平面碰撞与强激光加载下金属铝的层裂行为

在轻气炮和神光Ⅱ强激光装置上开展了金属铝的层裂实验。针对激光打靶层裂实验中样品自由面速度剖面后期振荡容易丢失问题,改进靶设计,获得很好效果。利用轻气炮加载和强激光加载层裂实验应变率的显著差异,并通过数值模拟,讨论了在建立具有预测能力的理论建模中需要关注的损伤成核、演化与汇合问题中的材料特性与应变率相关特性因素。结果表明,对于我们以前建立的动态损伤与断裂模型,微孔洞成核的平均半径、阈值压力、成核速率相关参数以及微孔洞长大的阈值压力等具有材料特性属性,但微孔洞的表面能以及决定材料发生完全层裂的临界损伤度等具有明显的应变率效应。另外,分析还发现,虽然层裂强度具有明显的应变率效应,但是在样品层裂当地,样品由持续拉伸向收缩转变的临界行为,取决于一个很小的临界损伤,这个临界值很可能是材料常数,与应变率无关。     

Dynamic void nucleation and growth in solids: A self-consistent statistical theory

We present a framework for a self-consistent theory of spall fracture in ductile materials, based on the dynamics of void nucleation and growth. The constitutive model for the material is divided into elastic and “plastic” parts, where the elastic part represents the volumetric response of a porous elastic material, and the “plastic” part is generated by a collection of representative volume elements (RVEs) of incompressible material. Each RVE is a thick-walled spherical shell, whose average porosity is the same as that of the surrounding porous continuum, thus simulating void interaction through the resulting lowered resistance to further void growth. All voids nucleate and grow according to the appropriate dynamics for a thick-walled sphere made of incompressible material. The macroscopic spherical stress in the material drives the response in all volume elements, which have a distribution of critical stresses for void nucleation, and the statistically weighted sum of the void volumes of all RVEs generates the global porosity. Thus, macroscopic pressure, porosity, and a distribution of growing microscopic voids are fully coupled dynamically. An example is given for a rate-independent, perfectly plastic material. The dynamics of void growth gives rise to a rate effect in the macroscopic material even though the parent material is rate independent.     

一种基于空穴聚集的层裂模型

基于如下假设，给出了层裂过程中的应力松弛方程，并建立了一种基于空穴聚集的延性层裂模型:在层裂早期，微空穴的主要效应是减小应力作用面积；在层裂后期，应力按空穴聚集时的应力-空隙度依赖关系减小。把P.F.Thomason、D.L.Tonks等及S.Cochran等给出的依赖于应力（压力）的层裂空隙度方程分别耦合于守恒方程、计及损伤的状态方程及本构方程，建立了求解所有变量包括损伤的封闭方程组。这种基于空穴聚集的层裂模型已被应用于一维层裂试验的数值模拟。模型中的层裂强度及临界损伤度初始可以估计，最终的确定将使数值模拟结果与实测的速度（或应力）剖面以及观测的层裂面上的损伤基本一致。分别基于D.L.Tonk等及S.Cochran等给出的依赖于压力的层裂空隙度方程所作的一维层裂试验数值模拟结果基本一致，而与基于P.F.Thomason给出的依赖于应力的层裂空隙度方程所作的相应数值模拟结果有明显差异。     

Determination and interpretation of statistics of spatially resolved waveforms in spalled tantalum from 7 to 13 GPa

A suite of impact experiments was conducted to assess spatial variability in the dynamic properties of tantalum, on length scales of tens of microns to a few millimeters. Two different sample types were used: tantalum processed to yield a uniform refined grain structure (grain size ∼20 μm) with a strong axisymmetric {1 1 1} crystallographic texture, and tantalum processed to yield an equiaxial structure with grain size ∼42 μm. Impact experiments were conducted loading the samples to stress levels from 6 to 12 GPa, which are well above the Hugoniot Elastic Limit (HEL), then pulling the sample into sufficient tension to produce spall. These stress levels were specifically chosen to investigate the spall behavior of tantalum at levels ranging from the incipient spall stage to significantly above the spall strength, focusing on microstructural phenomena. A recently developed spatially resolved velocity interferometer known as the line-imaging VISAR allowed the point-to-point variability of the spall strength to be determined. Specifically, we have been able to determine in real time the nucleation and growth of void defect structures that lead to the eventual spallation or delaminating of the plate. Experiments indicate that the nucleation and growth process is time-dependent and heterogeneous since a time-dependent distribution of defects is measured. This strongly suggests that the spall strength of the material is not a single-valued function. When fitted to Weibull failure statistics, the results indicate a similar mean value and variability for the spall strength of both types of tantalum. The spatial dependence of the material distension of the spalled tantalum is also deduced, in the approximation of uniaxial strain.     

延性金属层裂自由面速度曲线特征多尺度模拟研究

以延性金属钽为研究对象,对钽在平板撞击下的层裂行为进行了多尺度下的数值模拟研究,从微观视角对自由面速度曲线上的典型特征进行了新的解读。在宏观尺度,对比分析了光滑粒子流体动力学法（smootfied particle hydrodynamics, SPH）与Lagrange网格法以及几种本构模型的模拟结果及其适用性。通过与实验数据的对比表明,Steinberg-Cochran-Guinan本构模型在层裂模拟中与实验数据吻合较好,通过改变加载条件获得了不同应变率下的自由面速度曲线,分析了不同应变率下的自由面速度曲线中的典型特征。在微观尺度,采用分子动力学方法获得层裂区域内损伤演化情况,揭示了宏观尺度自由面速度曲线典型特征所蕴含的物理内涵。分析表明,层裂表现为材料内部微孔洞形核、长大和聚集的损伤演化过程,自由面速度曲线上的典型特征与层裂区域的损伤演化过程存在密切关联。Pullback信号是层裂区域内微孔洞形核的宏观表征;自由面速度曲线的下降幅值在一定程度上反映了微孔洞的形核条件,由此计算得到的层裂强度实际上是微孔洞的形核强度。此外,Pullback信号后的速度回跳速率反映了微损伤演化的速率。     

Damage of ductile materials deforming under multiple plastic or viscoplastic mechanisms

This work presents a model to represent ductile failure (i.e. failure controlled by nucleation, growth and coalescence) of materials whose irreversible deformation is controlled by several plastic or viscoplastic deformation mechanisms. In addition work hardening may result from both isotropic and kinematic hardening. Damage is represented by a single variable representing void volume fraction. The model uses an additive decomposition of the plastic strain rate tensor. The model is developed based on the definition of damage dependant effective scalar stresses. The model is first developed within the generalized standard material framework and expressions for Helmholtz free energy, yield potential and dissipation potential are proposed. In absence of void nucleation, the evolution of the void volume fraction is governed by mass conservation and damage does not need to be represented by state variables. The model is extended to account for void nucleation. It is implemented in a finite element software to perform structural computations. The model is applied to three case studies: (i) failure by void growth and coalescence by internal necking (pipeline steel) where plastic flow is either governed by the Gurson–Tvergaard–Needleman model or the Thomason model, (ii) creep failure (Grade 91 creep resistant steel) where viscoplastic flow is controlled by dislocation creep or diffusional creep and (iii) ductile rupture after pre-compression (aluminum alloy) where kinematic hardening plays an important role.     

A closed-form criterion for dislocation emission in nano-porous materials under arbitrary thermomechanical loading

Our traditional view of void nucleation is associated with interface debonding at second-phase particles. However, under extreme dynamic loading conditions second-phase particles may not necessarily be the dominant source of void nucleation sites. A few key experimental observations of laser spall surfaces support this assertion. Here, we describe an alternative mechanism to the traditional view, namely shock-induced vacancy generation and clustering followed by nanovoid growth mediated by dislocation emission. This mechanism only becomes active at very large stresses. It is therefore desirable to establish a closed-form criterion for the macroscopic stress required to activate dislocation emission in porous materials. Following an approach similar to Lubarda and co-workers, we derive the desired criterion by making use of stability arguments applied to the analytic solutions for the elastic interactions of dislocations and voids. Our analysis significantly extends that of Lubarda and co-workers by accounting for a more general stress state, finite porosity, surface tension, as well as temperature and pressure dependence. The resulting simple stress-based criterion is validated against a number of molecular dynamics simulations with favorable agreement.     

伴随微孔洞生长的裂纹弹塑性定常扩展

裂纹在韧性材料中扩展时,将们随着微孔洞的萌生和生长,孔洞的萌生和深化将直接影响着材料的总体断裂韧性和强度,以往的研究主要集中在将裂纹的扩展刻划为微孔洞的萌生、生长和汇合这样一个过程。从传统的断裂过程区模型出发研究微孔洞的萌生和生长对材料总体断裂韧性的影响,通过采用Ｇｕｒｓｏｎ模型,建立塑性增量本构关系,然后针对定常扩展情况直接进行分析,孔洞对材料断裂韧性的影响由本构关系刻划,而在孔洞汇合模型中,上     

Heterogeneous deformation and spall of an extruded tungsten alloy: plate impact experiments and crystal plasticity modeling

The role of microstructure in the dynamic deformation and fracture of a dual phase, polycrystalline tungsten alloy under high-rate impact loading is investigated via experiments and modeling. The material studied consists of pure tungsten crystals embedded in a ductile binder alloy comprised of tungsten, nickel, and iron. The tungsten crystals are elongated in a preferred direction of extrusion during processing. Plate impact tests were conducted on samples oriented either perpendicular or parallel to the extrusion direction. Spatially resolved interferometric data from these tests were used to extract wave propagation behavior and spall strength dependent upon position in the sample microstructure. Finite element simulations of impact and spall in digitally reproduced microstructural geometries were conducted in parallel with the experiments. Finite deformation crystal plasticity theory describes the behavior of the pure tungsten and binder phases, and a stress- and temperature-based cohesive zone model captures fracture at grain and phase boundaries in the microstructure. In results from both experiments and modeling, the grain orientations affect the free-surface velocity profile and spall behavior. Some aspects of distributions of free-surface velocity and spall strength among different microstructure configurations are qualitatively similar between experimental and numerical results, while others are not as a result of differing scales of resolution and modeling assumptions. Following a comparison of experimental and numerical results for different microstructures, intergranular fracture is identified as an important mechanism underlying the spall event.     

The effects of thermal softening and heat conduction on the dynamic growth of voids

This paper seeks to examine the dynamic growth of a single void in an elastic–plastic medium through analytical and numerical approaches. Particular attention is paid to the instability of void growth, and to the effects of inertia, thermal softening and heat conduction. A critical stress is known to exist for the unstable growth of voids. The dependence of this critical stress on material properties is examined, and this critical stress is demonstrated to correspond to the lower limit for the ductile spall strength in many materials. The effects of heat conduction on the dynamic growth of voids strongly depend on the time and length scales in the early stages of the dynamic void growth.     

Simplified model for prediction of dynamic damage and fracture of ductile materials

A simplified model for prediction of dynamic damage and fracture of ductile material has been proposed. The plastic flow of matrix and the void growth are dealt with separately after we show that two separated loading sub-surfaces and corresponding normality rules for matrix and damage exist. The equation of the loading sub-surface for the matrix plastic flow is derived by the means of introducing a mapping damage-free solid of matrix material, whose constitutive relation is supposed to have been determined via Hopkinson bar experiments. Based on the results of recovered experiments the law of damage evolution is phenomenally established. The model has been applied to predict some spall experiments carried out on tantalum, and results show it predicts the experiments very well.     

混凝土材料的层裂特性

利用Hopkinson压杆作为实验设备,通过试件后面吸收杆上应变波形研究了混凝土材料的层裂特性。不同强度混凝土在不同加载率下的实验结果表明,混凝土层裂强度与其压缩强度以及加载速率有关,给出了层裂强度和压缩强度以及加载率之间关系的经验公式,并指出不同加载速度下混凝土裂纹扩展方式不同是层裂强度率效应的主要原因。加载压缩波损伤的影响、重复加载实验以及多次层裂的顺序都表明,损伤对混凝土的层裂过程有重要影响。     

弹体贯穿混凝土数值模拟的改进材料模型

研究混凝土结构在冲击载荷下的力学特性对武器以及防护结构的设计和评估具有重要意义,而合适的材料模型可以更准确地预测混凝土结构的力学行为和破坏模式。因此,本文中提出了一种改进的混凝土塑性损伤材料模型来描述其在冲击载荷下的力学响应。该改进模型考虑了压力-体积应变关系、应变率效应、洛德角效应和塑性损伤累积对混凝土材料力学特性的影响,并引入了一个与损伤相关的硬化/软化函数来描述压缩状态下的应变硬化和软化行为。随后,通过对3个独立的强度面进行线性插值得到了该改进模型的破坏强度面,并采用部分关联流动法则考虑了混凝土材料的体积膨胀特性。最后,开展了单个单元在不同加载条件下和弹体贯穿钢筋混凝土靶的数值模拟,验证了该改进模型的可行性、准确性以及预测性能提升。     

Continuum modeling of a porous solid with pressure-sensitive dilatant matrix

The pressure-sensitive plastic response of a material has been studied in terms of the intrinsic sensitivity of its yield stress to pressure and the presence and growth of cavities. This work focuses on the interplay between these two distinctly different mechanisms and the attendant material behavior. To this end, a constitutive model is proposed taking both mechanisms into account. Using Gurson's homogenization, an upper bound model is developed for a voided solid with a plastically dilatant matrix material. This model is built around a three-parameter axisymmetric velocity field for a unit sphere containing a spherical void. The void is also subjected to internal pressure; this can be relevant for polymeric adhesives permeated by moisture that vaporizes at elevated temperatures. The plastic response of the matrix material is described by Drucker–Prager's yield criterion and an associated flow rule. The resulting yield surface and porosity evolution law of the homogenized constitutive model are presented in parametric form. Using the solutions to special cases as building blocks, approximate models with explicit forms are proposed. The parametric form and an approximate explicit form are compared against full-field solutions obtained from finite element analysis. They are also studied for loading under generalized tension conditions. These computational simulations shed light on the interplay between the two mechanisms and its enhanced effect on yield strength and plastic flow. Among other things, the tensile yield strength of the porous solid is greatly reduced by the internal void pressure, particularly when a liquid/vapor phase is the source of the internal pressure.     

On probabilistic aspects in the dynamic degradation of ductile materials

Dynamic loadings produce high stress waves leading to the spallation of ductile materials such as aluminum, copper, magnesium or tantalum. The main mechanism used herein to explain the change of the number of cavities with the stress rate is nucleation inhibition, as induced by the growth of already nucleated cavities. The dependence of the spall strength and critical time with the loading rate is investigated in the framework of a probabilistic model. The present approach, which explains previous experimental findings on the strain-rate dependence of the spall strength, is applied to analyze experimental data on tantalum.     

无氧铜层裂的实验与数值研究

利用一级气体炮对国产的无氧铜（OFHC）进行了平板撞击致层裂实验,3 mm厚的OFHC飞片撞击6 mm厚的OFHC靶,采用锰铜应力计记录试样/有机玻璃（PMMA）界面附近的应力历史,获得试样发生层裂的信息。软回收试样,观测回收试样的层裂片。采用基于空穴聚集的层裂模型,数值模拟这些平板撞击致层裂实验。数值模拟的应力剖面以及试样层裂片厚度与实验结果基本一致。此外,对于国外相关的OFHC层裂实验,采用基于空穴聚集的层裂模型也作了相应的数值模拟,并进行了比较。     

PROGRESSIVE FRAGMENT MODELING OF FAILURE WAVE IN CERAMICS UNDER PLANAR IMPACT LOADING

Polycrystalline ceramics have heterogeneous meso-structures which result in high singularity in stress distribution. Based on this, a progressive fragment model was proposed which describes the failure wave formation and propagation in shocked ceramics. The governing equation of the failure wave was characterized by inelastic bulk strain with material damage and fracture. And the inelastic bulk strain consists of dilatant strain from nucleation and expansion of microcracks and condensed strain from collapse of original pores. Numerical simulation of the free surface velocity was performed in good agreement with planar impact experiments on 92.93％ aluminas at China Academy of Engineering Physics. And the longitudinal, lateral and shear stress histories upon the arrival of the failure wave were predicted, which present the diminished shear strength and lost spall strength in the failed layer.     

Effect of the grain size on the macroscopic response of aluminum to shock loading

Shock tests of two lots of a 1420 aluminum-lithium alloy are performed. The mean grain size is 24 μm in the first lot and 1.6 μm in the second lot obtained by the method of equal-channel angular pressing. Two characteristics of dynamic strength of the material were determined in experiments on the high-velocity impact of flat samples: threshold of dynamic stability with respect to compression on the fore front of the compression pulse and spall strength of the material. The materials of both types have an identical threshold of dynamic stability with respect to compression, whereas the spall strength of the microcrystalline alloy is 20% greater than the spall strength of the polycrystalline alloy. The reason is the consumption of energy on structure formation in the coarse-grain material in passing to a larger-scale structural level (in the case with a fine-grain material, such a structure is available in the initial state). The experiments reveal the presence of a second plastic front whose amplitude is approximately 10% of the first plastic front. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 135–146, November–December, 2007.     

A physical model for nucleation and early growth of voids in ductile materials under dynamic loading

Spall fracture and other rapid tensile failures in ductile materials are often dominated by the rapid growth of voids. Recent research on the mechanics of void growth clearly shows that void nucleation may be represented as a bifurcation phenomenon, wherein a void forms spontaneously followed by highly localized plastic flow around the new void. Although thermal, viscoplastic, and work hardening effects all play an essential role in the earliest stages of nucleation and growth, the flow becomes dominated by spherical radial inertia, which soon causes all voids to grow asymptotically at the same rate, regardless of differences in initial conditions or constitutive details, provided only that there is the same density of matrix material and the same excess loading history beyond the cavitation stress.These two facts, initiation by bifurcation at a cavitation stress, at which a void first appears, and rapid domination by inertia, are used to postulate a simple, but physically realistic, model for nucleation and early growth of voids in a ductile material under rapid tensile loading. A reasonable statistical distribution for the cavitation stress at various nucleation sites and a simple similarity solution for inertially dominated void growth permit a simple calculation of the initiation and early growth of porosity in the material.Parametric analyses are presented to show the effect that loading rate, peak loading stress, density of nucleation sites, physical properties of the material, etc. have on the applied pressure and distribution of void sizes when a critical porosity is reached.     

Damage evolution of ductile material under impact loading

Nucleation, growth and coalescence of micro-voids result in the fracture of materials. Most mathematical models neglect nucleation and introduce initial damage, assuming it as a material constant. However, the original damage, which is formed during material working, is a material constant. The initial damage is a model parameter and depends on the load. Apparently, the predictability of such a model is poor.This paper made comparison and analysis of the four classical void growth models and showed their similarities. At the beginning of damage evolution, all the models follow a linear relationship in the form , where c is the size of micro voids and k is a parameter which relates the material and loading condition. With the concept of statistical micro-damage and the assumption of uniform void radius for new voids, a damage evolution equation was deduced based on the above void growth model. With this equation the effects of nucleation and growth at the beginning of the damage stage on the whole process of damage evolution can be calculated. The transition time from the nucleation dominant phase to the growth dominant phase can be determined. When the transition time is applied to the damage failure model of ductile material proposed by Johnson, the initial damage (f₀), a model parameter in the original model, can also be determined. The results of the derived damage evolution equation agree well with the previous research results.