Stress-dependent ultrasonic scattering in polycrystalline materials

Spatial and directional characterization of wire and arc additive manufactured aluminum alloy using phased array ultrasonic backscattering method

Pores, grains, or textures can collectively cause microstructural inhomogeneity and anisotropy in metallic materials fabricated by additive manufacturing. In this study, a phased array ultrasonic method is developed to characterize the inhomogeneity and anisotropy of wire and arc additively manufactured components by performing both beams focusing and steering. Two backscattering features, i.e., the integrated backscattering intensity and the root mean square of the backscattering signals, are employed to quantify the microstructural inhomogeneity and anisotropy, respectively. An experimental investigation is performed using an aluminum sample fabricated by wire and arc additive manufacturing. The ultrasonic measurements, performed on wire and arc additive manufactured 2319 aluminum alloy, show that the sample is inhomogeneous and weakly anisotropic. Metallography, electron backscatter diffraction, and X-ray computed tomography are used to verify the ultrasonic results. An ultrasonic scattering model is used to identify the influence of grains on the backscattering coefficient. Compared with a wrought aluminum alloy, the complex microstructure in additively manufactured material significantly influence the backscattering coefficient, and the presence of pores cannot be neglected in ultrasonic-based nondestructive evaluation for wire and arc additive manufactured metals.

The effect of external load on ultrasonic wave attenuation in steel bars under bending stresses

The stress state in deformed solids has a significant impact on the attenuation of an ultrasonic wave propagating through the medium. Measuring a signal with certain attenuation characteristics can therefore provide useful diagnostic information about the stress state in the structure. In this work, basic principles behind a novel attenuation-based diagnostic framework are introduced. An experimental study on steel bars under three-point bending was carried out, and finite element analyses were used to numerically model the experiments. Obtained test results showed a strong correlation between the external load and the ultrasonic signal energy, which decreases with increasing load. A similar but positive correlation appeared between the level of attenuation of longitudinal ultrasonic wave signals and the external load, which allowed for efficient estimation of the mid-span bending moment. Upon proper calibration of testing equipment, the change in ultrasonic signal energy can therefore be used as an indicator of the external load level. As a result, this effect has potential applications in non-destructive structural health monitoring frameworks.

A New Axial Stress Measurement Method for High-Strength Short Bolts Based on Stress-Dependent Scattering Effect and Energy Attenuation Coefficient

The accurate estimation of axial stresses is a major problem for high-strength bolted connections that needs to be overcome to improve the assembly quality and safety of aviation structures. However, the conventional acoustoelastic effect based on velocity-stress dependence is very weak for short bolts, which leads to large estimation errors. In this article, the effect of axial stress on ultrasonic scattering attenuation is investigated by calculating the change in the energy attenuation coefficient of ultrasonic echoes after applying axial preload. Based on this effect, a stress-dependent attenuation estimation model is developed to measure the bolt axial stress. In addition, the spectrum of the first and second round-trip echoes is divided into several frequency bands to calculate the energy attenuation coefficients, which are used to select the frequency band sensitive to the axial stress changes. Finally, the estimation model between axial stress and energy attenuation coefficients in the sensitive frequency band is established under 20 steps of axial preloads. The experimental results show that the energy attenuation coefficient in the sensitive band corresponds well with axial stress. The average relative error of the predicted axial stress is 6.28%, which is better than that of the conventional acoustoelastic effect method. Therefore, the proposed approach can be used as an effective method to measure the axial stress of short bolts in the assembly of high-strength connections.

Influence of residual stress and texture on the resonances of polycrystalline metals

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.

Attenuation and velocity of elastic waves in polycrystals with generally anisotropic grains: Analytic and numerical modeling

Better understanding of elastic wave propagation in polycrystals has interest for applications in seismology and nondestructive material characterization. In this study, a second-order wave propagation (SOA) model that considers forward multiple scattering events is developed for macroscopically isotropic polycrystals with equiaxed grains of arbitrary anisotropy (triclinic). It predicts scattering-induced wave attenuation and dispersion of phase velocity. The SOA model implements the generalized two-point correlation (TPC) function, which relates to the actual numeric TPC of simulated microstructure. The analytical Rayleigh and stochastic asymptotes for both attenuation and phase velocity are derived for triclinic symmetry grains, which elucidate the effects of the elastic scattering factors and the generalized TPC in different frequency regimes. Also, the computationally efficient far field approximation attenuation model is obtained for this case; it shows good agreement with the SOA model in all frequency ranges. To assess the analytical models, a three-dimensional (3D) finite element (FE) model for triclinic polycrystals is developed and implemented on simulated 3D triclinic polycrystalline aggregates. Quantitative agreement is observed between the analytical and the FE simulations for both the attenuation and phase velocity. Also, the quasi-static velocities obtained from the SOA and FE models are in excellent agreement with the static self-consistent velocity.

Attenuation and Phase Velocity of Elastic Wave in Textured Polycrystals with Ellipsoidal Grains of Arbitrary Crystal Symmetry

This study extends the second-order attenuation (SOA) model for elastic waves in texture-free inhomogeneous cubic polycrystalline materials with equiaxed grains to textured polycrystals with ellipsoidal grains of arbitrary crystal symmetry. In term of this work, one can predict both the scattering-induced attenuation and phase velocity from Rayleigh region (wavelength >> scatter size) to geometric region (wavelength << scatter size) for an arbitrary incident wave mode (quasi-longitudinal, quasi-transverse fast or quasi-transverse slow mode) in a textured polycrystal and examine the impact of crystallographic texture on attenuation and phase velocity dispersion in the whole frequency range. The predicted attenuation results of this work also agree well with the literature on a textured stainless steel polycrystal. Furthermore, an analytical expression for quasi-static phase velocity at an arbitrary wave propagation direction in a textured polycrystal is derived from the SOA model, which can provide an alternative homogenization method for textured polycrystals based on scattering theory. Computational results using triclinic titanium polycrystals with Gaussian orientation distribution function (ODF) are also presented to demonstrate the texture effect on attenuation and phase velocity behaviors and evaluate the applicability and limitation of an existing analytical model based on the Born approximation for textured polycrystals. Finally, quasi-static phase velocities predicted by this work for a textured polycrystalline copper with generalized spherical harmonics form ODF are compared to available velocity bounds in the literature including Hashin–Shtrikman bounds, and a reasonable agreement is found between this work and the literature.

Pressure influence on elastic wave attenuation in polycrystalline 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 wave propagation predictions for polycrystalline materials using three-dimensional synthetic microstructures: Phase velocity variations

In most theoretical work related to effective properties of polycrystals, the media are assumed to be infinite with randomly oriented grains. Therefore, the bulk material has absolute isotropy because each direction includes an infinite number of grains with infinite possibilities for grain orientation. However, real samples will always include a finite number of grains such that the inspection volume will have some associated anisotropy. Thus, bounds on the bulk properties are expected for a given measurement. Here, the effect of the number of grains on the variations of elastic anisotropy is studied using synthetic polycrystals comprised of equiaxed cubic grains (17 volumes with 100 realizations each). Voigt, Reuss, and self-consistent techniques are used to derive the effective elastic modulus tensor. The standard deviation of the average elastic modulus is then quantified for several materials with varying degrees of single-crystal anisotropy and is shown to be inversely proportional to the square root of the number of grains. Finally, the Christoffel equation is used to study the relevant phase velocities. With appropriate normalization, a master curve is derived with respect to the finite sample size, which shows the expected variations of phase velocity for the longitudinal, fast shear, and slow shear modes.

Enhanced Ultrasonic Flaw Detection using an Ultra-high Gain and Time-dependent Threshold

In an attempt to improve the ultrasonic testing capability of a conventional C-scan system, a flaw detection method using an ultra-high gain is developed in this paper. A time-dependent threshold for image segmentation is applied to identify automatically material anomalies present in the sample. A singly-scattered response (SSR) model is used with extreme value statistics to calculate the confidence bounds of grain noise. The result is a time-dependent threshold associated with the grain noise that can be used for segmentation. Ultrasonic imaging experiments show that the presented method has advantages over a traditional fixed threshold approach with respect to false positives and missed flaws. The results also show that a low gain is adverse to the detection of micro-flaws with subwavelength dimensions. The forward model is expected to serve as an effective tool for the probability of detection (POD) of flaws and the inspection of coarse-grained materials in the future.

Iterative solution to bulk wave propagation in polycrystalline materials

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.