Theoretical and experimental investigation of the photoacoustic effect in solids with residual stresses

Modern experiment and theory in the field of residual stress detection by the photoacoustic method are summarized and analyzed. A multimode approach based on the simultaneous application of several photothermal and photoacoustic methods is proposed for the study of thermal and thermoelastic effects in solids with residual stress. Some experimental results obtained within the framework of this approach for Vickers indentation zones in ceramics are presented. The effect of annealing on the photoacoustic, piezoelectric signal for ceramics and the influence of the given external loading on the behavior of the photoacoustic signal near the radial crack tips is investigated. It is experimentally shown that both compressive and shear stresses contribute to the photoacoustic signal near the radial crack tips. The model of the photoacoustic, thermoelastic effect in solids with residual stress is proposed. It is based on the modified Murnaghan model of non-linear elastic bodies, which takes into account a possible dependence of the thermoelastic constant on stress. This model is further developed to explain the photoacoustic signal behavior near the radial crack tips. It is demonstrated that this model of the photoacoustic effect agrees qualitatively with the available experimental data.     

Effect of an external mechanical load on elastic stresses near radial cracks in Al<Subscript>2</Subscript>O<Subscript>3</Subscript>-SiC-TiC ceramics: Photoacoustic study

The variation of the photoacoustic signal near the mouths of radial cracks in Vickers-indented externally loaded Al₂O₃-SiC-TiC ceramics is studied. A theoretical model of a photoacoustic signal that is recorded near the mouths of vertical cracks is suggested. Indentation zones in Al₂O₃-SiC-TiC ceramics are visualized by laser scanning photoacoustic microscopy. The sensitivity of the photoacoustic method with piezoelectric detection of signals to both normal and shear stresses acting on a crack is demonstrated. Experimental and theoretical data for the effect of external stresses on the photoacoustic signal near the mouths of radial cracks are compared. For the ceramics under study, agreement is fairly good. It is shown that the strain coefficients near the mouths of vertical cracks can be determined from photoacoustic experimental data.     

Application of optical parametric oscillators to photoacoustic studies in semiconductors

The results of the application of an optical parametric oscillator to photoacoustic studies of semiconductors are reported. The investigation of the photoacoustic signal, waveform and amplitude in Ge, Si, GaAs, GaSb in the 450–1770 nm range allows to make conclusions about the contribution of thermoelastic and deformation mechanisms to pressure pulse formation. At shorter wavelengths, the usual thermoelastic mechanism of acoustic-signal generation is prevailing. At longer wavelengths, for photon energies close to the energy gap, the efficiency of pressure generation in semiconductors with negative deformation potential (Ge, GaAs, GaSb) grows up sharply because of the transition to volume absorption and turning on the deformation mechanism. The experimentally measured values of the photoacoustic pressure are in good agreement with the result of quantitative estimations.     

Method of bimodal photoacoustic and ultrasound microscopy for simultaneous structural and functional diagnostics of biotissues

The excitation of external electrode of focused photoacoustic (PA) detector by the backscattered laser radiation can ensure a cost-effective upgrade from single-modality PA microscopy to dual-modality PA/US imaging. In this work we approbated thermoelastic generation of probing ultrasonic pulses for bimodal photoacoustic (PA) and optically mediated Ultrasound (US) microscopy in vivo, using single optical pulse delivered from tunable laser to form both PA and US A-scans. The presented results of bimodal in vivo visualization of rat brain provide with the experimental evidence, that the proposed approach can be used for both functional and structural bioimaging simultaneously.     

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)     

Photoacoustic cavitation in spherical and cylindrical absorbers

Photomechanical damage in absorbing regions or particles surrounded by a non-absorbing medium is investigated experimentally and theoretically. The damage mechanism is based on the generation of thermoelastic pressure by absorption of pulsed laser radiation under conditions of stress confinement. Principles of photoacoustic sound generation predict that the acoustic wave generated in a finite-size absorbing region must contain both compressive and tensile stresses. Time-resolved imaging experiments were performed to examine whether the tensile stress causes cavitation in absorbers of spherical or cylindrical shape. The samples were absorbing water droplets and gelatin cylinders suspended in oil. They were irradiated with 6-ns-long pulses from an optical parametric oscillator. Photoacoustic cavitation was observed near the center of the absorbers, even if the estimated temperature caused by absorption of the laser pulse did not exceed the boiling point. The experimental findings are supported by theoretical simulations that reveal strong tensile stress in the interior of the absorbers, near the center of symmetry. Tensile stress amplitudes depend on the shape of the absorber, the laser pulse duration, and the ratio of absorber size to optical absorption length. The photoacoustic damage mechanism has implications for the interaction of ns and sub-nslaser pulses with pigmented structures in biological tissue. Received: 9 October 1998 / Accepted: 5 January 1999 / Published online: 31 March 1999     

Microcavity dynamics during laser-induced spallation of liquids and gels

Photomechanical fracture induced by thermoelastic stress waves is an important mechanism of tissue ablation by short laser pulses. In this study, we present experimental investigations of the fracture process in ductile, water-containing materials and compare the results with a theoretical calculation. The model describes cavitation caused by the negative part of a bipolar thermoelastic stress wave. Pulses from aQ-switched, frequency-doubled Nd:YAG laser with 8 ns duration were used to irradiate dyed water and gelatine with variable absorption coefficient. Cavitation and ablation were observed with various time-resolved methods such as stress detection, video imaging and an optical pump-probe technique for the detection of individual cavities. Quantitative agreement between experiment and simulation could be achieved in the case of cavity lifetimes, especially at low laser fluence where the bubble density is low and no coalescence takes place. An increase of the threshold energy density for ablation with rising absorption coefficient and a distortion of the thermoelastic wave in the presence of cavitation were experimentally observed and could be qualitatively explained by use of the simulation. The results obtained in this study should facilitate the choice of the optimal laser parameters for photomechanical tissue ablation.     

Free vibration analysis of a hanged clamped-free cylindrical shell partially submerged in fluid: The effect of external wall,internal shaft,and flat bottom

The free flexural vibration of a hanged clamped-free cylindrical shell with various boundary conditions partially submerged in a fluid is investigated. Specifically, the effects of the boundary conditions such as the existence of the external wall, internal shaft, and bottom on the natural vibration characteristics of the partially submerged cylindrical shell are investigated both theoretically and experimentally. The fluid is assumed to be inviscid and irrotational. The cylindrical shell is modeled by using the Rayleigh–Ritz method based on the Sanders shell theory. The kinetic energy of the fluid is derived by solving a boundary-value problem related to the fluid motion. The theoretical predictions were in good agreement with the experimental results validating the theoretical approach developed in this study. The effects of the external wall, internal shaft, and bottom on the natural vibration characteristics can be neglected when its boundaries are not very close to the shell structure.     

Thermoelastic damping in torsion microresonators with coupling effect between torsion and bending

Predicting thermoelastic damping (TED) is crucial in the design of high Q MEMS resonators. In the past, there have been few works on analytical modeling of thermoelastic damping in torsion microresonators. This could be related to the assumption of pure torsional mode for the supporting beams in the torsion devices. The pure torsional modes of rectangular supporting beams involve no local volume change, and therefore, they do not suffer any thermoelastic loss. However, the coupled motion of torsion and bending usually exists in the torsion microresonator when it is not excited by pure torque. The bending component of the coupled motion causes flexural vibrations of supporting beams which may result in significant thermoelastic damping for the microresonator. This paper presents an analytical model for thermoelastic damping in torsion microresonators with the coupling effect between torsion and bending. The theory derives a dynamic model for torsion microresonators considering the coupling effect, and approximates the thermoelastic damping by assuming the energy loss to occur only in supporting beams of flexural vibrations. The thermoelastic damping obtained by the present model is compared to the measured internal friction of single paddle oscillators. It is found that thermoelastic damping contributes significantly to internal friction for the case of the higher modes at room temperature. The present model is validated by comparing its results with the finite-element method (FEM) solutions. The effects of structural dimensions and other parameters on thermoelastic damping are investigated for the representative case of torsion microresonators.     

Effects of intrinsic anharmonicity in the Mie–Grüneisen equation of state and higher order corrections

The usual quasiharmonic Mie–Grüneisen (MG) equation of state is modified by the inclusion of ‘intrinsic anharmonicities’, which have been considered up to now primarily in the high temperature limit. A comparison with experimental data for the rare gas solids, Ar, Kr and Xe and for MgO reveals that the anharmonic contributions cannot be represented perfectly within the MG approximation. A small but significant modification of the MG approach is presented to estimate intrinsic anharmonic contributions within a mean-field approximation for the thermal part of the internal energy. This estimate results in reasonable interpolations to low temperatures, where quantum effects are dominant. The present approach is also compared with more restricted recent theoretical results.     

Infrared-laser photoacoustic spectroscopy

This paper reviews the applications of IR-laser photoacoustics to trace-gas monitoring as well as to spectroscopic studies on absorbing liquids.In the first part we present a stationary, dual-beam CO-laser and a mobile CO₂-laser photoacoustic system which have both been applied to the monitoring of various gaseous pollutants. Emphasis is put on selectivity, sensitivity and on temporal resolution. Novel cell designs and experimental techniques and an iterative procedure for the analysis of photoacoustic spectra of multicomponent mixtures are introduced. New results are presented for measurements on car and industrial exhausts as well as on ambient air.The second part is devoted to theoretical and experimental photoacoustic studies on strongly absorbing liquids, in particular on the investigation of different boundary conditions. A characteristic enhancement of the photoacoustic signal in the liquid is obtained if a liquid or solid surface layer is present. This new phenomenon permits the analysis of surface films with a thickness of ⩾ 1 μm. Furthermore, the photoacoustic in-situ monitoring of the polymerization process on a liquid surface is presented for the first time.     

Energy efficiency of near infrared cobalt luminscence in ZnSe:Co determined by a photoacoustic method

The paper presents results of computations of the energy efficiency of the cobalt luminescence in ZnSe:Co determined by the photoacoustic method. The transmission spectra, photoacoustic experimental and theoretical spectra, and the frequency dependence on the photoacoustic amplitude characteristics are presented. From them, the energy efficiency of Co²⁺ the near infrared luminescence (3200 nm) was computed in the frame of new proposed photoacoustic model of computations of the luminescence energy efficiency.     

Bulk-wave and guided-wave photoacoustic evaluation of the mechanical properties of aluminum/silicon nitride double-layer thin films

The development of devices made of micro- and nano-structured thin film materials has resulted in the need for advanced measurement techniques to characterize their mechanical properties. Photoacoustic techniques, which use pulsed laser irradiation to nondestructively induce very high frequency ultrasound in a test object via rapid thermal expansion, are suitable for nondestructive and non-contact evaluation of thin films. In this paper, we compare two photoacoustic techniques to characterize the mechanical parameters of edge-supported aluminum and silicon nitride double-layer thin films. The elastic properties and residual stresses in such films affect their mechanical performance. In a first set of experiments, a femtosecond transient pump–probe technique is used to investigate the Young’s moduli of the aluminum and silicon nitride layers by launching ultra-high frequency bulk acoustic waves in the films. The measured transient signals are compared with simulated transient thermoelastic signals in multi-layer structures, and the elastic moduli are determined. Independent pump–probe tests on silicon substrate-supported region and unsupported region are in good agreement. In a second set of experiments, dispersion curves of the A₀ mode of the Lamb waves that propagate along the unsupported films are measured using a broadband photoacoustic guided-wave method. The residual stresses and flexural rigidities for the same set of double-layer membranes are determined from these dispersion curves. Comparisons of the results obtained by the two photoacoustic techniques are made and discussed.     

Theory of amplitude-dependent internal friction and acoustoplastic effect in shape memory alloys

Mechanisms of amplitude-dependent internal friction and the acoustoplastic effect in shape memory alloys are discussed in terms of the previously developed theory of diffuse thermoelastic martensitic transformations. The amplitude dependences of these effects are found for different temperatures and applied stresses.     

Elasticity and inelasticity of silicon nitride/boron nitride fibrous monoliths

A study is reported on the effect of temperature and elastic vibration amplitude on Young’s modulus E and internal friction in Si₃N₄ and BN ceramic samples and Si₃N₄/BN monoliths obtained by hot pressing of BN-coated Si₃N₄ fibers. The fibers were arranged along, across, or both along and across the specimen axis. The E measurements were carried out under thermal cycling within the 20–600°C range. It was found that high-modulus silicon-nitride specimens possess a high thermal stability; the E(T) dependences obtained under heating and cooling coincide well with one another. The low-modulus BN ceramic exhibits a considerable hysteresis, thus indicating evolution of the defect structure under the action of thermoelastic (internal) stresses. Monoliths demonstrate a qualitatively similar behavior (with hysteresis). This behavior of the elastic modulus is possible under microplastic deformation initiated by internal stresses. The presence of microplastic shear in all the materials studied is supported by the character of the amplitude dependences of internal friction and the Young’s modulus. The experimental data obtained are discussed in terms of a model in which the temperature dependences of the elastic modulus and their features are accounted for by both microplastic deformation and nonlinear lattice-atom vibrations, which depend on internal stresses.     

On the calculation of nonstationary mechanical stresses formed in solid objects upon laser energy absorption by the thermoelastic mechanism

A general approach to calculating nonstationary thermoelastic stresses generated in solid objects as a result of absorption of the laser radiation energy is worked out in the quasi-static approximation. In the 3D model, analytic expressions are derived for the radial and tangential stress tensor components on the surface of the object.     

Theoretical analysis of off beam quartz-enhanced photoacoustic spectroscopy sensor

Off beam quartz-enhanced photoacoustic spectroscopy (OB-QEPAS) sensors are based on a recently developed approach to off-beam photoacoustic (PA) detection which employs a quartz tuning fork (QTF) as an acoustic transducer. A microresonator (mR) with a side slit in the middle is used to enhance PA signal. This paper describes a theoretical model of an OB-QEPAS-based sensor. By deriving the acoustic impedances of the mR at two ends and the side slit in the middle in the model, we obtain a formula for numerically calculating the optimal mRs' parameters of OB-QEPAS-based sensor. We use the model to calculate the optimal mRs' lengths with respect to the resonant frequency of the QTF, acoustic velocities inside mRs, inner diameters of mRs, and acoustic conductivities of the mRs' side slits, and found out that the calculated results closely match experimental data. We also investigated the relationship between the mR selected in “on beam” QEPAS, OB-QEPAS, and an acoustic resonator (AR) excited in its first longitudinal mode used in conventional photoacoustic spectroscopy (PAS).     

Grain boundary segregation and relaxation in nano-grained polycrystalline alloys

The present study carries out systematic thermodynamics analysis of Grain Boundary(GB)segregation and relaxation in NanoGrained(NG)polycrystalline alloys.GB segregation and relaxation is an internal process towards thermodynamic equilibrium,which occurs naturally in NG alloys without any applied loads,causes deformation and generates internal stresses.The analysis comprehensively investigates the multiple coupling effects among chemical concentrations and mechanical stresses in GBs and grains.A hybrid approach of eigenstress and eigenstrain is developed herein to solve the multiple coupling problem.The analysis results indicate that the GB stress and grain stress induced by GB segregation and relaxation can be extremely high in NG alloys,reaching the GPa level,which play an important role in the thermal stability of NG alloys,especially via the coupling terms between stress and concentration.The present theoretic analysis proposes a novel criterion of thermal stability for NG alloys,which is determined by the difference in molar free energy between a NG alloy and its reference single crystal with the same nominal chemical composition.If the difference at a temperature is negative or zero,the NG alloy is thermal stable at that temperature,otherwise unstable.     

一种基于双波长的光声测温技术

光声测温是一种利用光声效应来进行温度监控的新方法,具有非侵入式、高灵敏度和探测深度较深等优点.但现有的单波长光声测温方法极易受到系统及测量环境干扰而导致测量精度降低.为了解决这一问题,本文提出了一种双波长光声温度测量方法.在光声测温理论的基础上,分析推导了双波长光声测温的基本原理,并进行了仿体及离体组织样品的双波长光声测温实验.实验结果显示,与传统单波长模式相比,双波长模式下的光声温度测量误差明显减小,测量精度平均提高35%以上.研究结果表明双波长光声测温方法能够有效提高光声温度测量的精度和稳定性,可作为一种更精准的光声温度监控方法应用于医疗手术等领域.