A split Hopkinson pressure bar technique to determine compressive stress-strain data for rock materials

This paper presents a split Hopkinson pressure bar technique to obtain compressive stress-strain data for rock materials. This technique modifies the conventional split Hopkinson bar apparatus by placing a thin copper disk on the impact surface of the incident bar. When the striker bar impacts the copper disk, a nondispersive ramp pulse propagates in the incident bar and produces a nearly constant strain rate in a rock sample. Data from experiments with limestone show that the samples are in dynamic stress equilibrium and have constant strain rates over most of the test durations. In addition, the ramp pulse durations can be controlled such that samples are unloaded just prior to failure. Thus, intact samples that experience strains beyond the elastic region and postpeak stresses can be retrieved for microstructural evaluations. The paper also presents analytical models that predict the time durations for sample equilibrium and constant strain rate. Model predictions are in good agreement with measurements.     

The complete process of large elastic-plastic deflection of a cantilever

An extension of the Elastica theory is developed to study the large deflection of an elastic-perfectly plastic horizontal cantilever beam subjected to a vertical concentrated force at its tip. The entire process is divided into four stages: I.elastic in the whole cantilever; II.loading and developing of the plastic region; III.unloading in the plastic region; and IV.reverse loading. Solutions for stages I and II are presented in a closed form. A combination of closed-form solution and numerical integration is presented for stage III. Finally, stage IV is qualitatively studied. Computed results are given and compared with those from small-deflection theory and from the Elastica theory.     

多阶变截面杆的弹性稳定计算

本文研究单阶和多阶截面杆在集中和分布轴向荷载作用下的弹性稳定计算方法,首次给出了其整体稳定和局部稳定的解析解.     

Blast wave measurements close to explosive charges

The paper reports the results of experimental measurements of the reflection pressures close to spherical charges of TNT. These measurements were made using a pressure bar technique. Charge weights of up to 3.6 kg were used, with the reflecting plane in the range 25 to 300 mm from the charge surface.A possible wave interaction model is discussed, to account for the observed pressure profiles, and its qualitative correctness checked by means of numerical simulation.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

DEVELOPMENT OF EXPERIMENTAL METHODS FOR IMPACT TESTING BY COMBINING HOPKINSON PRESSURE BAR WITH OTHER TECHNIQUES

The split Hopkinson pressure bar（SHPB） technique and the wave propagation inverse analysis（WPIA） technique are both extensively used to experimentally investigate the impact behavior of materials, although neither of them alone provides a fully satisfactory analysis. In the present paper, attention is given to new experimental techniques by incorporating a damagemodified constitutive model into the SHPB technique and combining the Hopkinson pressure bar（HPB） technique with WPIA. First, to distinguish the response due to dynamic constitutive behavior and the response due to dynamic damage evolution, the SHPB method incorporating a damage-modified constitutive model is developed, including an explicit damage-modified Zhu–Wang–Tang model and an implicit damage-modified constitutive model. Second, when the SHPB results become invalid, a method of combining new Lagrange inverse analyses with the HPB technique is developed, including cases of the HPB arranged in front of a long specimen and behind the specimen. As examples of these new methods, typical results are given for nonlinear viscoelastic polymers and concretes considering damage evolution, a super-elastic Ti–Ni alloy with phase transformation and an aluminum foam with shock waves propagating within it.     

A numerical study on the deformation and fracture modes of steel projectiles during Taylor bar impact tests

A heterogeneous material model based on macro-mechanical observations is proposed for simulation of fracture in steel projectiles during impact. A previous experimental study on the deformation and fracture of steel projectiles during Taylor bar impact tests resulted in a variety of failure modes. The accompanying material investigation showed that the materials used in the impact tests were heterogeneous on scales ranging from microstructure as investigated with SEM to variation in fracture strains from tensile tests. A normal distribution is employed to achieve a heterogeneous numerical model with respect to the fracture properties. The proposed material model is calibrated based on the tensile tests, and then used to independently simulate the Taylor bar impact tests. A preliminary investigation showed that the simulations are sensitive to assumptions regarding the anvil behaviour and friction properties. A flexible anvil and a yield-limited friction law are shown to be necessary to correctly reproduce the experimental behaviour. The proposed model is then shown to be capable of correctly reproducing all fracture modes but one, and also predict critical impact velocities for projectile fracture with reasonable accuracy. Fragmentation at velocities above the critical velocity is not well reproduced due to excessive element erosion. Measures to make the element erosion process more physical are proposed and discussed with their respective drawbacks. The use of a simple fracture criterion in combination with an element erosion technique accentuates the effect of distributing the fracture parameter.     

Energy as a Fifth Dimension

A recent analysis of the experimental data on some physical phenomena ruled by the four fundamental interactions (electromagnetic, weak, strong and gravitational) seems to show the possibility of describing such interactions in terms of a deformation of the usual Minkowski spacetime, with a metric whose coefficients do depend on the energy of the process considered. In this paper, we show that such results can be accounted for in terms of a Kaluza-Klein-like scheme, based on a five-dimensional Riemannian space in which energy plays the role of the fifth dimension. The corresponding five-dimensional Einstein equations in vacuum are solved in some cases of physical relevance and it is shown that all the phenomenological metrics describing the four fundamental forces are recovered as special cases of the classes of solutions found. Possible developments of the formalism are also briefly outlined.     

基准光栅重构傅里叶变换轮廓术

应用傅里叶轮廓变换术进行三维形貌测量中,为了获得待测物体的高度相位信息,通常需要采集两幅图像.因此当光学系统发牛变动时,必须重新采集基准光栅图像,不利于快速测量.提出一种从变形光栅图像中获取基准光栅图像信息的测量方法.首先在变形光栅图像中记录基准光栅信息,然后通过傅里叶分析提取基准光栅频率信息,通过图像分析获得基准光栅相位信息,最后重构出一幅完整的基准光栅图像,实现三维物体形貌测量.实验结果验证了该方法的可行的.     

99氧化铝陶瓷在不同应变率下的破碎特性

开展了99氧化铝陶瓷在不同应变率下的轴向压缩实验,通过对相应应变率下的试件碎片进行软回收,并结合筛余法对碎片进行几何表征,获得了不同应变率下的碎片尺寸分布曲线和试件破坏的能量吸收过程,建立了颗粒陶瓷的外力功与相对破碎率之间的关系。采用数字图像相关(Digital image correlation,DIC)技术获取了不同应变率下沿加载方向的应变场,并结合能量吸收过程和碎片级配表现分析了破坏模式。实验结果表明:99氧化铝陶瓷的破坏强度与应变率呈正相关,在中应变率下,能量吸收率与应变率呈负相关,由于能量吸收机制的改变,样品初始为劈裂破坏;当应变率达到401 s^?1时,破坏模式变为劈裂-粉碎混合破坏;随着应变率继续增大,试件变为粉碎破坏,颗粒平均粒径减小,碎片尺寸趋同,应力集中的影响逐渐减弱。分析了能量、破坏过程、碎片分布之间的关系,最终获得了碎片分布规律以及破碎特性。     

Boosts in an Arbitrary Direction and Maximal Causal Velocities in a Deformed Minkowski Space

We discuss boosts in a deformed Minkowski space, i.e., a four-dimensional spacetime with metric coefficients depending on nonmetric coordinates (in particular on the energy). The general form of a boost in an arbitrary direction is derived in the case of space anisotropy. Two maximal trivector velocities are mathematically possible, an isotropic and an anisotropic one. However, only the anisotropic velocity has physical meaning, being invariant indeed under deformed boosts.