Modelling of spall damage in ductile materials and its application to the simulation of plate impact on copper

A statistical model of dynamic spall damage due to void nucleation and growth is proposed for ductile materials under intense loading, which takes into account inertia, elastic-plastic effect, and initial void size. To some extent, void interaction could be accounted for in this approach. Based on this model, the simulation of spall experiments for copper is performed with the Lagrangian finite element method. The simulation results are in good agreement with experimental data for the free surface velocity profile, stress record behind copper target, final porosity, and void concentrations across the target. The influence of elastic-plastic effect upon the damage evolution is explored. The correlation between the damage evolution and the history of the stress near the spall plane is also analyzed.     

Modelling of spall damage in ductile materials and its application to the simulation of the plate impact on copper

A statistical model of dynamic spall damage due to void nucleation and growth is proposed for ductile materials under intense loading, which takes into account inertia, the elastic-plastic effect, and initial void size. To some extent, void interaction could be accounted for in this approach. Based on this model, the simulation of spall experiments for copper is performed by using the Lagrangian finite element method. The simulation results are in good agreement with experimental data for the free surface velocity profile, stress record behind copper target, final porosity, and void concentrations across the target. The influence of elastic-plastic effect upon the damage evolution is explored. The correlation between the damage evolution and the history of the stress near the spall plane is also analyzed.     

基于孔洞体胞模型铸造镁合金ML308的本构方程

铸造镁合金不可避免地包含许多微孔洞,这些微孔洞在材料的后续加工及服役过程中将发生演化,并对材料的力学行为产生重要影响.基于球形孔洞体胞模型,提出微孔洞长大及形核方程,它们构成微孔洞的演化方程.根据孔洞演化将造成材料性质弱化的物理机制,将微孔洞演化以弱化函数的形式引入到非经典弹塑性本构方程,得到考虑孔洞演化的铸造镁合金弹塑性本构方程.发展与本构方程相应的有限元数值分析程序,用其模拟了铸造镁合金ML308的微孔洞演化及力学行为,计算结果与实验结果符合较好. 关键词： 铸造镁合金 孔洞体胞模型 孔洞演化方程 本构方程     

基于微孔洞长大惯性机制的动态拉伸断裂模型构建

 采用圆柱体胞模型分析方法,对球形微孔洞在不同加载应变率条件下的动力学响应行为进行了有限元分析,计算结果表明：在微孔洞稳定增长阶段,惯性对微孔洞的快速增长起着关键性作用,其它因素的影响基本可以忽略,微孔洞半径增长率与平均应力的平方根成正比。提出了一个微孔洞增长惯性机制的损伤度演化方程,结合逾渗软化函数描述微孔洞聚集行为,从而构建了一个新的动态拉伸断裂模型,并通过自定义材料模型子程序,把断裂模型嵌入LS-DYNA程序中,对无氧铜平板撞击层裂实验进行了数值模拟研究,计算结果与实验结果的比较令人满意,初步检验了新模型的实用性。     

基于单孔洞近似的高纯铝部分层裂实验的数值模拟研究

基于单孔洞近似,对不同撞击速度下高纯铝的部分层裂实验进行了数值模拟研究,讨论了微孔洞长大对波传播的影响及其在自由面速度波剖面上的表现. 通过分析微孔洞周围的应力场变化,认识到实测自由面速度波剖面出现"回跳"特征并不能说明材料发生完全层裂,其直接原因是样品内部微孔洞长大所引起的局部卸载效应. 将计算得到的自由面速度波剖面和微孔洞相对体积与实验结果进行了对比分析,发现两者均符合很好,表明采用单孔洞增长来近似描述部分层裂样品中随机损伤发展及其对波传播的影响是可行的. 关键词： 层裂 孔洞增长 自由面速度波剖面 微孔洞相对体积     

单晶铜在动态加载下空洞增长的分子动力学研究

冲击载荷下延性材料的损伤是材料中微空洞的产生和长大演化的结果.利用分子动力学模拟 方法对延性金属单晶铜中单个空洞在动态加载下的演化发展进行了研究，得到了空洞增长过 程中的应力分布及空洞增长演化随冲击强度变化的规律.模拟结果表明，动态加载下的前期 压缩过程对后期拉伸应力场作用下的空洞增长演化特征有不可忽视的影响，微空洞增长的阈 值则与单晶实验中层裂强度随拉伸应力作用时间减少而增加的趋势相一致. 关键词： 层裂 分子动力学 动态加载 空洞     

Morphological evolution and migration of void in bi-piezoelectric interface based on nonlocal phase field method

This paper reports the result of investigation into the morphological evolution and migration of void in bi-piezoelectric material interface by utilizing nonlocal phase field model and finite element method (FEM), where the small scale effect containing the long-range forces among atoms is considered. The nonlocal elastic strain energy and the nonlocal electric energy around the void are firstly calculated by the finite element method. Then based on the finite difference method (FDM), the thermodynamic equilibrium equation containing the surface energy and anisotropic diffusivity is solved to simulate the morphological evolution and migration of elliptical void in bi-piezoelectric films interface. Results show that the way of load condition plays a significant role in the evolution process, and the boundary of void's long axis gradually collapses toward the center of ellipse. In addition, the evolutionary speed of left boundary gradually decreases with scale effect coefficient growth. This work can provide references for the safety evaluation of piezoelectric materials in micro electro mechanical system.     

Electrochemical effects of isolated voids in uranium dioxide

We present a model to study the electrochemical effects of voids in oxide materials under equilibrium conditions and apply this model to uranium dioxide. Based on thermodynamic arguments, we claim that voids in uranium dioxide must contain oxygen gas at a pressure that we determine via a Kelvin equation in terms of temperature, void radius and the oxygen pressure of the outside gas reservoir in equilibrium with the oxide. The oxygen gas within a void gives rise to ionosorption and the formation of a layer of surface-charge on the void surface, which, in turn, induces an influence zone of space charge into the matrix surrounding the void. Since the space charge is carried in part by atomic defects, it is concluded that, as a part of the thermodynamic equilibrium of oxides containing voids, the off-stoichiometry around the void is different from its remote bulk value. As such, in a uranium dioxide solid with a void ensemble, the average off-stoichiometry level in the material differs from that of the void-free counterpart. The model is applied to isolated voids in off-stoichiometric uranium dioxide for a wide range of temperature and disorder state of the oxide.     

Surface morphological response of crystalline solids to mechanical stresses and electric fields

Surface morphological evolution under the action of external fields is a fascinating topic that has attracted considerable attention within the surface science community over the past two decades. In addition to the interest in a fundamental understanding of field-induced nonlinear response and stability of surface morphology, the problem has been technologically significant in various engineering applications such as microelectronics and nanofabrication. In this report, we review theoretical progress in modeling the surface morphological response of stressed elastic solids under conditions that promote surface diffusion and of electrically conducting solids under surface electromigration conditions. A self-consistent model of surface transport and morphological evolution is presented that has provided the basis for the theoretical and computational work that is reviewed. According to this model, the surface morphological response of electrically conducting elastic solids to the simultaneous action of mechanical stresses and electric fields is analyzed. Emphasis is placed on metallic surfaces, including surfaces of voids in metallic thin films.Surfaces of stressed elastic solids are known to undergo morphological instabilities, such as the Asaro–Tiller or Grinfeld (ATG) instability that leads to emanation of crack-like features from the surface and their fast propagation into the bulk of the solid material. This instability is analyzed theoretically, simulated numerically, and compared with experimental measurements. The surface morphological evolution of electrically conducting, single-crystalline, stressed elastic solids under surface electromigration conditions is also examined. We demonstrate that, through surface electromigration, a properly applied and sufficiently strong electric field can stabilize the surface morphology of the stressed solid against both crack-like ATG instabilities and newly discovered secondary rippling instabilities; the effects of important parameters, such as surface crystallographic orientation, on the surface morphological response to the simultaneous action of an electric field and mechanical stress also are reviewed. In addition, electromigration-driven surface morphological response is analyzed systematically, focusing on the current-driven surface morphological evolution of voids in metallic thin films; this analysis has been motivated largely by the crucial role of void dynamics in determining the reliability of metallic interconnects in integrated circuits and has led to the interpretation of a large body of experimental observations and measurements. The electromigration-driven translational motion of morphologically stable voids, effects of current-driven void dynamics on the evolution of the electrical resistance of metallic thin films, and current-driven void–void interactions also are reviewed. Furthermore, theoretical studies are reviewed that demonstrated very interesting current-driven nonlinear void dynamics in stressed metallic thin films, including the inhibition of electromigration-induced instabilities due to the action of biaxial tensile stress, and stress effects on the electromigration-driven translational motion of morphologically stable voids.Complex, oscillatory surface states under surface electromigration conditions have been observed in numerical studies. In this report, emphasis is placed on void surfaces in metallic thin films, for which stable time-periodic states have been demonstrated. It is shown that increasing parameters such as the electric-field strength or the void size past certain critical values leads to morphological transitions from steady to time-periodic states; the latter states are characterized by wave propagation on the surface of a void that migrates along the metallic film at constant speed. The transition onset corresponds to a Hopf bifurcation that may be either supercritical or subcritical, depending on the symmetry of the surface diffusional anisotropy as determined by the crystallographic orientation of the film plane. It is also shown that, in the case where the Hopf bifurcation is subcritical, the simultaneous action of mechanical stress leads the current-driven void morphological response to the stabilization of chaotic attractors; in such cases, as the applied stress level increases, the void dynamics is set on a route to chaos through a sequence of period-doubling bifurcations. The observation of current-driven chaotic dynamics in homoepitaxial islands also is discussed.     

一个新的损伤演化方程及其在层裂中的应用

 采用统计细观损伤力学方法,基于延性金属断裂过程的孔洞演化机理,提出一个新的损伤演化方程,该方程在一定的条件下与由空心球体胞模型导出的损伤方程形式相同。在此基础上,将新的损伤演化方程编入一维Lagrange有限差分动力学程序,对OFHC铜的平板对称正碰撞层裂实验进行了数值模拟,计算结果与实验吻合得较好。     

惯性及弹塑性效应对延性金属材料层裂损伤的影响

本文以空心球壳模型为基础,在飞片加载条件下,讨论了惯性、弹塑性效应以及初始孔洞大小对材料层裂损伤的影响.分析结果表明,在研究材料层裂损伤问题时,惯性、弹塑性效应以及初始孔洞大小的影响是不能忽略的,特别是初始孔洞大小的影响.同时,鉴于初始孔洞大小的重要影响,本文尝试给出了一个分析初始孔洞尺寸的方法. 关键词： 层裂损伤 惯性 弹塑性效应 初始孔洞     

Irradiation-induced void evolution in iron:A phase-field approach with atomistic derived parameters

A series of material parameters are derived from atomistic simulations and implemented into a phase field(PF) model to simulate void evolution in body-centered cubic(bcc) iron subjected to different irradiation doses at different temperatures.The simulation results show good agreement with experimental observations — the porosity as a function of temperature varies in a bell-shaped manner and the void density monotonically decreases with increasing temperatures; both porosity and void density increase with increasing irradiation dose at the same temperature. Analysis reveals that the evolution of void number and size is determined by the interplay among the production, diffusion and recombination of vacancy and interstitial.     

利用高能离子模拟研究反应堆结构材料中的辐照效应

简要介绍了载能粒子辐射损伤对反应堆结构材料性能的影响,阐述了载能粒子束特别是高能离子束开展模拟研究的优势,并举例说明了国内利用高能重离子模拟研究反应堆结构材料辐射效应取得的进展。实验结果和理论分析表明,载能离子特别是高能离子辐照非常适合用于模拟研究反应堆结构材料中由粒子辐射引起的材料微观结构和宏观性能变化,是模拟研究反应堆结构材料辐射效应的非常有效的手段。 Radiation damage in structural materials of fission/fusion reactors is mainly attributed to the evolution of intensive atom displacement damage induced by energetic particles （ n, α and/or fission fragments） and highrate helium doping by direct α particle bombardments and/or （n, α） reactions. It can cause severe degradation of reactor structural materials such as surface blistering, bulk void swelling, deformation, fatigue, embrittlement, stress erosion corrosion and so on that will significantly affect the operation safety of reactors. However, up to now, behavior of structural materials at the end of their service can hardly be fully tested in a real reactor. In the present paper, damage process in reactor structural materials is briefly introduced, then the advantages of energetic ion implantation/irradiation especially high-energy heavy ion irradiation are discussed, and several typical examples on simulation of radiation effects in reactor candidate structural materials using high-energy heavy ion irradiations are introduced. Experimental results and theoretical analysis suggested that irradiation with energetic particles especially high-energy heavy ions is a very useful technique for simulating the evolution of microstructures and macro-properties of reactor structural materials.     

Nonlinear theory of void formation in colloidal plasmas

A nonlinear time-dependent model for void formation in colloidal plasmas is proposed. For experimentally relevant initial conditions, the model describes the nonlinear evolution of a zero-frequency linear instability that grows rapidly in the nonlinear regime and subsequently saturates to form a void. A number of features of the model are consistent with experimental observations under laboratory and microgravity conditions.     

Phase resolved PD patterns in treeing in the presence of voids

One of the important aspects of insulation condition monitoring through partial discharge (pd) detection is the need to establish a trend in the discharge pattern for a given insulating system. Treeing is one of the principal routes to failure in insulating materials, and its growth is accompanied by pd activity. In this work, a study of the evolution of the phase resolved pd patterns during the various stages of tree growth in the presence of void is undertaken. Air-filled artificial voids are injected into the polymer, and their effect on the growth of a pre-existing tree observed. The pd patterns were seen to change drastically on tree channels reaching the void. The tree channel reaching the void was seen to undergo intense pd activity followed by widening of the channel. Electrical pd detection is performed simultaneously with online visual observation of tree growth with a high resolution high speed camera.     

Modulation of Void Motion Behavior in a Magnetized Dusty Plasma

Based on fluid equations,we show a time-dependent self-consistent nonlinear model for void formation in magnetized dusty plasmas.The cylindrical configuration is applied to better illustrate the effects of the static magnetic field,considering the azimuthal motion of the dusts.The nonlinear evolution of the dust void and the rotation of the dust particles are then investigated numerically.The results show that,similar to the unmagnetized one-dimensional model,the radial ion drag plays a crucial role in the evolution of the void.Moreover,the dust rotation is driven by the azimuthal ion drag force exerting on the dust.As the azimuthal component of ion velocity increases linearly with the strength of the magnetic field,the azimuthal component of dust velocity increases synchronously.Moreover,the angular velocity gradients of the dust rotation show a sheared dust flow around the void.     

A phase-field modeling of void swelling in the Austenitic stainless steel

Two-dimensional phase-field simulations of void swelling in the Austenitic stainless steel were performed for irradiated materials. A numerical model was established for void swelling with an implementation of the elasticity effect, and we examined the roles of the applied stress and grain boundary sink strength and Frenkel defect recombination in determining the void swelling rate. The obtained results were compared with the existing experimental observations.     

改进的部分子演化模型及其对EMC效应和核Drell－Yan过程的解释

用解析方法证明了部分子演化模型可为双重Ｘ重新标度模型提供物理基础，进而利用修正的Ａｌｔｅｒａｌｌｉ－Ｐａｒｉｓｉ方程描述小ｘ区域的核遮蔽和反遮蔽效应，以改进部分子演化模型，使我们不必引入核遮蔽因子便可统一地描述ＥＭＣ效应、核遮蔽和反遮蔽效应．最后，利用改进的部分子演化模型相当好地解释了核Ｄｒｅｌｌ－Ｙａｎ过程的实验数据．     

Stochastic void coarsening

The random nature of diffusing jumps and cascade occurrence produce stochastic fluctuations of the point-defect fluxes. The effect of such fluctuations on the kinetics of void growth is investigated in the present paper. It is found that the non-linear coupling between the stochastic fluctuations and the void sizes may lead to the instability of void evolution within the mean-field theory, when the sizes of voids and their growth rates are both relatively small. The growth rate of voids becomes dominated by the stochastic component, causing the smaller voids to shrink away. This effect is investigated in terms of a non-equilibrium phase transition induced by a purely random stochastic noise. The derived conditions for this non-equilibrium transition are compared favourably with experimental observations. Received: 5 June 2000 / Accepted: 9 October 2000 / Published online: 21 March 2001