Thermoelastic Source Research Articles

Finite-Element Analysis of Laser-Generated Ultrasounds for Wave Propagation and Interaction with Surface-Breaking Cracks

ABSTRACT A finite-element method was used to simulate the wave propagation of laser-generated ultrasound and its interaction with surface-breaking cracks in an elastic material. The thermoelastic laser line source on the material surface was approximated as a shear dipole and loaded as nodal forces in the plane-strain finite element (FE) model. The shear dipole FE model was tested for the generation of ultrasound on the surface with no defect. The model was found to generate the Rayleigh surface wave and to give the correct directivity patterns for longitudinal and shear bulk waves. The model was then extended to examine the interaction of laser-generated ultrasound with surface-breaking cracks of various depths. Both fixed and scanning laser sources (SLS) were considered. For the case of the fixed source, the crack-reflected Rayleigh waves were monitored to detect a crack. In the SLS technique, the laser-generated signal arriving at the Rayleigh wave speed was monitored as the laser source was scanned. The proposed model clearly reproduced the experimentally observed features that can be used to characterize the presence of surface-breaking cracks.

Line source representation for laser-generated ultrasound in an elastic transversely isotropic half-space

Theoretical and experimental results are presented for a laser line source in an elastic, transversely isotropic half-space. The thermoelastic source (laser source) is represented as an appropriately weighted shear stress dipole applied at the sample surface. The plane of isotropy coincides with the half-space boundary. Analytical expressions representing the out-of-plane displacements for the surface wave and for the epicentral cases are given for all crystal classes that exhibit elastic transverse isotropy. In addition, quasianalytical results are given for observation points off the epicentral axis. Theoretical wave forms for all of the source/observation geometries considered are compared with experimental wave forms generated in single crystal zinc samples. The close comparison between experiment and theory confirms, for this particular line source orientation and crystal symmetry, that a laser line source is accurately modeled using an equivalent boundary stress.

Investigation of surface acoustic wave propagation on a sphere using laser ultrasonics

Using the noncontact laser ultrasonic technique, we investigate the propagation of surface acoustic waves on a sphere (SSAW). A finite thermoelastic line source gives rise to combined focusing and reversal effects. As for propagation on a cylinder surface, the reversal of the SSAW pulse is explained by the dispersion of the high frequency components of the laser-generated acoustic pulse. The focusing effect, due to the curvature of the surface, depends on the angular aperture of the source. From diffraction theory, optimal conditions for diffraction free propagation are derived, both in harmonic and pulse regimes. On a steel sphere of radius 25mm, Rayleigh waves excited by a 20ns YAG laser pulse focused onto a 3mm line propagate with a nearly constant amplitude.

Analysis of thermoelastic and dissipative effects related to the fatigue of 2024 T3 aluminium alloy

In this paper the fatigue phenomena of 2024 T3 aluminium alloy were studied in terms of thermal and calorimetric effects during uniaxial cyclic loading. Thermoelastic coupling sources and dissipation were separately estimated by using infrared thermal data and a local simplified form of the heat equation. The simplifications are essentially based on the assumption that the uniaxial fatigue test remains homogeneous until a macroscopic fatigue crack occurs within the gauge section of the specimen. Heat sources were then compared to predictions derived from mechanical data by assuming a linear isotropic thermoelastic behaviour of the material and by neglecting the influence of thermomechanical couplings on the hysteresis area of fatigue cycles.

Laser-induced acoustic landmine detection

Laser-induced acoustic (LIA) imaging is a new approach for underground object detection, especially for shallow buried landmine detection. This noncontact detection technique is based on a pulsed laser initiating photo-acoustic interaction in the ground. If sufficient photon energy couples into the ground, generating acoustic signals larger than seismic noise, a high enough mismatch of acoustic impedance between background media and target could provide a clear acoustic image revealing both the target’s position and the 3-D shape information to reduce false alarms. In this paper, we present a model for laser-induced acoustic wave generation, including models of photo-acoustic sources and propagation of sound waves in media, to obtain a better understanding of basic physics behind the process. A photon-induced thermoelastic source and a photon-induced plasma source are investigated. Also, an investigation was performed in terms of attenuation, angular distribution, and phase velocities, and experimental results are reported and compared with theoretical analysis.

Laser-generated thermoelastic acoustic sources in anisotropic materials

An analytical model appropriate for thermoelastic generation of acoustic waves in anisotropic materials is presented for both plane and line sources. The interaction of acoustic waves produced by subsurface sources with the bounding surface is accounted for using a method of images. For the plane source case, analytical solutions are found that form an appropriate basis for an angular spectrum of plane waves. For the line source case and for specific crystal symmetries and source orientations, it is shown in the limit of strong optical absorption, a buried line source is equivalent to applying a shear stress dipole at the bounding surface. However, contrary to the isotropic case, the character and strength of the equivalent surface stress is a function of propagation direction.

Interaction of a scanning laser-generated ultrasonic line source with a surface-breaking flaw

The scanning laser source (SLS) technique has been proposed recently as an effective way to investigate small surface-breaking cracks. By monitoring the amplitude and frequency changes of the ultrasound generated as the SLS scans over a defect, the SLS technique has provided enhanced signal-to-noise performance compared to the traditional pitch-catch or pulse-echo ultrasonic methods. In previous work, either a point source or a short line source was used for generation of ultrasound. The resulting Rayleigh wave was typically bipolar in nature. In this paper, a scanning laser line source (SLLS) technique using a true thermoelastic line source (which leads to generation of monopolar surface waves) is demonstrated experimentally and through numerical simulation. Experiments are performed using a line-focused Nd:YAG laser and interferometric detection. For the numerical simulation, a hybrid model combining a mass-spring lattice method (MSLM) and a finite difference method (FDM) is used. As the SLLS is scanned over a surface-breaking flaw, it is shown both experimentally and numerically that the monopolar Rayleigh wave becomes bipolar, dramatically indicating the presence of the flaw.

Calorimetric analysis of dissipative and thermoelastic effects associated with the fatigue behavior of steels

The fatigue of dual phase steel was examined in terms of calorimetric effects in order to match the energy manifestations of fatigue and constitutive equations drawn up in a thermomechanical framework. A simplified method, assuming a homogeneous fatigue test, is proposed to determine heat source development from a temperature field provided by an infrared camera. Thermoelastic and dissipative sources were then separately identified. Experimental results concerning thermoelastic effects are in close agreement with theoretical estimates. Dissipation depends on the loading frequency and stress amplitude applied to the fatigue specimen. However, as the marked decrease in dissipation observed when testing a block at high stress was not easily interpretable in terms of material effects, we questioned the homogeneous fatigue test assumption.

Development of a Flexible Laser Ultrasonic Probe

Ultrasonics is a widely used nondestructive testing technique, which is often applied off-line for weld quality inspection. Laser ultrasonic (LU) inspection systems have the potential for on-line application, providing the means to identify unacceptable welds as they are formed. Because LU systems are non-contacting, they can be used for testing moving specimens or for operation in hazardous and/or high temperature environments. A highly versatile system can be created when an optical fiber delivery system is incorporated into the design. Introduction of a focusing objective increases the allowable working distance and permits stronger generation using material ablation as the generating mechanism. This paper describes the development of a laser ultrasonic probe using an optical fiber delivery system with a distal end, focusing objective. The optical fiber delivery system can be configured as a single fiber source, a linear array (fiber bundle) or a phased array. Results include experimentally obtained directivity patterns demonstrating ultrasonic generation using ablation sources. Thermoelastic source results are also included. This paper demonstrates the potential of the fiber tool and presents an overview of the weld control scheme.

Acoustic Fields of Bulk Acoustic Waves Excited by Phase Velocity Scanning of Laser Interference Fringes

Directivity and generation efficiency of transverse and longitudinal bulk acoustic waves (BAWs) excited by phase velocity scanning (PVS) of laser interference fringes were theoretically investigated. Formulas were derived for the BAW generation based on scanning interference fringes (SIF) which were produced by intersecting two coherent laser beams with different frequencies on an opaque specimen. It was deduced that the amplitude of the BAW was proportional to the product of the scanning length of the SIF and the directivity pattern due to the thermoelastic line source. Unidirectionality of the BAW generated by the SIF was theoretically verified in an ideal state.

TIME DOMAIN MODELING OF AXISYMMETRIC WAVE PROPAGATION IN ISOTROPIC ELASTIC MEDIA WITH CEFIT — CYLINDRICAL ELASTODYNAMIC FINITE INTEGRATION TECHNIQUE

The Elastodynamic Finite Integration Technique (EFIT), originally developed by Fellinger et al.,1–3 represents a stable and efficient numerical code to model elastic wave propagation in linearly-elastic isotropic and anisotropic, homogeneous and heterogeneous as well as dissipative and nondissipative media. In previous works, the FIT discretization of the basic equations of linear elasticity, Hooke's law and Cauchy's equation of motion, was exclusively carried out in Cartesian coordinates. For problems in cylindrical geometries it is more suitable to use cylindrical coordinates. By that, axisymmetric problems can be treated in a two-dimensional staggered grid in the r,z-plane. The paper presents an EFIT version for axisymmetric problems in cylindrical coordinates called Cylindrical EFIT (CEFIT). After demonstrating the accuracy of the numerical code by a comparison between simulation results and analytical solutions, different examples of application are given. These examples include modeling of sound fields of ultrasonic transducers, thermoelastic laser sources, geophysical borehole probes, impact-echo measurements in layered media, and load simulations of the European Spallation Source (ESS) mercury target.

Time Domain Modeling of Axisymmetric Wave Propagation in Isotropic Elastic Media With Cefit - Cylindrical Elastodynamic Finite Integration Technique

The Elastodynamic Finite Integration Technique (EFIT), originally developed by Fellinger et al.,1–3 represents a stable and efficient numerical code to model elastic wave propagation in linearly-elastic isotropic and anisotropic, homogeneous and heterogeneous as well as dissipative and nondissipative media. In previous works, the FIT discretization of the basic equations of linear elasticity, Hooke's law and Cauchy's equation of motion, was exclusively carried out in Cartesian coordinates. For problems in cylindrical geometries it is more suitable to use cylindrical coordinates. By that, axisymmetric problems can be treated in a two-dimensional staggered grid in the r,z-plane. The paper presents an EFIT version for axisymmetric problems in cylindrical coordinates called Cylindrical EFIT (CEFIT). After demonstrating the accuracy of the numerical code by a comparison between simulation results and analytical solutions, different examples of application are given. These examples include modeling of sound fields of ultrasonic transducers, thermoelastic laser sources, geophysical borehole probes, impact-echo measurements in layered media, and load simulations of the European Spallation Source (ESS) mercury target.

Mixed matrix formulation for the analysis of laser-generated acoustic waves by a thermoelastic line source

An analytical model has been developed for the generation of bulk and surface acoustic waves at the surface of an isotropic solid by an infinite thermoelastic laser line source. This model is based on the mixed matrix formulation. It leads to expressions in closed form for the longitudinal and transverse bulk displacements and also for the Rayleigh wave components. A comparison with other models shows that the mechanical effect of the free surface reduces the strength of the two dipoles of force equivalent to the point thermoelastic source. For Rayleigh waves, quantitative agreement has been found with a numerical model and with experiments previously carried out on a duraluminum plate.

Experimental and theoretical waveforms of Rayleigh waves generated by a thermoelastic laser line source

An analytical model has been developed for the generation of surface acoustic (Rayleigh) waves in an isotropic solid by a thermoelastic laser line source. For a Gaussian light intensity profile, this model leads to an expression in closed form for the normal surface displacement of the Rayleigh wave either in the near field or in the far field domain. Quantitative agreement has been found for experiments carried out with an interferometric optical probe on a duraluminum plate.

Laser-ultrasound detection systems: a comparative study with Rayleighwaves

Using laser-generated Rayleigh waves in the thermoelastic regime asan ultrasonic source, a range of ultrasonic detector systems have beenevaluated experimentally for their sensitivity. Systems examined were thosebased on electromagnetic acoustic transducers (EMATs), a non-steady statephoto-emf detector, a confocal Fabry-Pérot interferometer (CFPI) and adifferential optical beam deflection (OBD) detector. These detector systemshad their own range of frequency responses within the range of approximately100 kHz to 140 MHz. However, experimental conditions in this study limited theupper frequency range to 22 MHz. For comparison, signal-to-noise ratios werenormalized with respect to both the experimental bandwidth, and, in the caseof laser detection, the incident laser intensity. Results showed that forremote monitoring at a distance greater than 0.2 m, optical systems based onthe photo-emf detector and the CFPI offered similar performances from amachine-finished aluminium surface. OBD measurements are not possible on sucha surface. However, for typical stand-off distances of 0.25 mm or less,cost-effective EMATS provided an alternative form of detector.

Point-source representation for laser-generated ultrasound in an elastic, transversely isotropic half-space

A point-source representation for laser-generated ultrasound in an elastic, transversely isotropic half-space is developed. This representation is comprised of a set of boundary conditions that approximates a thermoelastic point source located on the bounding surface of the half-space. An analytical expression representing the displacements for wave propagation along the symmetry axis is given for zinc where the bounding surface is the plane of transverse isotropy. The displacements obtained from theory are compared to experimental wave forms generated in a sample of single crystal zinc.

Unconstrained Hamiltonian formulation of general relativity with thermo-elastic sources

A new formulation of the Hamiltonian dynamics of the gravitational field interacting with (non-dissipative) thermo-elastic matter is discussed. It is based on a gauge condition which allows us to encode the six degrees of freedom of the `gravity + matter'-system (two gravitational and four thermo-mechanical ones), together with their conjugate momenta, in the Riemannian metric and its conjugate ADM momentum . These variables are not subject to constraints. We prove that the Hamiltonian of this system is equal to the total matter entropy. It generates uniquely the dynamics once expressed as a function of the canonical variables. Any function U obtained in this way must fulfil a system of three, first-order, partial differential equations of the Hamilton - Jacobi type in the variables . These equations are universal and do not depend upon the properties of the material: its equation of state enters only as a boundary condition. The well posedness of this problem is proved. Finally, we prove that for vanishing matter density, the value of U goes to infinity almost everywhere and remains bounded only on the vacuum constraints. Therefore the constrained, vacuum Hamiltonian (zero on constraints and infinity elsewhere) can be obtained as the limit of a `deep potential well' corresponding to non-vanishing matter. This unconstrained description of Hamiltonian general relativity can be useful in numerical calculations as well as in the canonical approach to quantum gravity.

The elastodynamic finite integration technique for waves in cylindrical geometries

This paper deals with the elastodynamic finite integration technique for axisymmetric wave propagation in a homogeneous and heterogeneous cylindrical medium (CEFIT). This special variant of a finite difference time domain (FDTD) scheme offers a suitable method to calculate real three-dimensional problems in a two-dimensional staggered grid. In order to test the accuracy of the numerical CEFIT code, problems for which analytical solutions are available are presented. These solutions involve wave propagation in an elastic plate, the scattering of a plane longitudinal wave by a spherical obstacle, and ultrasound generation by a thermoelastic laser source. For the latter problem experimental results are included. The CEFIT code also allows the treatment of more complicated problems. Further possible applications are the investigation of elastic waves generated in an acoustic microscope, the simulation of impact-echo measurements in multi-layer systems, axisymmetric wave propagation in arbitrary bodies of revolution, the calculation of elastic wave fields of longitudinal wave transducers with a circular aperture, and the investigation of multi-layer models for particulates.

Laser-generated ultrasound in single-crystal Mindlin-type plates: theory and experiment

A Mindlin-type plate theory, appropriate for laser-line irradiation of a single-crystal plate with cubic symmetry, is developed to predict the temporal displacement profile in the far-field of the laser source. The [100] crystal axis coincides with the plate normal and the [010] crystal axis is inclined at an angle to the laser-line source. A formal solution for the out-of-plane displacements is obtained using Laplace and Fourier transforms. Both thermoelastic and non-thermal photostrictive source mechanisms are considered. For the particular problem of photostrictive generation, the spatial and temporal dependence are recovered using a hybrid analytical and numerical inversion scheme. Experimental data for a single crystal silicon plate, obtained via pulse laser generation and interferometric detection, is compared with theory.

Relaxation of thermal stresses by dislocation flow and multiplication in the continuous casting of silicon

A semi-analytical model is proposed for simulating thermal stress generation during experimental continuous casting of polycrystalline silicon billets for photovoltaic applications. The geometry is axi-symmetric and the temperature field is formulated using three parameters. The thermoelastic stress source is given by the plane strain approximation. The Alexander and Haasen model, based on the classical Orowan equation, expresses the plastic relaxation and the associated multiplication of dislocations. This set of approximations allows us to discuss separately the influence of the withdrawal rate and of the thermal parameters on the variation along the billet of both the stress and the dislocation density.