测量三阶弹性常数的非线性声学方法

三阶弹性常数反映了固体弹性在二级近似下的非线性性质，它在固体物理和材料特性的确认和评估中起着重要作用。着重介绍了测量三阶弹性常数的超声二次谐波激发方法。     

各向同性和立方对称物体的高阶弹性系数和物态方程

 本文给出了物态方程可由实验测定的二阶弹性常数（SOEC），三阶弹性常数（TOEC）和四阶弹性常数（FOEC）表述。     

用相速度测量数据反演单向纤维增强复合材料板的弹性常数

基于横向各同性均匀介质中平观波相速度的解析表达式，用声速测量数据，通过失代阻尼最小二乘法来反演单向纤维增强复合材料板的弹性常数，数值实现中，运用了奇异值分解（ＳＶＤ）方法以改善计算的精度和稳定性。用模型计算的声速数据和实测的声速数据均进行了弹性常数的反演，结果表明了反演算法是有效的。     

过渡金属铝化物FeAl和CoAl弹性性质的第一性原理研究

本文通过第一性原理计算(密度泛函理论结合均匀形变方法)得到过渡金属铝化物FeAl和CoAl的二阶和三阶弹性常数,这些弹性常数是通过拟合计算出的能量与应力关系得到的。计算结果和理论数据及实验值符合的很好。接下来本文又研究了FeAl和CoAl在不同压强下的弹性性质。不同压强下的弹性常数Cij,体模量B,剪切模量G,泊松比σ 也成功的得到了。B/G比值和柯西压强 PC 都表明在零压下FeAl和CoAl表现出脆性。在压强小于60GPa的情况下,增大压强可以增强它们的韧性,但它们始终表现为脆性。     

高压下非晶碳的弹性性质

 本文报导了利用10 MHz超声脉冲“回波重合法”，测量非晶碳的声速及其在1 GPa压力以内的变化规律，得到非晶碳的二阶弹性常数（SOEC）、三阶弹性常数（TOCE）及组合的四阶弹性常数（FOEC），从而进一步计算和研究非晶碳的Gruneisen常数γ，德拜温度θ_D，比热以及在高压下的状态变化。     

稀土硼化物LaB6晶体材料的弹性性质和力学性能

利用密度泛函理论和Birch-Murnaghan物态方程,系统分析了LaB6晶体材料的弹性常数参数、体弹性模量、剪切弹性模量及其他力学性能。结果表明:LaB6晶体具有较大的弹性常数参数C11,说明在此主轴应力方向上具有较大的弹性常数;同时它还具有较大的体弹性模量,并且体弹性模量具有各向同性,剪切弹性模量具有各向异性;LaB6晶体的杨氏模量为227.85 GPa,泊松比为0.26,体剪弹性模量比值达到1.44,表明其脆性较强,不易发生弹性形变;LaB6晶体的硬度达到11.56 GPa,平均弹性波速达4.87 km/s。LaB6的带隙宽度为0.20 eV,呈金属性,内部电子具有较强的局域性,La和B之间具有较强的共价键成分。     

单向纤维增强复合板弹性常数的反演方法研究

利用小波变换和人工神经网络技术,对激光激发单向纤维增强复合板产生的兰姆波信号进行分析,进而反演出单向纤维增强复合板的弹性常数。对小波变换和神经网络算法加以优化以提高反演结果的准确性,并分别对纤维方向和垂直于纤维方向的实验波形进行弹性常数的反演,两个方向的反演结果十分吻合。研究表明,利用该方法可直接从激光激发兰姆波的瞬态实验波形中反演出复合板的弹性常数,既不用事先知道兰姆波各模式传播的群速度,也不必采用传统的最小二乘法拟合色散曲线来反演弹性常数。     

钛合金（TC-6）二阶和三阶弹性常数

 用脉冲回波重叠法测量了钛合金（TC-6）的二阶、三阶弹性常数。实验中发现dμ/dp<0（p<0.17 GPa）,dμ/dp>0（p>0.17 GPa）。     

高压下碳化钨压砧走时的测量

 在常温、实验压力为0～3 GPa条件下,利用脉冲反射法测量了纵波在碳化钨压钻中的走时,结果发现,随实验压力升高,碳化钨压砧的走时线性减少。碳化钨压砧被压缩是引起碳化钨压砧的走时减少的主要原因。实验压力（p/GPa）与碳化钨压砧走时减少量（Δt/μs）之间的关系为：Δt=(0.022 33±0.000 81)p。运用这个关系式可以对所测量的岩石弹性波速度进行校正,以获得更为精确的岩石弹性波速度。     

具有六方晶系结构的多晶体材料弹性常数——Y弹性常数

利用最近提出的新的物理参量——Ｙ弹性常数,将其应用于具有六方晶系结构的多晶体材料.推导了六方晶系结构的多晶体材料之Ｙ弹性常数,通过算例与具有六方晶系结构的多晶体材料之X射线弹性常数进行了比较.运用这个Ｙ弹性常数进一步推导出的多晶体材料整体之机械弹性常数的表达式与Kneer的研究结果中的表达式虽然形式不同,但针对具体材料所计算的结果却完全符合. 关键词： Y弹性常数 六方晶系 多晶体材料     

铝在校正高压下物质弹性波速测量上的应用

 自从在紧装式六面顶高压装置上建立了高温超高压下弹性波速的测量方法之后，已经获得了大量的有关岩石矿物的波速数据，利用这些波速数据解决了许多地质问题。然而，其高压弹性波速数据的精度没有解决，一直无法校正上、下顶砧的真正走时。根据弹性理论和标准物质铝的有关弹性参数，计算出铝的波速与压力的关系，然后，根据铝的波速与压力的关系推导出上、下顶砧的实际走时，校正后测量的较低压力下铁的波速与前人的资料吻合很好，并且铁的波速与压力也具有较好的非线性关系。因而，今后可以根据标准物质铝和铁来校正上、下顶砧的走时，从而获得物质在高压下更加精确的波速数据。     

Macroscopic theory of elasticity of fourth order elastic constants of cubic structure solids

The macroscopic theory of elasticity is extended to determine the fourth order elastic constants. The expressions for the small amplitude sound wave velocity and for a natural velocity, in statically stressed media, are derived in terms of second, third and fourth order elastic constants.     

Ultrasonic characterization of Cu-Al-Ni single crystals lattice stability in the vicinity of the phase transition

Measurements of elastic constants of the austenite phase when approaching the phase transformation either upon cooling or stressing is of the crucial interest for the shape memory alloy field. Acoustic properties (wave velocity and also attenuation changes) of the Cu-Al-Ni single crystal were investigated in situ during stress-induced martensitic transformation at constant (room) temperature. The parent austenite cubic lattice of the Cu-Al-Ni exhibits very high elastic anisotropy (anisotropy factor A approximately 12). The measurements were made using nine combinations of (i) applied uniaxial compression in a given crystal direction, (ii) the wave propagation and (iii) polarization vectors. The chosen configurations are sufficient for evaluation of all independent third order elastic constants (TOEC). The longitudinal modes were also measured by the immersion technique, using the transducer pair in a water tank installed on the testing machine. The device works as "a ultrasonic extensometer" measuring a transverse strain of the specimen. The dependencies of both natural and initial wave velocities on the applied stress may be evaluated. Three elastic constants of the stress-induced martensite were determined. The elastic properties were found to vary with the increasing stress above the Ms transformation temperature, which is interpreted as a precursor for the martensitic transformation. The onset of the transformation was additionally identified from the acoustic emission measurement.     

Ultrasonic wave propagation in IIIrd group nitrides

The ultrasonic attenuation in hexagonal structured (wurtzite) third group nitrides (GaN, AlN and InN) has been evaluated at 300 K for an ultrasonic wave propagating along the unique axis of the crystal. Higher order elastic constants of these materials are calculated using the Lennard-Jones potential for the determination of ultrasonic attenuation. The ultrasonic velocity, Debye average velocity, thermal relaxation time and acoustic coupling constant are evaluated along the z-axis of the crystal using the second order elastic constants and other related parameters. The contributions of the elastic constants, thermal conductivity, thermal energy density, ultrasonic velocity and acoustic coupling constant to the total attenuation are studied. On the basis of the ultrasonic attenuation, it can be concluded that the AlN is more ductile than either GaN or InN at 300 K. Orientation dependent characterization has been achieved by calculation of the orientation dependent ultrasonic velocity, Debye average velocity and thermal relaxation time for the materials.     

Measurements of Young’s and shear moduli of rail steel at elevated temperatures

The design and modelling of the buckling effect of Continuous Welded Rail (CWR) requires accurate material constants, especially at elevated temperatures. However, such material constants have rarely been found in literature. In this article, the Young’s moduli and shear moduli of rail steel at elevated temperatures are determined by a new sonic resonance method developed in our group. A network analyser is used to excite a sample hanged inside a furnace through a simple tweeter type speaker. The vibration signal is picked up by a Polytec OFV-5000 Laser Vibrometer and then transferred back to the network analyser. Resonance frequencies in both the flexural and torsional modes are measured, and the Young’s moduli and shear moduli are determined through the measured resonant frequencies. To validate the measured elastic constants, the measurements have been repeated by using the classic sonic resonance method. The comparisons of obtained moduli from the two methods show an excellent consistency of the results. In addition, the material elastic constants measured are validated by an ultrasound test based on a pulse-echo method and compared with previous published results at room temperature. The measured material data provides an invaluable reference for the design of CWR to avoid detrimental buckling failure.     

Third order elastic constants of NaCl

A brief review is given of the meaning of the third order elastic constants and of the general significance of the anharmonic parameters for mechanical and thermodynamic properties. The measurements of the third order elastic constants of NaCl and KCl by Chang and of NaCl by Swartz are described. In each case the changes in ultrasonic velocities were observed as a function of applied uniaxial stress. More recently a program in beam mixing has been initiated by Dunham to study the third order constants of NaCl through the conversion efficiency of the T+T →L interaction.     

Test of hyperelasticity in highly nonlinear solids: sedimentary rocks

We report measurements of three-wave mixing amplitudes on systems whose third order elastic constants have also been measured by means of the elastoacoustic effect. Because attenuation and diffraction are an important aspect of our measurement technique we analyze our results using a modified Khoklhov-Zabolotskaya-Kuznetsov equation in the frequency domain. We find that the value of beta so deduced for polymethyl methacrylate agrees quite well with that predicted from the stress dependent sound speed measurements, establishing that polymethyl methacrylate may be considered as a hyperelastic solid. The beta values of sedimentary rocks, though they are typically 2 orders of magnitude larger than, e.g., polymethyl methacrylates, are still a factor 3-10 less than those predicted from the elastoacoustic effect.     

Lattice dynamics,third order elastic constants and low temperature lattice thermal expansion of zirconium

The lattice dynamics and the anharmonic properties of the hexagonal Zirconium are worked out using Keating's approach. The dispersion curves are fitted using twelve second order parameters and the six second order elastic constants are evaluated. The ten third order elastic constants are calculated using five third order parameters. The experimental measurements on the pressure derivatives of the second order elastic constants in Zirconium are in good agreement with the calculated values. The low-temperature limit of the lattice thermal expansion is calculated which agrees well with the value obtained from thermal expansion data. The variation of the generalised GPs of the elastic modes with the direction of propagation is illustrated by polar diagram.     

用赝势方法计算简单金属的弹性常数

本文利用单参数Heine-Abarenkov模型势及Hubbard-Sham介电函数计算了七种简单金属(Li,Na,K,Rb,Cs,Al和Pb)的二阶与三阶弹性常数,两个可调参数用零温零压下晶体的弹性常数C₄₄与晶格常数的实验值来确定,计算结果与实验值或其他作者的理论计算值符合得比较好,尤其是Al的三阶弹性常数,本文的计算结果比其他作者的计算结果更接近于实验值。 关键词：     

Third-order elastic constants of diamond determined from experimental data

The pressure derivatives of the second-order elastic constants (SOECs) of diamond were determined by analyzing previous sound velocity measurements under hydrostatic stress [McSkimin and Andreatch, J. Appl. Phys., vol. 43, 1972, pp. 2944] [4]. Our analysis corrects an error in the previously reported results. Using the corrected pressure derivatives, together with published data for the nonlinear elastic response of shock-compressed diamond [Lang and Gupta, Phys. Rev. Lett., vol. 106, 2011, pp. 125502] [3], a complete and corrected set of third-order elastic constants (TOECs) is presented that differs significantly from TOECs published previously.