Frequency-dependent tensile and compressive effective moduli of elastic solids with distributed penny-shaped microcracks

This paper develops micromechanics models to estimate the tensile and compressive elastic moduli of elastic solids containing randomly distributed penny-shaped microcracks. The crack faces are open under tension and closed under compression. When the crack faces are closed, they may slide against one another following Coulomb’s law of dry friction. The micromechanics models provide analytical expressions of the tensile and compressive moduli for both static and dynamic cases. It is found that the tensile and compressive moduli are different. Further, under dynamic loading, both compressive and tensile moduli are frequency dependent. As a by-product, the micromechanics models also predict wave attenuation in the dynamic case. Numerical simulations using the finite element method are conducted to validate the micromechanics models.     

Ultrasonic measurements of microelectronic molding compounds

We report ultrasonic measurements on commercial molding compounds used in the microelectronic industries. The elastic moduli of epoxy resins loaded with silica particles have been measured using ultrasonic wave propagation. Precise measurements of velocity propagation and attenuation were carried out in a large temperature (4–420 K) and frequency (1–100 MHz) ranges. The influence of frequency on the attenuation is discussed.     

Ultrasonic wave propagation in two-phase media: Spherical inclusions

The scattering theory, recently developed via the extended method of equivalent inclusion, is used to study the propagation of time-harmonic waves in two-phase media of elastic matrix with randomly distributed elastic spherical inclusion materials. The elastic moduli and mass density of the composite medium are determined as functions of frequencies when given properties and concentration of the spheres and the matrix. Velocities and attenuation of ultrasonic waves in two-component media are determined. An averaging theorem that requires the equivalence of the strain energy and the kinetic energy between the effective medium and the original matrix with inhomogeneities is employed to derive the effective moduli and mass density. The functional dependency of these quantities upon frequencies and concentration provides a method of data analysis in ultrasonic evaluation of material properties. Numerical results for effective moduli, velocity and/or attenuation as functions of concentration of spherical inclusion material, or porosity, are graphically displayed.     

Ultrasonic properties of fluorosilicate glass-ceramics at cryogenic temperatures

The longitudinal ultrasonic wave velocity and attenuation, and shear wave velocity for machinable fluorosilicate glass-ceramic (MACOR) samples (regular shelf stock, annealed to 900°C, and 1000°C for 10 hrs) were measured as the functions of frequency and temperature with the pulse-echo method. The frequency and temperature range used were 5 MHz to 50 MHz, and 100 K to 300 K respectively. Both velocities for three samples decrease linearly with temperature, and the ultrasonic attenuation increases linearly with the frequency square, and decreases monotonically with increasing temperature. These data were used to calculate the elastic moduli, Lame parameter, and Poisson's ratio for the materials.     

An acoustic study of the relaxation properties of ZhK-1282 nematic liquid crystals in the vicinity of the nematic-isotropic phase transition

The viscous and elastic properties of a ZhK-1282 nematic liquid crystal (NLC) were studied in a temperature interval from 290 to 360 K by method of ultrasonic spectroscopy in the 3–63 MHz frequency range. The temperature dependences of the NLC density and shear viscosity are presented. The results of measurements of the velocity and attenuation of ultrasound and the shear viscosity were used to calculate the volume viscosity coefficient, the moduli of dilatation and isothermal compressibility, the relaxation times of the elastic and viscous properties, and the corresponding critical characteristics of the given NLC.     

Semi—IPN复合材料的弹性性能和内耗的超声测定

本文用超声浸液法测量了单向纤维增强热塑性树脂及其半互穿聚合物网络(Semi-IPN)复合材料的杨氏模量、剪切模量、泊松比和内耗,并对不同树脂、纤维和Semi-IPN中共混组成比对弹性性能的影响进行了研究。     

Al2O3f／Al复合材料的超声特性

测定了体积含量Ｖｆ不同（５．４，９．１和１３．６％）的Ａｌ２Ｏ３短纤维增强的铝基复合材料的纵波声速，横波声速和密度，并由此得出它们的切变模量μ和杨氏模量Ｅ，结果发现，随Ｖｆ增加，纵波声速减小，横波声速增加，与纯铝相比，μ和Ｅ均明显增大，还给出纵波超声声速和超声衰减在１００～３００Ｋ温区内的温度响应曲线。     

Stress waves in a linear viscoelastic cylinder

Steady-state solutions of stress waves travelling in a linear viscoelastic cylinder of infinite length are obtained by a method almost similar to Pochhammer-Chree's.

Torsional, longitudinal, and flexural waves are considered. The results acquired are in the form in which complex elastic moduli and propagation constant appear in place of corresponding quantities in elastic solutions. Corrections of the Rayleigh type for phase velocity and attenuation constant are also derived.     

Dynamic Acousto-Elasticity in a Fatigue-Cracked Sample

Dynamic acousto-elasticity (DAE) provides a unique way to observe nonlinear elastic features over an entire dynamic stress cycle including hysteresis and memory effects, detailing the full nonlinear behavior under tension and compression. This supplemental information cannot be observed with conventional nonlinear ultrasonic methods such as wave frequency mixing or resonance measurements, since they measure average, bulk variations of modulus and attenuation versus strain level. Where prior studies have employed DAE in volumetrically nonlinear materials (e.g., rocks, bone with distributed micro-crack networks), here we report results of DAE on the application to a single localized nonlinear feature, a fatigue crack, to characterize the nonlinear elastic response in regions of the crack length, tip, and undamaged portions of an aluminum sample. Linear wave speed, linear attenuation and third order elastic moduli (i.e., nonlinear parameters) each indicate a sensitivity to the presence of the crack, though in unique manners. The localized nature of the DAE measurement and its potential for quantifying all of the third order elastic constants makes it a promising technique for both detecting cracks, as well as providing quantitative information on the effect of the cracks on the material integrity.     

Elastic properties of rubber particles in toughened PMMA: ultrasonic and micromechanical evaluation

Ultrasonic measurements and micromechanical models are used to evaluate elastic properties of rubber particles dispersed in toughened polymers. Ultrasonic phase velocities and attenuation spectra of rubber-toughened poly(methyl methacrylate) (PMMA) with different rubber particle fractions are measured for longitudinal as well as transverse waves. The ultrasonic properties of rubber-toughened PMMA are found to depend markedly on the rubber particle fraction. The bulk and shear moduli determined from the measured velocities are in turn used to estimate those moduli of the particles based on existing micromechanics models, namely the three-phase model and the Hashin–Shtrikman upper and lower bounds. The bulk modulus of the particle estimated by the three-phase model is found to be in close agreement with the result of previous investigators. Implications of the Hashin–Shtrikman bounds for the particle moduli are also examined.     

氢对钛晶体弹性模量影响的第一原理研究

为了研究氢对钛晶体弹性模量的影响,采用基于密度泛函理论的第一原理赝势平面波方法对α-Ti、β-Ti、不同钛-氢原子比的α-Ti-H和β-Ti-H晶体模型进行了完全几何优化,计算了优化后晶体的弹性模量,通过差分电荷密度分析了氢影响钛晶体弹性模量的作用机理.计算得到的Ti/H原子比为16∶1的α-Ti-H晶体的弹性模量小于α-Ti晶体,而Ti/H原子比为8∶1的α-Ti-H晶体的弹性模量大于α-Ti晶体.不同Ti/H原子比的β-Ti-H晶体的弹性模量均大于β-Ti晶体.研究表明,氢降低了低氢含量的α-Ti-H晶体的弹性模量,提高了β-Ti-H晶体的弹性模量.     

Micro and macro material symmetries in generalized continua

Material symmetry restrictions on constitutive moduli of anisotropic elastic solids formed by different modes of aggregation (i.e. with material elements having micro and macro domains characterized by scales of different length) are investigated. An analysis is presented of the combined influence of anisotropy, substructure orientation, and long-range-order nonlocal interactions. Starting with a suitable attenuation function, a constitutive theory is constructed for a nonlocal-polar elastic solid possessing orthotropy at the nonlocal-polar level and transverse isotropy at the local polar level.     

Dynamic mechanical and ultrasonic properties of polyurea

Dynamic mechanical analysis (DMA) and ultrasonic measurements were carried out to study the temperature and frequency dependences of viscoelastic properties of polyurea. Master curves of Young’s storage and loss moduli were developed from the DMA data. Relaxation spectra were subsequently calculated by means of two approximate models, and the apparent activation energy of molecular rearrangements was also determined based on the temperature dependence of the time-temperature shift factor. Velocity and attenuation of longitudinal and shear ultrasonic waves in polyurea were measured in the 0.5-2 MHz frequency range between −60 and 30 °C temperatures. The complex longitudinal and shear moduli were computed from these measurements. Combining these results provided an estimate of the complex bulk and Young’s moduli at high frequencies. The results of the DMA and temperature and frequency shifted ultrasonic measurements are compared and similarities and deviations are discussed.     

MgO-Al2O3-SiO2-TiO2-Y2O3玻璃的弹性模量

根据硬盘基板用材料的要求，制备了MgO-Al2O3-SiO2-TiO2-Y2O3高弹性模量玻璃（120GPa)，玻璃的弹性模量随组成的变化服从Makishima-Mackenzie理论，MgO,Al2O3,TiO2,Y2O3等具有较高单位体积离解能的氧化物有利于提高玻璃的弹性模量，但玻璃弹性模量的理论计算值低于测试值，这是因为Makishima-Mackenzie理论没有考虑玻璃内阳离子的具体配位，对MgO,Y2O3堆积密度因子的堆导存在误差，因此利用Makishima-Mackenzie理论发展高弹性模量玻璃时应对MgO,Y2O3等氧化物的计算进行修正。     

Ultrasonic evaluation of fatigue damage in metal matrix composites

This paper describes an experimental nondestructive technique for fatigue damage assessment in metal matrix composites by measuring ultrasonic phase velocity and attenuation. A [0/90] SiC/Ti---15V---3Cr---3Al---3Sn metal matrix composite is considered as a model system. Cyclic loading at 50 and 70% of the ultimate sample strength were used until failure. The ultrasonic phase velocities and attenuations were measured periodically and found to be very sensitive to fatigue damage. The fatigue-induced changes in the composite elastic constants were calculated from the measured ultrasonic velocity data. For samples heat treated prior to fatigue (815°C) above the matrix β transus (about 760°C), the dominant damage mechanism is debonding of the fiber/matrix interface. We found that when samples were fatigued for less than 50% of the lifetime, the reduction of the composite moduli was linearly dependent on the number of fatigue cycles, which is explained by extension of interfacial partial debonds. This was supported by micromechanical analysis based on a partial disbond model. The rate of decrease in the composite moduli in the second half of the fatigue life was found to be lower, which may serve as a basis for estimation of the remaining fatigue life of the composite from ultrasonic velocity and attenuation measurements. The attenuation data was obtained in directions perpendicular to the fiber. A single-fiber scattering model has been used to explain the effect of the fiber/matrix interface on attenuation. Good correlation between attenuation and moduli measurements was observed.     

不同拉压模量及软化特性材料的球形孔扩张问题的统一解

对于具有不同的拉压模量及软化特性的岩土类材料,提出了不同拉压模量及软化特性的控制参数,采用双剪统一强度理论推导了球形孔扩张问题的应力及位移的统一解.分析了模量、模型和软化等控制参数对球形孔扩张时的扩张压力、塑性区开展规律及应力场的影响.结果表明:圆孔极限扩张压力,塑性区的发展规律,应力场,位移场等均随着模量控制参数、模型参数及软化参数的变化而变化,因此若采用经典的弹性理论、单一的模型参数及传统的不考虑应变软化来对岩土类的工程材料进行设计计算,必会带来较大的误差.     

Study on Dynamic Behavior and Tensile Strength of Concrete Using 1D Wave Propagation Characteristics

Concrete structures are usually fractured under dynamic loadings, so it is important to have a clear knowledge of their dynamic behavior and tensile strength. First, the principle of one-dimensional (1D) stress wave reflection and superposition at free surface is briefed, and the spalling test method based on the Hopkinson bar is presented. Then, the attenuation law of stress wave is explored and the dynamic tensile/compressive moduli of concrete are evaluated according to the wave propagation experiment. Lastly, the influences of strain rate on the spalling tensile strength and failure patterns of concrete are further analyzed. The testing results demonstrate that the attenuation of stress wave accords with an exponential law when propagating in the concrete bar. The difference between the dynamic elastic moduli of concrete in tension and in compression is minor. Spalling tensile strength is sensitive to strain rate, and there is an obvious linear correlation between dynamic increase factor (DIF) and strain rate in a log-log plot for strain rate above 1.0/s; a single fracture occurs at low strain rate, while multiple fractures are detected with increasing strain rate.