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。     

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     

层错四面体对单晶铜层裂行为影响的分子动力学研究

层错四面体是一种典型的三维空位型缺陷,广泛存在于受辐照后的面心立方金属材料中,对材料的力学性能有显著的影响.目前,关于层错四面体对辐照材料层裂行为的影响还缺乏深入系统的研究.本文使用分子动力学方法模拟了含有层错四面体的单晶铜在不同冲击速度下的层裂行为,对整个冲击过程中的自由表面速度及微结构演化等进行了深入的分析.研究发现,层错四面体在冲击波作用下会发生坍塌,并进一步诱导材料产生位错、层错等缺陷.在中低速度加载下,层错四面体坍塌引起的缺陷快速向周围扩展,为孔洞提供了更宽的形核区域,促进了孔洞的异质成核,造成材料层裂强度大幅度减小.当冲击速度较高时,层错四面体坍塌导致的局部缺陷对材料的层裂强度不再有明显影响.     

延性材料动态拉伸断裂早期连通过程的逾渗描述

 借鉴逾渗理论,提出了新的应力松弛函数,简称PR函数（Percolation-Release Function）,用以描述断裂发生前由于微孔洞连通而引起的快速应力松弛过程,具有较为明确的物理意义。通过其与损伤度函数模型进行耦合,对无氧铜和45钢平板撞击层裂进行了数值模拟。结果表明：数值计算不仅有效地再现了界面的应力历史和自由面速度历史,而且再现了靶中的损伤分布;新的逾渗松弛函数具有较好的适用性。     

加载应力幅值对高纯铜动态损伤演化特性研究

研究了加载应力幅值对延性金属高纯无氧铜动态损伤演化特性的影响. 层裂实验在一级轻气炮上开展, 利用不同的飞片击靶速度实现不同加载应力幅值(2.5 GPa, 2.75 GPa和3.75 GPa), 采用DISAR位移干涉诊断技术测量样品自由面的速度剖面, 利用基于白光轴向色差的表面轮廓测试技术测试软回收的样品截面. 结果显示: 随着加载应力幅值的升高, 层裂强度几乎没有变化, 但自由面速度剖面上Pull back信号后的回跳速率和幅值显著增大, 损伤演化速率显著升高.进一步分析表明: 延性金属动态损伤演化过程中微孔洞成核对加载应力幅值单一因素不敏感, 但加载应力幅值是微孔洞长大和聚集的主导因素之一.     

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     

一种新的概念性层裂模型

 在重建Cochran-Banner模型的基础上提出了一种新的概念性层裂模型。这种新模型仅保留Cochran-Banner模型中的强度函数,重新定义损伤,并抛弃了基本假设：一旦微损伤形成,使微损伤演化远远易于使固体进一步体积应变,进而修正了差分微元中固体比容的计算。在新的模型中,一旦拉伸应力达到层裂强度,重新定义的损伤将由强度函数确定的应力松弛方程、计及损伤的能量守恒方程、状态方程以及本构方程等一系列封闭方程组确定。新模型中也仅包含两个参数：层裂强度及临界损伤度,它们的确定能使在一定初、边值条件下的层裂试验的数值计算结果与实验测得的靶自由面速度历史或靶-低阻抗界面应力历史以及回收观测的层裂面上的损伤一致。强调指出,选定强度函数或应力松弛方程提供了确定损伤的可能,同时排除了任何外加的损伤演化方程。     

The characteristics of void distribution in spalled high purity copper cylinder under sweeping detonation

The effects of different peak compression stresses (2–5 GPa) on the spallation behaviour of high purity copper cylinder during sweeping detonation were examined by Electron Backscatter Diffraction Microscopy, Doppler Pins System and Optical Microscopy techniques. The velocity history of inner surface and the characteristics of void distributions in spalled copper cylinder were investigated. The results indicated that the spall strength of copper in these experiments was less than that revealed in previous reports concerning plate impact loading. The geometry of cylindrical copper and the obliquity of incident shock during sweeping detonation may be the main reasons. Different loading stresses seemed to be responsible for the characteristics of the resultant damage fields, and the maximum damage degree increased with increasing shock stress. Spall planes in different cross-sections of sample loaded with the same shock stress of 3.29 GPa were found, and the distance from the initiation end has little effect on the maximum damage degree (the maximum damage range from 12 to 14%), which means that the spallation behaviour was stable along the direction parallel to the detonation propagation direction under the same shock stress.     

The void nucleation mechanism within lead phase during spallation of leaded brass

The incipient spall behaviours of Cu-34%Zn-3%Pb leaded brass samples with annealed and cryogenic-treated conditions were loaded using one-stage light gas gun experiments. The effect of Pb-phase on dynamic damage nucleation in leaded brass specimens was investigated by means of optical microscopy, scanning electron microscopy and x-ray computer tomography. It was found that the voids of incipient spall were mainly nucleated in the interior of the lead (no tensile stress would be produced within lead according to the impact theory) instead of nucleated at the phase interface as expected by quasi-static damage fracture theory. A nucleation model is proposed in the present work that is the asymmetry high compression zones in the centre of the lead-phase were formed by the rarefaction wave convergence effects of matrix/quasi-spherical lead interface, which caused adiabatic temperature rise that exceeded melting point of lead due to severe plastic deformation, finally led to local melting and void nucleation. In addition, the spall strength and damage rate increased with the increase in the Pb-phase number.     

Molecular dynamics simulation on elastoplastic properties of the void expansion in nanocrystalline copper

Influences of different factors on the elastic-plastic properties of nanocrystalline copper containing a void are studied by the molecular dynamics method. The radius of the circular plate is 30a, while the radius of the void is 5a (a is 0.3615 nm for the lattice constant of bulk copper). The effects of crystal orientation, the void ellipticity, loading rate, and temperature of nanocrystalline copper are discussed. The elastic-plastic deformation of nanocrystalline under inner pressure is investigated in this research. The plastic zone is determined according to the dislocation nucleation from the edge of the void. The simulation results show that there are different deformation mechanisms under different crystal orientations, and the nanocrystalline copper can be strengthened by changing the void shape, decreasing the loading rate, and lowering the temperature. And the plastic zone initiation and growth are further explained. The change of different conditions has a great influence on plastic zone.     

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     

Effect of grain size and arrangement on dynamic damage evolution of ductile metal

Plate-impact experiments have been carried out to examine the effect of grain size and grain arrangement on the damage evolution of ultrapure aluminum. Two groups of samples, "cross-cut" and "longitudinal-cut," are obtained from the rolled aluminum rod along different directions. The peak compressive stress is approximately 1.25 GPa-1.61 GPa, which can cause incipient spall damage that is correlated to the material microstructure. The metallographic analyses of all recovered samples show that nearly all damage nucleates at the grain boundaries, especially those with larger curvature. Moreover, under lower shock stress, the spall strength of the "longitudinal-cut" sample is smaller than that of the "crosscut" sample, because the different grain sizes and arrangement of the two samples cause different nucleation, growth, and coalescence processes. In this study, the difference in the damage distribution between "longitudinal-cut" and "cross-cut" samples and the causes for this difference under lower shock-loading conditions are also analyzed by both qualitative and semi-quantitative methods. It is very important for these conclusions to establish a reasonable and perfect equation of damage evolution for ductile metals.     

关于自由面速度剖面解读层裂问题的几点商榷

 基于对层裂问题的理解和相关文献,就自由面速度剖面解读层裂问题的局限性提出了一些看法。指出：自由面速度剖面测量给出的层裂破坏过程是间接信息,而不是直接信息,用它确定的理论模型和数值模拟参数,也许并没有真实地反映层裂过程的物理本质;层裂强度常被人们用来表征材料在高应变率下的抗拉伸能力,但是在目前的层裂强度计算公式中没有考虑损伤介质对波剖面传播的影响,使得计算结果明显偏低;传统的单点测量得到的结果有很大的局限性,对于层裂问题,采用概率评估或者置信度评估,也许更符合真实情况。建议：为了全面真实地评价层裂问题中的物理、力学过程,应该加快发展更多的实验探测和诊断技术,尤其是对内部损伤状态的观测。     

非一维应变冲击加载下高纯铜初始层裂行为

提出了一种锥形靶层裂实验新方法,开展非一维应变冲击条件下高纯铜初始层裂行为实验研究,讨论了锥形靶内部损伤分布特征及其与自由面速度典型特征之间的内禀关系.结果显示:1)初始层裂的锥形靶内部出现了连续损伤区,损伤区扩展方向与锥面平行,从锥底到锥顶呈现了不同的损伤状态,从微孔洞独立长大到局部聚集,最后形成宏观裂纹,这种损伤状态分布特征归因于锥形靶内部拉伸应力幅值和持续时间的空间演化;2)通过锥形靶横截面损伤度定量统计分析,揭示损伤演化早期的微孔洞成核与早期长大过程是随机的,而损伤演化后期的微孔洞聚集过程具有显著的局域化特征;3)不同位置处实测的自由面法向粒子速度剖面呈现出典型的层裂Pull-back信号,但是通过与内部损伤分布特征对比,揭示基于Pull-back速度获得高纯铜层裂强度本质是微孔洞成核阈值应力,Pull-back回跳速度斜率反映了损伤演化速率,Pull-back回跳幅值与损伤度引起的应力松弛密切相关.     

钽的层裂实验数值模拟

 采用连续介质力学基唯象模型模拟分析了钽的平板撞击层裂行为。该模型包括了材料的非线性弹性（状态方程）、率相关塑性和孔洞的形核及生长等多种效应，并且采用一种对角隐式Runge-Kutta方法来求解本构率方程组，提高了热粘塑性本构关系计算的稳定性及精度。将数值模拟结果和相关实验数据进行了对比分析，结果表明，对于样品中的拉应力峰值明显高于材料层裂强度的实验（中、高速平板撞击实验），理论模型具有较好的预估能力，但对于临界层裂问题（低速平板撞击实验），该模型对材料损伤与失效过程的描述可能不够准确，需要进一步改进。     

损伤度函数模型用于3种钢层裂的二维数值模拟

 把损伤度函数模型嵌入到二维有限元程序DEFEL中，并对3种钢（HR-2钢、2169钢及45钢）的平板撞击层裂实验进行了数值模拟，在模拟中计及材料的屈服硬化效应和Bauschinger效应的影响，较好地再现了实测自由面的速度历史，同时给出了样品中的损伤分布及其发展。在数值模拟中发现，断裂面附近所受最大拉应力介于由声学近似解析计算的层裂强度和从三项式固体状态方程出发得出的断裂理论值之间，并对三者之间的差异作了分析，表明数值模拟结果是合理的。     

Dynamic fracture of copper under the action of a relativistic high-current electron beam

This paper presents the results of investigations of the dynamic spall fracture of bulk (2–6 mm) copper targets under the action of a relativistic high-current electron beam (1.3 MeV electron energy, 50 ns pulse duration, ∼10¹⁰ W/cm² power density) generated by the SINUS-7 accelerator. By numerical simulation with the use of the BETAIN1 software package it has been found that the amplitude of the stress wave formed is 6 GPa and the deformation rate is 5·10⁵ s⁻¹. As established experimentally, there is a practically linear relationship between the thickness of the target and the thickness of the spalled layer. Comparison of the experimental data and the simulation results has shown that the spall strength of copper under the given conditions is 1.3 GPa, which is in good agreement with the data available in the literature. Analysis performed with the use of fractographic teqniques has revealed that in the case of recrystallized copper the size of the spall pits formed inside the grains is four times greater than the size of the pits formed on the grain boundaries. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 69–74, July, 2006.     

高纯铜初始层裂的微损伤特性研究

本文对平面冲击加载下高纯铜初始层裂的微损伤特性进行了研究. 利用准三维的表面轮廓测试技术, 对冲击加载“软回收”的样品截面进行测试. 通过对测试数据的重构、量化和统计分析, 结果表明: 拉伸应力持续时间和加载应力幅值的增加, 都会加剧样品内部损伤局域化程度. 样品内损伤区域宽度是亚微米尺度的损伤演化的结果, 并且亚微米尺度的演化速率随着拉伸应变率的增加而单调递增. 通过统计获得了样品内微损伤的尺寸分布特征, 并分析了其与损伤演化进程的关联.     

AD95陶瓷的层裂强度及冲击压缩损伤机理研究

采用激光位移干涉测试技术测量了AD95 陶瓷在一维应变冲击压缩下的自由面或样品/窗口界面粒子速度剖面, 确定了层裂强度及其与加载应力的变化关系, 在此基础上讨论了冲击压缩损伤程度与加载应力的关系. 研究结果表明: AD95陶瓷发生冲击压缩损伤的阈值应力约为3.7 GPa, 小于其雨贡纽弹性极限(HEL, 约5.47 GPa); 小于阈值应力不发生冲击压缩损伤, 层裂强度随加载应力的增加逐渐增大; 大于阈值应力冲击压缩损伤快速发展, 层裂强度迅速降低; 在HEL附近层裂强度降低到零, 丧失了抗拉能力, 表明材料发生了严重的冲击压缩损伤.