Liyong Yang

Ultrasonic characterization of microstructure evolution during processing

Many cold‐working processes for polycrystalline metals cause alignment of the grains with a single symmetry axis. This type of microstructure is called fiber texture. The existence of a preferred orientation of the grains has a significant influence on the propagation and scattering of ultrasonic waves, which are often used for material inspection. Knowledge of the wave attenuation of such textured materials is of both theoretical and practical interest to nondestructive testing and materials characterization. In this article, the quantitative relations between fiber texture and wave attenuations of hexagonal crystals are presented. The texture is characterized by a Gaussian distribution function that contains a single parameter that governs the transition of the texture from perfectly aligned crystals to statistically isotropic. Under this assumption, the materials of interest have a varying degree of transverse isotropy representative of processing conditions. Simple expressions for the attenuations of ...

Attenuation of ultrasonic waves in rolled metals

Scattering of ultrasonic waves in polycrystals with texture is studied in this article. The attenuations of the three wave modes are determined as a function of dimensionless frequency and propagation direction, respectively, for given orientation distribution coefficients (ODCs). The calculation is done in the case of a statistically orthorhombic sample made up of cubic crystallites. The wave propagation and scattering model is formulated by the Dyson equation using an anisotropic Greens function approach. Within the limits of the first-order smoothing approximation, the Dyson equation is solved in the spatial Fourier transform domain. The results presented are shown to be directional dependent, frequency dependent, and especially dependent on the texture coefficients (ODCs) for the quasilongitudinal and two quasishear waves. The theoretical results presented may be used to improve the understanding of the microstructure during recrystallization processes.

Elastic wave propagation and scattering in solids with uniaxially aligned cracks

In this article, elastic wave propagation and scattering in a solid medium permeated by uniaxially aligned penny-shaped microcracks are studied. The crack alignment refers to the case in which the unit normals of all cracks are randomly oriented within a plane of isotropy. The analysis is restricted to the limit of the noninteraction approximation among individual cracks. Explicit expressions for attenuations and wave speeds of the shear horizontal, quasilongitudinal, and quasishear vertical waves are obtained using stochastic wave theory in a generalized dyadic approach. The ensemble average elastic wave response is governed by the Dyson equation, which is solved in terms of the anisotropic elastic Greens dyadic. The analysis of expressions is limited to frequencies below the geometric optics limit. The resulting attenuations are investigated in terms of the directional, frequency, and damage dependence. In particular, the attenuations are simplified considerably within the low frequency Rayleigh regime. Finally, numerical results are presented and discussed in terms of the relevant dependent parameters.

Scattering of elastic waves in damaged media

The scattering of elastic waves in a medium with damage from microcracking is discussed. The influence of damage from penny-shaped microcracks within a homogeneous medium is considered. The microcracks are assumed to be randomly oriented and uniformly distributed. Explicit expressions are derived for the attenuation of longitudinal and shear elastic waves in terms of the damage parameter and the effective elastic moduli of the medium. A generalized tensor-based approach is used such that the results are coordinate free. The derivation is based upon diagrammatic methods. The problem is formulated in terms of the Dyson equation, which is solved for the mean field response within the limits of the first-order smoothing approximation. The longitudinal and shear attenuations are discussed in terms of their frequency dependence and damage dependence. In particular, the attenuations are shown to scale linearly with the damage parameter.

Granular layers on vibrating plates: Effective bending stiffness and particle-size effects

Acoustic methods of land mine detection rely on the vibrations of the top plate of the mine in response to sound. For granular soil (e.g., sand), the particle size is expected to influence the mine response. This hypothesis is studied experimentally using a plate loaded with dry sand of various sizes from hundreds of microns to a few millimeters. For low values of sand mass, the plate resonance decreases with added mass and eventually reaches a minimum without particle size dependence. After the minimum, a frequency increase is observed with additional mass that includes a particle-size effect. Analytical nondissipative continuum models for granular media capture the observed particle-size dependence qualitatively but not quantitatively. In addition, a continuum-based finite element model (FEM) of a two-layer plate is used, with the sand layer replaced by an equivalent elastic layer for evaluation of the effective properties of the layer. Given a thickness of sand layer and corresponding experimental resonance, an inverse FEM problem is solved iteratively to give the effective Youngs modulus and bending stiffness that matches the experimental frequency. It is shown that a continuum elastic model must employ a thickness-dependent elastic modulus in order to match experimental values.

Wave attenuations in solids with perfectly aligned cracks

The theory of wave propagation and scattering in cracked media is applied to study the wave attenuations in an isotropic solid medium containing perfectly aligned penny-shaped microcracks. The unit normals of all cracks are assumed parallel to a given direction. The wave scattering model is formulated using an anisotropic Green’s dyadic approach. Explicit expressions are derived for attenuations of the three wave modes in terms of the microcrack density. Numerical results are presented and discussed. In particular, comparisons of the attenuation results presented in this letter with previous results for the Rayleigh limit are given.

Influence of particle size on the vibration of plates loaded with granular material

Acoustic methods of land mine detection rely on the vibrations of the top plate of the mine in response to sound. For granular soil (e.g., sand), it is expected that particle size will influence the mine response. This hypothesis is studied experimentally using a plate loaded with dry sand of various sizes from hundreds of microns to a few millimeters. For low values of sand mass, the plate resonance decreases and eventually reaches a minimum without particle size dependence. After the minimum, the frequency increase with additional mass includes a particle-size effect. Analytical continuum models for granular media applied to this problem do not accurately capture the particle-size effect. In addition, a continuum-based finite element model (FEM) of a two-layer plate is used with the sand layer replaced by an equivalent elastic layer. For a given thickness of the sand layer and corresponding experimental resonance, an inverse FEM problem is solved iteratively. The effective Youngs modulus and bending stiffness of the equivalent elastic layer that match the experimental frequency are found for every layer thickness. Smaller particle sizes are shown to be more compliant in bending. The results clarify the importance of particle size on acoustic detection methods.

Effect of particle friction on the vibrations of a plate loaded with granular media

Acoustic methods have recently been shown to hold promise for detection of nonmetallic mines. These methods rely on the vibration response of the soil‐plate system. The influence of particle size on the frequency response was previously illustrated using sieved sand as the loading material. Here, the influence of particle friction is studied using spherical glass beads. The first resonance of a plate was measured as a function of layer mass for a layer of monodispersed glass beads of various sizes (from 38 μm to 2.5 mm). The plate exhibited the same qualitative behavior as with sand loading but the response was quantitatively different. In particular, the minimum frequency attained for the glass bead layer was consistently higher than that for sand. However, the dependence on particle size followed the similar trends. Mechanisms related to both interparticle friction and layer‐plate interface friction were explored. Experimental results with a roughened plate indicate that the resonance behavior is not de...

Propagation of elastic waves in hexagonal crystals with fiber texture

Many cold‐working processes for polycrystalline metals cause alignment of the grains with a single symmetry axis called fiber texture. The existence of a preferred orientation of the grains has a big influence on the propagation and scattering of ultrasonic waves, which are often used for materials inspection. Knowledge of the wave attenuation of such textured materials is of both theoretical and practical interest to nondestructive testing and materials characterization. In this presentation, the quantitative relations between fiber texture and wave attenuations of hexagonal crystals are presented. The texture is characterized by a Gaussian distribution function that contains a single parameter that governs the transition of the texture from statistically isotropic to fiber texture. Under this assumption, the materials of interest have a varying degree of transverse isotropy representatives of processing conditions. Simple expressions for the attenuations of the three modes of waves are given in a concis...

Effect of particle size on the vibration of plates loaded with granular material

Acoustic methods of landmine detection are emerging as reliable techniques that are especially well suited for non‐metallic mines. These methods rely on the vibrations of the top plate of the mine as it responds to the acoustic excitation. The plate response is complicated by the interaction with the surrounding soil. If the loading soil is granular (e.g., sand), it is expected that particle size will influence the mine response. Experimental results related to this hypothesis are presented here. The first resonant frequency of a sand‐loaded plate is measured as a function of sand mass for dry sand of various sizes covering a range from hundreds of microns to a few millimeters. For low values of sand mass, the plate resonance decreases and eventually reaches a minimum. In this regime, there is no dependence on particle size. After the minimum, the frequency increases with additional mass. In this regime, a particle size effect is observed. Models are also presented to support and explain experimental resu...