Modeling the propagation of ultrasonic waves in the interface region between two bonded elements

An important task in nondestructive materials evaluation is the development of techniques to characterize the bond quality of adherent joints. Binding forces are nonlinear and cause a nonlinear modulation of transmitted and reflected ultrasonic waves. As a consequence, the higher harmonics generated by an insonified monochromatic wave give information about the adhesive bonds. The local binding forces in thin bonded interfaces can be obtained by the amplitudes of the ultrasonic waves of the insonified frequency and its higher harmonics as transmitted through the interface. Additional phase measurements may enable one to obtain the evaluation of the full hysteretic cycle of the interaction force. In order to gain a deeper understanding of the interface region and to improve the technique, numerical simulations of the ultrasonic wave propagation through specimens of two bonded elements can be used. A simple model based on the local interaction simulation approach (LISA) is described in this contribution, and a comparison between the results of the simulations and the experimental data is presented. Besides its intrinsic relevance for NDE, the problem considered in this paper may be very useful to analyze and test models for the simulation of ultrasonic wave propagation in nonclassical nonlinear mesoscopic elastic materials.     

A unified treatment of nonclassical nonlinear effects in the propagation of ultrasound in heterogeneous media

Recent experiments on rocks and other materials, such as soil, cement, concrete and damaged elastic materials, have led to the discovery of nonlinear (NL) hysteretic effects in their elastic behaviour. These observations suggest the existence of a NL mesoscopic elasticity universality class, to which all the aforementioned materials belong. The purpose of the present contribution is to search for the basic mathematical roots for nonclassical nonlinearity, in order to explain its universality, classify it and correlate it with the underlying meso- or microscopic interaction mechanisms. In our discussions we explicitly consider two quite different kinds of specimens: a two-bonded-elements structure and a thin multigrained bar. It is remarkable that, although the former includes only one interface and the latter very many interstices, the same "interaction box" formalism can be applied to both. Another important result of the proposed formalism is that the spectral contents of an arbitrary system for any input amplitude may be predicted, under certain assumptions, from the result of a single experiment at a higher amplitude.     

PC bond cleavage of (silox)3NbPMe3 (silox = tBu3SiO) under dihydrogen leads to (silox)3Nb=CH2, (silox)3Nb=PH or (silox)3NbP(H)Nb(silox)3, and CH4

Photolysis of the equilibrium mixture (silox)3NbPMe3 (1) + H2 (1-3 atm) right arrow over left arrow (silox)3Nb(Heq)2 (2e, tbp)/(silox)3Nb(Ht)2 (2t, pseudo-Td) + PMe3 causes PC bond cleavage. Depending on conditions, various amounts of (silox)3Nb=CH2 (3), (silox)3Nb=PH (5-H), (silox)3Nb=PMe (5-Me), (silox)3Nb=P(H)Nb(silox)3 (9, precipitated if N2 is present; X-ray), (silox)3NbH (4, active only through equilibration with 2e,t), and CH4 are produced. Addition of PH3 to 1 provides an independent route to 5-H; its deprotonation gives [(silox)3NbP]Li (6), whose methylation yields 5-Me. Early conversion 3:5-H ratios of approximately 3:1 suggest that initial PC bond activation is slow relative to subsequent PC bond cleavages. Addition of HPMe2 and H2PMe to 1 generates (silox)3HNbPMe2 (7) and (silox)3HNbPHMe (8), respectively, and both degrade faster than PMe3. A mechanism based around sequential PC or CH oxidative addition, followed by 1,2-elimination events, is proposed. The limiting step in the decomposition of all PMe3 is a slow hydrogenation of 3 to regenerate 2e,t and produces CH4. Hydrides 2e,t are likely to be the photolytically active species.     

Theα-α′ phase transition of hydrogen in elastically anisotropic cubic metals

The formulation of the statistical mechanics of the - phase transition in hydrogenmetal-systems is extended in such a way as to include the elastic anisotropy of the host crystal. The corresponding reduction of symmetry leads to qualitative modifications of the results. Depending on hydrogen concentration and temperature, phases with homogeneous,C ₃- andC ₂-symmetric equilibrium hydrogen distributions are formed. The transitions between these phases are investigated, and the relation of their orders and the corresponding changes in symmetry is studied. Differences between isotropic and anisotropic systems are discussed.     

Mechanically Regularized FE DIC for Heterogeneous Materials

In situ tensile tests in a scanning electron microscope (SEM) have been conducted on a 8-layer 5-harness satin carbon fibre and epoxy matrix composite to observe the first stages of damage at the scale of fibres and matrix. A speckle pattern based on a suspension of alumina particles was applied onto the surface of the specimen to facilitate the use of digital image correlation (DIC). Local and finite element (FE) DIC are compared on pictures acquired during the tensile tests, with and without a speckle pattern. FE DIC with mechanical regularization was found to be the only approach able to measure displacement fields at a fine enough resolution in both cases. This method, initially created for homogeneous materials, was then adapted to heterogeneous materials. First, a microstructure consistent mesh was created and used for correlation purposes. Second, the difference between the mechanical properties of the constituents is taken into account in the mechanical regularization. Last, the accuracy of the method is analysed. The adaptation presented herein was proved to be able to measure displacement fields in the matrix between fibres with an error of 10 nm (a fifth of a pixel) and to detect the initiation of the first damage mechanisms by means of the mechanical residuals.

     

Quantitative determination of contact stiffness using atomic force acoustic microscopy

Atomic force acoustic microscopy is a near-field technique which combines the ability of ultrasonics to image elastic properties with the high lateral resolution of scanning probe microscopes. We present a technique to measure the contact stiffness and the Young's modulus of sample surfaces quantitatively, with a resolution of approximately 20 nm, exploiting the contact resonance frequencies of standard cantilevers used in atomic force microscopy. The Young's modulus of nanocrystalline ferrite films has been measured as a function of oxidation temperature. Furthermore, images showing the domain structure of piezoelectric lead zirconate titanate ceramics have been taken.     

Long-range interaction of point defects with arbitrary dipole tensors in a sphere

The elastic field of lattice defects in a sphere with a free surface is studied. The interaction energy of two arbitrary point defects in an elastically isotropic crystal is expanded in terms of spherical harmonics. Separate expressions are given for the infinite material contribution and for the surface term. The bearing of the results on phase transitions in defect-systems is discussed.     

Olefin substitution in (silox)3M(olefin) (silox = (t)Bu3SiO; M = Nb, Ta): the role of density of states in second vs third row transition metal reactivity

The substitution chemistry of olefin complexes (silox)3M(ole) (silox = (t)Bu3SiO; M = Nb (1-ole), Ta (2-ole); ole = C2H4 (as 13C2H4 or C2D4), C2H3Me, C2H3Et, cis-2-C4H8, iso-C4H8, C2H3Ph, cC5H8, cC6H10, cC7H10 (norbornene)) was investigated. For 1-ole, substitution was dissociative (deltaG(double dagger)(diss)), and in combination with calculated olefin binding free energies (deltaG(o)(bind)), activation free energies for olefin association (deltaG(double dagger)(assoc)) to (silox)3Nb (1) were estimated. For 2-ole, substitution was not observed prior to rearrangement to alkylidenes. Instead, activation free energies for olefin association to (silox)3Ta (2) were measured, and when combined with deltaG(o)(bind) (calcd), estimates of olefin dissociation rates from 2-ole were obtained. Despite stronger binding energies for 1-ole vs 2-ole, the dissociation of olefins from 1-ole is much faster than that from 2-ole. The association of olefins to 1 is also much faster than that to 2. Linear free energy relationships (with respect to deltaG(o)(bind)) characterize olefin dissociation from 1-ole, but not olefin dissociation from 2-ole, and olefin association to 2, but not olefin association to 1. Calculated transition states for olefin dissociation from (HO)3M(C2H4) (M = Nb, 1'-C2H4; Ta, 2'-C2H4) are asymmetric and have orbitals consistent with either singlet or triplet states. The rearrangement of (silox)3Nb(trans-Vy,Ph-cPr) (1-VyPhcPr) to (silox)3Nb=CHCH=CHCH2CH2Ph (3) is consistent with a diradical intermediate akin to the transition state for substitution. The disparity between Nb and Ta in olefin substitution chemistry is rationalized on the basis of a greater density of states (DOS) for the products (i.e., (silox)3M + ole) where M = Nb, leading to intersystem crossing events that facilitate dissociation. At the crux of the DOS difference is the greater 5dz2/6s mixing for Ta vs the 4dz2/5s mixing of Nb. This rationalization is generalized to explain the nominally swifter reactivities of 4d vs 5d elements.     

Ultrasonic radiation in dynamic force microscopy

In dynamic force microscopy the cantilever of an atomic force microscope is vibrated at ultrasonic frequencies in the range of several 10 kHz up to several MHz while scanning a sample surface. The amplitude and phase of the cantilever vibration as well as the shift of the cantilever resonance frequencies provide information about local sample surface properties. In several operation modes of dynamic force microscopy, for example force modulation microscopy, tapping mode or atomic force acoustic microscopy, the sensor tip is in contact with the sample at least during a fraction of its vibration cycle. The periodic indentation of the tip with the sample surface generates ultrasonic waves. In this paper, the ultrasonic radiation of a vibrating cantilever into a sample and its contribution to the damping of the cantilever vibration are calculated. The theoretical results are compared to experiments.     

Thermodynamics, kinetics, and mechanism of (silox)3M(olefin) to (silox)3M(alkylidene) rearrangements (silox = tBu3SiO; M = Nb, Ta)

Olefin complexes (silox)(3)M(ole) (silox = (t)Bu(3)SiO; M = Nb (1-ole), Ta (2-ole); ole = C(2)H(4), C(2)H(3)Me, C(2)H(3)Et, C(2)H(3)C(6)H(4)-p-X (X = OMe, H, CF(3)), C(2)H(3)(t)Bu, (c)C(5)H(8), (c)C(6)H(10), (c)C(7)H(10) (norbornene)) rearrange to alkylidene isomers (silox)(3)M(alk) (M = Nb (1=alk), Ta (2=alk); alk = CHMe, CHEt, CH(n)Pr, CHCH(2)C(6)H(4)-p-X (X = OMe, H, CF(3) (Ta only)), CHCH(2)(t)Bu, (c)C(5)H(8), (c)C(6)H(10), (c)C(7)H(10) (norbornylidene)). Kinetics and labeling experiments suggest that the rearrangement proceeds via a delta-abstraction on a silox CH bond by the beta-olefin carbon to give (silox)(2)RM(kappa(2)-O,C-OSi(t)Bu(2)CMe(2)CH(2)) (M = Nb (4-R), Ta (6-R); R = Me, Et, (n)Pr, (n)Bu, CH(2)CH(2)C(6)H(4)-p-X (X = OMe, H, CF(3) (Ta only)), CH(2)CH(2)(t)Bu, (c)C(5)H(9), (c)C(6)H(11), (c)C(7)H(11) (norbornyl)). A subsequent alpha-abstraction by the cylometalated "arm" of the intermediate on an alpha-CH bond of R generates the alkylidene 1=alk or 2=alk. Equilibrations of 1-ole with ole' to give 1-ole' and ole, and relevant calculations on 1-ole and 2-ole, permit interpretation of all relative ground and transition state energies for the complexes of either metal.