On the uniqueness and sensitivity issues in determining the elastic and plastic properties of power-law hardening materials through sharp and spherical indentation

A systematic study of the uniqueness, reversibility and sensitivity issues associated with seven indentation-based methods of property extraction demonstrates that: (i) The indentation algorithms generally identify the elastic and plastic properties of materials uniquely for most materials. (ii) The indentation forward algorithms (wherein the indention responses are determined from the elastic and plastic properties of the indented materials) and the reverse algorithms (wherein the elastic and the plastic properties of materials are extracted from the indentation responses) are distinct for each indentation method and are internally consistent in that the differences in the elastic and plastic properties determined through the reverse analysis and the ‘true’ material properties are generally small for a large number of materials, for each of the seven methods. (iii) While the differences in the indentation response parameters predicted by each of the seven indentation methods (for a particular material) could be small, there could be considerable dispersion in the elastic and plastic properties predicted by the reverse algorithms of the seven methods (for a particular set of indentation response parameters). (iv) In the forward analysis, small uncertainties in the elasto-plastic properties lead to small uncertainties in the predictions of the indentation response of materials. The sensitivity distribution is generally heterogeneous and symmetric across positive and negative variations in the material elasto-plastic properties. (v) In the reverse analysis, the elastic modulus exhibits low sensitivity, while the yield strength and the strain-hardening exponent generally exhibit high sensitivity to uncertainties in the indentation response parameters. The sensitivity distribution is heterogeneous and asymmetric across positive and negative variations in the indentation response parameters. (vi) The representative stresses are fairly robust to uncertainties in the indentation response parameters. Consequently, dual sharp and spherical indentation methods, which identify multiple representative stresses, exhibit reduced sensitivity in the determination of the plastic properties.     

Investigations of thickness-shear mode elastic constant and damping of shunted piezoelectric materials with a coupling resonator

Shear-mode piezoelectric materials have been widely used to shunt the damping of vibrations where utilizing surface or interface shear stresses. The thick-shear mode(TSM) elastic constant and the mechanical loss factor can change correspondingly when piezoelectric materials are shunted to different electrical circuits. This phenomenon makes it possible to control the performance of a shear-mode piezoelectric damping system through designing the shunt circuit. However, due to the difficulties in directly measuring the TSM elastic constant and the mechanical loss factor of piezoelectric materials, the relationships between those parameters and the shunt circuits have rarely been investigated. In this paper, a coupling TSM electro–mechanical resonant system is proposed to indirectly measure the variations of the TSM elastic constant and the mechanical loss factor of piezoelectric materials. The main idea is to transform the variations of the TSM elastic constant and the mechanical loss factor into the changes of the easily observed resonant frequency and electrical quality factor of the coupling electro–mechanical resonator. Based on this model, the formular relationships are set up theoretically with Mason equivalent circuit method and they are validated with finite element(FE) analyses. Finally, a prototype of the coupling electro–mechanical resonator is fabricated with two shear-mode PZT5 A plates to investigate the TSM elastic constants and the mechanical loss factors of different circuit-shunted cases of the piezoelectric plate. Both the resonant frequency shifts and the bandwidth changes observed in experiments are in good consistence with the theoretical and FE analyses under the same shunt conditions. The proposed coupling resonator and the obtained relationships are validated with but not limited to PZT5 A.     

Mass spring lattice modeling of the scanning laser source technique

The scanning laser source (SLS) technique is a promising new laser ultrasonic tool for the detection of small surface-breaking defects. The SLS approach is based on monitoring the changes in laser generated ultrasound as a laser source is scanned over a defect. Changes in amplitude and frequency content have been observed for ultrasound generated by the laser over uniform and defective areas. In this paper, the SLS technique is simulated numerically using the mass spring lattice model. Thermoelastic laser generation of ultrasound in an elastic material is modeled using a shear dipole distribution. The spatial and temporal energy distribution profiles of typical pulsed laser sources are used to model the laser source. The amplitude and spectral variations in the laser generated ultrasound as the SLS scans over a large aluminum block containing a small surface-breaking crack are observed. The experimentally observed SLS amplitude and spectral signatures are shown to be captured very well by the model. In addition, the possibility of utilizing the SLS technique to size surface-breaking cracks that are sub-wavelength in depth is explored.     

Acoustic field excited by a pulsed laser line source in a cylinder

The excitation and propagation of the acoustic waves in an elastic cylinder are studied by laser ultrasonics both theoretically and experimentally. The theoretical analysis of the two-dimensional acoustic field excited by a pulsed laser line source impacting on the generatrix of an elastic cylinder is presented. The dispersive properties for both cylindrical Rayleigh wave and the higher modes--whispering gallery (WG) modes are analyzed in detail. The numerical transient displacement waveforms for a detecting point located another terminal of the cylinder diameter opposite the source are calculated. The experimental excitation and detection of the acoustic waves in an aluminum cylinder are carried out on a laser ultrasonic system, which mainly consists of a Q-switched Nd:YAG laser and a laser interferometer. The wave components of bulk waves and surface waves (cylindrical Rayleigh waves and WG modes) are analyzed by comparing the numerical and experimental waveforms. The results are in good agreement.     

Elastic waves in fibre composite laminates

This paper considers the propagation of elastic waves in an eight-ply quasi-isotropic laminate arising from line sources of dislocation located at each of the seven interfaces in turn. The line source sets up a straight crested wave travelling along the laminate in a direction normal to the load line, and the elastodynamic equations within each layer are solved by taking the Laplace transform with respect to time and the Fourier transform with respect to the spatial coordinate in the direction of propagation. The resulting system of six first-order differential equations in each layer is solved to obtain the transforms of the displacement and stress components throughout the laminate. The time history of any displacement or stress component at any location may then be recovered by numerical inversion of the double transform. Examples are shown of the time history of the normal displacement of the top surface of the laminate at a distance of 20 plate thicknesses from the plane of action of the sources. The numerical inversion involves a summation over different modes of Rayleigh-Lamb waves in the laminate and contributions to the overall response from some of the individual modes are displayed.     

Acoustic emission during laser annealing of silicon single crystals

The acoustic response of silicon single crystals to the action of a millisecond laser pulse, with an excitation wavelength 1.06 μm, has been investigated. It has been discovered for the first time that additional acoustic emission, delayed in time with respect to the photoacoustic response, is observed for laser energy flux density above the threshold corresponding to surface melting. The delay time depends linearly on the laser radiation power and varies from one to tens of milliseconds. It is shown, by comparing the parameters of the acoustic emission with the dynamical development of thermoelastic stresses in the laser action zone as well as with the kinetics of melting of the irradiated surface, that crack formation under the action of the thermoelastic stresses is the source of the additional acoustic emission. Fiz. Tverd. Tela (St. Petersburg) 39, 505–509 (March 1997)     

Wave field localization in a prestressed functionally graded layer

Characteristic features of wave field formation caused by a surface source of harmonic vibration in a prestressed functionally graded layer are investigated. It is assumed that the elastic moduli and the density of the material vary with depth according to arbitrary laws. The initial material of the medium is represented by a model hyperelastic material with third-order elastic moduli. The boundary-value problem for a set of Lamè equations is reduced to a set of Cauchy problems with initial conditions, which is solved by the Runge–Kutta–Merson method modified to fit the specific problem under study. Considering shear vibrations of a functionally graded layer as an example, effects of the type of its inhomogeneity, variations in its properties, and nature of its initial stressed state on the displacement distribution in depth are investigated. Special attention is paid to characteristic features of displacement localization in a layer with an interface-type inclusion near critical frequencies. A direct relation between the inhomogeneous layer structure and the type of displacement localization in depth is demonstrated. It is found that the role of initial stresses and variations in material parameters considerably increases in the vicinities of critical frequencies.     

Experimental determination of third-order elastic constants of diamond

To determine the nonlinear elastic response of diamond, single crystals were shock compressed along the [100], [110], and [111] orientations to 120 GPa peak elastic stresses. Particle velocity histories and elastic wave velocities were measured by using laser interferometry. The measured elastic wave profiles were used, in combination with published acoustic measurements, to determine the complete set of third-order elastic constants. These constants represent the first experimental determination, and several differ significantly from those calculated by using theoretical models.     

Forced vibration of a damped sandwich beam subjected to moving forces

The response of a sandwich beam subjected to moving forces (constant as well as pulsating) is analyzed by the use of Fourier and Laplace transforms and compared with the response of an equivalent elastic beam. The results indicate that the critical speed of force on a sandwich beam is always greater than that on an elastic beam of identical mass per unit length and flexural rigidity, and depends on its geometric and shear parameters. For subcritical speeds, the maximum deflection of a sandwich beam is shown to occur earlier than that of an equivalent elastic beam. An increase in the core shear stiffness is shown to be beneficial in reducing the dynamic magnification of the central deflection of the sandwich beam.     

Elastic constants of layers in isotropic laminates

The individual laminae elastic constants in multilayer laminates composed of dissimilar isotropic layers were determined using ultrasonic-resonance spectroscopy and the linear theory of elasticity. Ultrasonic resonance allows one to measure the free-vibration response spectrum of a traction-free solid under periodic vibration. These frequencies depend on pointwise density, laminate dimensions, layer thickness, and layer elastic constants. Given a material with known mass but unknown constitution, this method allows one to extract the elastic constants and density of the constituent layers. This is accomplished by measuring the frequencies and then minimizing the differences between these and those calculated using the theory of elasticity for layered media to select the constants that best replicate the frequency-response spectrum. This approach is applied to a three-layer, unsymmetric laminate of WpCu, and very good agreement is found with the elastic constants of the two constituent materials.     

Reconstruction of the dynamic contact stresses in an elastic layer from the displacements of its free surface

An inverse problem on the reconstruction of the wave field of contact stresses produced by an external load in an elastic layer from the displacements of its free surface is considered for the model of forced steady-state vibrations in the approximation of plane deformations. The solution is constructed using two approaches: (1) a reduction of the problem to the Fredholm integral equation of the first kind with the use of the Tikhonov regularization and (2) an expansion of the solution in a discrete set of waves. It is shown that both approaches are approximately equivalent in the model under consideration. Possibilities for an adequate reconstruction of the source field from far-zone measurements of a finite number of propagating wave modes are analyzed.     

Simulation of elastic displacement of surface during laser short pulse heating of gold

The laser short pulse heating initiates nonequilibrium heating of the substrate material, which in turn results in the thermal stresses developing in the region below the surface. The surface temperature can be measured possibly through the monitoring of the resulting surface displacement. This requires in detail investigation into the surface displacement and surface temperature rises across the heated spot during the laser short pulse heating process. In the present study, the laser short pulse heating of gold surface is considered and the temperature rise at the surface and elastic displacement of the surface are investigated. The spatial and temporal distributions of surface displacement and surface temperature are predicted and the elastic response of the substrate material due to temperature rise is explored. It is found that the temporal and spatial distributions of the surface displacement do not follow the temperature rise at the surface. Consequently, care should be taken when measuring the temperature rise at the surface by means of monitoring the surface displacement during a laser short pulse heating process.     

Equivalent charge of photons and neutrinos in a plasma

It is suggested that it is possible to define an equivalent electric charge for an intense laser pulse (which can be described as a photon bunch) propagating in a plasma. It is also shown that this equivalent charge can be a source of new radiation processes in an inhomogeneous plasma. The results are extended to the case of a neutrino bunch, which is coupled to the plasma by weak nuclear forces.     

The effect of fractional thermoelasticity on a two-dimensional problem of a mode I crack in a rotating fiber-reinforced thermoelastic medium

This article is concerned with the effect of rotation on the general model of the equations of the generalized thermoe- lasticity for a homogeneous isotropic elastic half-space solid, whose surface is subjected to a Mode-I crack problem. The fractional order theory of thermoelasticity is used to obtain the analytical solutions for displacement components, force stresses, and temperature. The boundary of the crack is subjected to a prescribed stress distribution and temperature. The normal mode analysis technique is used to solve the resulting non-dimensional coupled governing equations of the problem. The variations of the considered variables with the horizontal distance are illustrated graphically. Some particular cases are also discussed in the context of the problem. Effects of the fractional parameter, reinforcement, and rotation on the varia- tions of different field quantities inside the elastic medium are analyzed graphically. Comparisons are made between the results in the presence and those in the absence of fiber-reinforcing, rotating and fractional parameters.     

The effect of rotation on plane waves in generalized thermo-microstretch elastic solid with one relaxation time for a mode-I crack problem

The present paper is aimed at studying the effect of rotation on the general model of the equations of the generalized thermo-microstretch for a homogeneous isotropic elastic half-space solid,whose surface is subjected to a Mode-I crack problem.The problem is studied in the context of the generalized thermoelasticity Lord-S hulman’s (L-S) theory with one relaxation time,as well as with the classical dynamical coupled theory (CD).The normal mode analysis is used to obtain the exact expressions for the displacement components,the force stresses,the temperature,the couple stresses and the microstress distribution.The variations of the considered variables through the horizontal distance are illustrated graphically.Comparisons of the results are made between the two theories with and without the rotation and the microstretch constants.     

Proposal of refined interface models and their application for free-edge effect

Two interface models based on physical considerations are proposed to analyze the freeedge effects in unidirectional multilayered composites. The first model is a transition behavior law describing the graded properties of the interlayer between two adjacent layers. It is defined according to the stacking direction and based on a microscopic analysis of the fiber distribution in the vicinity of the interlayer. Used in a numerical simulation, this model gives accurate stress distributions in the laminate, including the interlaminar stresses at the free-edge that are not singular. The second model utilizes an interface law, defined on the material surface, resulting from the asymptotic resolution of an elastic problem pertaining to the interlayer and simulating a very thin flexible layer. This model also gives no singular free-edge interlaminar stresses close to those obtained with the first model.     

Analysis of crack propagation data for a strain ageing and a stabilized mild steel tested under R=0 and R=−1 loading conditions

Comparative studies of crack propagation in a strain ageing and a stabilized mild steel were carried out under axial loadings of the R = 0 and R = ?1 types. The results show the rate of fatigue crack propagation is dependent on both the tensile and the compressive stresses in the fatigue cycles, the compression stresses being less effective than the equivalent tensile stresses in causing crack growth. An equation is presented relating the rate of fatigue crack growth to a stress intensity range which is factored to allow for the variations in fatigue damage associated with the tensile and compressive parts of the stress cycle.     

Generation of a uniform line source using a binary filter

A uniform or nearly uniform 10 mm long line source has been generated from a gaussian laser beam using a binary filter. This is done by processing the binary filter throughout a well corrected optical system, so that the equivalent of a continuous inverse gaussian filter is obtained at the final image plane. This equivalent continuous filter generates a uniform line source with maximum conversion efficiency of 50%.     

Effect of porosity on the laser induced damage threshold of porous anodic alumina films

Thermal stress of porous alumina films has been simulated by finite element method based on thermal transfer equation and thermal stress formulas. The influence of equivalent thermal conductivity and elastic modulus on laser induced damage threshold (LIDT) has been studied. It was found that the biggest circumferential tensile stress will be small with the porosity from 15% to 35%, and it effectively improves the LIDT. The equivalent thermal conductivity and LIDT decreases with the increase of porosity. The equivalent elastic modulus decreases and LIDT increase with the increase of porosity.     

基于能量转换原理的磁电层合材料低频磁电响应分析

提出了一种基于能量转换原理的磁致伸缩/压电层合材料低频磁电响应模型,并对不同层合结构的磁电响应特性进行了对比研究.该模型假定层合材料层间能量传递通过层间剪切力来实现,利用应力函数法分析了磁致伸缩层和压电层的应力与应变,求出了磁致伸缩层的应变能和存储磁场能以及压电层的应变能和电场能;利用Hamilton最小能量原理求出了层间剪切力的大小,获得了开路状态下层合材料的低频磁电响应模型.发现磁电电压系数与磁致伸缩材料的磁导率、泊松比、磁机耦合系数以及压电材料的泊松比、机电耦合系数等有关,并对这些参数的影响进行了分析.同时对两层和三层结构的层合材料磁电特性进行了对比研究,发现层合结构不同则获得的磁电系数公式不同,用相应的公式计算得到的误差才会最小.研究结果表明,本文的理论误差小于6.5%,与其他方法相比,本文的理论模型能更好地描述磁电层合材料的低频磁电响应特性.