线黏弹性球面发散应力波的频率响应特性

基于线黏弹性球面波Laplace域的理论解, 得到了不同传播距离处粒子速度、粒子位移、应力、应变等力学量的传递函数。以标准线性固体模型为例, 重点讨论了粒子速度频率响应函数的传播特征, 指出随着传播距离的增加, 粒子速度幅频响应函数的高频响应会低于低频响应, 而在理想弹性条件下, 粒子速度幅频响应函数的高频响应一直高于低频响应。以弹性半径为0.025 m的空腔爆炸为例, 采用Laplace数值逆变换方法对粒子速度波形的演化进行了分析, 给出了粒子速度强间断幅值及粒子速度峰值随传播距离变化的衰减规律曲线, 指出黏弹性介质中粒子速度幅值的衰减曲线介于理想弹性介质中粒子速度幅值衰减曲线和黏弹性介质中粒子速度强间断幅值衰减曲线之间。     

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.     

多孔材料吸能行为对相对密度和冲击速度的依赖性

多孔材料是一种优异的吸能缓冲材料,但由于其变形模式的非单一性以及动态应力应变曲线的难获取性,其吸能行为对相对密度和冲击速度的依赖性关系还并不完全明朗。本文基于不需要提前作本构假定的波传播法,开展了多孔材料的吸能行为研究。采用多孔材料的细观有限元模型进行Taylor冲击虚拟实验,获取全场质点速度时程曲线,结合Lagrange分析法得到多孔材料的局部应力应变信息,进而探讨了动态吸能性能对材料相对密度和冲击速度的依赖性。研究结果表明多孔材料的吸能行为可依据变形模式分为三个阶段。在冲击模式下,多孔材料单位体积吸能与相对密度成线性增加关系,此时惯性起主导作用;在过渡模式下,惯性的主导作用减弱,单位体积吸能量的增加速率随相对密度的增加而减弱;在准静态模式下,多孔材料只能发生微小的变形,其吸能很少。本文进一步获得了区别于多孔材料准静态应力-应变曲线的动态应力-应变状态曲线,并考察了其与相对密度之间的关系。结果表明：随着相对密度的增加,多孔材料的动态压实应变将变小,而动态塑性平台应力将提高。     

Coupled thermoelasticity with non-zero thermal boundary conditions

We consider one-dimensional wave propagation in a thermoelastically coupled half space. The boundary conditions involve an application of a non-zero temperature or temperature gradient. The strain, temperature, stress and particle velocity are obtained and compared when both time and distance are large. The ratios of the temperature to the strain, the stress to the strain, and the particle velocity to the strain are found to be the same for all the six cases considered.     

In-fiber doppler velocimeter for velocity measurements of moving surfaces

An optical fiber Doppler velocimeter using a 3×3 coupler with a large path imbalance Mach-Zehnder interferometer for passive demodulation of Doppler wavelength shifts is demonstrated. The particle velocity on the free surface end of the Hopkinson bar is directly obtained using the all-fiber Doppler velocimeter. These data show good agreement with the particle velocity predicted using strain gage data combined with one-dimensional stress wave propagation theory.     

On the response of rubbers at high strain rates—II. Shock waves

In this series of papers, we examine the propagation of waves of finite deformation in rubbers through experiments and analysis; in the present paper, Part II, attention is focused on the propagation of one-dimensional tensile shock waves in strips of latex and nitrile rubber. Tensile wave propagation experiments were conducted at high strain rates by holding one end fixed and displacing the other end at a constant velocity. A high-speed video camera was used to monitor the motion and to determine the evolution of strain and particle velocity in rubber strips. Shock waves have been generated under tensile impact in prestretched rubber strips; analysis of the response yields the tensile shock adiabat for rubbers. The propagation of shocks is analyzed by developing an analogy with the theory of detonation; it is shown that the condition for shock propagation can be determined using the Chapman-Jouguet shock condition.     

Dynamic tensile characterization of pig skin

The strain-rate dependent response of porcine skin oriented in the fiber direction is explored under tensile loading. Quasi-static response was obtained at strain rates in the range of 10-3s-1to 25 s-1. Characterization of the response at even greater strain rates is accomplished by measuring the spatio-temporal evolution of the particle velocity and strain in a thin strip subjected to high speed impact loading that generates uniaxial stress conditions. These experiments indicate the formation of shock waves; the shock Hugoniot that relates particle velocity to the shock velocity and the dynamic stress to dynamic strain is obtained directly through experimental measurements, without any assumptions regarding the constitutive properties of the material.     

Dynamic stress intensity factor K III and dynamic crack propagation characteristics of anisotropic materials

Based on the mechanics of anisotropic materials, the dynamic propagation problem of a mode Ⅲ crack in an infinite anisotropic body is investigated. Stress, strain and displacement around the crack tip are expressed as an analytical complex function, which can be represented in power series. Constant coefficients of series are determined by boundary conditions. Expressions of dynamic stress intensity factors for a mode Ⅲ crack are obtained. Components of dynamic stress, dynamic strain and dynamic displacement around the crack tip are derived. Crack propagation characteristics are represented by the mechanical properties of the anisotropic materials, i.e., crack propagation velocity M and the parameter ~. The faster the crack velocity is, the greater the maximums of stress components and dynamic displacement components around the crack tip are. In particular, the parameter α affects stress and dynamic displacement around the crack tip.     

Dynamic crack tip fields and dynamic crack propagation characteristics of anisotropic material

Based on mechanics of anisotropic material, the dynamic crack propagation problem of I/II mixed mode crack in an infinite anisotropic body is investigated. Expressions of dynamic stress intensity factors for modes I and II crack are obtained. Components of dynamic stress and dynamic displacements around the crack tip are derived. The strain energy density theory is used to predict the dynamic crack extension angle. The critical strain energy density is determined by the strength parameters of anisotropic materials. The obtained dynamic crack tip fields are unified and applicable to the analysis of the crack tip fields of anisotropic material, orthotropic material and isotropic material under dynamic or static load. The obtained results show Crack propagation characteristics are represented by the mechanical properties of anisotropic material, i.e., crack propagation velocity M and fiber direction α. In particular, the fiber direction α and the crack propagation velocity M give greater influence on the variations of the stress fields and displacement fields. Fracture angle is found to depend not only on the crack propagation but also on the anisotropic character of the material.     

预置圆孔膨胀环动态断裂行为研究

利用中心线起爆膨胀环加载技术,采用分幅摄影技术观测了20号钢圆环在准一维拉伸作用下,预置圆孔缺陷临近区域的动态断裂特征。获得了高应变率下圆孔的变形、裂纹的萌生及扩展过程。并采用LS-DYNA3D有限元程序分步建模,将驱动器对膨胀环的冲击压力简化为直接作用于圆环内壁的压力历史,以此模拟了整个断裂过程。通过实验图像,得到裂纹尖端的位移以及速度随时间变化的曲线。结果表明,宏观可见裂纹出现于应力集中最大处,裂纹扩展速度随时间振荡,数值模拟与实验结果吻合较好。     

Dynamic stress intensity factor KⅢ and dynamic crack propagation characteristics of anisotropic materials

Based on the mechanics of anisotropic materials,the dynamic propagation problem of a mode Ⅲ crack in an infinite anisotropic body is investigated.Stress,strain and displacement around the crack tip are expressed as an analytical complex function,which can be represented in power series.Constant coefficients of series are determined by boundary conditions.Expressions of dynamic stress intensity factors for a mode Ⅲ crack are obtained.Components of dynamic stress,dynamic strain and dynamic displacement around the crack tip are derived.Crack propagation characteristics are represented by the mechanical properties of the anisotropic materials,i.e.,crack propagation velocity M and the parameter α.The faster the crack velocity is,the greater the maximums of stress components and dynamic displacement components around the crack tip are.In particular,the parameter α affects stress and dynamic displacement around the crack tip.     

固体介质中球形发散波的实验装置

建立了用于固体介质中球形发散波传播规律研究的实验技术 ,球形波源是当量为 0 .12gTNT和 0 .4 9gTNT的微型炸药球 ,波后粒子速度测计是圆环型电磁粒子速度计。用该实验和测量系统在有机玻璃和花岗岩中进行了大量的实验研究 ,实验的重复性很好。利用微型炸药球可在较小的样品中模拟较大比距离范围内的波传播。利用圆环型电磁粒子速度计可使输出信号幅度不受波强度因几何发散而快速衰减的影响 ,而且信号输出反映了波面上一条圆环线处介质动力学状态的综合平均结果。该技术的这些突出优点对研究固体介质 (特别是非均匀固体介质 )中球形发散波传播规律和相应的材料动力学特性研究具有重要意义。圆环型电磁粒子速度计测量技术同样适用于固体介质中圆柱形发散波的情况。     

On the response of rubbers at high strain rates—I. Simple waves

In this series of papers, we examine the propagation of waves of finite deformation in rubbers through experiments and analysis; in the present paper, Part I, attention is focused on the propagation of one-dimensional waves in strips of natural, latex and synthetic, nitrile rubber. Tensile wave propagation experiments were conducted at high strain rates by holding one end fixed and displacing the other end at a constant velocity. A high-speed video camera was used to monitor the motion and to determine the evolution of strain and particle velocity in rubber strips. Analysis of the response through the theory of finite waves indicated a need for an appropriate constitutive model for rubber; by quantitative matching between the experimental observations and analytical predictions, an appropriate instantaneous elastic response for the rubbers was obtained. This matching process suggested that a simple power-law constitutive model was capable of representing the high strain-rate response for both rubbers used.     

高应变率下ZrB2-SiC陶瓷复合材料压缩力学性能实验研究

采用分离式霍普金森压杆装置,测试了高应变率下ZrB2-20%SiC陶瓷复合材料的动态压缩力学性能,应变率范围为900s^-1~3000s^-1。结果表明:ZrB2-20%SiC陶瓷复合材料的动态压缩强度与临界应变均随应变率的增大而增加,2950s^-1时压缩强度与临界应变比981s^-1时分别增大了88.72%和148.85%;应变率对ZrB2-20%SiC陶瓷复合材料的动态压缩应力-应变曲线与破坏机理影响显著,应变率为1134s^-1时,ZrB2-20%SiC陶瓷复合材料破坏模式以裂纹扩展为主,应变率为2861s^-1时,多裂纹扩展为该材料的主要破坏机理;应变率越高,试件的损伤程度越大,压缩试件碎片尺寸越小,压缩应力-应变曲线的非线性越明显。     

岩石偏心圆孔单裂纹平台圆盘的动态裂纹扩展与止裂

针对平台圆环构型的优点, 提出偏心圆孔单裂纹平台圆盘(cracked eccentrically holed flattened disc, CEHFD), 该试样具有更长的断裂路径。利用霍普金森压杆加载系统, 径向冲击CEHFD试样, 完成Ⅰ型动态断裂实验。砂岩试样表面粘贴应变片和裂纹扩展计, 用于监测裂纹动态起裂、扩展和止裂的全过程。实验表明, 在整个断裂过程中, 裂纹非匀速扩展, 裂纹扩展速度在裂纹起裂后加速上升, 在裂纹止裂前有明显的减速, 与地震时断层的动态破裂全过程完全吻合。采用实验-数值-解析法得到动态应力强度因子, 其时间历程呈现先增大后减小的趋势。根据断裂过程不同时刻, 得到相应的动态起裂韧度、扩展韧度及止裂韧度。在动态断裂全过程中, 动态扩展韧度为速度的函数, 变化趋势与速度一致, 随着时间先增大后减小; 动态起裂韧度大于动态止裂韧度, 止裂韧度随着裂纹最大扩展速度的增大而降低, 并且有较大的离散性。     

多孔铁电陶瓷冲击压缩响应与损伤演化的离散元数值模拟

采用flat-joint粘结模型，建立多孔铁电陶瓷在一维应变冲击压缩下的PFC (particle flow code)颗粒流离散元模型，通过数值模拟再现了平板撞击实验中实测的自由面速度剖面历史，并揭示了多孔铁电陶瓷在冲击压缩下的响应过程与损伤演化机制。多孔铁电陶瓷在冲击压缩下的响应过程可分4个阶段:弹性变形、失效蔓延、冲击压溃变形、冲击Hugoniot平衡状态；其中，失效蔓延的内在机制是由剪切裂纹的成核与增长，而冲击压溃变形的主要机制是孔洞的塌缩以及层状剪切裂纹的形成与扩展；冲击速度与孔隙率对铁电陶瓷的响应有显著的影响，Hugoniot弹性极限强烈依赖于孔隙率，但与冲击速度的大小无关，宏观损伤累积随着冲击速度和孔隙率的增加而增加。     

Deformation trapping due to thermoplastic instability in one-dimensional wave propagation

One-dimensional shear wave propagation in a half-space of a nonlinear material is considered. The surface of the half-space is subjected to a time dependent but spatially uniform tangential velocity. The half-space material exhibits strain hardening, thermal softening and strain rate sensitivity of the flow stress. For this system, a well-defined band of intense shear deformation can develop adjacent to the loaded surface, even though the material has no imperfections or other natural length scale. Representative particle velocity and strain profiles, which have been obtained numerically, are described for several different models.     

The dependence of crack velocity on the critical stress in fracture

The constant velocity of crack propagation in PMMA is investigated in terms of the fracture stress for both continuously increasing loading (strain rate ?=0.59×10^?4 s^?1) and dynamic loading (strain rate ?=0.35 s^?1). It was found that the constant crack velocity increases with increasing fracture stress and that it depends on the loading conditions (continuously increasing or dynamic loading). In particular, it was found that the increase of the constant velocity for the static loading case is higher than for the dynamic one. However, in both cases, the constant velocity reaches a limiting value for stresses higher than a certain level.     

用改进的基于质点速度测量的拉格朗日分析方法研究尼龙动态力学特性

采用改进的基于质点速度波形测量的拉格朗日分析方法,研究了率型材料的动态力学性能.首先用高磁感应强度的钕铁硼强滋材料研制出新型磁电式粒子速度计,其性能高于前人文献所报道的性能.其次,在理论分析和数值模拟的基础上得出,用实测的质点速度波形来求应力波形时,实测的应力边界是不可缺少的.在实际研究中,要同时测得质点速度以及应力量...     

冲击压缩下氧化铝陶瓷中破坏阵面的传播

进行了平面冲击波压缩下氧化铝陶瓷中破坏阵面的实验测试和理论探索. 通过氧 化铝陶瓷的平板碰撞实验，借助VISAR测试系统测量了试件自由面的质点速度历程，并对回 收试件进行了电镜扫描观察. 质点自由面速度历程曲线表明，氧化铝陶瓷材料中存在破坏阵 面的传播. 考察了破坏阵面的传播特性，给出了陶瓷材料的动态破坏模型，并对破坏阵面的 传播进行了数值分析.