Elastic Property Measurement Using Rayleigh-Lamb Waves

Abstract

A nondestructive technique is described for the measurement of elastic constants of isotropic plates using ultrasonic Rayleigh-Lamb waves. The experimental method employs continuous harmonic waves and a pair of variable-angle contact transducers in pitch-catch mode. The phase velocity of the R-L waves at a particular frequency is determined from the phase shift over a measured path length. This simple experimental technique can measure phase velocity over the range 1–10 mm/μs with an error of less than 0.5% over a frequency range of 50 kHz-2 MHz. Individual symmetric and antisymmetric modes can be generated through the selection of transducer angle and frequency. Young's modulus and Poisson's ratio for the material are calculated from measurements of frequency and phase velocity by a nonlinear least squares solution to the dispersion equations. The sensitivity of the nonlinear least squares function to the measurement region of the dispersion curve is investigated. It was found that estimations of material properties are more accurate and less sensitive to small experimental errors when only selected frequencies and R-L modes are used in the least squares calculation. This technique is demonstrated with several isotropic materials and with both thick (6 mm) and thin (0.8 mm) plates. Values for elastic constants determined by the contact transducer Lamb wave technique compare favorably with values measured using the pulse-echo-overlap method. The uncertainty in measurements of Young's modulus and Poisson's ratio was less than 1% and 2%, respectively. The technique has advantages over more traditional methods for measuring elastic properties when it is desirable to use wavelengths greater than the plate thickness, when properties may vary with frequency, or when it is necessary to measure in-plane elastic properties of thin plate structures.     

Analysis of the resistance of high-E,low-E brittle composites to failure by thermal shock

By means of the inclusion of a dispersed phase with low Young's modulus, the generally low thermal stress resistance of brittle materials for high-temperature structures can be improved significantly. An analysis of this improvement on the basis of continuum and micromechanical theory is presented in this paper. The low-E phase is shown to cause a significant decrease in Young's modulus, with a negligible effect in the coefficient of thermal expansion. The relative change in thermal conductivity is a function of the thermal conductivity of the dispersed phase. The tensile fracture stress is reduced significantly, primarily due to the mismatch in elastic properties, with smaller effects due to the mismatches in the coefficient of thermal expansion and thermal conductivity. The relative changes in Young's modulus and tensile fracture stress are such as to result in an increase in the strain-at-fracture and a simultaneous decrease in the elastic energy at fracture, the driving force for catastrophic crack propagation. The accompanying increase in fracture energy also contributes to the improvement of thermal shock resistance. By changing the size of the low-E inclusion, tradeoffs can be made between strain-at-fracture and elastic energy at fracture.     

Atomic force microscopy of 3T3 and SW-13 cell lines: An investigation of cell elasticity changes due to fixation

Mechanical properties of single cells are of increasing interest both from a fundamental cell biological perspective and in the context of disease diagnostics. In this respect, atomic force microscopy (AFM) has become a powerful tool for imaging and assessing mechanical properties of biological samples. However, while these tests are typically carried out on chemically fixed cells, the most important data is that on living cells. The present study applies AFM technique to assess the Young's modulus of two cell lines: mouse embryonic fibroblasts (NIH/3T3) and human epithelial cancer cells (SW-13). Both living cells and those fixed with paraformaldehyde were investigated. This analysis quantifies the difference between Young's modulus for these two conditions and provides a coefficient to relate them. Knowing the relation between Young's modulus of living and fixed cells, allows carrying out and comparing data obtained during steady-state measurements on fixed cells that are more frequently available in the clinical and research settings and simpler to maintain and probe.     

Laser-assisted synthesis of Ti–Mo alloys for biomedical applications

This paper presents the results of a laser-based combinatorial investigation of the Ti–Mo system, aiming at finding alloys with promising properties for orthopedic applications. Variable powder feed rate laser cladding was applied to synthesize Ti–xMo alloys with composition continuously varying in the range of 4–19 wt.% Mo. Screening was performed on the basis of the alloys' mechanical properties, in particular hardness and Young's modulus, measured by microindentation tests. Microstructural analysis showed that alloys with Mo content between 4 and 8 wt.% are composed of acicular martensite and retained β-phase, the proportion of the later phase increasing with increasing Mo content. Alloys with Mo content of 10 wt.% and higher consist entirely of β phase. All the alloys present a Mo segregation pattern indicating that solidification occurred with a cellular solid–liquid interface. Though β-phase alloys present lower values of Young's modulus and hardness than α′- or α″- containing alloys, minimum values of Young's modulus (75 GPa) and hardness (240 VHN) were achieved for the Ti–13 wt.% Mo alloy.     

Elastic property measurement using Rayleigh-Lamb waves

A nondestructive technique is described for the measurement of elastic constants of isotropic plates using ultrasonic Rayleigh-Lamb waves. The experimental method employs continuous harmonic waves and a pair of variable-angle contact transducers in pitch-catch mode. The phase velocity of the R-L waves at a particular frequency is determined from the phase shift over a measured path length. This simple experimental technique can measure phase velocity over the range 1–10 mm/µs with an error of less than 0.5% over a frequency range of 50 kHz-2 MHz. Individual symmetric and antisymmetric modes can be generated through the selection of transducer angle and frequency. Young's modulus and Poisson's ratio for the material are calculated from measurements of frequency and phase velocity by a nonlinear least squares solution to the dispersion equations. The sensitivity of the nonlinear least squares function to the measurement region of the dispersion curve is investigated. It was found that estimations of material properties are more accurate and less sensitive to small experimental errors when only selected frequencies and R-L modes are used in the least squares calculation. This technique is demonstrated with several isotropic materials and with both thick (6 mm) and thin (0.8 mm) plates. Values for elastic constants determined by the contact transducer Lamb wave technique compare favorably with values measured using the pulse-echo-overlap method. The uncertainty in measurements of Young's modulus and Poisson's ratio was less than 1% and 2%, respectively. The technique has advantages over more traditional methods for measuring elastic properties when it is desirable to use wavelengths greater than the plate thickness, when properties may vary with frequency, or when it is necessary to measure in-plane elastic properties of thin plate structures.     

基于AFM纳米硬度测量系统的实验

为了解决用AFM自身压痕软件进行纳米硬度测量时无法直接获得载荷-压深曲线和由于受到扫描陶管扫描范围的限制而进行多点压痕实验范围有限的问题,建立了三维微动工作台和原子力显微镜相结合的纳米压痕硬度测量系统.基于该系统,对单晶薄膜材料进行了单点压痕实验,得出该系统适合进行纳米硬度测量的结论;并对薄膜材料的纳米硬度和弹性模量进行了分析,讨论了尺寸效应对两者的影响.另外,进行了40×40的点阵压痕实验,得到了材料整个压痕面的三维形貌图和三维硬度图.     

Effects of mass density on the microhardness and modulus of tetrahedral amorphous carbon films

Tetrahedral amorphous carbon (ta-C) films were deposited by filtered cathodic vacuum arc technique with substrate negative bias setting in the range of 0–200 V. The film density, hardness and Young's modulus were respectively obtained from the X-ray reflectivity and nanoindentation measurements. A maximum value of density was identified in the middle range of incident ion energy. Correlations between the density and elastic behavior of the films were then discussed theoretically based on the constraint-counting model of Philips and Thorpe. The measured Young's modulus and hardness almost vary linearly with the increasing density which agrees quite well with the theoretic predictions.     

Measurement of mechanical properties of multilayer coatings by nanoindentation

Abstract

Multilayer protective coatings of alternate aluminium and titanium diboride TiB₂ layers have been tested by nanoindentation to measure both hardness and Young's modulus values. The initial results show that the values obtained depend upon the depth of indentation. An alternative view is presented to show that by considering the percentage of each coating in contact with the indenter a single relationship between either hardness or Young's modulus and the amount of aluminium layer penetrated can be produced. This technique allows the influence of the percentage ceramic on the results obtained to be identified. Comparison of the nanoindentation results with three point bending tests show how the coating structure influences the results obtained.     

Micromorphology and nanomechanical characteristics of sputtered aluminum thin films

Micromorphology and nanoindentation properties of sputtered aluminum thin films are presented. The field emission scanning electron microscope, atomic force microscopy (AFM) and nanoindentation results are presented for films prepared at a substrate temperature ranging between 44.5 °C and 100 °C. A multifractal approach on the microstructure is presented to comprehend the micromorphology of the films. The roughness decreases, whereas fractal dimension increases as the temperature increases. The hardness and Young's modulus do not exhibit any predictable trend. Hardness and Young's modulus exhibit a linear relationship.     

Mechanical Behavior of Multilayered Nanoscale Metal‐Ceramic Composites

Single and multilayered structures at nano‐length scale are very attractive materials due to their high strength, toughness, and wear resistance relative to conventional laminated composites. In this study, single layered Al, SiC, and multilayered Al/SiC composites were synthesized by DC/RF magnetron sputtering. The microstructure of the multilayered structures was characterized by scanning electron microscopy (SEM). The elastic and plastic behavior of single and multilayered materials was investigated by nanoindentation and tensile testing. For nanoindentation, an analytical model was employed to subtract the contribution of the Si substrate, in order to extract the true modulus of the films. Finite element simulations were employed to confirm the analytical predictions and to investigate the anisotropic elastic behavior of the multilayered composite. It was concluded that while indentation provides reasonable Young's modulus and hardness values in monolithic layers, it does not provide the true modulus of the multilayered materials because of their inherent anisotropy.     

Revisiting the Buckling Metrology Method to Determine the Young's Modulus of 2D Materials

Measuring the mechanical properties of 2D materials is a formidable task. While regular electrical and optical probing techniques are suitable even for atomically thin materials, conventional mechanical tests cannot be directly applied. Therefore, new mechanical testing techniques need to be developed. Up to now, the most widespread approaches require micro‐fabrication to create freely suspended membranes, rendering their implementation complex and costly. Here, a simple yet powerful technique is revisited to measure the mechanical properties of thin films. The buckling metrology method, that does not require the fabrication of freely suspended structures, is used to determine the Young's modulus of several transition metal dichalcogenides (MoS₂, MoSe₂, WS₂, and WSe₂) with thicknesses ranging from 2 to 10 layers. The obtained values for the Young's modulus and their uncertainty are critically compared with previously published results, finding that this simple technique provides results which are in good agreement with those reported using other highly sophisticated testing methods. By comparing the cost, complexity, and time required for the different methods reported in the literature, the buckling metrology method presents certain advantages that make it an interesting mechanical test tool for 2D materials.     

On the measurement of pile-up corrected hardness based on the early Hertzian loading analysis

Nanoindentation has been used to gain insight into the elastic/plastic contact responses of material at very small scales. The Oliver and Pharr's analysis (W.C. Oliver and G.M. Pharr, J. Mater. Res. 7 (1992) 1564) on the nanoindentation curve, however, can be meaningless when plastically deformed material piles around the indented points. This study suggests a measuring methodology of the real contact area enlarged by the material pile-up and its corresponding mechanical properties; the pile-up corrected contact area can be calculated inversely from the reduced modulus formulation with input information of the independently determined Young's modulus based on the Hertzian loading analysis. This contact correction relaxed overestimates in the elastic modulus and hardness interpreted from the nanoindentation curve and yielded actual mechanical properties comparable to the literature values of a (100) tungsten monocrystal. In addition, theoretically estimated upheaval amount of the contact boundary in this study was nearly consistent with the average pile-up height measured from an atomic-force microscope.     

Low-cycle fatigue of 1Cr–18Ni–9Ti stainless steel and related weld metal under axial, torsional and 90° out-of-phase loading

The fatigue behaviour of base metal and weld joints of 1Cr–18Ni–9Ti stainless steel has been studied under uniaxial, torsional and 90° out‐of‐phase loading. A significant degree of additional hardening is found for both base metal and weld metal under 90° out‐of‐phase loading. Both base metal and weld metal have the same cyclic stable stress–strain relationship under torsional cyclic loading and 90° out‐of‐phase cyclic loading. Base metal exhibits higher cyclic stress than weld metal under uniaxial loading, and Young's modulus and yield stress of weld metal are smaller than those of base metal. Weld metal exhibited lower fatigue resistance than base metal under uniaxial and torsional loading, but no significant difference was found between the two materials under 90° out‐of‐phase loading. A large scatter of fatigue life is observed for weld metal, perhaps because of heterogeneity of the microstructure. The Wang–Brown (WB) damage parameter and the Fatemi–Socie (FS) damage parameter, both based on the shear critical plane approach, were evaluated relative to the fatigue data obtained.     

High-throughput characterization of mechanical properties of Ti-Ni-Cu shape memory thin films at elevated temperature

Hardness and Young's moduli values for Ti_xNi_90−xCu₁₀ (37 at.% < x < 67 at.%) thin films from a continuous composition spread type materials library, annealed at 500 °C for 1 h, were determined at room temperature (martensitic state) and 80 °C (austenitic state) using high-throughput nanoindentation experiments. These values are found to increase as the compositions deviate from Ti contents close to 50 at.%. The increases in hardness is correlated to the presence of Ti-rich and (Ni,Cu)-rich precipitates resulting in precipitate hardening and grain size refinement (Hall-Petch effect). The increase of the Young's moduli is rationalized by considering the significantly higher Young's moduli of the different precipitate phases and applying the rule of mixtures. The contributions of the precipitate phases and the matrix to the combined Young's modulus were estimated by evaluating the load-displacement curves in detail. The obtained results are in good agreement with the Young's moduli determined from thin film curvature measurements [R. Zarnetta et al., Smart Mater. Struct. 19 (2010) 65032]. Thus, the experimental restrictions for nanoindentation experiments at elevated temperatures are concluded to not adversely affect the validity of the results.     

Structures and properties of Ti alloys after double implantation

The paper presents new results on investigation of structure and physical-mechanical properties of near surface layers of titanium alloys after (W⁺, Mo⁺) ion implantation and subsequent thermal annealing under 550 °C for 2 h. Using back scattering (RBS) of helium ions and protons, scanning electron microscopy (SEM) with microanalysis (EDS), (WDS), proton (ion) induced X-ray emission (PIXE), X-ray phase analysis (XRD) with a grazing incidence geometry (0.5° angle), measurements of nanohardness and elastic modulus, friction wear (cylinder-plate), measurements of corrosion resistance in a salt solution, we investigated the VT-6 samples, and determined their fatigue resistance under cyclic loads. Double increase of hardness, decrease of wear and increased fatigue resistance were found, which was related to the formation of small dispersion (nanodimension) nitride, carbonitride, and intermetalloid phases.     

Application of carbon extraction replicas in grain-size measurements of high-strength steels using TEM

In this paper, the application of carbon extraction replicas in grain-size measurements is introduced and discussed. Modern high-strength microalloyed steels, used as structural or pipeline materials, have very small grains with substructures. Replicas used in transmission electron microscopes can resolve the grain boundaries and can be used for systematic measurement of grain size in cases where the small size of the grains pushes the resolution of conventional optical microscopes. The grain-size variations obtained from replicas are compared with those obtained from optical and scanning electron microscopy. An emphasis is placed on the importance of using the correct technique for imaging and the optimal magnification. Grain-size measurements are used for estimation of grain-boundary strengthening contribution to yield strength. The variation in grain size is also correlated with hardness in the base metal of several microalloyed steels, as well as the fine-grained heat-affected zone of a weld structure with several heat inputs.     

Combination of normal and lateral force-displacement measurements as a new technique for the mechanical characterization of surfaces and coatings

Nanoindentation with Vickers or Berkovich tips has become an established technique for the measurement of hardness and Young's modulus. Also the use of spherical indenters has attracted more and more attention for the determination of the Young's modulus and yield strength. However, these techniques are still far away from the conditions in a real applications where usually normal forces are combined with lateral forces in a tribological system. Therefore, often scratch and wear tests are used additionally to characterize the mechanical behavior. However, conventional techniques, which apply lateral forces, have the disadvantage that they often do not deliver characteristic and comparable material parameters which are independent of the measurement conditions and which can serve as input parameters for the modeling with analytical or finite element methods. This shall be overcome by a new technique, which will allow the measurement of lateral force-displacement curves with the same accuracy like conventional nanoindentation can do in normal direction. The realization of two independent measurements with the same tip at the same sample position will allow the calculation of more unknown material parameters than before. The use of spherical indenters with forces at which elastic or beginning plastic deformation takes place makes it easier to combine the measurements with analytical stress calculations and to derive critical material parameters. As a first step towards the abovementioned characterization method, a new nanomechanical tester with a high-resolution measurement of force and displacement in normal and lateral direction was developed and tested.     

Nanoindentation mapping of mechanical properties of cement paste and natural rocks

This paper reports a study to assess nanoindentation mapping of mechanical properties of cement paste and natural rocks. Initial work seems to show that mechanical property mapping by nanoindentation is feasible and can be related to microscopic information. Further work is however required on the effect of indent size and spacing. Such a testing technique can be very useful for materials with different phases to study the intrinsic properties of each component, and also the interaction and properties of the interfacial regions of different phases. The values of Young's modulus and hardness of the individual mineral phases were also determined by statistically analysing a large number of experimental data.     

船用TA5钛合金激光焊接接头组织和性能研究

采用IPG光纤激光器对8 mm厚的TA5钛合金进行激光自熔焊接,并对焊接接头的微观组织和力学性能进行分析。结果表明,激光焊接接头表面成形连续、均匀、无飞溅,内部无气孔和裂纹等缺陷。母材组织为细小均匀的等轴α相;焊缝区组织主要由粗大的β柱状晶粒、大量的针状马氏体α'以及少量的板条马氏体组成;热影响区组织主要由等轴α相、少量的针状马氏体α'和少量的残余β组成;在熔合线的边界,柱状晶粒与等轴晶粒联生结晶、外延生长,保证了焊接接头的稳定连接。焊接接头各区域的显微硬度差异较大,最高硬度出现在熔合线附近,焊缝区和热影响区的显微硬度明显高于母材的。对拉伸断裂部位进行观察,拉伸断裂发生在远离焊缝的母材处,这说明激光焊接接头的抗拉强度与母材等强或者略高于母材的,这与大量针状马氏体形成的网篮组织有直接的关系。      

Electron microscopy of inertia-friction weldments in a rapidly solidified Al-Fe-Mo-V alloy

The microstructures of inertia-friction weldments in a rapidly solidified, powder metallurgy Al-8.7Fe-2.8Mo-1V alloy were characterized using light and transmission electron microscopy. Extensive plastic deformation at the weld interface during the welding process was shown to fracture and disperse relatively coarse, spherical dispersoids present in the original base-metal microstructure, thereby resulting in a refined dispersoid size in this region. These fine dispersoids promoted an increase in hardness at the weld interface as compared to the unaffected base metal. Local regions of nonuniform interface deformation at the weld outer periphery resulted in a heterogeneous microstructure comprised of adjacent regions of high and low dispersoid density. The dispersoid-lean regions were characterized by appreciably coarsened alpha grains and a hardness well below that of the base metal. The greater extent of dispersoid-lean regions in welds produced with low axial force promoted preferential weld interface failure during three-point bend testing, while the near absence of these regions in welds produced with high axial force promoted failure in the unaffected base metal remote from the weld.