Material aspects of dynamic neck retardation

Neck retardation in stretching of ductile materials is promoted by strain hardening, strain-rate hardening and inertia. Retardation is usually beneficial because necking is often the precursor to ductile failure. The interaction of material behavior and inertia in necking retardation is complicated, in part, because necking is highly nonlinear but also because the mathematical character of the response changes in a fundamental way from rate-independent necking to rate-dependent necking, whether due to material constitutive behavior or to inertia. For rate-dependent behavior, neck development requires the introduction of an imperfection, and the rate of neck growth in the early stages is closely tied to the imperfection amplitude. When inertia is important, multiple necks form. In contrast, for rate-independent materials deformed quasi-statically, single necks are preferred and they can emerge in an imperfection-free specimen as a bifurcation at a critical strain. In this paper, the interaction of material properties and inertia in determining neck retardation is unraveled using a variety of analysis methods for thin sheets and plates undergoing plane strain extension. Dimensionless parameters are identified, as are the regimes in which they play an important role.     

Neck development in metal/elastomer bilayers under dynamic stretchings

Dynamic stretching of bilayer plates comprised of an elastomer layer bonded to a metal layer is studied with emphasis on neck development under plane strain. Neck retardation and multiple necks in the metal layer are promoted by the elastomer layer under quasi-static conditions and also by inertia in the all-metal layer under dynamic stretching. The present study explores the interaction of these two effects under the assumption that ductility is unlimited. The study reveals the roles of the elastomer modulus, the metal strength and the rate of stretching in giving rise to necking retardation.     

Dynamic neck development in a polymer tube under internal pressure loading

The initiation and growth of necks in polymer tubes subjected to rapidly increasing internal pressure is analyzed numerically. Plane strain conditions are assumed to prevail in the axial direction. The polymer is characterized by a finite strain elastic–viscoplastic constitutive relation and the calculations are carried out using a dynamic finite element program. Numerical results for neck development are illustrated and discussed for tubes of various thicknesses. The sensitivity to the wave number of the thickness imperfections is studied with a focus on comparing a long wave length imperfection and a short wave length imperfection. After some thinning down at the necks, the mode of deformation switches to neck propagation along the circumference of the tube. A case is shown in which the necks have propagated along the entire tube wall, so that network locking in the polymer results in high stiffness against further expansion of the tube. The rate dependence of the necking behavior gives noticeable differences in neck development for slow loading versus fast loading.     

粗晶LY-12合金准超塑性单轴拉伸模拟

在试验的基础上，利用Chaboche本构模型对LY-12准超塑性单轴拉伸变形进行数值模拟，对其能够实现大延伸率的力学现象进行分析，由于材料具有高应变速率敏感指数，颈缩不发生在标距中间，而是有多处出现颈缩，不同颈缩相互的松弛作用对变形起重要作用，模拟和试验都表明，温度一定，不同应变速率下，颈缩发生的位置和颈缩程度不同，从而最大破坏延伸率也不同，利用该模型可以预测粗晶LY—12材料的超塑性变形能力和可能破坏的部位。     

Biomechanical Simulation to Compare the Blood Hemodynamics and Cerebral Aneurysm Rupture Risk in Patients with Different Aneurysm Necks

In this study, one normal subject and two patients suffering from a cerebral aneurysm with circular and elliptical necks are analyzed by using the fluid-structure interaction (FSI) method. Although the blood hemodynamics parameters increase after the occurrence of the disease, the largest increase is in the wall shear stress (by a factor of 4.1–6.5) as compared to the normal subject. The increase in these parameters for patients with a circular neck is more pronounced than that with an elliptical neck. The blood flow becomes slightly more turbulent after the occurrence of the cerebral aneurysm, though it still remains in the range of the laminar flow and the pulsatility of the blood flow in patients is 28–45% greater than that of the normal subject. Finally, the results show that the risk of vessel rupture in the cerebral aneurysm with a circular neck is 40.8% higher than that in the case of the cerebral aneurysm with an elliptical neck.     

大直径SHPB弥散效应的二维数值分析

采用轴对称动态有限元HONDO程序对大直径SHPB装置中压杆横向泊松效应引起的应力波弥散进行二维数值分析,并从以下三个方面讨论波形弥散的影响：（1）SHPB装置中压杆直径和杆长对弥散结果（主要是升时）的影响;（2）压杆中的波形弥散对试件应力-应变曲线的影响;（3）弥散对试件应变率的影响。分析表明,在直径SHPB弥散效应对实验结果的影响很大,必须考虑。     

Necking evolution in dynamically stretched bars: New experimental and computational insights

This paper presents new results on dynamic neck evolution in steel bars of varying diameters. Dynamic tensile tests were carried out in a Kolsky apparatus using cylindrical steel specimens with various cross-section diameters ranging from 1.5 mm to 4 mm. A high speed digital camera was used to record the deformation of the specimen during the loading process. Video recording of the tests enabled accurate experimental measurements of the necking evolution, specifically its growth rate as a function of the diameter. The experiments show that increasing the specimen cross-section slows down the neck development. This behavior has been further investigated using two different kinds of numerical calculations: (1) axisymmetric finite element simulations and (2) one-dimensional finite difference computations. While the finite difference model only considers the normal stress along the longitudinal direction of the bar, the finite element model does not entail any simplification on the stress state of the specimen during the loading process. In agreement with the experiments, the finite element calculations show a decrease of the necking growth rate with the increase in the cross-section of the sample. On the contrary, the damping effect of the specimen cross-section on the necking evolution is not captured by the finite difference computations. We postulate that this result comes from the one-dimensional nature of the finite difference model. This work uncovers, by means of combined experiments and modelling, the key role played by stress multiaxiality in the growth rate of dynamic necks.     

细颈倾角对挠性接头力学性能影响分析

为确定某单平衡环挠性接头的最佳细颈倾角,对挠性接头进行了力学性能分析。首先给出了挠性接头的离散动力学模型,然后利用ANSYS仿真分析软件对不同细颈倾角结构的挠性接头进行了抗冲击能力和等刚度的力学性能分析,得出了细颈倾角在30°～60°范围内的冲击响应和等刚度性能。最后结合两种力学性能分析可知:当细颈倾角为44°时,该挠性接头在加速度幅值为40g、脉宽为11ms冲击条件下的轴向最大响应应力为448MPa,径向最大响应应力为584MPa;在该倾角情况下挠性接头由不等刚度造成的g2项误差优于0.06(°)/h。综合两方面的性能指标可最终确定挠性接头的最佳细颈倾角为44°。     

仿鸡脖子刚柔耦合结构的仿生机理及大变形建模

观察表明,禽类颈部普遍具有刚柔耦合的特点,在运动过程中,可以辅助身体运动,使得头部产生大变形.在机器人、航空航天等领域普遍需要具有大变形、变刚度等特征的结构实现相关功能.受禽类脖子结构的启发,提出了一种仿鸡脖子刚柔耦合结构,阐明仿鸡脖子的仿生机理并建立大变形模型.首先,从鸡颈部的生物解剖出发,发现仿鸡脖子结构势必具有多自由度刚柔耦合的特征,因此,根据鸡脖子骨骼的构型构造出单节仿生标准单元,根据肌肉的连接方式厘清节间弹性连接,建立起仿鸡脖子刚柔耦合结构的力学模型;然后,通过定义连接矩阵描述节间弹性元件的分布和作用,由此得到任意运动下的标准单元的力平衡方程;最后,选取了几种具有代表性的工况,通过有限元分析验证理论建模方法的准确性并展示结构的非线性变刚度特征;在4种典型平面弯曲工况下得到不同变形与发力肌肉群的对应关系.文章提出的仿鸡脖子刚柔耦合结构建模具有仿生机理清晰、适合大变形计算及结构具有非线性刚度特征等特点,也解释了禽类颈部变形机理.     

Numerical simulation of the divergent flow regime in a circular contraction flow of a viscoelastic fluid

A numerical method is used to study the influence of inertia and elongational properties on the vortex growth in the flow of a viscoelastic fluid through a four-to-one contraction. It appears that the vortex growth regime and the divergent flow regime, which are observed in experiments for some fluids, can be found for a choice of the material parameters where both the elongational stresses and the inertia forces are large for the flow rate considered. After studying the type and the vorticity it is concluded that the appearance of a divergent flow regime is likely to be a critical phenomenon (i.e., a change of type for a critical velocity) and that large elongational stresses are essential as well.     

Dynamic fracture of concrete compact tension specimen: Experimental and numerical study

Compared to quasi-static loading concrete loaded by higher loading rates acts in a different way. There is an influence of strain-rate and inertia on resistance, failure mode and crack pattern. With increase of loading rate failure mode changes from mode-I to mixed mode. Moreover, theoretical and numerical investigations indicate that after the crack reaches critical velocity there is progressive increase of resistance and crack branching. These phenomena have recently been demonstrated and discussed by O?bolt et al. (2011) on numerical study of compact tension specimen (CTS) loaded by different loading rates. The aim of the present paper is to experimentally verify the results obtained numerically. Therefore, the tests and additional numerical studies on CTS are carried out. The experiments fully confirm the results of numerical prediction discussed in O?bolt et al. (2011). The same as in the numerical study it is shown that for strain rates lower than approximately 50/s the structural response is controlled by the rate dependent constitutive law, however, for higher strain rates crack branching and progressive increase of resistance is observed. This is attributed to structural inertia and not the rate dependent strength of concrete. Maximum crack velocity of approximately 800 m/s is measured before initiation of crack branching. The comparison between numerical and experimental results shows that relatively simple modeling approach based on continuum mechanics, rate dependent microplane model and standard finite elements is capable to realistically predict complex phenomena related to dynamic fracture of concrete.     

离心惯性力效应对超临界二氧化碳干气密封流场与密封特性影响分析

为揭示离心惯性力效应对S-CO₂干气密封流场与密封特性的影响规律,以螺旋槽干气密封为研究对象,引用考虑离心惯性力效应的Reynolds方程,在考虑气膜真实气体效应、黏度随压力与温度双重变化的同时,基于N-S方程与能量守恒定律,建立了绝热状态下考虑离心惯性力效应作用的能量控制方程. 然后,采用有限差分法对压力控制方程与能量控制方程进行耦合求解,并对考虑离心惯性力效应与没有考虑离心惯性力效应下的压力分布、温度分布以及密封特性进行了分析讨论. 研究表明:离心惯性力效应具有削弱流场内压力与温度的作用;从避免凝结流动角度考虑,离心惯性力效应引起的温降将不利于S-CO₂干气密封;考虑离心惯性力效应作用时,气膜开启力在不同槽深与转速下存在最佳工况点,泄漏率随着转速的增加显著减小,而离心惯性力效应与膜厚之间没有强交互作用;考虑离心惯性力效应作用的气膜开启力、泄漏率、出口温度均比不考虑离心惯性力效应作用的小,且这种差异随着转速的增大而增加,而随着膜厚的变化没有改变. 这些结果为进一步研究S-CO₂干气密封奠定了一定的理论基础.      

Dynamic fracture of concrete – compact tension specimen

The behavior of concrete structures is strongly influenced by the loading rate. Compared to quasi-static loading concrete loaded by impact loading acts in a different way. First, there is a strain-rate influence on strength, stiffness, and ductility, and, second, there are inertia forces activated. Both influences are clearly demonstrated in experiments. Moreover, for concrete structures, which exhibit damage and fracture phenomena, the failure mode and cracking pattern depend on loading rate. In general, there is a tendency that with the increase of loading rate the failure mode changes from mode-I to mixed mode. Furthermore, theoretical and experimental investigations indicate that after the crack reaches critical speed of propagation there is crack branching. The present paper focuses on 3D finite-element study of the crack propagation of the concrete compact tension specimen. The rate sensitive microplane model is used as a constitutive law for concrete. The strain-rate influence is captured by the activation energy theory. Inertia forces are implicitly accounted for through dynamic finite element analysis. The results of the study show that the fracture of the specimen strongly depends on the loading rate. For relatively low loading rates there is a single crack due to the mode-I fracture. However, with the increase of loading rate crack branching is observed. Up to certain threshold (critical) loading rate the maximal crack velocity increases with increase of loading rate, however, for higher loading rates maximal velocity of the crack propagation becomes independent of the loading rate. The critical crack velocity at the onset of crack branching is found to be approximately 500 m/s.     

用三线摆测定物体对非质心轴的转动惯量

对三线摆的线性近似模型和转动惯量计算公式的由来作了简要说明. 分析了三线摆扭振系统 质心偏移对转动惯量测试的影响，给出了扭振系统质心与三线摆中心轴对齐的判别准则和用 三线摆测定物体对非质心轴转动惯量的工程实用方法. 通过工程实例说明了该方法的有效性 与可靠性. 最后讨论了提高转动惯量实测精度的几项具体措施.     

Static and dynamic snap-through behaviour of an elastic spherical shell

The deformation and snap-through behaviour of athin-walled elastic spherical shell statically compressed on aflat surface or impacted against a flat surface are studied theoretically and numerically in order to estimate the influenceof the dynamic effects on the response.A table tennis ballis considered as an example of a thin-walled elastic shell.Itis shown that the increase of the impact velocity leads to avariation of the deformed shape thus resulting in larger deformation energy.The increase of the contact force is causedby both the increased contribution of the inertia forces andcontribution of the increased deformation energy.The contact force resulted from deformation/inertia ofthe ball and the shape of the deformed region are calculated by the proposed theoretical models and compared withthe results from both the finite element analysis and somepreviously obtained experimental data.Good agreement isdemonstrated.     

A numerical study on the rate sensitivity of cellular metals

Metallic foams have non-linear deformation behavior, which make them attractive in many applications. Many experimental researches on the dynamic behavior and rate sensitivity of cellular metals have been reported in the literature, but they contain conflicting, and sometimes confusing, conclusions on the strain-rate and inertia effect of cellular metals. In this paper, the dynamic crushing behavior of 2D Voronoi honeycomb is studied by finite element method. The influences of inertia, strain hardening and strain-rate hardening of metal matrix on the deformation mode and plateau stress of the honeycomb are investigated. Three deformation modes are found in different velocity ranges. According to the numerical results, it is found that the plateau stress increases significantly with the increase of impact velocity due to non-uniform deformation induced by inertia. The strain-hardening effect is slight in our numerical tests and the rate effect of the honeycomb is obviously weaker than that of the cell wall material.     

Determining the moments of inertia of large bodies from vibrations in elastic suspension

To ensure the maneuvering capabilities of aircraft and high-speed sea vessels, designers should know the moments of inertia of their massive parts. But since the structure of some elements such as power units is very complicated, it is impossible to determine their moments of inertia analytically. Thus the problem of measuring the moments of inertia of massive large bodies arises. To this end, a measuring bench was designed in N. E. Zhukovskii Central Institute for Aerohydrodynamics (TsAGI) on the basis of a new method for determining the body moments of inertia from vibrations in the elastic suspension [1]. In this connection, it is necessary to develop the corresponding mathematical algorithms for determining the moments of inertia.In this paper, we develop mathematical algorithms for determining the body moments of inertia by using methods for identification of linear systems in the state space [2–5]. We present three versions of solving the problem of determining the body moments of inertia depending on the information about the method for exciting the vibrations or about the body parameters and the rigidity of the bench springs. We study the influence of damping on the accuracy of determining the moments of inertia. Numerical results are given for a specific system.     

铝蜂窝的动态力学性能及影响因素

采用显式动力有限元方法研究了具有不同胞元结构的六角形铝蜂窝在冲击荷载下的力学性能,讨 论了铝蜂窝的变形模式和动态承载力以及影响因素。通过改变胞壁夹角得到5种不同的胞元结构,计算采用 了3种冲击速度。结果表明,在准静态变形模式下,胞元的几何因素对铝蜂窝的承载力起主导作用;一旦蜂窝 的变形呈现动态模式后,惯性效应显著,对蜂窝承载力起决定作用,胞元几何因素的影响不再明显;在过渡模 式下,惯性效应与几何因素共同主导蜂窝的动态承载力,并且冲击速度越高,惯性效应的影响越大。     

Ductility of thin metal films on polymer substrates modulated by interfacial adhesion

When a laminate of a thin metal film on a tough polymer substrate is stretched, the metal film may rupture at strains ranging from a few percent to a few tens of percent. This variation in the ductility of the metal film is modulated by the adhesion of the metal/polymer interface. To study this modulation, here we use the finite element method to simulate the co-evolution of two processes: debonding along the interface and necking in the metal film. We model the interface as an array of nonlinear springs, and model the metal and the polymer as elastic–plastic solids. The simulation shows that necking of the film is accommodated mainly by interfacial sliding, rather than interfacial opening. Depending on the resistance of the interface to sliding, the metal film can exhibit three types of tensile behavior: the film slides and ruptures at a small strain by forming a single neck, the film slides and deforms to a large strain by forming multiple necks, and the film deforms uniformly to a very large strain without sliding and necking.     

A low‐dimensional spectral approach for transient axisymmetric free‐surface flow inside thin cavities of arbitrary shape

A low‐dimensional spectral method is used to solve the transient axisymmetric free surface flow inside thin cavities of arbitrary shape. The flow field is obtained on the basis of the lubrication equations, which are expanded in terms of orthonormal functions over the cavity gap. The formulation accounts for nonlinearities stemming from inertia and front location. The work is of close relevance to the filling stage during die casting, and injection molding, or the flow inside annular (extrusion) dies. Both flows under an imposed flow rate, and an imposed pressure at the cavity entrance are examined. The influence of inertia, aspect ratio, gravity, and wall geometry on the evolution of the front, flow rate, and pressure is assessed particularly in the early stage of flow, when a temporal behavior of the ‘boundary‐layer’ type develops. The multiple‐scale method is applied to obtain an approximate solution at small Reynolds number, Re. Comparison with the exact (numerical) solution indicates a wide range of validity for the multiple‐scale approach, including the moderately small Re range. Copyright © 2002 John Wiley & Sons, Ltd.