Recent Progress in Ultrasonic Nondestructive Characterization of Material Microstructures: A Review

The scattering and attenuation of high frequency ultrasonic wave in polycrystalline materials such as metal and ceramics have implication of material microstructures. Many studies have recently developed sophisticate forward models that corelate ultrasonic scattering and attenuation with different types of polycrystalline materials. Furthermore, some studies have proposal effective methodologies to nondestructively determine polycrystal microstructures from ultrasonic measurements, namely solving the inversion problems. Its applications cover titanium alloys in aerospace, carbon steels in transportation, additively manufactured components and machineries, to name a few. This paper reviews recent progress in ultrasonic nondestructive characterization of metal microstructures, including voids, grain size, crystallographic texture and grain boundary.


Introduction
Polycrystalline materials including metals and ceramics are materials that consist of numerous grains in the micro scale level, and they thus are heterogeneous materials in the micro scale.Polycrystalline materials may be anisotropic in the macro scale level when crystallographic texture exists (grains align in a preferred direction) [1], [2].Due to the variance of physical properties, polycrystalline materials are used in engineering structures such as pipeline, pressure vessel and machineries, and functional materials, such as semiconductors and magnets [2].The applications of polycrystalline materials range from aerospace, defense, semiconductor, machinery, energy industry and transportation.
When ultrasonic waves propagate in a heterogeneous polycrystalline material, several interesting ultrasound-microstructure interaction phenomena will happen, including velocity dispersion, scattering, and attenuation [3]- [8].For an intact polycrystal, ultrasonic scattering occurs at the boundaries between adjacent grains (scatters) because of the abrupt change in elastic constant matrices between two neighboring grains and the scattering further leads to wave beam attenuation.Furthermore, the scattering is ubiquitously and it may be picked up in an arbitrary direction with an ultrasonic transducer [9].A measure of scattering strength is called scattering cross-section [10], which depends on several factors such as ultrasonic wave frequency, scatter size and grain anisotropy.When defects such as inclusion, crack or porosity exist in the polycrystalline material, wave-defect interaction, and wave-grain interaction both exist.In this scenario, the incident wave is not only scattered on the grain boundaries but also on the defect/grain interface, namely both defect and grain act as scatters.Typically, the defect-caused scattering surpasses the grain scattering by several orders owing to stronger elasticity contrast between defect and polycrystalline matrix and it thus dominates the scattering phenomenon, which explains the observation in the ultrasonic nondestructive testing.Therefore, the ultrasonic scattering signals includes valuable information about the microstructure such as defect size and grain size.Due to physical nonlinearity of polycrystalline materials, ultrasonic waves that have finite amplitude would cause harmonics and other complex wave-microstructure interactions.However, nonlinear wave is out of the scope of this article.
The practical needs of nondestructive characterization of polycrystalline materials, especially metals, attract much attention from researchers.The state-of-art approach is to develop forward model for a specific type of polycrystalline microstructure and then develop inverse model to retrieve the microstructure information from ultrasonic measurement results.Recent progress in forward models quantitatively explains ultrasonic scattering in intact polycrystalline materials that are made of triclinic symmetry grains and these with crystallographic texture [8].Furthermore, the numerical modeling of ultrasound scattering in polycrystalline material thrill and it offer great insight into wave scattering [7], [11].Additionally, the scattering of bulk wave and surface Rayleigh wave have been studies quantitatively [12].It is worth mentioning that in most cases inversion of microstructure relay on analytical model where the relationship between ultrasonic scattering or attenuation and grain size is expressed explicitly.
Recent progress in ultrasonic nondestructive characterization of microstructures is significant and opens many opportunities to solve industrial challenges.It covers nondestructive characterization of additively manufactured component [13], [14], metal microstructures with elongated grains, crystallographic texture [15], residual stress, and metals with inhomogeneous microstructure [7].Ultrasonic characterization has become a valuable tool to ensure the quality and integrity of metal components through various manufacturing processes such as additively manufacturing, casting, sintering, and welding.Through advancements in analytical modeling, numerical modeling, advanced signal processing technique and ultrasonic inversion algorithm, researchers are expanding the applications of ultrasonic characterization method in metal microstructure.This paper will give a detailed review about these advancements.

Analytical Modeling
Several types of rigorous analytical models such as Karal & Keller model [16], perturbation theory [17]- [19], and spectral function method [20], [21] exist.Weaver type forward model [22] is the most popular analytical modeling for ultrasonic nondestructive characterization of metal microstructures.This type of model assumes single scattering and weak scattering in polycrystalline material.Thus, the scattering inducted attenuation results from an assembly of scattering events on individual grains.Due to the randomness of the grain orientation, the scattering on a single beam path may not be repeatable from one location to another but the statistical average is an important metric to quantify the scattering strength of the polycrystalline material.This is different from the wave scattering form a single inclusion (Figure 1) where the scattered wave field can be solved explicitly.The ultrasonic scattering or attenuation from a polycrystal is a function of grain shape, single crystal elastic constants and two-point correlation function.Current forward models have considered different grain shapes [23]- [26] and arbitrary crystal symmetries [27], [28].The two-point correlating function describes the elastic tensor correlation at two random points and normally it is split into tensorial part and a geometric part [22].The tensorial part for elastic constants has been derived for triclinic grains [8], [29], [30] while the geometric part is a probabilistic function related to grain size and morphology [23], [31], [32].An example of two-point correlation function is shown in Figure 2. It is worthy to mention that some studies proposed empirical attenuation models that work well for grain size determination [33], [34].

Numerical Modeling
Most studies on numerical modeling of wave propagation in polycrystalline material use finite element method (FEM) and representative elementary volume (RVE).Recent progress on wave scattering in polycrystalline using finite element method is significant because it verifies analytical forward models more rigorously than experiments [24], [25], [27], [35]- [37].In most cases, the polycrystalline material microstructure is approximated by threedimensional synthetic microstructures.The synthetic microstructures are called Voronoi tessellation grains.The real microstructures (Figure 3a) may have abnormal grain shape and grain size while the Voronoi tessellation grains (Figure 3b) have to be in convex shape.Furthermore, the Voronoi tessellation grains have been adopted in many driplines to ensemble grain structures [38].Solving the wave scattering form polycrystalline materials in FEM needs to mesh the individual grains and set up proper boundary conditions [37], [39].The solver may also require a large amount of computation resources such as CPU and memory, especially on 3D models.Many studies have found that the analytical model and the FEM have good agreement [7], [27], [35], [40] and one comparison example between FEM and analytical models [27] is shown in Figure 4, which lays a foundation for ultrasonic nondestructive characterization of grain size by inversion.

Ultrasonic Inversion Algorithm
Ultrasonic inversion to retrieve microstructure information can be achieved either by physics-based model [9], [41]- [45] or by machine learning model [46].Typically, the physics-based inversion model is developed based on forward model and it has explicit physical explanation and relatively wide applications, for example, one inversion model may be applicable to various types of metals.The machine learning model is purely achieved by training and cross validation on a large amount of experimental data.It may be more accurate on a specific case, but the machine learning model training may be time consuming and numerous experimental measurements are costly.Besides, the machine learning model has to be trained again when it is deployed to a new alloy even if transfer learning can be conducted.
In most cases, the grain size can be determined from ultrasonic measurements by nonlinear function fitting, but grain clusters in titanium alloy cause extra complexity in model-based inversion [44].This problem requires careful design of inversion algorithm and a thorough study about the reliability and uniqueness of the inversion method.Therefore, the same study [44], proposed an inversion methodology that uses ultrasonic backscattering and attenuation data to retrieve cluster sizes and morphology.Additional study has also been conducted on the reliability of the inversion method, namely add noise to the ultrasonic data and validate the inversion outputs as shown in Figure 5.For a single phase cubic polycrystalline material, the ultrasonic inversion method can provide more information other than grain size.Simultaneous characterization of grain size and elastic constants has been achieved on polycrystalline copper [43], with a novel inversion method and inversion results are validated by comparison with other resources.
Characterization of grain size distribution is a challenge to model-based inversion because grain size impact on attenuation is subtitle at certain frequency ranges [4], [47].However, machine learning model has solved this challenge on aluminum alloy as reported in Ref. [46] where laser ultrasonic method is employed to measure the attenuation and random swarm optimization has been used to find the best weights and activation for the neural network.
The neural network proposed in a study [46], which has 11 inputs and 2 output and the corresponding neural network is reconstructed in Figure 6.

Applications of Ultrasonic Nondestructive Characterization
This section discusses recent progress in nondestructive characterization of microstructure, with a focus on linear ultrasound techniques, for the metal components fabricated by advanced manufacturing including additive manufacturing.

Voids and Defects Inspection for Additive Manufacturing
Additive manufacturing, also known as 3D printing, has evolved rapidly over the past decades and accelerated the fabrication of intricate components across different industries, including aerospace, defense, and healthcare.Comment AM methods cover powder bed fusion (PBF), directed energy deposition (DED), binder jetting, and wire ace additive manufacturing.One example setup for WAAM is shown in Figure 7.Although AM provides numerous benefits, such as reduced waste and complex geometry, AM components often encompass defects and complex microstructures due to the fast cooling of the molten pool in the layer-by-layer deposition process.Such defects and undesired microstructures are detrimental to the mechanical properties of the AM parts.Therefore, reducing defects and ensuring microstructure quality of manufactured parts remains a challenge.Ultrasonic testing (UT) has approved to be a versatile and effective method for assessing structural integrity of AM parts and has gained significant attention recently due to its capability to detect defects, characterize microstructures, and measure residual stresses within AM components.A review of ultrasonic testing applications in additive manufacturing, including defect inspection, material property characterization, and process control [14], has been reported, and it highlights the significance of UT in quality control of additively manufactured components.In addition, high frequency ultrasonic NDE has been proposed to determine the material properties of additively manufactured components such as material strength, and elastic modulus [48].

Defect or Void Inspection
Ultrasonic non-destructive evaluation (NDE) techniques are critical in inspecting defects and material inconsistencies of AM components that can compromise their performance and reliability.Normally, porosity is a major in AM part, for example, the porosity in the steel sample in Figure 8. Ultrasonic wave scattering is sensitive to various types of defects, including porosity, cracks, and delamination.Advanced signal processing techniques, such as machine learning and tomography, allow accurate defect sizing and localization.In ultrasonic testing of AM component evaluation, the selections of transducer type ultrasonic frequency, and inspection setup are crucial in determining the sensitivity and resolution of the inspection.High-frequency ultrasound (5 MHz range) performs well for inspecting micro-scale defects and fine grain microstructures, while low frequency ultrasound is suitable for bulk material evaluation.
High frequency UT has been used to evaluate the voids of additively manufactured parts [48] and phased array ultrasonic testing (PAUT) has been employed towards in-situ defect monitoring for metallic additive manufacturing components [49].In addition, ultrasonic scattering inspection has been proposed as an approach for improved methods of additive manufacturing.Ultrasonic immersion testing has also been investigated to evaluate artificial defects in AM turbine blades, where a 15 MHz focused immersion transducer attached to a positioning system is used to scan the specimen and scattering signals at individual spots are collected and analyzed to detect defects [50].
Generally, UT utilizes bulk waves to inspect volumetric defects or characterize macro level material properties and special angled UT transducers must be used to generate and receive surface or near surface waves such as Rayleigh wave and creeping wave for surface defect inspection.However, such surface inspection method may surfer limited sensitivity because of high wave attenuation and surface roughness.A recent study [51] proposed acoustic meta surface lens (MSL) to detect near surface defects in additively manufactured components and great sensitivity has been achieved with MSL in the detection of near surface defects.
Deep learning-empowered ultrasonic testing has been proposed to assess the porosity of AM parts with rough surfaces [52].Rough surface affects the ultrasonic wave penetration into the AM metal, causing low signal-to-noise (SNR).The study [52] found that CNN assisted ultrasonic testing can overcome the low SNR issue and performs best for detecting the porosity in unpolished AM parts.
Laser ultrasonic method has been used to inspect AM components [53].The results demonstrate that it is a promising approach for the non-contact inspection of AM components.Furthermore, the inspection results have been verified by X-ray computed tomography (CT) and ultrasonic immersion testing (UIT).Multimodal imaging is to combine ultrasonic imaging with other imaging modalities, such as X-ray computed tomography (CT) or thermography of AM components.This multimodal approach provides comprehensive information about the defects and grain structure of the AM part [54].
These studies above have demonstrated the ability of ultrasonic method to detect surface and internal defects in AM components and have approved that ultrasonic scattering-based method is a promising method for defect inspection of AM parts.Ultrasonic method has also been employed to determine the elasticity of additive manufactured Inconel 625 specimens [55].Furthermore, recent studies have evaluated the properties of advanced engineering materials, such as titanium, Inconel, and composites by ultrasonic method [14].

Process Control
Online and offline ultrasonic inspection has been used for the process control of additive manufacturing.One study [56] proposed a smart AM test block for online process control and offline materials characterization using ultrasonic NDE.
Real-time monitoring of AM processes by ultrasonic sensing has gained much attention, specific techniques include phased array ultrasound [49], [57] and laser ultrasonic method [53].By continuously assessing the quality of each layer during deposition, manufacturers can identify defects early in the production process for manufacturing parameters optimization.
In conclusion, recent studies have demonstrated that ultrasonic testing performs well in evaluating the quality of AM components.Ultrasonic method including PAUT, immersion ultrasonic, MSL, laser ultrasound and machine learning based UT has been applied to defect inspection, material characterization, residual stresses, and process control of additively manufactured components and it has shown great potential in large scale industrial applications.
Although ultrasonic scattering-based method has shown great promise in the inspection of additively manufactured components, several challenges still exist: 1) anisotropic materials due to crystallographic texture in the AM which can complicate the interpretation of ultrasonic signals.2) lack of Standards and Qualification to ensure reliability and consistency across various industries.3) High-Temperature Environments for in situ ultrasonic nondestructive evaluation.

Grain Size and Grain Morphology
Statistical elastic wave scattering amplitude at grain boundaries in polycrystalline media can be quantified as a function of grain structure, and such an analytical model can be used to determine microstructural properties from ultrasonic measurement.The coherent wave attenuation and diffuse-field scattering events have been extensively investigated [31], [44], [58].In all studies, the scattering amplitude shows a clear dependence on grain size, grain shape, and grain size distribution.Analytical models applicable to predicting grain scattering are often developed assuming dependent scattering on a single spatial length scale, namely mean grain diameter.
Nondestructive characterization of average grain size and morphology using ultrasonic scattering or scattering induced attenuation has been reported by numerous studies [6], [26], [45], [59]- [61].The characterization of mean grain sizes has been achieved by analyzing the attenuation of high-frequency ultrasonic waves generated and received by a Laser Ultrasonics System (LUS) setup [62].Additionally, LUS has been used to estimate grain size and composition in steel at elevated temperatures.Typical ultrasonic characterization method based on attenuation coefficient, which has been applied to determine mean grain size, is less sensitive to grain size distribution.However, a particle swarm optimization neural network has been proposed to estimate grain size distribution in aluminum alloy [46], namely mean and standard deviation in the log-normal function.The In another paper, experimental ultrasonic backscattering data have been used to inversely determine grain size in metal alloys using laser ultrasonic technique [63].The method is based on the explicit relationship between the ultrasonic attenuation coefficient and the mean grain diameter.In one research [63] a model has been developed to retrieve the grain size based on the centroid frequency shift of ultrasonic wave echoes.The characterization results have been verified by metallographic inspections in α-titanium.Furthermore, ultrasonic nondestructive techniques have been used to characterize average grain size and to assess mechanical properties of metals, which is more practical than other methods.
The nondestructive characterization of grain size using ultrasonic attenuation in 316L stainless steel has been studied [33], the relationship between wave attenuation and the grain size is quantified as a power law.The results indicate that ultrasonic attenuation can be used as a nondestructive method to evaluate the grain size of stainless steel.But anther study [45], has used the second-order attenuation model and grain-scale 3D finite element modelling to investigate the capabilities and limitation of ultrasonic attenuation-based characterization method.
A reliable inversion methodology for ultrasonic nondestructive characterization of titanium alloy with clusters of preferentially oriented near alpha grains has been developed using immersion ultrasound [44].An example of immersion ultrasonic system and ultrasonic signal is shown in Figure 9.The two-step inversion methodology is based on the ultrasonic attenuation coefficient and the backscattering amplitude.The ultrasonic inversion methodology is validated by comparing the results with those obtained by the electron backscatter diffraction.It illustrates that the ultrasonic nondestructive method is an efficient and accurate tool to characterize titanium alloys with clusters of preferentially oriented grains [44].

Crystallographic Texture and 3D Grain Boundary
Crystallographic texture refers to the preferred orientation of crystalline grains within a material crystallographic texture in metals profoundly influences material properties and performance such as mechanical, thermal, and magnetic properties.The common methods for quantitative crystallographic texture characterization are x-ray diffraction, neutron diffraction and EBSD [64].EBSD is only suitable for characterizing the orientations of surface grains while X ray diffraction has limited penetration depth.Neutron diffraction is capable of characterizing texture of bulky samples up to several centimeter thickness [65].A quantitative measure of crystallographic texture is the orientation distribution function (ODF), which is a summation of harmonic functions with different order [66].The coefficients of the harmonic functions are called orientation distribution coefficients (ODCs) [67].Ultrasonic techniques have become a feasible tool to evaluate crystallographic texture in metals [68], [69].The primary technique to assess crystallographic texture in metals is the measurement of ultrasonic phase velocity.A polycrystalline material with texture would exhibit anisotropic elastic constants and the degree of anisotropy is governed by the extent of crystallographic texture.When ultrasonic wave penetrates this material in different directions, the resulting ultrasonic velocity would show direction dependence.These changes can be quantified by Christoffel equation [68], [69].
Generally, one needs to measure the ultrasonic phase velocities in multiple angles and back calculate the ODCs based on the analytical expressions between ODF and ultrasonic velocities.
To obtain a quantitative description of crystallographic texture in 3D space, it is essential to design an effective algorithm to reconstruct the orientation distribution function (ODF) from ultrasonic measurements.The ultrasonic characterization of crystallographic texture in a bulk sample has been implemented by a deconvolution method [70].
The surface grain orientation can be determined from inversion of surface wave velocities that measured by laser ultrasonic method [71] and it can achieve good resolution as EBSD.The Brillouin scattering in laser ultrasound is another approach to determine grain orientation of surface grains and it relies on super high frequency ultrasound at micron level spatial resolution, as shown in Figure 10.In addition, the grain boundary of subsurface grains [72] also can be reconstructed based on Brillouin scattering as shown in Figure 11.

Residual Stress and Inhomogeneity
Residual stresses happen in AM components because of the rapid solidification and thermal gradients during the manufacturing process.There is a good correlation between ultrasonic velocity and residual stress amplitude due to acoustoelastic effect.Ultrasonic wave velocity measurement has been used to evaluate residual stress quantitatively in aluminum alloy [73].Surface longitudinal wave method using a pair of angle beam transducers is also a reliable method to measure residual stress [74].Ultrasonic scattering or attenuation map at local area also can be an indicator of microstructure heterogeneity.A uniform microstructure would cause uniform scattering strength over the sample while a sample with inhomogeneous microstructure would result in variance in ultrasonic scattering map pattern.For example, the titanium sample exhibits heterogenous microstructure due to forging while its scattering map also shows distinct pattern from one side to the other as shown in Figure 12.This study [44], has approved that the ultrasonic scattering pattern has good correlation with microstructure heterogeneity.X Axis (mm) 0.01200 0.01500 0.01800 0.02100 0.02400 0.02700 0.03000 0.03300 0.03600

Conclusions
Polycrystalline materials have served as critical structural and functional materials in various industries such as transportation, semiconductor industry and clean energy.The microstructure of a polycrystalline material needs careful design to achieve its desired properties.Thus, microstructure characterization is an indispensable tool to ensure microstructure quality.Compared to optical microstructure characterization, ultrasound based nondestructive microstructure characterization has several advantages and it becomes prevalent in industrial applications.This paper reviews recent work in ultrasonic nondestructive characterization of metal microstructures, including the principle and detailed applications.All the papers demonstrated that ultrasonic nondestructive characterization is indeed a practical method to solve industrial challenges.The future trends in ultrasonic nondestructive characterization will be more focused on materials with complex microstructures such as additively manufactured components and functionally graded materials.

Figure 1 .
Figure 1.Demonstration of longitudinal plane wave scattering from a single inclusion

Figure 2 .
Figure 2. Two-point correlation function for polycrystalline materials.

Figure 3 .
Figure 3. (a) microstructure image by optical microscopy and (b) synthetic microstructure by Voronoi tessellation grains.

Figure 4 .
Figure 4. Comparison between analytical model and numerical model for validation of analytical model.

Figure 5 .
Figure 5. Diagram for studying the reliability of the ultrasonic model-based inversion.

Figure 6 .
Figure 6.A reconstructed diagram for the fully connected neural network mentioned with 11 input neurons, 10 neurons on the hidden layer and two output neurons.

Figure 9 .
Figure 9. Configuration of immersion ultrasonic testing and an example of ultrasonic backscattering signal.
deep learning model does not require a physical model and avoids the requirement of developing complicated attenuation model for grain size distribution.