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The properties of crystalline materials can be described mathematically by tensors whose components are generally known as property constants. Tabulations of these constants in terms of the independent components are well known for common material properties (e.g. elasticity, piezoelectricity etc.) aptly described by tensors of lower rank (e.g. ranks 2–4). General relationships between constants of higher rank are often unknown and sometimes reported incorrectly. A computer program is developed here to calculate the property constant relationships of a property of any order, represented by a tensor of any rank and point group. Tensors up to rank 12, e.g. the tensor of sixth-order elastic constants c_{_{6}i\,j\,k\,l\,m\,n\,p\,q\,r\,s}, can be calculated on a standard computer, while ranks higher than 12 are best handled on a supercomputer. Output is provided in either full index form or a reduced index form, e.g. the Voigt index notation common to elasticity. As higher-order tensors are often associated with nonlinear material responses, the program provides an accessible means to investigate the important constants involved in nonlinear material modeling. The routine has been used to discover several incorrect relationships reported in the literature.

Metal additive manufacturing is a fabrication method that forms a part by fusing layers of powder to one another. An energy source, such as a laser, is commonly used to heat the metal powder sufficiently to cause a molten pool to form, which is known as the melt pool. The melt pool can exist in the conduction or the keyhole mode where the material begins to rapidly evaporate. The interaction between the laser and the material is physically complex and difficult to predict or measure. In this article, high-speed X-ray imaging was combined with immersion ultrasound to obtain synchronized measurements of stationary laser-generated melt pools. Furthermore, two-dimensional and three-dimensional finite-element simulations were conducted to help explain the ultrasonic response in the experiments. In particular, the time-of-flight and amplitude in pulse-echo configuration were observed to have a linear relationship to the depth of the melt pool. These results are promising for the use of ultrasound to characterize the melt pool behavior and for finite-element simulations to aid in interpretation.

Efficient nondestructive qualification of additively manufactured (AM) metallic parts is vital for the current and future adoption of AM parts throughout several industries. Resonant ultrasound spectroscopy (RUS) is a promising method for the qualification and characterization of AM parts. Although the adoption of RUS in this setting is emerging, the influence of residual stress and texture, which are both very common in AM parts, is not well understood. In this article, a stress- and texture-dependent constitutive relation is used to study the influence on free vibrational behavior in a RUS setting. The results that follow from using the Rayleigh-Ritz method and finite element analysis suggest that residual stress and texture have a significant impact on the resonance frequencies and mode shapes. These results support the potential of using RUS to sense texture and residual stress in AM parts. Additionally, these results suggest that RUS measurements could be misinterpreted when the stress and texture are not accounted for, which could lead to a false positive/negative diagnosis when qualifying AM parts.

This article reconsiders traditional topics in nonlinear elastic waves and nonlinear ultrasonics. Herein, higher-order coupling between finite initial deformation and finite amplitude waves are considered. To allow for coupling, a large-on-large deformation model is developed and used to generate the equations of motion relative to the deformed and undeformed material configurations. Thus, the equations of motion provide a single setting to describe topics in nonlinear elastic waves such as acoustoelasticity, second harmonic generation, and coupling relations between these topics. The model is evaluated to recover the traditional linearized acoustoelastic relations and predicted second harmonic amplitudes. Then, the so-called large acoustoelasticity theory is developed for anisotropic materials with specific results given for isotropic materials. Last, the stress influence on second harmonic generation is presented.

PANDA (anti-proton annihiliation at Darmstadt) is planned to be one of the four main experiments at the future international accelerator complex FAIR (Facility for Antiproton and Ion Research) in Darmstadt, Germany. It is going to address fundamental questions of hadron physics and quantum chromodynamics using cooled antiproton beams with a high intensity and and momenta between 1.5 and 15 GeV/c. PANDA is designed to reach a maximum luminosity of 2 × 1032 cm−2 s. Most of the physics programs require an excellent particle identification (PID). The PID of hadronic states at the forward endcap of the target spectrometer will be done by a fast and compact Cherenkov detector that uses the detection of internally reflected Cherenkov light (DIRC) principle. It is designed to cover the polar angle range from 5° to 22° and to provide a separation power for the separation of charged pions and kaons up to 3 standard deviations (s.d.) for particle momenta up to 4 GeV/c in order to cover the important particle phase space. This document describes the technical design and the expected performance of the novel PANDA disc DIRC detector that has not been used in any other high energy physics experiment before. The performance has been studied with Monte-Carlo simulations and various beam tests at DESY and CERN. The final design meets all PANDA requirements and guarantees sufficient safety margins.

Binder jet printing (BJP) is a promising additive manufacturing method with benefits in sustainability, material selection, and geometric design freedom. However, issues related to part quality persist, necessitating reliable inspection and characterization strategies. Traditional protocols involving sectioning and extensive sample preparation may miss crucial information about a components’ microstructure due to volumetric variations. This study explores ultrasonic inspection of binder jet SS316L tensile specimens containing spatially varying grain size and porosity by measurement of longitudinal wave speed and attenuation. The ability of ultrasound to detect porosity is evaluated by cross referencing wave speed and attenuation data with porosity data gathered from x-ray computed tomography (XCT). Three-dimensional pore volumes were collapsed into two-dimensional maps such that ultrasound and XCT could be compared in a point-by-point fashion. After tensile testing, the location of failure was compared against wave speed and attenuation extremes. The results show the potential of ultrasound as well as important considerations related to the inspection of additively manufactured parts with complex microstructures.

Ultrasonic scattering-based measurements are commonly used as sensitive tools for non-destructive evaluation (NDE) of metals. Existing analytical models can predict ultrasonic wavespeed and attenuation for statistically homogeneous metals exhibiting spatially dependent elastic constants. These models rely on two-point statistics that correspond to first-order smoothing approximation (FOSA) of the mass operator series present in the governing Dyson equation. The FOSA-based prediction agrees well with finite element (FE) results for a wide range of polycrystalline metals at ultrasonic frequencies in the stochastic regime. However, discrepancies become more pronounced with increasing single-crystal elastic anisotropy even at low frequencies in the Rayleigh limit. For example, a difference of 70% is present for Lithium. In this presentation, the next order or third-order smoothing approximation (TOSA) is introduced, and Rayleigh-limit attenuations and wavespeeds are derived analytically. In this context, the TOSA accounts for four-point correlation functions and, thus, a higher degree of multiple scattering effects are included. This presentation will focus on key points and assumptions pertaining to the derivation for results including the TOSA. The TOSA-based model improves predictions of longitudinal attenuation by more than 11% and 4% for polycrystalline Lithium or Nickel, respectively. Future extensions to higher frequencies and multiphase polycrystals will be described.

Advancements in manufacturing processes, such as metal 3D printing, are deeply reliant on our understanding of the resulting internal features and microstructures that dictate material behavior. Microstructure characterization is often relegated to techniques that require extensive sample sectioning and surface preparation, which are inherently limited to a small portion of the bulk material. In this presentation, I will show how elastic wave propagation methods (namely, ultrasonic testing) can be combined with physics-based models to extract microstructural parameters in fit-for-service parts. Example results are given for binder jet printed metals (namely, stainless steel 316 and SS316 infiltrated with bronze) where microstructure is characterized over large volumes nondestructively. These methods are correlated to both destructive metrics of microscale features and mechanical properties, which are linked to processing conditions and sample geometry. Finally, I will provide a broader outlook for the impact these techniques may have on the development and implementation of quality assurance protocols for additively manufactured parts.

Intrinsic to most metal additive manufacturing (AM) processes are melt pools generated from directed energy sources like lasers. Melt pools are critical as they function to join powder layers to previous layers during the process. Their criticality extends deeper as most porosity in AM parts stems from melt pool behavior while melt pool solidification dictates the parts’ microstructure. Significant breakthroughs in metal AM are severely hindered by the lack of access to experimental tools to study melt pools and modeling that do not fully capture the complex physics. Thus, melt pool related defects are often difficult to predict in occurrence and location while determining optimal process parameters to eliminate defects is extremely challenging and costly. Furthermore, the many exciting opportunities such as realizing new AM alloys, developing gradient materials/structure, and tailoring microstructure to intended applications are possible only with further understanding of melt pool behavior. With these clear needs, in-process acoustics have been proposed as plausible experimental tools for studying melt pool behavior. This presentation will provide an overview of the current activity in this area in addition to the specific needs the acoustics community can potentially address.

Resonant Ultrasound Spectroscopy (RUS) is a mature and reliable technique for measuring the elastic stiffness constants of anisotropic materials. In highly processed materials such as additively manufactured metal parts, the anisotropic stiffnesses arrive from microstructures that contain grains with preferred orientations, which can result from directionally dependent thermal or mechanical processes. The connection between elastic stiffnesses and microstructure suggest the potential for RUS being used as a tool to characterize microstructure. This presentation will highlight modeling and experimental measurements in this direction. The RUS model is developed from a micromechanical foundation and includes structure-property linkages between the microstructure’s orientation distribution function and the macroscopic elastic constitutive behavior. The micromechanical basis allows efficient creation of a complete catalog containing all possible resonant behavior (resonant frequencies and mode shapes) of polycrystalline samples as a function of the possible textures. The second part of the presentation will focus on connecting experimentally measured resonances and mode shapes to a particular catalog entry. The inclusion of mode shape imaging in the analysis is expected to offer additional detail and potential for expanded characterization beyond texture and elastic stiffnesses.

The current work investigates early material changes that manifest in aluminum alloy 7075 subjected to fatigue loading. Tension-tension specimens linearly tapered in width were exposed to cyclic loading with compliance and eddy current measurements made in-situ, while nano-indentation, surface potential, x-ray diffraction, and ultrasonic response were made ex-situ. Early stage damage progression was evaluated at various size scales and used to estimate a remaining life in real time. Baseline, in-situ, and post failure measurements were compared and analyzed as a function of fatigue cycles. Eddy current and compliance measurements showed a strong correlation between signal strength and fatigue life with eddy current providing a more precise signal per specimen. Microscale electrical measurements showed a link between surface potential and regions of the specimen that experienced higher tensile stress. Results are discussed with an emphasis on multiscale damage detection and identification due to fatigue cycling, while highlighting the most promising techniques for improving structural durability and real-time state monitoring.

In this paper, we will report about the implementation of the self-consistent Kröner–Eshelby model for the calculation of X-ray elastic constants for general, triclinic crystal symmetry. With applying appropriate symmetry relations, the point groups of higher crystal symmetries are covered as well. This simplifies the implementation effort to cover the calculations for any crystal symmetry. In the literature, several models can be found to estimate the polycrystalline elastic properties from single crystal elastic constants. In general, this is an intermediate step toward the calculation of the polycrystalline response to different techniques using X-rays, neutrons, or ultrasonic waves. In the case of X-ray residual stress analysis, the final goal is the calculation of X-ray Elastic constants. Contrary to the models of Reuss, Voigt, and Hill, the Kröner–Eshelby model has the benefit that, because of the implementation of the Eshelby inclusion model, it can be expanded to cover more complicated systems that exhibit multiple phases, inclusions or pores and that these can be optionally combined with a polycrystalline matrix that is anisotropic, i.e., contains texture. We will discuss a recent theoretical development where the approaches of calculating bounds of Reuss and Voigt, the tighter bounds of Hashin–Shtrikman and Dederichs–Zeller are brought together in one unifying model that converges to the self-consistent solution of Kröner–Eshelby. For the implementation of the Kröner–Eshelby model the well-known Voigt notation is adopted. The 4-rank tensor operations have been rewritten into 2-rank matrix operations. The practical difficulties of the Voigt notation, as usually concealed in the scientific literature, will be discussed. Last, we will show a practical X-ray example in which the various models are applied and compared.

Structural health monitoring and nondestructive inspection techniques typically assess the lifecycle and reliability of high-value aerospace, mechanical, and civil systems. Maintenance and inspection intervals are typically time-based and dependent on the structural health monitoring/nondestructive inspection technique to detect macroscale damage resulting from fatigue or environmental damage. The current work proposes an integrated materials-structures-dynamics approach for providing state awareness of structural health. The proposed approach shifts the conventional structural health monitoring/nondestructive inspection focus of searching for cracks to a health state awareness based on tracking changes in the energetics of the materials-structures-dynamics states. Energy variations are tracked in a cantilevered structure exposed to nonlinear harmonic oscillation, where the strain energy of the beam was derived and used to determine a health state index. Nanoindentation was used to probe the near-surface mechanical properties of the beam to characterize local material variations as a function of fatigue cycles. A nonlinear ultrasonic approach was considered in order to connect the local material behavior changes to the variations in the dynamic performance of the beam. The intent of the investigation was to connect the traditionally detached materials, structural, and dynamics approaches to structural health monitoring/nondestructive inspection, while providing a framework for enabling damage precursor detection.

A measurement of the double-polarization observable E for the reaction $$\gamma p\rightarrow \pi ^0 p$$ γ p → π 0 p is reported. The data were taken with the CBELSA/TAPS experiment at the ELSA facility in Bonn using the Bonn frozen-spin butanol (C$$_4$$ 4 H$$_9$$ 9 OH) target, which provided longitudinally-polarized protons. Circularly-polarized photons were produced via bremsstrahlung of longitudinally-polarized electrons. The data cover the photon energy range from $$E_\gamma =600$$ E γ = 600 to 2310 MeV and nearly the complete angular range. The results are compared to and have been included in recent partial wave analyses.

Resonant ultrasound spectroscopy (RUS) is a mature and robust technique for the nondestructive characterization of the elastic properties of solids capable of providing the elastic constants of anisotropic crystalline solids. The traditional method is based on assuming that the solid is linear elastic and, therefore, obeys a linearized Hookean constitutive relationship (Hooke’s law). In this article, an alternative constitutive law is provided that allows for an initial strain or prestrain to be present stemming from residual stress. Then, the constitutive relationship is integrated into the RUS framework. The model is demonstrated using a realistic prestrain field obtained by simulating shot-peening processing of a polycrystalline Cu sample. The sensitivity of the resonances to the developed prestrain is established and discussed. This work allows researchers to consider the influence of initial strain or residual stress in their samples and the potential influence on accurate elastic constant estimates. The model also supports the potential of RUS for the nondestructive characterization of prestrain in materials.

Traditionally, the acoustoelastic effect refers to the influence of stress in a solid on an elastic wave's phase velocity. Since the phase velocity can be represented by the real part of the complex wave number, a natural question arises regarding the effect of stress on the imaginary part or dissipation of the wave. In this article, the influence of pressure on the elastic wave's attenuation in polycrystalline materials is modeled. The constitutive behavior of an initially stressed solid is coupled into Weaver's scattering-based attenuation model [J. Mech. Phys. Solids 38, 55-86 (1990)]. As a result, the pressure-dependent longitudinal and shear wave attenuation coefficients are unveiled. As the traditional stress-free attenuation coefficients depend on the degree of single-crystal elastic anisotropy, it is shown that the pressure influence on attenuation depends on the anisotropy of the single-crystal's third-order or nonlinear elastic constants. Analysis of the model indicates linkages between pressure derivatives of velocity and attenuation to the material's linear and nonlinear elastic anisotropy, crystal structure, and type of atomic bonding.

Ultrasonic backscattering from polycrystalline materials with elongated grains is investigated. A normal incident line-focus transducer is employed such that refracted longitudinal and transverse waves are focused within the polycrystal and scatter at grain boundaries back to the transducer. A ray-based scattering model is developed to explain the dependence of the statistics of scattering measurements on grain elongation. The spatial variance of measured scattered signals from Al alloy (7475-T7) is compared to the model. This work promotes the ultrasonic backscatter technique for monitoring grain elongation of metals using one transducer with access to a single sample face.

Ultrasonics are viable tools to monitor internal microstructure of polycrystalline metals. Recently, the need for such tools has dramatically increased as metallic additively manufactured (AM) materials are rapidly becoming common in engineered structures. Nondestructive techniques like X-ray CT and ultrasonics are increasingly being used as a quality control step to help assure performance. Ultrasonics can also be used to help improve and develop AM processes by integration as an in situ method to assess the relationship between part microstructure and process parameters. This presentation will cover the development of two in situ ultrasonic techniques aimed at improving the state of the art in metal AM. First, ultrasound is employed to monitor keyhole melt pool dynamics in Al6061 samples. In this application, a high-frequency ultrasonic shear wave scatters from the liquid-solid boundary of the melt pool, which allows us to monitor keyhole initiation, melt pool depth, fluctuations in depth, and solidification. The sensitivity was confirmed through ground truth measurements using simultaneous synchrotron x-ray imaging. Then, progress on using in situ diffuse ultrasonic scattering on Gr91 powder bed fusion parts will be highlighted. The microstructure sensitivity of diffuse scattering is thought to be able to discern the formation of different microstructures during the manufacturing process.

Resonant ultrasound spectroscopy (RUS) is a standard technique for experimentally measuring the elastic constants of anisotropic elastic materials. Traditionally, the influence of internal or residual stresses on the measurement of elastic constants is not taken into consideration. However, it is well-known that residual stress can impart a small variation in the phase velocity of ultrasonic bulk waves, which is known as the acoustoelastic effect. Thus, it is plausible that residual stress will influence the resonances of samples measured during RUS. In this presentation, the elastodynamic theory for describing free vibrations is reformulated by using a stress-dependent constitutive relationship. The model culminates in an eigenvalue problem with a stiffness matrix being dependent on the spatially varying residual stress field within the domain of the sample. The model is evaluated by considering a realistic residual stress distribution. Results show the degree at which frequencies of resonance depend on the residual stress. While accounting for residual stress is expected to improve the estimates of elastic constants, there is also potential to use RUS as a tool to assess and characterize the residual stress present in samples.

This article reevaluates two foundational models for bulk ultrasonic wave propagation in polycrystals. A decoupling of real and imaginary parts of the effective wave number permits a simple iterative method to obtain longitudinal and shear wave attenuation constants and phase velocity relations. The zeroth-order solution is that of Weaver [J. Mech. Phys. Solids 38, 55-86 (1990)]. Continued iteration converges to the unified theory solution of Stanke and Kino [J. Acoust. Soc. Am. 75, 665-681 (1984)]. The converged solution is valid for all frequencies. The iterative method mitigates the need to solve a nonlinear, complex-valued system of equations, which makes the models more robust and accessible to researchers. An analysis of the variation between the solutions is conducted and is shown to be proportional to the degree of inhomogeneity in the polycrystal.

A measurement of the double-polarization observable E for the reaction \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma p\rightarrow \pi ^0 p$$\end{document}γp→π0p is reported. The data were taken with the CBELSA/TAPS experiment at the ELSA facility in Bonn using the Bonn frozen-spin butanol (C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_4$$\end{document}4H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_9$$\end{document}9OH) target, which provided longitudinally-polarized protons. Circularly-polarized photons were produced via bremsstrahlung of longitudinally-polarized electrons. The data cover the photon energy range from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E_\gamma =600$$\end{document}Eγ=600 to 2310 MeV and nearly the complete angular range. The results are compared to and have been included in recent partial wave analyses.

Ultrasound is a prominent nondestructive testing modality for the detection, localization, and sizing of defects in engineering materials. Often, inspectors analyze ultrasonic waveforms to determine if echoes, which stem from the scattering of ultrasound from a defect, exceed a threshold value. In turn, the initial selection of the threshold value is critical. In this letter, a time-dependent threshold or upper bound for the signal envelope is developed based on the statistics governing the scattering of ultrasound from microstructure. The utility of the time-dependent threshold is demonstrated using experiments conducted on sub-wavelength artificial defects. The results are shown to enhance current nondestructive inspection practices.

We report an in-depth look into commonly applied theories describing the propagation of ultrasound in polycrystalline materials. The analysis indicates that integrals involving multiple spatial derivatives on the tensor of the Green’s function were inappropriately defined as a result of neglecting its singularity. The subsequent impact is demonstrated via an instability in the dispersion relations for two-phase polycrystals having locally isotropic constituents. Evaluation of the dispersion relation reveals non-physical values of negative attenuation in certain cases. Correcting these terms accounts for strong property fluctuations and provides quantitative error estimates for the velocity dispersion and attenuation constants.

The $\overline{{\rm{P}}}\mathrm{ANDA}$ (anti-Proton ANnihiliation at DArmstadt) experiment will be one of the four flagship experiments at the new international accelerator complex FAIR (Facility for Antiproton and Ion Research) in Darmstadt, Germany. $\overline{{\rm{P}}}\mathrm{ANDA}$ will address fundamental questions of hadron physics and quantum chromodynamics using high-intensity cooled antiproton beams with momenta between 1.5 and 15 GeV/c and a design luminosity of up to 2 × 1032 cm−2 s−1. Excellent particle identification (PID) is crucial to the success of the $\overline{{\rm{P}}}\mathrm{ANDA}$ physics program. Hadronic PID in the barrel region of the target spectrometer will be performed by a fast and compact Cherenkov counter using the detection of internally reflected Cherenkov light (DIRC) technology. It is designed to cover the polar angle range from 22° to 140° and will provide at least 3 standard deviations (s.d.) π/K separation up to 3.5 GeV/c, matching the expected upper limit of the final state kaon momentum distribution from simulation. This documents describes the technical design and the expected performance of the $\overline{{\rm{P}}}\mathrm{ANDA}$ Barrel DIRC detector. The design is based on the successful BaBar DIRC with several key improvements. The performance and system cost were optimized in detailed detector simulations and validated with full system prototypes using particle beams at GSI and CERN. The final design meets or exceeds the PID goal of clean π/K separation with at least 3 s.d. over the entire phase space of charged kaons in the Barrel DIRC.

The Hashin-Shtrikman bounds on the elastic constants have been previously calculated for polycrystalline materials with crystallites having general elastic symmetry (triclinic crystallite symmetry). However, the calculation of tighter bounds and the self-consistent estimates of these elastic constants has remained unsolved. In this paper, a general theoretical expression for the self-consistent elastic constants is formulated. An iterative method is used to solve the expression for the self-consistent estimates. Each iteration of the solution gives the next tighter set of bounds including the well-known Voigt-Reuss and Hashin-Shtrikman bounds. Thus, all of the bounds on the elastic constants and the self-consistent estimates for any crystallite symmetry are obtained in a single, computationally efficient procedure. The bounds and self-consistent elastic constants are reported for several geophysical materials having crystallites of monoclinic and triclinic symmetries. HighlightsA homogenization model for the elastic constants of polycrystals is given.An iterative solution produces the effective bulk and shear modulus.Voigt-Reuss and Hashin-Shtrikman bounds are obtained within the iterative solution.Self-consistent elastic constants are obtained when the iterative solution converges.The model applies to isotropic polycrystals containing crystallites of any symmetry.

Bound nuclear systems with two units of strangeness are still poorly known despite their importance for many strong interaction phenomena. Stored antiprotons beams in the GeV range represent an unparalleled factory for various hyperon-antihyperon pairs. Their outstanding large production probability in antiproton collisions will open the floodgates for a series of new studies of systems which contain two or even more units of strangeness at the PANDA experiment at FAIR. For the first time, high resolution gamma-spectroscopy of doubly strange Lambda Lambda-hypernuclei will be performed, thus complementing measurements of ground state decays of Lambda Lambda-hypernuclei at J-PARC or possible decays of particle unstable hypernuclei in heavy ion reactions. High resolution spectroscopy of multistrange Xi(-) -atoms will be feasible and even the production of Omega(-) -atoms will be within reach. The latter might open the door to the vertical bar S vertical bar = 3 world in strangeness nuclear physics, by the study of the hadronic Omega(-) -nucleus interaction. For the first time it will be possible to study the behavior of Xi(+) in nuclear systems under well controlled conditions. (C) 2016 Elsevier B.V. All rights reserved.

Elastic wave scattering is used to study polycrystalline media for a wide range of applications. Received signals, which include scattering from the randomly oriented grains comprising the polycrystal, contain information from which useful microstructural parameters may often be inferred. Recently, a mode-converted diffuse ultrasonic scattering model was developed for evaluating the scattered response of a transverse wave from an incident longitudinal wave in a polycrystalline medium containing equiaxed single-phase grains with cubic elastic symmetry. In this article, that theoretical mode-converted scattering model is modified to account for grain elongation within the sample. The model shows the dependence on scattering angle relative to the grain axis orientation. Experimental measurements were performed on a sample of 7475-T7351 aluminum using a pitch-catch transducer configuration. The results show that the mode-converted scattering can be used to determine the dimensions of the elongated grains. The average grain shape determined from the experimental measurements is compared with dimensions extracted from electron backscatter diffraction, an electron imaging technique. The results suggest that mode-converted diffuse ultrasonic scattering has the potential to quantify detailed information about grain microstructure.

Stress-dependent elastic moduli of polycrystalline materials are used in a statistically based model for the scattering of ultrasonic waves from randomly oriented grains that are members of a stressed polycrystal. The stress is assumed to be homogeneous and can be either residual or generated from external loads. The stress-dependent elastic properties are incorporated into the definition of the differential scattering cross-section, which defines how strongly an incident wave is scattered into various directions. Nine stress-dependent differential scattering cross-sections or scattering coefficients are defined to include all possibilities of incident and scattered waves, which can be either longitudinal or (two) transverse wave types. The evaluation of the scattering coefficients considers polycrystalline aluminum that is uniaxially stressed. An analysis of the influence of incident wave propagation direction, scattering direction, frequency, and grain size on the stress-dependency of the scattering coefficients follows. Scattering coefficients for aluminum indicate that ultrasonic scattering is much more sensitive to a uniaxial stress than ultrasonic phase velocities. By developing the stress-dependent scattering properties of polycrystals, the influence of acoustoelasticity on the amplitudes of waves propagating in stressed polycrystalline materials can be better understood. This work supports the ongoing development of a technique for monitoring and measuring stresses in metallic materials.

Traditionally, the propagation of bulk elastic waves in anisotropic crystals or solids is governed by the displacement form of the elastodynamic wave equation. Phase velocities follow after transforming the wave equation into an eigenvalue problem, which gives the Christoffel equations, and solving for the roots of the characteristic polynomial. Alternatively, only a few researchers have considered a pure stress wave equation of motion to describe the propagation of waves in elastic solids. However, to our knowledge, the dual characteristic polynomial and its solutions based on a pure stress formalism has not been established previously. This presentation will outline the needed steps to reach and solve the dual characteristic polynomial. Phase velocity solutions follow from the formation of new principal invariants, which are functions of the elastic compliance constants and propagation directions. The dual formalism is proven consistent to the traditional displacement formalism through the use of sixth-rank Levi-Civitia identities. Lastly, possible extensions of this work will be highlighted.

The propagation and properties of Rayleigh waves on curved surfaces are investigated theoretically. The Rayleigh wave dispersion equation for propagation on a curved surface is derived as a parabolic equation, and its penetration depth is analyzed using the curved surface boundary. Reciprocity is introduced to model the diffracted Rayleigh wave beams. Simulations of Rayleigh waves on some canonical curved surfaces are carried out, and the results are used to quantify the influence of curvature. It is found that the velocity of the surface wave increases with greater concave surface curvature, and a Rayleigh wave no longer exists once the surface wave velocity exceeds the bulk shear wave velocity. Moreover, the predicted wave penetration depth indicates that the energy in the Rayleigh wave is transferred to other modes and cannot propagate on convex surfaces with large curvature. A strong directional dependence is observed for the propagation of Rayleigh waves in different directions on surfaces with complex curvatures. Thus, it is important to include dispersion effects when considering Rayleigh wave propagation on curved surfaces.

The polarization observables T , E , P , H , and G in photoproduction of η mesons off protons are measured for photon energies from threshold to W = 2400 MeV (T), 2280 MeV (E), 1620 MeV ( P , H ), or 1820 MeV (G), covering nearly the full solid angle. The data are compared to predictions from the SAID, MAID, JuBo, and BnGa partial-wave analyses. A refit within the BnGa approach including further data yields precise branching ratios for the Nη decay of nucleon resonances. A Nη-branching ratio of 0.33 ± 0.04 for N ( 1650 ) 1 / 2 − is found, which reduces the large and controversially discussed Nη-branching ratio difference of the two lowest mass J P = 1 / 2 − -resonances significantly.

The first measurements of the beam-target-helicity-asymmetries $E$ and $G$ in the photoproduction of $\omega$-mesons off protons at the CBELSA/TAPS experiment are reported. $E$ ($G$) was measured using circularly (linearly) polarised photons and a longitudinally polarised target. $E$ was measured over the photon energy range from close to threshold ($E_\gamma = 1108$~MeV) to $E_\gamma = 2300$~MeV and $G$ at a single energy interval of $1108 < E_\gamma, Comment: 6 pages, 6 figures