Molecular dynamics study of deformation and fracture of Bi-segregated copper bicrystals

The microprocesses of deformation and fracture of Bi-segregated copper bicrystals Σ33 ( ) 58.99°, Σ11 ( ) 50.48° and Σ9 ( ) 38.94° have been simulated by molecular dynamics in order to study the relationship between the grain boundary embrittlement (GBE) and grain boundary (GB) structure. It is shown that GBE is related to the segregated concentration and distribution of Bi atoms, while Bi segregation is related to the GB structure. Due to their different structures, the bicrystals Σ33, Σ11 and Σ9 show an increasing propensity for Bi segregated concentration. So under the action of external force, Σ33, Σ11 and Σ9 show transgranular ductile, intergranular tearing and intergranular brittle fracture modes, respectively. The subject supported by the Chinese Academy of Sciences and National Natural Science Foundation of China     

Molecular dynamics simulation of entropy and surface tension for grain boundary of α-Fe

The grain boundary is an interface and the surface tension is one of its important thermodynamic properties. In this paper, the surface tension of the ∑9 grain boundary for α-Fe at various temperatures and pressures is calculated by means of Computer Molecular Dynamics (CMD). The results agree satisfactorily with the experimental data. It is shown that the contribution of entropy to surface tension of grain boundary can be ignored. The project supported by the National Natural Science Foundation of China and the Science Foundation of Chinese Academy of Sciences.     

Molecular dynamics studies on the dislocation gliding near a tilt boundary

The gliding behavior of edge dislocation near a grain boundary (GB) in copper under pure shear stresses is simulated by using molecular dynamics(MD) method. Many-body potential incorporating the embedded atom method (EAM) is used. The critical shear stresses for a single disocation to pass across GB surface are obtained at values of σ _c =23MPa ∼ 68 MPa and 137MPa∼274 MPa for Ω=165 small angle tilt GB at 300K and 20K, respectively. The first result agrees with the experimental yield stress σ _y (=42MPa) quite well. It suggests that there might be one of the reasons of initial plastic yielding caused by single dislocation gliding across GB. In addition, there might be possibility to obtain yield strength from microscopic analysis. Moreover, the experimental value of σ _y at low temperature is generally higher than that at room temperature. So, these results are in conformity qualitatively with experimental fact. On the other hand, the Ω=25 GB is too strong an obstacle to the dislocation. In this case, a dislocation is able to pass across GB under relatively low stress only when it is driven by other dislocations. This is taken to mean that dislocation pile-up must be built up in front of this kind of GB, if this GB may take effect on the process of plastic deformation. The project supported by KM85-33 of Academia Sinica and the National Natural Science Foundation of China     

Molecular dynamics studies on the local disordering of Σ3 and Σ11 grain boundaries in aluminium bicrystal

Molecular dynamics (MD) simulations using Morse interaction potential are performed in studies of [110] symmetrical tilt grain boundary (GB) structures with mis-orientation angles 50.5°(Σ11), 129.5°(Σ11), 70.5°(Σ3) and 109.5°(Σ3) at various tempratures. The GB structures are found to start local disordering at about 0.5T _m (T _m is the melting point of aluminium) for 50.5°(Σ11), 0.32T _m for 129.5° (Σ11) and 0.38T _m for 70.5°(Σ3), respectively. These results agree with conclusions deduced from the anelastic measurements. But, for twin-boundary structure 109.5°(Σ3), this disordering has not been found even when temperature increases up to 0.9T _m . The project supported by the National Natural Science Foundation of China and Laboratory for Non-linear Mechanics of Continuous Media, Institute of Mechanics, Academia Sinica.     

Topology of the Integral Manifolds of the N-Body Problem with Positive Energy

The integral manifolds of the N-body problem are the level sets of energy and angular momentum. For positive energy and non-zero angular momentum, all level sets are diffeomorphic to a non-zero level set of angular momentum on the unit tangent bundle of the configuration space. The one complication that arises in attempting to describe this level set explicitly is the degeneracy at the syzygies of the equations that define angular momentum. In this work, we analyze the behavior of the angular momentum near syzygies, and show how to construct local coordinates near the syzygies. In particular, we show that the projection of the integral manifold onto the configuration space _c is a homotopy equivalence, and use this to compute the homology of the integral manifolds.     

Effects of grain boundary on irradiation-induced zero-dimensional defects in an irradiated copper

Grain boundaries(GBs) can serve as effective sinks for radiation-induced defects, thus notably influencing the service performance of materials. However, the effect of GB structures on the zero-dimensional defects induced by irradiation has not been fully elucidated. Here, the evolution of cascade collision in the single-crystal(SC),bicrystalline(BC), and twinned crystalline(TC) copper is studied by atomic simulations during irradiation. The spatial distributions of vacancies and interstitials a...     

A finite deformation analysis of polycrystal by considering the influence of grain boundary

By combining grain boundary (GB) and its influence zone, a micromechanic model for polycrystal is established for considering the influence of GB. By using the crystal plasticity theory and the finite element method for finite deformation, numerical simulation is carried out by the model. Calculated results display the microscopic characteristic of deformation fields of grains and are in qualitative agreement with experimental results.The project is supported by National Natural Science Foundation of China.     

Bifurcations and equilibria in the extended N-body ring problem

We consider the motion of an infinitesimal particle under the gravitational field of (n+1) bodies in ring configuration, that consist of n primaries of equal mass m placed at the vertices of a regular polygon, plus another primary of mass m₀=βm located at the geometric center of the polygon. We analyze the phase flow, determine the equilibria of the system, their linear stability and the bifurcations depending on the mass of the central primary (parameter β).This study is extended to the case when the central body is an ellipsoid or a radiation source. In this case, the topology of the problem is modified.     

A micromechanical model for polycrystalline creep with grain boundary cavitation

Summary  A micromechanical model is developed to describe effects such as combined power-law creep and diffusion, grain boundary sliding and cavitation in polycrystals. Several aspects of creep-constrained cavitation are taken into account such as diffusion in a cage of creeping matrix material and cavitating facets in a cage of creeping grains. Grain boundary sliding is modelled by distributed micro-shearcracks. It is shown that the different physical mechanisms and their interactions are functions of a well-defined material parameter λ, which can be related to the material length scale L introduced by Rice. Received 18 January 2000; accepted for publication 17 May 2000     

Building generalized open boundary conditions for fluid dynamics problems

This paper deals with the design of an efficient open boundary condition (OBC) for fluid dynamics problems. Such problematics arise, for instance, when one solves a local model on a fine grid that is nested in a coarser one of greater extent. Usually, the local solution U^loc is computed from the coarse solution U^ext, thanks to an OBC formulated as , where B_h and B_H are discretizations of the same differential operator (B_h being defined on the fine grid and B_H on the coarse grid). In this paper, we show that such an OBC cannot lead to the exact solution, and we propose a generalized formulation , where g is a correction term. When B_h and B_H are discretizations of a transparent operator, g can be computed analytically, at least for simple equations. Otherwise, we propose to approximate g by a Richardson extrapolation procedure. Numerical test cases on a 1D Laplace equation and on a 1D shallow water system illustrate the improved efficiency of such a generalized OBC compared with usual ones. Copyright © 2012 John Wiley & Sons, Ltd.     

Multiple time step molecular dynamics simulation for interaction between dislocations and grain boundaries

A multiple time step algorithm, called reversible reference system propagator algorithm, is introduced for the long time molecular dynamics simulation. In contrast to the conventional algorithms, the multiple time method has better convergence, stability and efficiency. The method is validated by simulating free relaxation and the hypervelocity impact of nano-clusters. The time efficiency of the multiple time step method enables us to investigate the long time interaction between lattice dislocations and low-angle grain boundaries.The project supported by the National Natural Science Foundation of China (the 973 Project 2004CB619304).     

Simulation of polycrystal deformation with grain and grain boundary effects

Modeling the strengthening effect of grain boundaries (Hall-Petch effect) in metallic polycrystals in a physically consistent way, and without invoking arbitrary length scales, is a long-standing, unsolved problem. A two-scale method to treat predictively the interactions of large numbers of dislocations with grain boundaries has been developed, implemented, and tested. At the first scale, a standard grain-scale simulation (GSS) based on a finite element (FE) formulation makes use of recently proposed dislocation-density-based single-crystal constitutive equations (“SCCE-D”) to determine local stresses, strains, and slip magnitudes. At the second scale, a novel meso-scale simulation (MSS) redistributes the mobile part of the dislocation density within grains consistent with the plastic strain, computes the associated inter-dislocation back stress, and enforces local slip transmission criteria at grain boundaries.Compared with a standard crystal plasticity finite element (FE) model (CP-FEM), the two-scale model required only 5% more CPU time, making it suitable for practical material design. The model confers new capabilities as follows:

(1)

The two-scale method reproduced the dislocation densities predicted by analytical solutions of single pile-ups.

(2)

Two-scale simulations of 2D and 3D arrays of regular grains predicted Hall-Petch slopes for iron of 1.2 ± 0.3 MN/m^3/2 and 1.5 ± 0.3 MN/m^3/2, in agreement with a measured slope of 0.9 ± 0.1 MN/m^3/2.

(3)

The tensile stress-strain response of coarse-grained Fe multi-crystals (9-39 grains) was predicted 2-4 times more accurately by the two-scale model as compared with CP-FEM or Taylor-type texture models.

(4)

The lattice curvature of a deformed Fe-3% Si columnar multi-crystal was predicted and measured. The measured maximum lattice curvature near grain boundaries agreed with model predictions within the experimental scatter.

     

Continuum framework for dislocation structure,energy and dynamics of dislocation arrays and low angle grain boundaries

We present a continuum framework for dislocation structure, energy and dynamics of dislocation arrays and low angle grain boundaries that are allowed to be nonplanar or nonequilibrium. In our continuum framework, we define a dislocation density potential function on the dislocation array surface or grain boundary to describe the orientation dependent continuous distribution of dislocations in a very simple and accurate way. The continuum formulations incorporate both the long-range dislocation interaction and the local dislocation line energy, and are derived from the discrete dislocation model. The continuum framework recovers the classical Read–Shockley energy formula when the long-range elastic fields of the low angle grain boundaries are canceled out. Applications of our continuum framework in this paper are focused on dislocation structures on static planar and nonplanar low angle grain boundaries and misfitting interfaces. We present two methods under our continuum framework for this purpose, including the method based on the Frank׳s formula and the energy minimization method. We show that for any (planar or nonplanar) low angle grain boundary, the Frank׳s formula holds if and only if the long-range stress field in the continuum model is canceled out, and it does not necessarily hold for a total energy minimum dislocation structure.     

A crack on the grain boundary — An analysis based on crystal plasticity theory

The influence of the mismatch of the lattice orientation on the deformation and stress fields of a crack located on the grain boundary is studied by means of the finite-element analysis taking account of finite deformatio and finite lattice rotation. The plane strain calculations for an fcc crystal subjected to mode I loading are performed on the basis of the crystalline plasticity described by a planar three-slip model. For the crack-tip shapes and the dominant deformation modes on slip systems, results of all the cases analysed here are in qualitative agreement with the earlier analytical and numerical solutions. Our results indicate that the lattice orientation difference may greatly influence the shear stress along the grain boundary which is related to grain-boundary sliding, while the normal stress along the grain boundary, which may induce cleavage fracture, is virtually insensitive to it. The influence of the lattice orientations on the crack-tip fields is also investigated under small-scale-yielding conditions and the comparison with the results of finite deformation is made.     

Morse Theory and Central Configurations in the Spatial N-body Problem

In the spirit of Palmore and Pacella, Morse Theory is used to obtain a lower bound for the number of central configurations in the spatial N-body problem. The homology of the configuration ellipsoid with the collision and collinear manifolds removed and the SO(3) symmetry quotiented out is calculated. As intermediate steps, homology calculations are carried out for several additional manifolds naturally arising in the N-body problem.     

虚边界元法的理论分析

通过平面位势问题,对虚边界元方法的理论基础进行了探讨性研究。在此基础上,给出虚边界与真实边界间的距离选取法,其实质是距离的选取依赖于边界的离散化。     

Apollonius coordinates,theN-body problem,and continuation of periodic solutions

This paper treats theN-body problem and its relation to various restricted problems. For each solution of the Kepler problem a generalization of the pulsating coordinates used to express the Hamiltonian of the elliptic restricted three-body problem is given. These coordinates are called Apollonius coordinates. The method of symplectic scaling is used to give a precise derivation of the elliptic restricted problem showing the precise asymptotic relationship between the restricted problem and the full three-body problem. This derivation obviates the proof of the fact that a nondegenerate periodic solution of the elliptic restricted three-body problem can be continued into the full three-body problem under mild nonresonance assumptions. Also, the method of symplectic scaling is used to give a precise derivation of the elliptic Hill lunar equation showing the precise relationship between the elliptic Hill lunar equation and the full three-body problem. A similar continuation theorem is established.     

近边界三维水下爆炸气泡动态特性研究

模拟了近壁、近自由面的水下爆炸气泡的非线性动态特性,假定水下爆炸气泡脉动阶段的流场是无旋、不可压缩的,采用高阶曲面三角形单元离散三维气泡表面,用边界积分法求解气泡的运动,在计算奇异积分时通过重新构造双层位势的主值积分消除双层奇异积分的奇异性,得到更精确的结果,并通过合理的加权方法精确的求解边界面上各节点的真实速度,结合弹性网格技术（elastic mesh technique, EMT）得到优化速度,在整个模拟过程中不需要采用数值光顺。将本文的三维模型与轴对称模型进行的对比分析表明,两种模型计算结果吻合很好,并用三维模型模拟了气泡与自由表面及圆筒的相互作用,水下爆炸气泡在自由表面及圆筒的联合作用下呈现出强非线性。     

Defect redistribution within a continuum grain boundary plasticity model

The mechanical response of polycrystalline metals is significantly affected by the behaviour of grain boundaries, in particular when these interfaces constitute a relatively large fraction of the material volume. One of the current challenges in the modelling of grain boundaries at a continuum (polycrystalline) scale is the incorporation of the many different interaction mechanisms between dislocations and grain boundaries, as identified from fine-scale experiments and simulations. In this paper, the objective is to develop a model that accounts for the redistribution of the defects along the grain boundary in the context of gradient crystal plasticity. The proposed model incorporates the nonlocal relaxation of the grain boundary net defect density. A numerical study on a bicrystal specimen in simple shear is carried out, showing that the spreading of the defect content has a clear influence on the macroscopic response, as well as on the microscopic fields. This work provides a basis that enables a more thorough analysis of the plasticity of polycrystalline metals at the continuum level, where the plasticity at grain boundaries matters.     

含氢原子缺陷晶界的剪切行为

针对4个α-Fe对称倾斜晶界,采用分子静力学考察了4个晶界中H原子偏析能的分布特征,并采用分子动力学方法研究了晶界内植入不同数量H原子对其在室温条件下剪切行为的影响.H原子通过随机方式植入界面内,利用植入H原子数量与晶界面积的比值来定义H原子面密度ρ.在含H原子晶界剪切行为分析过程中,重点考察了在不同H原子密度ρ下,4个晶界的初始塑性临界应力和晶界迁移位移的变化趋势以及4个晶界在加载过程中的微观变形机理.研究表明:晶界内的H原子偏析能明显偏低,4个晶界附近的H原子会自发向晶界内偏析;随着植入H原子数量的逐渐增多,晶界的初始塑性临界应力和后续变形阶段应力均会降低.晶界内植入H原子会从本质上改变晶界的微观变形机理,进而影响晶界在外载荷条件下的迁移属性.与不含H原子晶界的变形机理对比发现,加载过程中晶界的微结构会发生剧烈的演化,H原子的扩散和团簇化效应会导致晶界内出现纳米孔缺陷.