theory. The role that discrete dislocation plasticity can play in interpreting interface fracture properties in the presence of plastic flow is discussed.     

Nucleation of misfit dislocations and plastic deformation in core/shell nanowires

During fabrication of metal nanowires, an oxide layer (shell) that surrounds the metal (core) may form. Such an oxide-covered nanowire can be viewed as a cylindrical core/shell nanostructure, possessing a crystal lattice mismatch between the core and shell. Experimental evidence has shown that, in response to this mismatch, mechanical stresses induce plastic deformation in the shell and misfit dislocations nucleate at the core/shell interface. As a result, the mechanical, electrical and optoelectronic properties of the nanowire are affected. It is therefore essential to be able to predict the critical conditions at which misfit dislocation nucleation at the nanowire interface takes place and the critical applied load at which the interface begins deforming plastically. Two approaches are explored in order to analyze the stress relaxation processes in these oxide-covered nanowires: (i) energy considerations are carried out within a classical elasticity framework to predict the critical radii (of the core and shell) at which dislocation nucleation takes place at the nanowire interface; (ii) a strain gradient plasticity approach is applied to estimate the flow stress at which the interface will begin deforming plastically (this stress is termed “interfacial-yield” stress). The interfacial-yield stress, predicted by gradient plasticity, depends, among other material parameters, on the radii of the core and shell. Both approaches demonstrate how the geometric parameters of nanowires can be calibrated so as to avoid undesirable plastic deformation; in particular, method (i) can give the radii values that prevent misfit dislocation formation, whereas method (ii) can provide, for particular radii values, the critical stress at which interface deformation initiates.     

A discrete dislocation plasticity analysis of a single-crystal semi-infinite medium indented by a rigid surface exhibiting multi-scale roughness

Discrete dislocation plasticity was used to analyse plane-strain indentation of a single-crystal elastic–plastic semi-infinite medium by a rigid surface exhibiting multi-scale roughness, characterised by self-affine (fractal) behaviour. Constitutive rules of dislocation emission, glide and annihilation were used to model short-range dislocation interactions. Dislocation multiplication and the development of subsurface shear stresses due to asperity microcontacts forming between a single-crystal medium and a rough surface were examined in terms of surface roughness and topography (fractal) parameters, slip-plane direction and spacing, dislocation source density, and contact load (surface interference). The effect of multi-scale interactions between asperity microcontacts on plasticity is elucidated in light of results showing the evolution of dislocation structures. Numerical solutions yield insight into plastic flow of crystalline materials in normal contact with surfaces exhibiting multi-scale roughness.     

Computational Materials Chemistry at the Nanoscale

In order to illustrate how atomistic modeling is being used to determine the structure, physical, and chemical properties of materials at the nanoscale, we present here the results of molecular dynamics (MD) simulations on nanoscale assemblies of such materials as carbon nanotubes, diamond surfaces, metal alloy nanowires, and ceramics. We also include here the results of nonequilibrium MD simulations on the nanorheology of a monolayer of wear inhibitor self-assembled on two metal oxide surfaces, separated by hexadecane lubricant, and subjected to steady state shear.We also present recent developments in force fields (FF) required to describe bond breaking and phase transformations in such systems. We apply these to study of plasticity in metal alloy nanowires where we find that depending on the strain rate, the wire may deform plastically (forming twins), neck and fracture, or transition to the amorphous phase.     

刚体定点转动的张量描述

通过引入转动张量来描述刚体的定点转动,避免了在用角位移描述刚体定点转动时所遇到的问题,即角位移在它是有限大小和无限小时属性发生了变化.验证了对于刚体定点无限小转动,可以分别采用角位移矢量和转动张量描述,两者是等价的.     

EPR studies of a two-nitrogen-atom centre in natural,plastically-deformed diamond

The hyperfine structure of an EPR system in a natural, brown diamond implies that the system is due to a centre containing two nitrogen atoms on almost equivalent sites. X-ray topographic evidence shows that the sample has been plastically deformed and it is suggested that a possible model for the defect is that of an ionized, substitutional N pair with a dislocation nearby.     

Optofluidic variable aperture

A variable aperture has been fabricated and demonstrated using polydimethylsiloxane-based optofluidic technology. The device consists of a deformable membrane, an air pressure chamber, a cavity filled with light-absorbing liquid, and a rigid transparent upper plate. The working principle of the device is based on the deformable capability of the thin membrane structure and its resultant contact with the rigid plate. The contact area can be easily controlled by varying the air volume introduced and hence can serve as a light transmission aperture. Experimental results show that aperture diameter can be continuously changed from zero to 6.35 mm.     

An elastic-plastic contact model for line contact structures

Although numerical simulation tools are now very powerful,the development of analytical models is very important for the prediction of the mechanical behaviour of line contact structures for deeply understanding contact problems and engineering applications.For the line contact structures widely used in the engineering field,few analytical models are available for predicting the mechanical behaviour when the structures deform plastically,as the classic Hertz’s theory would be invalid.Thus,the present study proposed an elastic-plastic model for line contact structures based on the understanding of the yield mechanism.A mathematical expression describing the global relationship between load history and contact width evolution of line contact structures was obtained.The proposed model was verified through an actual line contact test and a corresponding numerical simulation.The results confirmed that this model can be used to accurately predict the elastic-plastic mechanical behaviour of a line contact structure.     

Elastoplastic contact between randomly rough surfaces

I have developed a theory of contact mechanics between randomly rough surfaces. The solids are assumed to deform elastically when the stress sigma is below the yield stress sigma(Y), and plastically when sigma reaches sigma(Y). I study the dependence of the (apparent) area of contact on the magnification. I show that in most cases the area of real contact A is proportional to the load. If the rough surface is self-affine fractal (Hurst exponent H) the whole way up to the lateral size L of the nominal contact area, then (assuming no plastic deformation) A approximately L(H).     

多元件粘弹性土模型条件下桩的纵向振动特性与时域响应

研究了桩侧土为4元件粘弹性模型(分别采用两个Voigt体串联或两个Maxwell体并联)及其简化条件下(可简化成多种三元件粘弹性模型)桩土系统的振动特性,并求得了桩顶在瞬态半正弦脉冲荷载作用下,桩的时域纵向响应的半解析解,同时结合基桩完整性检测的机械阻抗法和反射波法研究了各主要模型参数对时域及频域响应曲线的影响。试算分析表明,当采用两个Voigt体串联模型时,桩的振动特性主要受参数较小的一个控制,较大的一个则起辅助作用。而当采用双Maxwell体并联上模型时,在Maxwell体中,串联的弹簧和阻尼器通过相互耦合发挥作用,即弹簧系数的增加可表现为传统Voigt模型下阻尼作用的增强,而阻尼系数的增加则也可表现为传统Voigt模型下土刚度作用的增强,其中一个元件(弹簧或阻尼器)系数增加的极限状态(趋于无穷大)等效于另一个元件单独存在时的作用结果。研究结果表明,本文得到的理论成果相比于已有理论更加完善并能更好地反映客观实际。     

Effect of screening of the elastic field of the disclination located at the interface of two half-spaces by a dislocation ensemble

The self-consisted dynamics of a dislocation ensemble in the elastic field of the disclination located at the interface of two half-spaces has been considered for two cases, namely, for half-spaces with different densities of mobile dislocations and for a bicrystal where dislocations are absent in one half-space. The elastic energy W of the disclination screened by the dislocation ensemble has been calculated for the rectangular zone centered relative to the disclination. It has been shown that W increases as ～ $\sqrt R $ (R is the transverse size of the zone in the plastically deformed half-space).     

Static friction of sinusoidal surfaces: a discrete dislocation plasticity analysis

Discrete dislocation plasticity simulations are carried out to investigate the static frictional response of sinusoidal asperities with (sub)-microscale wavelength. The surfaces are first flattened and then sheared by a perfectly adhesive platen. Both bodies are explicitly modelled, and the external loading is applied on the top surface of the platen. Plastic deformation by dislocation glide is the only dissipation mechanism active. The tangential force obtained at the contact when displacing the platen horizontally first increases with applied displacement, then reaches a constant value. This constant is here taken to be the friction force. In agreement with several experiments and continuum simulation studies, the friction coefficient is found to decrease with the applied normal load. However, at odds with continuum simulations, the friction force is also found to decrease with the normal load. The decrease is caused by an increased availability of dislocations to initiate and sustain plastic flow during shearing. Again in contrast to continuum studies, the friction coefficient is found to vary stochastically across the contact surface, and to reach locally values up to several times the average friction coefficient. Moreover, the friction force and the friction coefficient are found to be size-dependent.     

刚体一般运动的描述

刚体的一般运动是刚体运动学中最复杂的一类运动,其求解通常需要借助欧拉定理或沙勒定理.通过这两个定理,我们可以把刚体的一般运动分解成较简单的定轴转动和平动.本文主要应用代数理论中的正交矩阵描述刚体的运动,并用代数语言分析了定点转动的本征问题,证明了欧拉定理.随后,将刚体的定点转动进行分解,并给出了物理图像和推导结论,完成...     

Finite element modelling of a rotating piezoelectric ultrasonic motor

The evaluation of the performance of ultrasonic motors as a function of input parameters such as the driving frequency, voltage input and pre-load on the rotor is of key importance to their development and is here addressed by means of a finite element three-dimensional model. First the stator is simulated as a fully deformable elastic body and the travelling wave dynamics is accurately reproduced; secondly the interaction through contact between the stator and the rotor is accounted for by assuming that the rotor behaves as a rigid surface. Numerical results for the whole motor are finally compared to available experimental data.