单轴应变：本构关系——它的内容、方法和意义

论述了单轴应变加载下固体中偏应力的基本含义和偏应力在本构关系研究中的意义。指出了加载-卸载波剖面测量在本构关系研究中的重要作用。建立了测量金属材料在平面冲击压缩下的剪切模量的基本方法,对表征固体材料弹性特性的剪切模量在冲击压缩状态下的物理含义做出了解释。根据剪切模量的一般性定义,建立了描写受冲击材料的准弹性-塑性卸载特性的有效剪切模量与纵波声速和横渡声速的关系。通过同时测量受冲击材料中的追赶稀疏波速度和波后粒子速度,获得了LY12铝在20～110GPa冲击压力和无氧铜在41～104GPa冲击压力下的声速和剪切模量,以及从冲击压缩状态卸载时沿着准弹性卸载路径的声速和有效剪切模量。 对目前广泛使用的描写单轴应变下固体材料的加载-卸载响应特性的SCG本构模型进行了分析,指出该本构关系的局限性,认为这种本构关系原则上不能用来描写受冲击材料的卸载过程。根据LY12铝和无氧铜的实验研究结果,对SCG本构关系中的剪切模量方程进行修正,讨论了修正的物理含义。修正后的方程与实验测量结果符合很好,在此基础上提出新的加载本构方程。 根据铝和铜沿着准弹性卸载路径的声速测量结果,提出了描写受冲击压缩固体的准弹性卸载的有效剪切模量方程和相应的屈服强度方程。建立了单轴应变下包含加载-卸载过程的新的本构方程。根据本文的实验测量结果,给出了铝合金和无氧铜卸载本构方程的解析形式,确定了相关参数。 依据文中提出的加载本构和卸载本构方程,对实验测量的6发LY12铝的波剖面、美国5发6061-T6铝合金的加载-卸载波剖面及冲击波衰减数据,进行了数值模拟计算和预测。计算中采用与本文测量相同的卸载本构参数,计算结果与实验结果符合很好,再现了这些波剖面的准弹性-塑性卸载行为和冲击波衰减行为。对3发无氧铜波剖面的计算模拟,也获得了令人满意的结果。 最后,从现象学出发,对发生在冲击波阵面内的弹-塑性屈服过程进行了分析,对固相区冲击波后材料的状态不在屈服面上的原因进行解释。     

钽和LY12铝的高压声速测量

应用两种不同的实验装置钽飞片/LY12铝缓冲层/LiF窗口和钽飞片/LiF窗口,采用逆向碰撞法测量了钽在110~131 GPa冲击压力下的纵波声速。实测的钽的声速结果与文献\[5\]报道的数据有较好的一致性。研究结果表明,作为缓冲层的LY12铝与LiF窗口的阻抗比较接近,使用缓冲层对钽的声速测量结果没有明显影响。实验测量同时获得了LY12铝在110 GPa和131 GPa冲击压力下的纵波声速。结合文献\[4\]的数据表明LY12铝在125～150 GPa冲击压力范围内,纵波声速随冲击压力的增加逐渐降低至体波声速。     

磁驱动准等熵压缩下LY12铝的强度测量

高压高应变率加载下材料的强度研究一直是冲击动力学的一个难题,目前动态载荷下材料的高压强度测量主要是基于平板撞击技术,冲击温升和应变率效应对材料强度的影响难以分离. 基于小型磁驱动加载装置CQ-4,开展了磁驱动准等熵压缩下LY12 铝的声速和强度测量的实验研究,讨论了考虑加载-卸载过程时磁驱动压缩实验的负载电极设计、实验样品设计、数据处理与分析等内容,并获得了12 GPa 压力范围沿加载-卸载路径的声速变化和峰值压力点的强度数据.      

单轴应变：本构关系——它的内容、方法和意义（续）

6卸载本构 6．1沿着准弹性卸载路径的有效剪切模量的变化规律 长期以来,Steinberg本构关系不仅被用来描写单轴应变加载过程,也被用来描写从冲击压缩状态卸载的过程,即模拟卸载波剖面。因此,Steinberg本构方程（5．1）和（5．2）中的应力P不仅表示冲击加载压力,     

延性材料平面冲击波基本实验数值模拟的若干问题

假设屈服强度正比于剪切模量,分别构建了四种强度模型,并用于数值模拟Ly12铝的平面冲击波试验的质点速度剖面以及钨合金的平面冲击波试验的锰铜计应力记录.研究发现,基于Steinberg等的屈服强度模型比较符合实验.还对平面冲击波试验的层裂现象进行了简化的数值模拟,其中,采用了该文作者所提出的一种基于空穴聚集的层裂模型,该模型的特点是分别引入了层裂过程的早期及后期应力松弛方程.     

准一维应变下Al2O3陶瓷动态压缩失效的实验研究

为了考察Al2O3陶瓷准一维应变下的力学性能,采用LY12铝套筒和45钢套筒对陶瓷试样进行了环向约束,在准静态和动态下分别进行了压缩实验,得到了材料的应力-应变曲线。实验结果表明,Al2O3陶瓷的轴向压缩强度基本上随围压的增大而增大,动态压缩加载下的轴向压缩强度随应变率增大而增大。Al2O3陶瓷在准一维应变下的破坏形式为裂纹破坏,准静态的脆性失效行为可以用Mohr-Coulomb失效准则来描述。     

双屈服面法测量金属材料动高压屈服强度的若干改进

在J.R.Asay等提出的双屈服面法（简称AC方法）测量动态屈服强度的基础上,对实验设计和数据处理做了部分改进。在实验设计方面,在满足实验物理设计的前提下,将 AC方法的卸载实验装置(双层飞片和双台阶样品)简化为单飞片和单台阶样品,以简化波系作用,并减少了声速测量不确定度的引入因素。在数据处理方面,发现由Lagrange声速和工程应变关系曲线外推求预冲击态的体积声速容易引入较大的不确定度,而通过Lagrange声速和粒子速度关系曲线可以更清晰地得到塑性卸载起始点,使图解法和积分法得到的屈服强度值趋于一致。利用改进后的AC方法,得到了低温退火后LY12铝在20.0 GPa预冲击压力下的屈服强度为0.6 GPa。     

预应力对LY12铝弹性前驱波的影响

通过过盈配合的热装配方法对LY12铝合金平面样品施加了径向预应力,采用平面飞片撞击方法获得了预应力对弹性前驱波的影响。结果表明:当飞片均以500 m/s的速度撞击样品时,压缩预应变为0(无预应变)、964.5×10-6和1 886.0×10-6时,弹性前驱波幅值分别为87.56、95.24、121.03 m/s,压缩预应力(变)提高了LY12铝弹性前驱波幅值。结合实验的特点,探讨了对样品施加静态径向预应力的数值模拟方法,结果表明,上升沿(100 μs)较为缓慢的加载可以达到与准静态加载应力分布一样的结果。采用该数值模拟方法给出和验证了弹性前驱波随压缩预应力增加而上升的计算结果,与实验结果较为吻合。     

超声瑞利波测试材料表面载荷应力的实验研究

实验研究了利用超声瑞利波传播特性测试材料表面应力的方法.在测试过程中采用回振法测声速,以分辨应力作用引起声速的徽小变化;并设计夹具实现探头与试样之间的稳定耦合和弹性接触,精简了实验机构,提高了实验精度.研究结果表明,在应力作用下,平行和垂直于应力方向传播的瑞利波发生了相应的变化:应力较小时,声速随应力变化较快;随着应力...     

超弹性镍钛形状记忆合金单轴相变棘轮行为的宏观唯象本构模型

超弹性镍钛形状记忆合金因其良好的力学性能以及独特的超弹性和形状记忆效应已广泛应用于土木工程、航空航天和生物医疗等多个领域,在实际服役环境中超弹性镍钛合金元件不可避免地会承受不同应力水平的循环载荷作用,亟待建立描述相变棘轮行为(即峰值应变和谷值应变随着正相变和逆相变循环的进行不断累积)的循环本构模型.为此,基于已有的超弹性镍钛形状记忆合金在不同峰值应力下的单轴相变棘轮行为实验研究结果,在广义黏塑性框架下,对Graesser等提出的通过背应力非线性演化方程反映超弹性镍钛形状记忆合金超弹性行为的一维宏观唯像本构模型进行了拓展,考虑了正相变和逆相变过程中特征变量的差异及其随循环的演化,以非弹性应变的累积量为内变量引入了正相变开始应力、逆相变开始应力、相变应变和残余应变的演化方程,同时通过峰值应力与正相变完成应力的比值来确定演化方程中的相关系数,建立了描述超弹性镍钛合金单轴相变棘轮行为的本构模型.将模拟结果与对应的实验结果进行对比发现,建立的宏观唯像本构模型能够合理地描述超弹性镍钛形状记忆合金的单轴相变棘轮行为及其峰值应力依赖性,模型的预测结果和实验结果吻合得很好.     

Elastic coefficients of aluminum as functions of the degree of compression in a shock wave

The velocities of elastic relief waves in commercial aluminum (AD1) and aluminum alloy (D16) samples compressed by a shock wave were measured by the most direct method. Using these results together with the relationship for the three-dimensional velocity of sound as a function of the intensity of the sound wave (derived on the assumption that the shock adiabat and the one-dimensional release isentrope coincide when expressed in pressure/mass-velocity coordinates), Young's modulus, the shear modulus, and the Poisson coefficient are calculated for shock-compressed aluminum.     

动高压加载下锆基金属玻璃强度测量

为了研究Zr₅₁Ti₅Ni₁₀Cu₂₅Al₉金属玻璃的高压强度特性,进行了平靶冲击实验。采用反向碰撞方式,运用DISAR技术测量金属玻璃样品/LiF窗口界面粒子速度剖面,分析粒子速度剖面获得了37~66GPa压力范围锆基金属玻璃的屈服强度和剪切模量。实验结果表明,在上述压力范围金属玻璃的屈服强度和剪切模量均显示出一定程度的压力硬化效应,分析表明金属玻璃冲击加载波阵面剪应力衰减并非由损伤/破坏或温度软化等因素导致。     

Effects of texture evolutions and point defects on ultrasonic waves under simple shear and pure shear

In this paper, longitudinal and transverse wave velocities propagating into aluminum alloy A6061 under simple shear and pure shear were studied experimentally. Compared with the same velocity change tendencies of transverse wave under simple shear and pure shear, longitudinal wave velocity shows different change tendencies under both shear states, regardless of the same shear strain states in two cases. Finite element analysis was performed and the analyzed results indicate that the transverse wave velocity depends on texture evolutions mainly, whereas the longitudinal wave velocity is sensitively influenced by point defects induced by cross-slips. Consequently, the longitudinal wave velocity showing a sensitive response to the point defects was examined by measuring longitudinal wave velocity changes propagating into Al single crystal subjected to the combination loads of equi-biaxial tension and compression.     

径向非均匀介质中圆形夹杂的动应力分析

基于复变函数理论,研究了径向非均匀弹性介质中均匀圆夹杂对弹性波的散射问题. 介质的非均匀性体现在介质密度沿着径向按幂函数形式变化且剪切模量是常数. 利用坐标变换法将变系数的非均匀波动方程转为标准亥姆霍兹(Helmholtz) 方程. 在复坐标系下求得非均匀基体和均匀夹杂同时存在的位移和应力表达式. 通过具体算例分析了圆夹杂周边的动应力集中系数(DSCF). 结果表明:基体与夹杂的波数比和剪切模量比,基体的参考波数和非均匀参数对动应力集中有较大的影响.      

U–6Nb shear stress relaxation in compression waves (IJP 585-AV)

When uranium alloyed with 6-wt% niobium (U–6Nb) is rapidly compressed in uniaxial strain experiments, shear stress is observed to relax with a characteristic time of 30 ± 7 ns. In shock wave experiments, this relaxation inhibits the development of an elastic precursor commonly seen in other materials. When U–6Nb is cold-rolled to pre-twin and significantly increase the density of dislocations in the material, stress relaxation effects are diminished suggesting that twinning causes relaxation in the un-worked material. Separate ramp wave compression experiments produce effects that agree with those observed in shock-loading experiments. A phenomenological model is introduced that allows accurate simulation of all experiments. Estimates of residual shear stress after relaxation are obtained.     

Effect of interface stress on the fracture behavior of a nanoscale linear inclusion along the interface of bimaterials

This paper investigates the influence of residual interface tension on the fracture behavior of a nanoscale linear interface inclusion in a bimaterial matrix. Solutions to the inclusion opening displacement and the energy release rate are obtained. The results show that the interface effect on the inclusion deformation and inclusion tip field are prominent at nanoscale. Especially, the residual interface stress has a dramatic influence on the energy release rate. It is also found that the importance of the interface effect depends on the size of the inclusion, the shear modulus ratios of the bimaterial. The inclusion opening displacement and the energy release rate can be reduced considerably by decreasing the inclusion length at nanoscale.     

Linear Elastic Wave Propagation in Unsaturated Sands,Silts, Loams and Clays

Due to its propitious material properties sandstone is the most studied porous medium for the investigation of linear wave propagation. However, in practical applications the behavior of other soil types, i.e., especially the three main soil types sand, silt, and clay, are much more important. Therefore, the model for partially saturated soils introduced by Albers (Habilitation Thesis, 2010a) is applied to 11 soil types classified in the German standard DIN 4220 to obtain information on the phase velocities and attenuations of the three longitudinal waves and the shear wave appearing in such media.     

FRACTURE ANALYSIS OF A FUNCTIONALLY GRADED STRIP UNDER PLANE DEFORMATION

In this paper the plane elasticity problem for a functionally graded strip containing a crack is considered. It is assumed that the reciprocal of the shear modulus is a linear function of the thickness-coordinate, while the Possion's ratio keeps constant. By utilizing the Fourier transformation technique and the transfer matrix method, the mixed boundary problem is reduced to a system of singular integral equations that are solved numerically. The influences of the geometric parameters and the graded parameter on the stress intensity factors and the strain energy release rate are investigated. The numerical results show that the graded parameters, the thickness of the strip and the crack size have significant effects on the stress intensity factors and the strain energy release rate.     

Multiple scattering of elastic waves in metal-matrix composite materials with high volume concentration of particles

A new approach is proposed to investigate the propagation of compressional (P) and shear (SV) waves in metal-matrix composite materials with high volume concentration of particles. The theory of quasicrystalline approximation and Waterman's T matrix formalism are employed to treat the multiple scattering resulting from the particles in composites. The addition theorem for spherical Bessel functions is used to accomplish the translation between different coordinate systems. The analytical expression of the Percus–Yevick correlation function is also given. Closed form solutions for the effective propagation constants and the dynamic effective elastic modulus of materials are obtained in the low frequency limit. At higher frequencies, only numerical results of them are presented. Numerical examples show that the phase velocities of P and SV waves in the composite materials with low volume concentration in the low frequency are in good agreement with the results in previous literatures. The effects of the incident wave number, the volume fraction of particles and the material properties of the particles and matrix on the dynamic effective elastic modulus are also examined.