Failure waves in glass under dynamic compression

Abstract

Plate impact (I-d strain) and bar impact (I-d stress) experiments were performed on soda lime glass and pyrex glass. Embedded manganin gauges were used to monitor stress-time profiles in both types of experiments. In the plate impact experiments we found that glass not only fails through inelastic (or densification) deformation, but also through a unique failure process which gives rise to a failure wave first observed by Kanel et al. in the Soviet Union in 1990. In the present work three independent observations were made that support the existence of failure wave in glass: (i) the spall strength below and above the HEL is zero behind the failure wave, (ii) a small recompression is present in the longitudinal gauge (embedded between glass and PMMA) profile due to the reflections of release waves from the advancing failure wave, and (iii) transverse stress (measured by transverse gauge) increases on the arrival of the failure wave. The transverse stress increases because the glass loses its shear strength as a result of the arrival of the failure wave. The speed of the failure wave is about 1.5–2mm/μs. In the experiments on pyrex bars we used high speed Imacon framing camera to monitor the speed of the failure front. We found that pyrex bars fail through a failure front propagating across the cross section of the bar. The speed of the failure front is a function of the impactor (pyrex bar or steel plate) velocity. The speed increases from 2.3 mm/μs, corresponding to impact velocity of 125 m/s, to 5.2mm/μs for impact velocity of 330 m/s.     

Soda lime玻璃材料中失效波形成和传播研究

 为了研究冲击载荷作用下Soda lime玻璃材料中失效波的形成和传播,通过轻气炮加载平板撞击实验,采用双螺旋锰铜压阻传感器,在一发实验中同时测量4种不同厚度试件背面与有机玻璃背板间界面处的纵向应力时程曲线,根据测量结果得到试件中失效波的传播轨迹。通过改变碰撞速度,对不同加载条件下的失效波形成和传播规律进行了研究,结果表明,Soda lime玻璃材料在冲击作用下产生失效波所需的延迟时间随冲击载荷的增加而减小,失效波传播速度随冲击载荷的增加而增加。最后采用弹性微裂纹统计模型描述冲击载荷作用下Soda lime玻璃的破坏机制,并将模型嵌入LS-DYNA有限元程序中,模拟试件在不同加载条件下的平板碰撞,所得横向应力和自由面粒子速度曲线均可用于表征失效波破坏现象。根据数值模拟结果分析失效波的传播轨迹,与实验测量结果符合较好。     

Impulsive fracture of silicon by elastic surface pulses with shocks

During nonlinear evolution of surface acoustic waves (SAWs) stress increases with propagation, and may cause fracture of brittle materials. This effect was used to evaluate the strength of crystalline silicon with respect to impulsive load in the nanosecond time scale without using seed cracks. Short SAW pulses propagating in the [11(macro)2] direction on the Si(111) plane induce fracture at significantly lower SAW amplitudes than the mirror symmetric wave propagating in the [112(macro)] direction. This effect is explained by the differences in elastic nonlinearity of the two propagation directions.     

A high-speed photographic study of fast cracks in shocked diamond

Six fracture surfaces have been observed extending at velocities between c_R (the Rayleigh wave velocity) and 1.3c_R in high-speed photographs of four diamond specimens. The diamonds were embedded in a transparent polymer and shocked in plate impact experiments. The measured velocities exceed limiting velocities proposed in theoretical and practical studies of single mode I cracks in diamond. The fracture surfaces probably extend by initiation and coalescence of multiple tensile fractures along a single cleavage plane. This mechanism is dependent on the suppression of cracks branching from the {111} growth plane in diamond and considers the population of flaws near a propagating crack tip.     

Elastic response of an acoustic coating on a rib-stiffened plate

This paper develops a three-dimensional analytical model of a fluid-loaded acoustic coating affixed to a rib-stiffened plate. The system is loaded by a plane wave that is harmonic both spatially and temporally. The model begins with Navier-Cauchy equations of motion for an elastic solid, which produces displacement fields that have unknown wave propagation coefficients. These are inserted into stress equations at the boundaries of the plate and the acoustic coating. These stress fields are coupled to the fluid field and the rib stiffeners with force balances. Manipulation of these equations develops an infinite number of indexed equations that are truncated and incorporated into a global matrix equation. This global matrix equation can be solved to determine the wave propagation coefficients. This produces analytical solutions to the systems’ displacements, stresses, and scattered pressure field. This model, unlike previously developed analytical models, has elastic behavior and thus incorporates higher order wave motion that makes it accurate at higher wavenumbers and frequencies. An example problem is investigated for three specific model results: (1) the dynamic response, (2) a sonar array embedded in the acoustic coating, and (3) the scattered pressure field. An expression for the high frequency limitation of the model is derived. It is shown that the ribs can have a significant impact on the structural acoustic response of the system.     

Thermoelastic wave induced by pulsed laser heating

In this work, a generalized solution for the thermoelastic plane wave in a semi-infinite solid induced by pulsed laser heating is developed. The solution takes into account the non-Fourier effect in heat conduction and the coupling effect between temperature and strain rate, which play significant roles in ultrashort pulsed laser heating. Based on this solution, calculations are conducted to study stress waves induced by nano-, pico-, and femtosecond laser pulses. It is found that with the same maximum surface temperature increase, a shorter pulsed laser induces a much stronger stress wave. The non-Fourier effect causes a higher surface temperature increase, but a weaker stress wave. Also, for the first time, it is found that a second stress wave is formed and propagates with the same speed as the thermal wave. The surface displacement accompanying thermal expansion shows a substantial time delay to the femtosecond laser pulse. On the contrary, surface displacement and heating occur simultaneously in nano- and picosecond laser heating. In femtosecond laser heating, results show that the coupling effect strongly attenuates the stress wave and extends the duration of the stress wave. This may explain the minimal damage in ultrashort laser materials processing. Received: 23 May 2000 / Accepted: 26 May 2000 / Published online: 20 September 2000     

Measurement of surface figure of plane optical surfaces with polarization phase-shifting Fizeau interferometer

A Fizeau interferometer based set up for measurement of surface forms of plane optical surfaces has been discussed. Phase shifting interferometry has been applied using polarization phase shifter. A linearly polarized (632.8 nm) He–Ne laser has been used as the source. Light reflected from the object and the reference/master surfaces are made circularly polarized in opposite senses by means of two properly oriented quarter wave retardation plates placed at appropriate positions, one inside and other outside the interference cavity of the interferometer, and phase shifts are introduced between the object and the reference/master waves by varying angular orientation of a polarizer/analyzer. Final result is made free from any residual wave-front aberrations introduced by the (intra-cavity) wave plate by subtracting phase values obtained by PSI technique between a high optical quality master surface and the reference surface from that obtained for the test object surface with respect to the same reference surface for each point of the interference field. Results are shown for a plane surface.Advantages of the technique presented are linearity and high accuracy in phase stepping, no perturbation of the interference cavity during the phase shifting and possibility of real time or dynamic interferometry.     

Investigation of a silicon-based one-dimensional phononic crystal plate via the super-cell plane wave expansion method

The super-cell plane wave expansion method is employed to calculate band structures for the design of a silicon-based one-dimensional phononic crystal plate with large absolute forbidden bands. In this method, a low impedance medium is introduced to replace the free stress boundary, which largely reduces the computational complexity. The dependence of band gaps on structural parameters is investigated in detail. To prove the validity of the super-cell plane wave expansion, the transmitted power spectra of the Lamb wave are calculated by using a finite element method. With the detailed computation, the band-gap of a one-dimensional plate can be designed as required with appropriate structural parameters, which provides a guide to the fabrication of a Lamb wave phononic crystal.     

二维晶格中激波的传播和自由面反射的分子动力学数值研究

本文用分子动力学方法研究和计算了面心晶体中沿(1、0、0)面或休心晶体中沿(1、1、0)面上激波的传播和自由面反射现象。在所研完的范围内(u_p=10~75×10⁴cm/sec)粒子速度沿平均值的振动是不衰减的,激皮的传播速度和波后粒子速度的平均值呈线性关系。激波在自由面反射后,自由表面附近的粒子速度为活塞速度的二倍,这和宏观力学结果相同。此外,还出现最外层分子不断地以更高的速度被抛离的现象,这和宏观测量的微物质喷射现象亦类似。在稍后的阶段,还显示出内部粒子间被拉开的"微断裂"现象。     

Ultrasonic SH wave velocity in textured aluminium plates

Neutron diffraction has been used to measure the crystallite orientation distribution function for a sample of rolled aluminium plate. Based on this study an expression is given for the ultrasonic velocity of the fundamental horizontally polarized shear (SH) wave propagating in the plane of the plate at an angle θ to the rolling direction. This expression is correct to second order in the leading texture component and is compared with the exact numerical result and with measurements of the SH wave velocity for this plate. In textured materials the group and phase velocities are not, in general, parallel and an expression for the angle between them is derived. Inclusion of this effect leads to better agreement between experiment and theory. The results have application to the texture-independent determination of stress with ultrasonics recently proposed by MacDonald and Thompson et al.     

金属薄板弹性各向异性检测

当平面声波入射到液体中的金属薄板上时，透射系数将随声波入射角变化，根据这一规律，能够准确地测定声波入射面与金属薄板交线方向上金属板材料的弹性常数，测得金属薄板面内不同方向的弹性常数，对金属薄板弹性各向异性情况将有一清蜥的认识，由于测试过程采用微机控制、数据采集和处理，实现了各向异性测量的全自动化，该方法测试时间短、所需样品小且加工方便，并可测试金属薄板弹性各向异性的均匀度。     

Real-time stress detection of monocrystalline silicon by laser irradiation using Mach–Zehnder interferometry

The effect of changes in laser-induced stress upon irradiation of monocrystalline silicon was studied in detail using Mach–Zehnder interferometer, high speed camera and computer processing system, real-time detection of stress distribution and stress evolvement under different laser fluences and pulse widths. After irradiation, the changes of interference fringes were used to calculate the stress value. The results show that the stresses increased with the increase of the laser fluence. The formation of stress could be explained using thermoelastic theory. The cleavage plane’s dislocation appears in the following sequence: (1 1 1) plane appears and then the dislocation slip of (1 1 0) cleavage plane appears. In addition, it is found that cleavage plane of (1 1 1) mainly exist in the spot and cleavage plane of (1 1 0) mainly exists in the vicinity of spot radius. Stress areas mainly exist in the thin layer on the surface of silicon. Furthermore, stress field was analysed by the finite-element method to get a better understanding of the formation and distribution of stress. Under the same experimental conditions, the numerical results are in agreement with the experimental values.     

Relationship between Rayleigh wave polarization and state of stress

This research develops an analytical model (using Stroh's formalism) to predict the affect of applied stress on the wave speed and the polarization of Rayleigh surface waves. Simulation results are then used to demonstrate that the polarization of a Rayleigh wave (which is reference-free) could be more sensitive than wave speed as an indicator of the state of stress.     

Local instability of a plate with a circular nanohole under uniaxial tension

The problem of the influence of surface tension on the local instability of a plate under tension is investigated by the example of an infinite plate with a circular nanohole. The method for solving the problem under consideration is based on a previously developed approach for solving problems on local buckling of a thin uniaxially stretched elastic sheet with variously shaped macroholes. The critical (Euler) load, at which the instability occurs, is sought by the Ritz method in framework of the linearized Karman set of equations based on the principle of virtual motions as the smallest positive load giving the minimum of the potential energy of the plate deformation. The generalized plane stress state of the plate with a nanohole is found for its application taking into account surface stresses. The linearized Gurtin-Murdoch relationships for the surface elasticity, the generalized Young-Laplace law, and the Goursat-Kolosov complex potentials are used when deriving analytical dependences for the stress in this plane problem. The deflection of the plate is represented by a double row satisfying the damping condition at infinity and ensuring freedom of motion of hole edges. Numerical calculations are performed for the aluminum plate. Two variants of the elastic properties of a circular hole are considered. Zones of compressing circumferential tensions near the edges of the circular hole with radii 1, 2, and 4 nm under uniaxial tension are constructed. It is shown that the account of the surface stresses decreases the critical load, which has a tendency to decrease in both cases with a decrease in the cut radius in a nanometer variation range.     

Sensitivity of Homogeneity Mapping of Dielectric Wafer Using Millimeter Waves

A plane electromagnetic wave normally falling on a surface of a dielectric plate has been considered to investigate the sensitivity of the dielectric constant homogeneity mapping in the dielectric wafer by measuring the phase and/or the amplitude of the millimeter wave reflected from or transmitted through it. Measurement conditions at which the highest sensitivity might be achieved are established. The sensitivity at Fabry-Perot resonance conditions as well as at frequency shifted from resonance has been considered.     

Rayleigh surface waves in a plate

In the article the analysis of a monochromatic elastic surface wave in an unlimited plate of limited thickness whose opposite surfaces are planar and mutually parallel, made of an elastic isotropic material of a constant density is described. Equations are calculated for the wave number calculation — speed of surface wave propagation, and an equation for the calculation of the vector components deformation (component trajectory) of the elastic medium.     

Watching ripples on crystals

We present a new method for imaging surface phonon focusing and dispersion at frequencies up to 1 GHz that makes use of ultrafast optical excitation and detection. Animations of coherent surface phonon wave packets emanating from a point source on isotropic and anisotropic solids are obtained with micron lateral resolution. We resolve rounded-square shaped wave fronts on the (100) plane of LiF and discover isolated pockets of pseudosurface wave propagation with exceptionally high group velocity in the (001) plane of TeO(2). Surface phonon refraction and concentration in a minute gold pyramid is also revealed.     

The effect of boundary conditions on guided wave propagation in two-dimensional models of healing bone

Guided wave propagation has recently drawn significant interest in the ultrasonic characterization of bone. In this work, we present a two-dimensional computational study of ultrasound propagation in healing bones aiming at monitoring the fracture healing process. In particular, we address the effect of fluid loading boundary conditions on the characteristics of guided wave propagation, using both time and time-frequency (t-f) signal analysis techniques, for three study cases. In the first case, the bone was assumed immersed in blood which occupied the semi-infinite spaces of the upper and lower surfaces of the plate. In the second case, the bone model was assumed to have the upper surface loaded by a 2mm thick layer of blood and the lower surface loaded by a semi-infinite fluid with properties close to those of bone marrow. The third case, involves a three-layer model in which the upper surface of the plate was again loaded by a layer of blood, whereas the lower surface was loaded by a 2mm layer of a fluid which simulated bone marrow. The callus tissue was modeled as an inhomogeneous material and fracture healing was simulated as a three-stage process. The results clearly indicate that the application of realistic boundary conditions has a significant effect on the dispersion of guided waves when compared to simplified models in which the bone's surfaces are assumed free.     

强激光加载铝材料动态损伤特性及其微介观结构观测

在神光-Ⅱ装置上利用强激光加载铝材料进行高应变率(高于106s-1)层裂实验,研究不同初始温度下高纯铝材料的动态损伤特性。采用任意反射面速度干涉仪测量样品自由面速度剖面,由自由面速度剖面计算纯铝样品层裂强度与屈服应力。结果表明:随着温度升高,材料层裂强度减小,屈服应力增大。对激光加载前后样品进行金相分析,观察不同初始温度下纯铝材料的微介观结构变化及其损伤特性。结果表明:随着温度升高,样品晶粒尺度缓慢增大,但在873K(近熔点)时晶粒尺度急剧增加;层裂面附近小孔洞数目较多,孔洞尺寸也较大,而远离层裂面处,孔洞数目相对较少,且尺寸也较小;材料的断裂方式随温度升高由沿晶断裂为主逐渐变为穿晶断裂为主。     

高纯铝层裂的自由面速度剖面特征分析

 采用任意反射面激光干涉测速（VISAR）系统,对高纯铝（纯度为99.999%）材料开展了层裂实验研究,获得了未完全层裂和完全层裂样品的自由面速度剖面。基于实验测量中观察到的层裂回跳（Pullback）信号的脉冲宽度、速度幅值差异以及回跳信号上升过程中的两次速度斜率变化特征,详细讨论了高纯铝材料从出现损伤到完全断裂的过程中波剖面演化的行为特征。结合“软回收”样品的细观分析,指出这些自由面速度变化特征可能与材料中应力波的能量释放速率以及材料中晶粒的断裂行为密切相关。研究结果可以为延性金属损伤断裂的演化过程提供有意义的认识。