一维快速拉伸下无氧铜的动态断裂与破碎

利用电磁膨胀环技术对无氧铜环进行了不同加载电压下的动态拉伸实验。对无氧铜在破碎前出现塑性失稳多重颈缩进行了初步分析,利用能量平衡的破碎理论给出了无氧铜环的破碎分布。三维数值模拟结果表明,颈缩区温升比非颈缩区高,且多重颈缩在环周上的分布服从泊松分布。     

45钢柱壳爆炸膨胀断裂的SPH模拟分析

金属柱壳爆炸膨胀断裂存在拉伸、剪切及拉剪混合等多种断裂模式,目前其物理机制及影响因素还不清晰。本文中采用光滑粒子流体动力学方法（smoothed particle hydrodynamics, SPH）对45钢柱壳在JOB-9003及RHT-901不同装药条件下的外爆实验进行了数值模拟,探讨柱壳在不同装药条件下发生的剪切断裂、拉剪混合断裂模式及其演化过程,模拟结果与实验结果一致。SPH数值模拟结果表明:在爆炸加载阶段,随着冲击波在柱壳内、外壁间来回反射形成二次塑性区,沿柱壳壁厚等效塑性应变演化呈凸形分布,壁厚中部区域等效塑性应变较内、外壁大;在较高爆炸压力（JOB-9003）作用下,柱壳断裂发生在爆轰波加载阶段,损伤裂纹从塑性应变积累较大的壁厚中部开始沿剪切方向向内、外壁扩展,形成剪切型断裂模式;而在RHT-901空心炸药加载下,虽然裂纹仍从壁厚中部开始沿剪切方向扩展,但随后柱壳进入自由膨胀阶段,未断区域处于拉伸应力状态,柱壳局部发生结构失稳,形成类似“颈缩”现象,裂纹从剪切方向转向沿颈缩区向外扩展,呈现拉剪混合断裂模式。拉伸裂纹占截面的比例与柱壳结构失稳时刻相关。可见,柱壳断裂演化是一个爆炸冲击波与柱壳结构相互作用的过程,不能简单将其作为一系列膨胀拉伸环处理。     

石英玻璃圆环高速膨胀碎裂过程的离散元模拟

采用离散元算法模拟了石英玻璃圆环受到外加动态载荷时的力学行为. 首先基于flat-jointed粘结模型,通过标准的单轴拉压、三点弯曲等数值实验来标定了石英玻璃的微观参数. 在此模型基础上,数值模拟再现了石英玻璃圆环在不同应变率下的膨胀碎裂过程. 为定量分析数值模拟结果,需要准确确定圆环的碎裂发生时刻. 模拟发现:伴随着石英玻璃圆环的断裂,圆环外表面粒子径向膨胀速度的时程曲线会发生突然升高然后下降的跳动;详细分析表明,这种跳动源自周向的脆性断裂诱发的卸载波(周向拉伸应力急剧下降)以及伴随而来的泊松膨胀,这种径向速度跳动现象为实验中检测脆性断裂发生时刻提供了可能. 进一步的数值研究表明:(1)石英玻璃圆环的断裂应变随着应变率的提高而增大,与韧性金属材料的膨胀环实验结果一致;(2)石英玻璃圆环的碎片平均质量随着应变率的增大而减小;(3)数值计算获得的碎片平均尺寸与已有的理论和实验结果比较吻合. 利用液压膨胀环实验装置对石英玻璃圆环进行了验证性实验,回收得到的碎片形貌及碎片个数与数值模拟的结果基本一致.      

石英玻璃圆环高速膨胀碎裂过程的离散元模拟

采用离散元算法模拟了石英玻璃圆环受到外加动态载荷时的力学行为.首先基于flat-jointed粘结模型,通过标准的单轴拉压、三点弯曲等数值实验来标定了石英玻璃的微观参数.在此模型基础上,数值模拟再现了石英玻璃圆环在不同应变率下的膨胀碎裂过程.为定量分析数值模拟结果,需要准确确定圆环的碎裂发生时刻.模拟发现:伴随着石英玻璃圆环的断裂,圆环外表面粒子径向膨胀速度的时程曲线会发生突然升高然后下降的跳动;详细分析表明,这种跳动源自周向的脆性断裂诱发的卸载波(周向拉伸应力急剧下降)以及伴随而来的泊松膨胀,这种径向速度跳动现象为实验中检测脆性断裂发生时刻提供了可能.进一步的数值研究表明:(1)石英玻璃圆环的断裂应变随着应变率的提高而增大,与韧性金属材料的膨胀环实验结果一致;(2)石英玻璃圆环的碎片平均质量随着应变率的增大而减小;(3)数值计算获得的碎片平均尺寸与已有的理论和实验结果比较吻合.利用液压膨胀环实验装置对石英玻璃圆环进行了验证性实验,回收得到的碎片形貌及碎片个数与数值模拟的结果基本一致.     

韧性材料冲击拉伸碎裂中的碎片尺寸分布规律

利用有限元方法模拟韧性金属圆环高速膨胀过程中的碎裂过程, 获得不同初始膨胀速度下碎片的样本集合. 通过对碎片的尺寸进行统计分析发现:(1)无论初始膨胀速度如何, 碎片的归一化尺寸分布具有相似性, 可以用一个具有初始阈值的Weibull分布描述, 近似地, 这个分布还可以简化为Rayleigh分布;(2)碎片尺寸的累积分布曲线呈现阶梯特性, 表现出较明显的"量子化"特性.在上述发现基础上, 建立一个Monte-Carlo模型:碎裂点来自于颈缩点, 颈缩之间的间距满足某种连续的Weibull分布, 而碎片的尺寸为随机的若干个颈缩间距之和.概率模拟表明:除非早期的颈缩间距分布很宽, 否则选择的离散性必然导致碎片尺寸分布呈现某种量子化特性.采用L04工业纯铝和无氧铜试件进行了爆炸膨胀碎裂实验, 回收得到的碎片尺寸分布结果与理论分析基本一致.     

可膨胀塑性本构方程及其在轴对称试棒韧性断裂分析中的应用

由于大应变和三轴张力的怍用,在许多韧性材料中将出现空洞的形成与扩展,从而产生塑性条件下的体积膨胀。本文提出了一组可以计及这类塑性可膨胀性的本构方程。利用轴对称试棒颈缩实验的结果、空洞模型的分析和计算模拟,可以标定方程中有关的切线模量值。为检验这类本构方程的合理性和核对所标定的模量数值,可再用之分析轴对称试棒的韧性断裂行为,以获取更逼近实验的结果。     

材料动态断裂碎片特性的理论描述

考虑裂纹间相互卸载作用，引入最小尺寸碎片概念。同时，假设断裂成核点随机分布于样品中，依据统计原理导出了一组完备的方程组，由此从理论上给出了碎片的数目及其大小分布关系式。与金属圆柱形壳体和圆环的膨胀破坏实验结果比较表明，该方程组对实验结果具有很好的预测能力。     

内部爆炸加载下柱壳的环周分裂数

基于有限长度柱壳的Gurney速度公式,以壳体平均半径估算平均应变率,同时考虑壳体剪切断裂时的断裂面长度与径向壁厚的差异,对Grady-Kipp方法进行了修正,得到柱壳剪切断裂模式下环周分裂数的完整表达式。利用修正方法分析得到的环周分裂数计算结果与实验数据分析结果符合更好。以20号低碳钢柱壳为例,对其在TNT爆炸加载下的膨胀断裂进行了三维数值模拟,得到的环周分裂数模拟结果与实验结果符合较好。     

基于偏析线的圆棒颈缩分析

本文基于拉伸圆棒颈缩后纵剖面上形成的偏析线(腐蚀后可见)提出了建立颈部最小截面上的应变场的方法。利用试验得到的有关数据,并借助于塑性全量理论及逐步插值积分法得到颈缩后材料的及最小截面上的应力场。计算结果反映了宏观断裂过程中微观结构变化所导致的应变“软化”现象。电镜观察表明:曲线上的极值点所对应的颈缩状态正反映了微结构中的次级空洞大量形成的阶段,紧随而来的是宏观断裂的到来,因此是一个与材料临界断裂有着密切关系的一个量。     

金属材料平面应变拉伸变形局部化有限元分析

本文对于涉及韧性金属大变形中颈缩与剪切带断裂一类高度非线性变形局部化问题进行了弹塑性有限元数值模拟。采用改进的Ｊ２形变理论微分形式公式与交叉三角形四边形单元有限元网格，详细研究了应变硬化指数及初始表面不均匀特性的平面应变拉伸颈缩和剪切带形成的综合影响，给出此类问题的断裂机制图。     

Effects of superimposed hydrostatic pressure on fracture in round bars under tension

The effect of superimposed hydrostatic pressure on fracture in round bars under tension is studied numerically using the finite element method based on the Gurson damage model. It is demonstrated that while the superimposed hydrostatic pressure has no noticeable effect on necking, it increases the fracture strain due to the fact that a superimposed pressure delays or completely eliminates the nucleation, growth and coalescence of microvoids or microcracks. The experimentally observed transition of the fracture surface, from the cup-cone mode under atmospheric pressure to a slant structure under high pressure, is numerically reproduced. It is numerically proved that the superimposed hydrostatic pressure has no effect on necking for a damage-free round bar under tension.     

光滑圆柱拉伸试件的颈缩分析

对Gurson本构方程作了初步的研究，并对圆柱光滑拉伸试件在颈缩阶段用Gurson本构方程做了大应变弹塑性有限元分析。讨论了颈缩区空穴形核、扩张、静水应力以及材料软化的问题，初步揭示了空穴的演化过程和材料的破坏机理。有限元分析的结果表明，颈缩阶段空穴长大聚合机理非常显著，而形核作用相对较弱。     

Perturbation solution of axisymmetric plastic problem I—Necking of a bar

In this paper, basing on the general equations of axisymmetric plastic problems deduced in ref. [11], and employing perturbation technique, the asymptotic analysis for the necking problem is given. The result will provide knowledge of distribution of stress and strain in whole plastic region, thus, it will lead to a better understanding of the necking phenomena in a tension specimen, such as the cup-cone type fracture.Communicated by Chien Wei-zang.     

高导无氧铜杆高应变率拉伸下的颈缩与断裂

采用Hopkinson拉伸实验装置和一种高速拉伸断裂实验新装置,对高导无氧铜(OFHC)杆件进行了一系列高应变率拉伸断裂试验.实验结果表明,局部化的断裂应变随拉伸速度增大并不明显增大,其断裂位置有随机性.存在一种临界拉伸速度,当冲击拉伸速度大于此值时,断裂即发生在冲击拉伸端附近,杆的其它部分几乎无应变.采用典型的Johnson-Cook本构关系,使用LS-DYNA程序进行一系列数值模拟,提出颈缩处直径收缩率达极值的颈缩失效判据,由此计算所得的局部化颈缩应变及断裂位置与试验回收结果有一定差别.     

Instability and failure of internally pressurized ductile metal cylinders

Forlong, ductile, thick-walled tubes under internal pressure instabilities and final failure modes are studied experimentally and theoretically. The test specimens are closed-end cylinders made of an aluminum alloy and of pure copper and the experiments have been carried out for a number of different initial external radius to internal radius ratios. The experiments show necking on one side of the tubes at a stage somewhat beyond the maximum internal pressure. All tubes, except for one aluminum alloy tube, failed by shear fracture under decreasing pressure. The aluminum alloy tubes exhibited localized shear deformations in the neck region prior to fracture and also occasionally surface wave instabilities. The numerical investigation is based on an elastic-plastic material model for a solid that develops a vertex on the yield surface, using representations of the uniaxial stress-strain curves found experimentally. In contrast to the simplest flow theory of plasticity this material model predicts shear band instabilities at a realistic level of strain. A rather sharp vertex is used in the material model for the aluminum alloy, while a more blunt vertex is used to characterize copper. The theoretically predicted bifurcation into a necking mode, the cross-sectional shape of the neck, and finally the initiation and growth of shear bands from the highly strained internal surface in the neck region are in good agreement with the experimental observations.     

A new approach for failure criterion for sheet metals

The interpretation of sheet forming simulations relies on failure criteria to define the limits of metal deformation. The common requirements for these criteria across a broad range of application areas have not yet been satisfied or fully identified, and a single criterion to satisfy all needs has not been developed. Areas where existing criteria appear to be lacking are in the comprehension of the effects of non-proportional loading, general non-planar and triaxial stress loading, and process and material mechanisms that differentiate between necking and fracture. This study was mainly motivated to provide an efficient method for the analysis of necking and fracture limits for sheet metals. In this paper, a model for the necking limit is combined with a model for the fracture limit in the principal stress space by employing a stress-based forming limit curve (FLC) and the maximum shear stress (MSS) criterion. A new metal failure criterion for in-plane isotropic metals is described, based on and validated by a set of critical experiments. This criterion also takes into consideration of the stress distribution through the thickness of the sheet metal to identify the mode of failure, including localized necking prior to fracture, surface cracking, and through-thickness fracture, with or without a preceding neck. The fracture model is also applied to the openability of a food can for AA 5182. The predicted results show very good agreement with the experimentally observed data.     

Mode I fracture of sheet metal

The perceived wisdom about thin sheet fracture is that (i) the crack propagates under mixed mode I & III giving rise to a slant through-thickness fracture profile and (ii) the fracture toughness remains constant at low thickness and eventually decreases with increasing thickness. In the present study, fracture tests performed on thin DENT plates of various thicknesses made of stainless steel, mild steel, 6082-O and NS4 aluminium alloys, brass, bronze, lead, and zinc systematically exhibit (i) mode I “bath-tub”, i.e. “cup & cup”, fracture profiles with limited shear lips and significant localized necking (more than 50% thickness reduction), (ii) a fracture toughness that linearly increases with increasing thickness (in the range of 0.5-). The different contributions to the work expended during fracture of these materials are separated based on dimensional considerations. The paper emphasises the two parts of the work spent in the fracture process zone: the necking work and the “fracture” work. Experiments show that, as expected, the work of necking per unit area linearly increases with thickness. For a typical thickness of , both fracture and necking contributions have the same order of magnitude in most of the metals investigated.A model is developed in order to independently evaluate the work of necking, which successfully predicts the experimental values. Furthermore, it enables the fracture energy to be derived from tests performed with only one specimen thickness. In a second modelling step, the work of fracture is computed using an enhanced void growth model valid in the quasi plane stress regime. The fracture energy varies linearly with the yield stress and void spacing and is a strong function of the hardening exponent and initial void volume fraction. The coupling of the two models allows the relative contributions of necking versus fracture to be quantified with respect to (i) the two length scales involved in this problem, i.e. the void spacing and the plate thickness, and (ii) the flow properties of the material. Each term can dominate depending on the properties of the material which explains the different behaviours reported in the literature about thin plate fracture toughness and its dependence with thickness.