Guided acoustic waves in thin epitaxial films: Experiment and inverse problem solution for NiTi.

Despite the fundamental and technological importance of the elastic constants, a suitable method for their full characterization in epitaxial films is missing. Here we show that transient grating spectroscopy (TGS) with highly k-vector-selective generation and detection of acoustic waves is capable of determination of all independent elastic coefficients of an epitaxial thin film grown on a single-crystalline substrate. This experimental setup enables detection of various types of guided acoustic waves and evaluation of the directional dependence of their speeds of propagation. For the studied model system, which is a 3µm thin epitaxial film of the NiTi shape memory alloy on an MgO substrate, the TGS angular maps include Rayleigh-type surface acoustic waves as well as Sezawa-type and Love-type modes, delivering rich information on the elastic response of the film under different straining modes. The resulting inverse problem, which means the calculation of the elastic constants from the TGS maps, is subsequently solved using the Ritz-Rayleigh numerical method. Using this approach, tetragonal elastic constants of the NiTi film and their changes with the austenite→martensite phase transition are analyzed.

Non-Hookean large elastic deformation in bulk crystalline metals.

Crystalline metals can have large theoretical elastic strain limits. However, a macroscopic block of conventional crystalline metals practically suffers a very limited elastic deformation of <0.5% with a linear stress-strain relationship obeying Hooke's law. Here, we report on the experimental observation of a large tensile elastic deformation with an elastic strain of >4.3% in a Cu-based single crystalline alloy at its bulk scale at room temperature. The large macroscopic elastic strain that originates from the reversible lattice strain of a single phase is demonstrated by in situ microstructure and neutron diffraction observations. Furthermore, the elastic reversible deformation, which is nonhysteretic and quasilinear, is associated with a pronounced elastic softening phenomenon. The increase in the stress gives rise to a reduced Young's modulus, unlike the traditional Hooke's law behaviour. The experimental discovery of a non-Hookean large elastic deformation offers the potential for the development of bulk crystalline metals as high-performance mechanical springs or for new applications via "elastic strain engineering."

Flexible and Tough Superelastic Co-Cr Alloys for Biomedical Applications.

The demand for biomaterials has been increasing along with the increase in the population of elderly people worldwide. The mechanical properties and high wear resistance of metallic biomaterials make them well-suited for use as substitutes or as support for damaged hard tissues. However, unless these biomaterials also have a low Young's modulus similar to that of human bones, bone atrophy inevitably occurs. Because a low Young's modulus is typically associated with poor wear resistance, it is difficult to realize a low Young's modulus and high wear resistance simultaneously. Also, the superelastic property of shape-memory alloys makes them suitable for biomedical applications, like vascular stents and guide wires. However, due to the low recoverable strain of conventional biocompatible shape-memory alloys, the demand for a new alloy system is high. The novel body-centered-cubic cobalt-chromium-based alloys in this work provide a solution to both of these problems. The Young's modulus of <001>-oriented single-crystal cobalt-chromium-based alloys is 10-30 GPa, which is similar to that of human bone, and they also demonstrate high wear and corrosion resistance. They also exhibit superelasticity with a huge recoverable strain up to 17.0%. For these reasons, the novel cobalt-chromium-based alloys can be promising candidates for biomedical applications.

Characterization of bonding quality of a cold-sprayed deposit by laser resonant ultrasound spectroscopy.

Resonant ultrasound spectroscopy was utilized to determine the mechanical properties of a planar interface between a cold-sprayed iron deposit and an aluminum alloy substrate. The measurements were done at room temperature and with a thermal cycle from room temperature to 500 °C. The properties of the interface were assessed by analyzing the resonant frequencies of a sandwich-like sample by means of a numerical model. While the as-sprayed deposit at the room temperature exhibited a perfect adhesion to the substrate, the thermal cycle led to deterioration of the properties due to precipitation of FeAl3 along the interface and subsequent cracking. The modal analysis enabled localization of the damage zone along the interfaces and simulating its temperature evolution during the cooling run.

Transformation Pathway upon Heating of Metastable ß Titanium Alloy Ti-15Mo Investigated by Neutron Diffraction.

A transformation pathway during thermal treatment of metastable ß Ti-15Mo alloy was investigated by in situ neutron diffraction. The evolution of individual phases α , ß , and ω was investigated during linear heating with two heating rates of 1.9 ∘ C / min and 5 ∘ C / min and during aging at 450 ∘ C . The results showed that with a sufficient heating rate (5 ∘ C / min in this case), the ω phase dissolves before the α phase forms. On the other hand, for the slower heating rate of 1.9 ∘ C / min , a small temperature interval of the coexistence of the α and ω phases was detected. Volume fractions and lattice parameters of all phases were also determined.

Structural characterization of semi-heusler/light metal composites prepared by spark plasma sintering.

A composite of powders of semi-Heusler ferromagnetic shape memory and pure titanium was successfully prepared by spark plasma sintering at the temperature of 950 °C. Sintering resulted in the formation of small precipitates and intermetallic phases at the heterogeneous interfaces. Various complementary experimental methods were used to fully characterize the microstructure. Imaging methods including transmission and scanning electron microscopy with energy dispersive X-ray spectroscopy revealed a position and chemical composition of individual intermetallic phases and precipitates. The crystalline structure of the phases was examined by a joint refinement of X-ray and neutron diffraction patterns. It was found that Co38Ni33Al29 decomposes into the B2-(Co,Ni)Al matrix and A1-(Co,Ni,Al) particles during sintering, while Al, Co and Ni diffuse into Ti forming an eutectic two phase structure with C9-Ti2(Co,Ni) precipitates. Complicated interface intermetallic structure containing C9-Ti2(Co,Ni), B2-(Co,Ni)Ti and L21-(Co,Ni)(Al,Ti) was completely revealed. In addition, C9-Ti2(Co,Ni) and A1-(Co,Ni,Al) precipitates were investigated by an advanced method of small angle neutron scattering. This study proves that powder metallurgy followed by spark plasma sintering is an appropriate technique to prepare bulk composites from very dissimilar materials.

Ultrasonic bandgaps in 3D-printed periodic ceramic microlattices.

The transmission of longitudinal ultrasonic waves through periodic ceramic microlattices fabricated by Robocasting was measured in the 2-12MHz frequency range. It was observed that these structures (scaffolds of tetragonal and hexagonal spatial arrangements with periodicity at length-scales of ∼100µm) exhibit well-detectable acoustic band structures with bandgaps. The locations of these gaps at relatively high frequencies were shown to be in close agreement with the predictions of numerical models, especially for tetragonal scaffolds. For hexagonal scaffolds, a mixing between longitudinal and shear polarizations of the propagation modes was observed in the model, which blurred the matching of the calculated band structures with the experimentally measured bandgaps.

Forward and inverse problems for surface acoustic waves in anisotropic media: a Ritz-Rayleigh method based approach.

We show that the Ritz-Rayleigh method can be used for calculation of velocity of surface acoustic waves (SAWs) propagating in a general direction of an anisotropic medium of arbitrary symmetry class. The main advantage of this method is that expanding the displacement field of SAW into a fixed functional basis transforms the calculation of SAW velocities into a simple linear eigenvalue problem. The correctness and reliability of the proposed approach are verified on experimental SAW data obtained for generally oriented planes of an indium phosphide single crystal. The same experimental datasets are then used to discuss the invertibility of the method, i.e. the possibility of determination of elastic coefficients from SAW measurements in general directions. It is shown that the SAW data obtained on a single generally oriented plane are sufficient for such an inverse calculation for a cubic material only if they are complemented by measurements of velocities of bulk quasi-longitudinal (qL) waves propagating along the same free surface. Moreover, when the SAW and qL data are available from three almost perpendicular faces of a single specimen, the complete elastic tensor (21 independent constants) can be inversely determined, without considering a priori any symmetry constraints to the material.

The effect of antiphase boundaries on the elastic properties of Ni-Mn-Ga austenite and premartensite.

The evolution of elastic properties with temperature and magnetic field was studied in two differently heat-treated single crystals of the Ni-Mn-Ga magnetic shape memory alloy using resonant ultrasound spectroscopy. Quenching and slow furnace cooling were used to obtain different densities of antiphase boundaries. We found that the crystals exhibited pronounced differences in the c' elastic coefficient and related shear damping in high-temperature ferromagnetic phases (austenite and premartensite). The difference can be ascribed to the formation of fine magnetic domain patterns and pinning of the magnetic domain walls on antiphase boundaries in the material with a high density of antiphase boundaries due to quenching. The fine domain pattern arising from mutual interactions between antiphase boundaries and ferromagnetic domain walls effectively reduces the magnetocrystalline anisotropy and amplifies the contribution of magnetostriction to the elastic response of the material. As a result, the anomalous elastic softening prior to martensite transformation is significantly enhanced in the quenched sample. Thus, for any comparison of experimental data and theoretical calculations the microstructural changes induced by specific heat treatment must be taken into account.

Anisotropic elasticity of DyScO3 substrates.

The full elastic tensor of orthorhombic dysprosium scandate (DyScO(3)) at room temperature was determined by resonant ultrasound spectroscopy (RUS). Measurements were performed on three 500 µm thick substrates with orientations (110), (100) and (001) in the Pbnm (a < b < c) setting. For this purpose, a modification of the RUS method was developed, enabling simultaneous processing of the resonant spectra of several platelet-shaped samples with different crystallographic orientations. The obtained results are compared with ab initio calculations and with elastic constants of other rare-earth scandates, and are used for discussion of the in-plane elasticity of the (110)-oriented substrate.

Sensitivity of the resonant ultrasound spectroscopy to weak gradients of elastic properties.

The applicability of resonant ultrasound spectroscopy on materials with weak spatial gradients in elastic coefficients and density is analyzed. It is shown that such gradients do not affect measurably the resonant spectrum but have a significant impact on the modal shapes. A numerical inverse procedure is proposed to explore the possibility of reconstructing the gradients from experimentally obtained modal shapes. This procedure is tested on synthetic data and applied to determine the gradient of the shear modulus in a continuously graded silicon nitride ceramic material. The results are in a good agreement with the gradient calculated for the examined material theoretically as well as with the results of other experimental methods.

Linearized forward and inverse problems of the resonant ultrasound spectroscopy for the evaluation of thin surface layers.

In this paper, linearized approximations of both the forward and the inverse problems of resonant ultrasound spectroscopy for the determination of mechanical properties of thin surface layers are presented. The linear relations between the frequency shifts induced by the deposition of the layer and the in-plane elastic coefficients of the layer are derived and inverted, the applicability range of the obtained linear model is discussed by a comparison with nonlinear models and finite element method (FEM), and an algorithm for the estimation of experimental errors in the inversely determined elastic coefficients is described. In the final part of the paper, the linearized inverse procedure is applied to evaluate elastic coefficients of a 310 nm thick diamond-like carbon layer deposited on a silicon substrate.

Determination of elastic coefficients of bone and composite materials by acoustic immersion technique.

Elastic properties of single parts of a human skeleton are necessary to know for modelling bone tissue-implants interactions as well as for diagnostic purposes. This paper contributes to the methodology of the evaluation of elastic properties of bones by the ultrasonic wave inversion. The method was developed on composite structures such as plates and cylindrical shells. Final results are then demonstrated on the bovine cortical bone specimen. Properties are supposed to exhibit an orthotropic or a transversally isotropic symmetry. Quasi-longitudinal and quasi-transversal waves are generated from the wave diffraction on the liquid/specimen interface. Wave velocity fields obtained by the ultrasonic scanning technique are used as an input to the inversion procedure for all elastic constants determination. Experimental results are confronted with the numerical modelling of the wave propagation and the stability of resulting data is evaluated by the statistical method based on the Monte-Carlo simulation. The suggested approach has a potential for the qualify of such measurements performed on fresh bones and also for improvement in-situ ultrasonic techniques.

Differential geometry of ray surfaces in anisotropic solids and its contribution to NDE: modelling and experiment.

Point-source/point-receiver techniques are one of the most widely used methods for nondestructive evaluation of anisotropic materials. The group velocities resulting from these techniques must be, for further inverse evaluation of elastic coefficients, geometrically converted into corresponding phase velocities. On the other hand, the phase velocities can be determined from a material's response to a line source. But, due to the anisotropy, the short line sources generated by cylindrical lenses are insufficient for reliable determination of the phase velocity. In this paper, a long line source is approximated by a set of linearly arranged point sources. As it follows from the differential geometry of ray surfaces, information obtained from such set of sources is sufficient for determination of phase velocities of both the quasi-transverse and the quasi-longitudinal modes of propagation. Moreover, this approach can be generalized for any arbitrary set of point sources only by employing a proper time-base transformation. The applicability of the presented approaches is illustrated on transversely isotropic and tetragonal fibrous composite materials.

Sensitivity analysis of an inverse procedure for determination of elastic coefficients for strong anisotropy.

The elastic coefficients of anisotropic solids are often evaluated from measurements of phase or group velocities of ultrasonic bulk waves by the usage of inverse optimizing procedures. This paper discusses the effects of various factors on such procedures results for transversely isotropic solids with considerably strong anisotropy. First, the inverse determination of all elastic coefficients of unidirectional CFRP composite is briefly outlined. Then the results of the optimization are treated as exact values and the sensitivity of the optimizing process versus main considered sources of inaccuracies is analyzed. Results of extensive simulations are presented to illustrate the effect of input data distortion, input data incompleteness, and geometrical conversion from experimentally obtained group velocities into corresponding phase velocities used as input data for the optimizing procedure. The paper takes note of how information about the elastic coefficients can be extracted from the different segments of the phase velocity surface. The stability versus input data distortion for inversion from group velocities and phase velocities is compared and the importance of reliable geometrical converting from group into phase velocities is illustrated. An novel method for geometrical conversion of distorted group velocity data into corresponding phase velocities based on affine combinations of low-order polynomials is presented and compared with piecewise or high-order polynomial fitting.