On the energy conservation and critical velocities for the propagation of a ＂steady-shock＂ wave in a bar made of cellular material

The propagation of shock waves in a cellular bar is systematically studied in the framework of continuum solids by adopting two idealized material models, viz. the dynamic rigid, perfectly plastic, locking （D-R-PP-L） model and the dynamic rigid, linear hardening plastic, locking （D-R-LHP-L） model, both considering the effects of strain-rate on the material properties. The shock wave speed relevant to these two models is derived. Consider the case of a bar made of one of such material with initial length L 0 and initial velocity v i impinging onto a rigid target. The variations of the stress, strain, particle velocity, specific internal energy across the shock wave and the cease distance of shock wave are all determined analytically. In particular the ＂energy conservation condition＂ and the ＂kinematic existence condition＂ as proposed by Tan et al. （2005） is re-examined, showing that the ＂energy conservation condition＂ and the consequent ＂critical velocity＂, i.e. the shock can only be generated and sustained in R-PP-L bars when the impact velocity is above this critical velocity, is incorrect. Instead, with elastic deformation, strain-hardening and strain-rate sensitivity of the cellular materials being considered, it is appropriate to redefine a first and a second critical impact velocity for the existence and propagation of shock waves in cellular solids. Starting from the basic relations for shock wave propagating in D-R-LHP-L cellular materials, a new method for inversely determining the dynamic stress-strain curve for cellular materials is proposed. By using e.g. a combination of Taylor bar and Hopkinson pressure bar impact experimental technique, the dynamic stress-strain curve of aluminum foam could bedetermined. Finally, it is demonstrated that this new formulation of shock theory in this one-dimensional stress state can be generalized to shocks in a one-dimensional strain state, i.e. for the case of plate impact on cellular materials, by simply making proper replacements of the elastic and plastic constants.     

Pulse shaping techniques for testing elastic-plastic materials with a split Hopkinson pressure bar

We present pulse shaping techniques to obtain compressive stress-strain data for elastic-plastic materials with a split Hopkinson pressure bar. The conventional split Hopkinson pressure bar apparatus is modified by placing a combination of copper and steel pulse shapers on the impact surface of the incident bar. After impact by the striker bar, the copper-steel pulse shaper deforms plastically and spreads the pulse in the incident bar so that the sample is nearly in dynamic stress equilibrium and has a nearly constant strain rate in the plastic response region. We present analytical models and data that show a broad range of incident strain pulses can be obtained by varying the pulse shaper geometry and striking velocity. For an application, we present compressive stress-strain data for 4340 R_c 43 steel.     

SnAgCu焊料的动态力学性能

对SnAgCu焊锡材料在应变率0.001、600、1 200、1 800 s-1下的拉伸和压缩力学性能进行了测试,得到了不同应变率下的应力应变曲线。结果表明,该材料不仅具有明显的应变率效应,而且其动、静态的塑性硬化模量差异很大。金相分析显示:准静态压缩时,塑性变形主要由晶粒的转动、变形和晶界的滑移控制;而动态压缩时,可观察到材料内部的枝状晶粒被折断为大量次级晶枝,呈现出明显不同于准静态情况下的变形机制。     

子弹撞击作用下固支浅圆拱的弹塑性动力响应

基于大变形动力学微分方程并利用有限差分离散分析,研究了子弹撞击作用下固支浅圆拱的弹塑性动力响应。通过对响应不同时刻内力分布特征的分析,阐明了圆拱的响应模式和变形机制。研究表明,弹塑性响应过程可分为六个阶段。在响应早期,拱的变形以塑性弯曲挠动由撞击点向拱根部传播为主;在响应后期,则主要以轴力主导下的轴向拉伸变形为主。在高速撞击下,塑性弯曲挠动的不均匀性可以引起浅拱的反向弯曲变形。固支浅圆拱的动力响应对撞击速度的某个变化范围非常敏感,在此范围内,撞击速度的较小增加可以导致响应的很快增长,但动力响应随撞击速度连续变化,未发生突然的跳跃失稳。本文中计算结果同实验数据吻合较好。     

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.     

Pressure-shear waves in 6061-T6 aluminum and alpha-titanium

Thepressure-shear plate impact technique is used to study material behavior at high rates of deformation. In this technique, plastic waves of combined pressure and shear stresses are produced by impact of parallel plates skewed relative to their direction of approach. Commercially pure alpha-titanium and 6061-T6 aluminum are tested under a variety of pressure and shear tractions by using different combinations of impact velocities and angles of inclination. A laser interferometer system is used to monitor simultaneously the normal and transverse components of motion of a point at the rear surface of the target plate. The experimental results are compared with numerical solutions based on an elastic/viscoplastic model of the material. Both isotropic and kinematic strain hardening models are used in the computations. The results indicate that unlike the normal velocity profiles, the transverse velocity profiles are sensitive to the dynamic plastic response and, thus, can be used to study material behavior at high strain rates. For the materials tested the results suggest that the flow stress required for plastic straining increases markedly with increasing strain rate at strain rates above 10⁴s^?1. Hydrostatic pressure of the order that exists in the tests (up to 2 GPa) does not affect the plastic flow in 6061-T6 aluminum and appears to have at most a minor effect on the deformation of the titanium.     

高温下轻质泡沫铝动态力学性能实验

对传统的分离式Hopkinson压杆装置加以改进,设计了一种长杆直接撞击Hopkinson杆的实验方案,检测出低波阻抗材料在高温动态加载下的应力均匀性。对轻质泡沫铝材料的实验表明,在同一撞击速度下,温度越高,试件两端的应力均匀性越差,增加温度与提高撞击速度均会导致泡沫铝材料冲击端与支撑端的应力不均匀性。根据高温下应力均匀性的实验结果,确定高温下试件均匀变形对应的冲击速度,再通过传统的分离式Hopkinson压杆实验得出泡沫铝在高温动态下的力学性能。     

Mechanism of buckling development and strain reversal occurrence in elastic–plastic cylindrical shells under axial impact

In order to clarify the mechanism of loading and unloading, buckling growth, and strain-reversal occurrence in elastic–plastic cylindrical shells that are impacted axially, non-linear dynamic equations in incremental form are derived and solved by using the finite difference method. The validity of the developed theory is verified by comparing theoretical and experimental results. From the calculation results, it is found that, at the initial stage of the impact process, the effective stress related to the middle-surface stresses in the part near the impacted end rises with time, and exhibits plastic loading. The radial restraints on the impacted end have obvious influence on the strain reversal occurrence at an early stage of the impact process. The effective modulus controls the post-buckling deformation of the shell, which contrasts with the situation for the bar to be impacted axially.     

起波钢筋高速动态拉伸力学性能研究

针对提高混凝土梁抗冲击爆炸性能的起波配筋新技术,采用理论分析与动态冲击拉伸试验相结合的方法,揭示了起波钢筋的快速拉伸变形作用机理,分析了拉伸速度、起波矢高等因素对起波钢筋抗拉强度的影响规律,确定了起波钢筋静态弹性极限强度计算方法。提出了起波钢筋等效拉伸应变率新概念,建立了弹性极限强度动力放大系数（dynamic increase factors,DIF）计算模型。研究结果表明,预先弯折起波使得钢筋在受力拉直过程中产生截面弯矩,起波钢筋的力学性能存在明显的应变率效应;起波钢筋弹性抗拉极限强度DIF随起波矢高的增高先增大后减小,存在一个最优起波设计矢高,可以使起波钢筋抗拉强度动态放大系数达到最大。研究成果可为进一步推动起波配筋技术在防护工程中的应用提供依据。     

一种基于SHPB的冲击膨胀环实验技术

设计了一种基于分离式Hopkinson压杆(SHPB)的冲击膨胀环实验装置,实验装置包括一个液压腔,一侧为驱动活塞,另一侧为圆环试件封闭。对活塞施加轴向冲击,利用液体体积近似不可压缩的特性,通过液压腔截面积的大比例缩小,将较低速度的对活塞冲击转化为圆环试件沿径向的高速膨胀,驱动试件发生拉伸变形直至断(碎)裂。使用这种冲击膨胀装置,获得了LY12铝环在不同撞击速度下碎裂过程的初步结果。实验结果显示,随着撞击速度增大,圆环试件碎裂产生的碎片的尺度减小,试件的表观断裂应变增加。这为研究材料的动态拉伸碎裂问题提供了一种加载方式。     

Electromagnetic velocity-transducer studies of plastic waves in aluminum bars

In this investigation, annealed aluminum rods were subjected to dynamic compressive impact loading of duration of the order of 560 μsec to study the propagation of longitudinal plastic waves, using an electromagnetic transducer to record particle velocities at four stations approximately three inches apart. Test results indicate that any given level of particle velocity propagates along the bar with a constant speed, not affected by the strain rate, within the range of strain rates encountered. Good agreement was found between the propagation speeds observed for different levels of velocity (averaged over all tests) and predictions of the von Kármán rate-independent plastic-wave-propagation theory based on a single dynamic stress-strain curve almost coinciding with the static curve.     

Effect of elastic target material on Taylor model

A theoretical model is proposed for a semi-infinite elastic bar struck axially by a flat-ended cylindrical projectile. The model is actually developed from the classical Taylor model except that the target is a semi-infinite bar with elastic behavior being considered. Particular attention is paid to the influence due to elastic wave propagation in the target bar on the energy partitioning between the projectile and target, which may result in the final length of the cylinder significantly different from the predictions of the classical Taylor model. The theoretical model is verified by numerical simulations, and the effects of several key non-dimensional parameters on the residual deformation and energy dissipation are discussed in detail. It is shown that the elastic effect of the target bar plays an important role in the prediction of plastic deformation of the cylindrical projectile.     

Outer synchronization of small-world networks by a second-order sliding mode controller

The current work presents an experimentally validated analytical model for low-velocity impact between a sphere and a plate. The model accounts for plastic deformation as well as flexural vibrations. The elastic phases are modeled with a nonlinear Hertzian contact model, and the plastic phase is linearized with a non-homogeneous expression. The results are compared against newly carried out experiments. The model well captures the effect of plate thickness-to-sphere diameter ratio, impact velocity, and material properties. The model’s generalized framework allows consideration for various expressions of contact parameters, critical velocity, and residual indentation. Moreover, the proposed methodology can be easily incorporated into particle-based or discrete element modeling approaches for granular flows to evaluate the real-time coefficient of restitution as opposed to assuming the constant value beforehand. Simplified relations are provided to assist in evaluating the coefficient of restitution.     

A coupling cross-section finite element model for torsion analysis of prismatic bars

A general finite element model has been developed for the analysis of prismatic bars subject to torsional loading by modelling only a small slice of the bar. Exact analytical coupling deformation relationships between the artificial cross-sections, which are independent of the position of axis of rotation, have been formulated. Three examples from the range of analyses that have been evaluated have been selected to demonstrate the accuracy and effectiveness of the method. Analyses for an orthotropic elastic square cross-section bar, an elastic–plastic circular cross-section shaft containing a radial crack, and geometrically nonlinear deformation of a thin-walled I-section beam are presented and compared with previous results, where available.     

端部受斜撞击作用悬臂梁的弹塑性动力响应模式

基于大变形动力控制方程并利用有限差分离散分析,研究了斜撞击作用下弹塑性悬臂梁的动力响应．通过对屈服函数以及弯矩、轴力在动力响应过程中分布规律的分析,阐明了斜撞击下恳臂梁的弹塑性动力响应模式和斜撞击的轴向分量对变形机制的影响．研究表明,弹塑性响应过程可划分为四个阶段,对应的变形模式为：“压缩塑性区扩展”模式,“广义移行塑性铰”和“压缩塑性区收缩”混合模式,“驻定塑性铰”模式,“弹性自由振动”模式．与刚塑性分析所假定的两相变形模式比较,弹塑性应响分析证实了响应早期的瞬态轴向压缩模式和梁根部“驻定塑性铰”模式的存在性,肯定了刚塑性分析所假定变形模式的主要特征．斜撞击的轴向分量在撞击发生的瞬时主导了梁的变形,使梁呈现同承受横向冲击明显小同的变形规律．随着响应的深入,轴向分量迅速衰减,其对截面屈服的贡献非常微弱,由横向分量引起的弯曲挠动在大部分时间内主导和控制梁的变形．数值计算结果表明,斜撞击载荷的质量、撞击速度和角度是影响梁动力响应的重要因素．     

On longitudinal impact V

Summary Although during the last twenty years there has appeared an immense literature on plastic deformation caused by longitudinal tensile or compressive impact, it is difficult to find papers with direct bearing on such engineering applications as riveting where the hammer and the anvil, between which the rivet is compressed, are so light that elastic pulses in hammer and anvil must be considered besides elastic and plastic pulses in the rivet. In this article such cases are treated by means of a graphical method developed from those given by Clark and Duwez and especially De Juhasz. It is shown how the amount, extension and efficiency of plastic straining are influenced by the energy, velocity, weight and form of the hammer, as well as by the form of the anvil, for different rivet lengths. For example, maximum efficiency in producing a prescribed plastic strain at the top of the rivet can be obtained by suitable choice of hammer diameter and velocity. The treatment is limited to rivets with stress-strain curves consisting of two straight lines. Some experiments on aluminium rivets with approximately this type of curve are reported, and the results agree reasonably well with the corresponding theoretical analysis.     

应力调整对石英玻璃珠低速冲击破碎行为的影响

结合高速摄影技术,应用SHPB加载装置,分别使用钢制、铝制和有机玻璃制3种透射杆,对直径约7.90、11.80、15.61 mm 3种尺寸的石英玻璃珠进行了低速冲击实验。根据不同透射杆条件下的玻璃珠破碎过程中的载荷-位移曲线,结合有限元软件计算玻璃珠在冲击作用下载荷的变化情况以及实验过程中玻璃珠的应变,探讨了应力调整对玻璃珠破碎过程的影响。结果表明:相同冲击条件作用下,改变透射杆的材料,会改变玻璃珠破碎过程中的载荷分布,即透射端边界波阻抗的改变会导致反射波发生改变,从而导致玻璃珠内部载荷发生变化;透射杆为铝材和有机玻璃材质时,玻璃珠在破碎过程中的载荷明显下降,在加载过程中伴随着垫块的变形,玻璃珠内部的应力调整时间变长;透射杆为钢杆时,玻璃珠的应变主要表现为两端最大,越靠近中间应变越小,对于透射杆为铝杆和有机玻璃杆的玻璃珠,透射端局部出现了卸载行为。采用有机玻璃透射杆之后,局部应力和变形降低的结果使得玻璃珠在经受较大的变形之后发生破碎,表明玻璃珠的破碎行为由局部变形和局部变形梯度共同控制。     

吸能包装模型结构的冲击响应

利用空气炮冲击实验对吸能包装结构的跌落过程进行模拟，进行了缩比模型的正撞和30°斜撞实验，针对模型实验进行了数值分析，获得了吸能包装结构模型在撞击过程中的应力分布和塑性变形，并将计算情况与实验结果进行了分析。结果表明:在撞击中吸能包装结构主要通过缓冲木材的塑性变形及外钢壳屈曲产生的塑性铰吸收能量，塑性变形主要集中于撞击端，而远离撞击端未见塑性变形；计算中木材本构参数采用顺纹方向压缩应力应变曲线具有一定的有效性。     

回转体高速倾斜入水的流场特性及结构响应

回转体高速入水过程涉及液体和固体的耦合作用，是一个复杂的非线性、非定常过程。为研究回转体高速入水的结构动响应及流场演变规律，本文中基于STAR-CCM+和ABAQUS平台，建立了回转体高速入水的双向流固耦合数值模型，开展了不同入水速度的回转体高速倾斜入水流固耦合数值计算。结果表明:数值计算的入水速度、位移曲线和空泡形态与实验结果良好吻合，验证了流固耦合方法的有效性；回转体倾斜高速入水的载荷先集中在触水部分边缘处，后集中于回转体底部中心处；流固耦合方法的入水冲击载荷峰值小于刚体的，弹性回转体的载荷曲线产生明显波动；撞水阶段，回转体空泡呈现不对称形态，随着入水加深，空泡不对称性变弱；入水速度60 m/s下，空泡发生表面闭合，回转体入水初速度越快，空泡表面闭合越晚；冲击载荷与入水速度有关，入水速度越大，峰值出现越早，震荡越明显，速度超过100 m/s时，回转体产生塑性形变。     

Elastic–plastic contact force history and response characteristics of circular plate subjected to impact by a projectile

A new elastic–plastic impact–contact model is proposed in this paper. By adopting the principle of minimum acceleration for elastic–plastic continue at finite deformation, and with the aid of finite difference method, the proposed model is applied in the problem of dynamic response of a clamped thin circular plate subjected to a projectile impact centrally. The impact force history and response characteristics of the target plate is studied in detail. The theoretical predictions of the impact force and plate deflection are in good agreements with those of LDA experimental data. Linear expressions of the maximum impact force/transverse deflection versus impact velocity are given on the basis of the theoretical results. The project supported by the National Natural Science Foundation of China (10532020).