Ultrasonic nondestructive material evaluation method and study on texture and cross slip effects under simple and pure shear states

Ultrasonic wave velocities propagating in a plastically deformed medium are known to depend upon its microstructural material properties. Therefore, the authors have proposed the theoretical modeling of an ultrasonic nondestructive method to evaluate plastically deformed states. In the present paper, we verify the proposed theoretical modeling of an ultrasonic nondestructive method and examine its accuracy by comparing the experimental results with the simulated subsequent yield surfaces, the longitudinal and transverse wave velocities under combined stress states of an aluminum alloy using internal state variables of an anisotropic distortional yield model which were determined to achieve a good fit for the experimental results of the longitudinal and transverse wave velocity changes under uniaxial tension test. As a special case, the velocity changes of longitudinal wave under pure shear state subjected to the combinations of tension and compression are also studied, it shows a different result compared with that of longitudinal wave velocity under torsional tests of thin thickness cylinders, i.e., simple shear state. The effects on ultrasonic wave velocity changes due to texture and cross slip under simple and pure shear states are studied via a finite element polycrystal model (FEPM).     

Body wave propagation in rotating elastic media

We investigate the propagation of elastic waves through an elastic medium submitted to an angular rotation Ω. Wave propagation is shown to be directly related to the Kibel number Ki=ω/Ω, where ω is the wave frequency. Two dispersive waves W₁ and W₂ are obtained which tend to the classical dilatational and shear waves, respectively, when Ki tends to infinity. Wave W₁ shows a cutoff frequency ω_c=Ω below which it does not propagate. The case of small angular rotation Ω is also studied. The corrections to be introduced to dilatational and shear waves are then shown to be of order O(Ki⁻¹).     

Mechanical response and texture evolution of AZ31 alloy at large strains for different strain rates and temperatures

In order to study the behavior of material under finite deformation at various strain rates, the responses of AZ31 Mg sheet are measured under uniaxial (tension and compression) and multiaxial (simple shear) loadings along rolling direction (RD), 45° to rolling direction (DD), 90° to rolling direction (TD), and normal to the sheet (ND) to large strains. The material exhibits positive strain rate sensitivity (SRS) at room and elevated temperatures; the SRS is more pronounced at high temperatures and lower strain rates. The r-value of the material under tensile loading at room temperatures is higher in TD at lower strain rate. Texture measurements on several failed specimens are reported under tension and simple shear after finite plastic deformation of about 20% equivalent strain. The as-received material exhibits a strong fiber with equal fractions of grains having the c-axis slightly tilted away from the sheet normal towards both +RD and −RD. Pole figures obtained after tensile loading along the rolling direction (RD) show that the texture of the material strengthens even at low strains, with c-axis perpendicular to the sheet plane and prism planes lining up in a majority of grains. However, the tensile loading axis along TD does not lead to similar texture strengthening; the c-axis distribution appears to be virtually unchanged from the virgin state. The pole figures obtained after in-plane compression along RD brings the c-axes of the grains parallel to the loading direction. The pole figures after simple shear loading show that the c-axis rotates to lie on the sheet plane consistent with a compression axis 45° away on the sheet plane.     

Optimal Bounds on Texture Coefficients

Let w be the orientation distribution function of a polycrystalline aggregate of crystallites with symmetry G _cr and with group of texture symmetry G _tex. In this paper we obtain a “recipe” on how to derive optimal bounds on the texture coefficients W _lmn associated with w. In particular, we find explicit bounds in the case in which G _tex is a group with orthorhombic symmetry and G _cr is either a group with cubic symmetry or a group with hexagonal symmetry. This revised version was published online in July 2006 with corrections to the Cover Date.     

立方晶粒正交板材瑞利波速与织构系数的关系

正交板材是由大量微小晶粒组成的正交多晶体材料,而多晶体中晶粒的取向分布(可通过取向分布函数中的织构系数来描述)影响着多晶体材料的力学性能,也必然影响着瑞利波的传播速度。将多晶体材料的织构系数引入到弹性张量中,通过特征值办法,采用线性化处理,推导出立方晶粒正交板材的瑞利波速与织构系数的关系式,在此基础上可通过正交板材瑞利波速的测量获得织构系数,并与通过超声横波纵波测得结果相比,吻合很好。     

On the propagation of elastic waves through composite media

Summary With the aid of an ultrasonic pulse technique, the propagation of elastic waves (longitudinal as well as transverse) through polyurethane rubbers filled with different amounts of sodium chloride particles was studied. The velocity of both longitudinal and transverse waves was found to increase with filler content. From the measured wave velocities, the effective modulus for longitudinal waves,L, bulk modulus,K, and shear modulus,G, were calculated according to the relations for a homogeneous isotropic material. All three moduli appear to be monotonously increasing functions of the filler content over the whole experimentally accessible temperature range (–70 °C to + 70 °C forL andK;}-70 °C to about –20 °C forG) and they, moreover, reflect the glassrubber transition of the binder.Poisson's ratio,, was found to decrease with increasing filler content and show a rise at the high temperature side of the experimentally accessible temperature range (about –20 °C) as a result of the approach of the glass-rubber transition.In addition to the velocities, the attenuation of both longitudinal and transverse waves was measured in the temperature ranges mentioned. It was found that in the hard region tan _L as well as tan _G are independent of the filler content within the accuracy of the measurements. In the rubbery region, however, tan _L, increases with increasing filler content.Finally, the experimental data are compared with a simple macroscopic theory on the elastic properties of composite media.     

Molecular orientation in sheared molten thermotropic random copolyester

The macromolecular alignment and texture orientation in sheared thermotropic copolyester were investigated using in situ wide-angle X-ray scattering (WAXS) and polarizing optical microscopy (POM). The molecular behavior was correlated with viscoelastic properties. The polymer is a random copolyester based on 60 mol% 1,4-hydroxybenzoic acid (B) and 40 mol% ethylene terephthalate (ET) units. X-ray scattering showed that the molecular chains were aligned along the flow direction. The degree of molecular orientation, , is an increasing function of the applied shear rate. However, rheo-optics showed that shear flow could not orient the polydomain texture, i.e., neither defect stretching nor elimination of defects was observed. Instead, shear compressed the microdomains and gave rise to long-range orientation correlations. Rheology showed that the nematic melt is viscoelastic, the loss modulus G″ dominates the elastic modulus G′, and the dynamic viscosity η* is shear thinning. Moreover, the steady shear viscosity, η, also behaved shear thinning, while the first normal stress difference N ₁ remained positive. The empirical Cox–Merz rule did not hold, , within the shear rate range studied. The microscopic and rheological properties suggest that B–ET is a flow-aligning nematic polymer.     

Shear stability studies on polymer-polymer and polymer-fibre mixtures

The shear stability of drag reducing polymer-polymer and polymer-fibre mixtures has been studied at a Reynolds number of 14,000 using a turbulent flow rheometer. The ratio of the drag reduction at a particular pass number to the initial drag reduction has been determined for the mixtures at various pass numbers and compositions in order to determine the effect of composition on the shear stability of the mixtures.It has been found in both cases that when there is a drastic difference in the shear stabilities of the constituents of the mixtures, the incorporation of a small amount of the less shear stable drag reducing agent reduces the shear stability drastically. On the other hand, when the shear stability of the constituents are of the same order, there is only a proportional change in the shear stability of the mixtures on addition of one component to the other. A correlation between the decay coefficient of the mixture (R _M ), the decay coefficients of the constituents (R ₁ andR ₂ ) and the weight fractions of the mixture components (W ₁ andW ₂) is suggested. An efficacious method for preparing asbestos fibre stock suspensions is also described.     

DNS Scrutiny of the <Emphasis Type="Italic">ζ</Emphasis>-<Emphasis Type="Italic">f</Emphasis> Elliptic-Relaxation Eddy-Viscosity Model in Channel Flows with a Moving Wall

In this paper we present a Direct Numerical Simulations (DNS) of channel flow with stationary and moving walls. Three cases, Poiseuille-type with U_W/U_b = 0.75, intermediate-type with U_W/U_b = 1.215, and Couette-type with U_W/U_b = 1.5 (U_W and U_b are the wall and the bulk velocity), were compared with the pure Poiseuille U_W/U_b = 0, at a bulk Reynolds number equal to 4,800 corresponding to Re _\uptau = 288_{\uptau} =288. The DNS results were used to scrutinize the capabilities of ζ-f eddy viscosity model (based on the elliptic relaxation concept) in reproducing the near-wall turbulence in non conventional flows where the shear stress structures are strongly different with respect to the cases used for models calibration. The ζ-f model (also in its basic formulation) demonstrated to have good prospects to reproduce the main phenomenology of such class of flows due to its built-in capabilities to account separately for the different (and opposite) near wall effects on turbulence: the damping due to viscosity and pressure reflection. The results of the computations demonstrated that standard ζ-f model can reasonably reproduce the phenomenology of these flows in terms of velocity and turbulent kinetic energy profiles and budgets.     

Micromechanical modelling of dry and saturated cement paste: Porosity assessment using ultrasonic waves

This article assesses the relationship between porosity and ultrasonic parameters of cement paste. It includes theoretical assessment of ultrasonic wave velocities of cement paste materials. Theoretical micromechanical models describing cement paste as a two-phase composite were detailed. Mechanical (bulk and shear moduli) and ultrasonic (longitudinal and transverse velocities) properties were evaluated. They were then, compared to the experimental ultrasonic properties measured on dry and fully water saturated samples with varying porosity First, the obtained micromechanical results showed that the correlation between acoustic velocity and porosity yielded the expected values: longitudinal and transverse velocities decrease with porosity. Secondly, the dilute inclusion model was able to represent the acoustic parameter of the cement paste only at low porosity, up to 20%. The self-consistent model under-estimated the measured ultrasonic properties for almost all porosity ranges. The Mori–Tanaka and the Kuster–Toksöz models succeeded in describing the acoustic parameters in dry and saturated states when assuming spherical shaped pores.     

Analytical and experimental evaluation of double-notch shear specimens of orthotropic materials

A finite-difference analysis of the state of stress in a double-notch interlaminar shear strength specimen is developed. The effects of geometry and material parameters on the stress distributions are investigated. It has been found that, in agreement with previous determinations,^1–7 a uniform distribution of shear stress on the fracture plane does not exist. The shear stress distribution becomes more uniform for increased material anisotropy and for small (L/T) ratios, whereL is the distance between the notches andT is the specimen thickness. Also, it has been determined that the notch size (W) and the distance from the notches to the loaded ends of the specimen (h) do not influence the stress distributions significantly. The effects of variations in the (L/T) ratio, the notch size (W), and the length (h) were investigated experimentally. For a graphite/epoxy laminate of 0/90-deg square wave it has been found that the apparent shear strength determined by double-notch shear tests decreases significantly with an increase in (L/T) ratio. The decrease in the apparent shear strength with an increase inh, however, is very small. Also, the apparent shear strength is not affected significantly by increasing the notch sizeW.     

A fretting fatigue crack detection feasibility study using shear wave non-destructive inspection

A study was conducted to assess the viability of using ultrasonic shear wave non-destructive inspection (NDI) methods to detect fatigue cracks nucleating in the vicinity of a contact regionin situ. Use of this method is hampered by the presence of electronic and acoustic noise in the laboratory environment and by the contact in the experimental configuration. A previously established fretting fatigue test fixture was selected, in which nominally flat pads are held in contact against a thin, flat specimen and gross sliding between the pad and specimen is eliminated. Experiments were performed with Ti-6Al-4V at 300 Hz andR=0.5 for average clamping stresses of 200 and 620 MPa, and applied fatigue stresses of 330 and 250 MPa. The shear wave response was monitored during each test, and the test was interrupted when changes in the waveform were thought to indicate a crack. Also, the effect of the contact load and the sensitivity of the technique under the contact conditions were assessed. For the lower clamping stress, a sizeable portion of life was spent nucleating cracks, and the propagation life was too short to allow interruption of the tests. At the higher clamping stress, cracks with surface lengths of ∼2.5 mm were detected on, 10 mm wide specimens in tests conducted using the shear wave NDI technique. While the presence of the contact produced changes in the ultrasonic waveform, additional changes occurred as the crack propagated that permitted crack detection. A simple waveform correlation was used post-test to quantify the waveform changes, and thereby validate the viability of this NDI method for use in contact regions. In the configuration used for this study, the shear wave NDI technique was insensitive to small cracks. Some refinements that could dramatically improve crack detection capability are discussed. The original color figures found in this article can be seen in the online verson of this article, or can be obtained from A. Hutson.     

Experimental Investigation of the Generation of Internal Waves by a Vertical Cylinder in a Near-Surface Pycnocline

A bench study of the amplitudes, mode composition, and phase structure of the internal waves generated by a vertical cylinder in the presence of a near-surface pycnocline has been performed; the pycnocline took the form of a stratified fluid layer located between two quasi-homogeneous layers of thicknesses h ₁ and h ₂=2h ₁. In the experiments, the cylinder traveled at velocities critical with respect to internal wave generation. Different cases of model submergence relative to the pycnocline are considered. The dependence of the mode structure and the amplitude-phase characteristics of the forced internal waves on the body velocity and its relative submergence is analyzed. The parameters of both steady and unsteady wave systems are studied.The data obtained make it possible to predict the forced wave parameters and the critical body velocities for given model dimensions and pycnocline parameters.     

Resolved shear stress intensity coefficient and fatigue crack growth in large crystals

Fatigue crack growth is caused primarily by shear decohesion due to dislocation motion in the crack tip region. The resolved shear stress, which drives dislocation in a crystal, is strongly orientation dependent, and therefore, the cyclic plastic deformation of the shear decohesion process is highly anisotropic.The crack planes are often inclined to the loading axis both in the inplane orientation and in the thickness direction. This inclination induces all three modes of the crack tip stress field, K_I, K_II, and K_III.Fatigue crack growth in large-grain Al 7029 aluminum alloy was studied. The crack tip stress fields of the test specimens are calculated with the finite element method. The values of K_I, K_II, and K_III are evaluated. The orientation of the crystal at a crack tip was determined with the Laue X-ray method. The crystal orientation and the calculated crack tip stress fields are used to compute the resolved shear stress intensity of each of the twelve slip systems of the crystal at the crack tip. The resolved shear stress field of a slip system is linearly proportional to the resolved shear stress intensity coefficient, RSSIC.The values of RSSIC thus evaluated are used to analyze the orientations of the crack plane and to correlate with the shear fatigue crack growth rate.     

Swirling turbulent flow through a curved pipe

An experimental study of a swirling turbulent flow through a curved pipe with a pipe-to-mean-bend radius ratio of 0.077 and a flow Reynolds number based on pipe diameter and mean bulk velocity of 50,000 has been carried out. A rotating section, six pipe diameters long, is set up at six diameters upstream of the curved bend entrance. The rotating section is designed to provide a solid-body rotation to the flow. At the entrance of the rotating section, a fully-developed turbulent pipe flow is established. This study reports on the flow characteristics for the case where the swirl number, defined as the ratio of the pipe circumferential velocity to mean bulk velocity, is one. Wall static pressures, mean velocities, Reynolds stresses and wall shear distribution around the pipe are measured using pressure transducers, rotating-wires and surface hot-film gauges. The measurements are used to analyze the competing effects of swirl and bend curvature on curved-pipe flows, particularly their influence on the secondary flow pattern in the crossstream plane of the curved pipe. At this swirl number, all measured data indicate that, besides the decaying combined free and forced vortex, there are no secondary cells present in the cross-stream plane of the curved pipe. Consequently, the flow displays characteristics of axial symmetry and the turbulent normal stress distributions are more uniform across the pipe compared to fully-developed pipe flows.List of symbols B calibration constant - e bridge voltage - e ₀ bridge voltage at zero flow - C _f total skin friction coefficient, = 2 _w/ W ₀ ² - D pipe diameter, = 7.62 cm - De Dean number, = ^1/2 Re - M angular momentum - n calibration constant - N _s swirl number, = D/2 W ₀ - r radial coordinate - R mean bend radius of curvature, = 49.5 cm - Re pipe Reynolds number, = DW ₀/ - S axial coordinate along the upstream (measured negative) and downstream (measured positive) tangent - U, V, W mean velocities along the radial, tangential and axial directions, respectively - u, v, w mean fluctuating velocities along the radial, tangential and axial directions, respectively - u, v, w root mean square normal stress along the radial, tangential and axial directions, respectively - v ^{ov2}, u^{ov2} normal stress along the tangential and radial direction, respectively - W ₀ mean bulk velocity, 10 m/s - W _c W measured at pipe axis - W total wall friction velocity, - total wall friction velocity measured at S/D = -18 - ,v vw, w7#x016B; turbulent shear stresses - pipe-to-mean-bend radius ratio, = D/2 R = 0.077 - axial coordinate measured from bend entrance - fluid kinematic viscosity - fluid density - _w mean total wall shear stress - instantaneous total wall shear - azimuthal coordinate measured zero from pipe hori zontal diameter near outer bend - angular speed of the rotating section     

Isoparametric shear spring element applied to crack patching and instability

In this work the isoparametric shear spring element is applied to the stress and energy analysis of a center-crack panel reinforced by a rectangular patch. In this model, only transverse shears are assumed to prevail in the adhesive layer. The stresses and crack-tip stress intensity factors are obtained for reinforcement on both sides and one side of the panel, and are found to be in agreement with those obtained by previous authors using the triangular shear spring element.Crack stability that tends to vary with patch thickness is determined from the local and global maximum of the minimum strain energy density function denoted, respectively, as [(dW/dV)_min^max]_L at point L and [(dW/dV)_min^max]_G at point G. The distance l between L and G gives the prospective path of subcritical crack growth and its magnitude provides a measure of the degree of crack stability. A patched panel with small l tends to be more stable than that with large l. By increasing the patch thickness beyond a certain value, l can be contained within the patch such that failure, if initiated, will be highly localized. Such a behavior is exhibited. Numerical results are provided to support the foregoing conclusion.     

Wave propagation in transversely isotropic porous piezoelectric materials

Wave propagation in porous piezoelectric material (PPM), having crystal symmetry 6 mm, is studied analytically. Christoffel equation is derived for the propagation of plane harmonic waves in such a medium. The roots of this equation give four complex wave velocities which can propagate in such materials. The phase velocities of propagation and the attenuation quality factors of all these waves are described in terms of complex wave velocities. Phase velocities and attenuation of the waves in PPM depend on the phase direction. Numerical results are computed for the PPM BaTiO₃. The variation of phase velocity and attenuation quality factor with phase direction, porosity and the wave frequency is studied. The effects of anisotropy and piezoelectric coupling are also studied. The phase velocities of two quasi dilatational waves and one quasi shear waves get affected due to piezoelectric coupling while that of type 2 quasi shear wave remain unaffected. The phase velocities of all the four waves show non-dispersive behavior after certain critical high frequency. The phase velocity of all waves decreases with porosity while attenuation of respective waves increases with porosity of the medium. The characteristic curves, including slowness curves, velocity curves, and the attenuation curves, are also studied in this paper.     

Interaction of an ultrasonic wave with a bubbly mixture

The interaction of an ultrasonic wave with a bubbly two-phase flow is studied both experimentally and theoretically. Brief theoretical reviews of acoustic wave generation by a piston and of the interaction of a plane wave with a single bubble are given. A theory relating ultrasonic wave transmission through a bubbly flow with two-phase flow parameters, notably the bubble size and the volumetric interfacial area, is derived and compared with preliminary data. The theoretical and experimental limitations concerning the application of ultrasonic transmission measurements to the study of bubbly flow are discussed in detail, and recommendations for future work in this area are made.Nomenclature A projected cross-sectional area of a bubble - a bubble radius - a _T emitter radius - c speed of sound - d equivalent bubble diameter - I intensity - I ₀ incident intensity - J ₀ Bessel function of zero order - J ₀ Bessel function of first order - j ₁ spherical Bessel function of the first kind and of order l - k wave number - n _l spherical Bessel function of the second kind (Nishi's notation) - n number of bubbles per unit volume or per unit area - P ₀ pressure amplitude at the emitter; equilibrium pressure in the liquid - p pressure perturbation - r spherical coordinate, radial distance to the x-axis - S total scattering cross-sectional area, surface of the piston - S _i scattering cross-sectional area of the i-th bubble - T transmittance - t time - U complex source strength divided by the source area - W ratio of radial distance from the axis on the emitter surface to the radius of the emitter - x axis coinciding with the direction of propagation of the plane wave; distance between the transducers - void fraction - interfacial area per unit volume - spherical coordinate - ultrasonic wavelength - density - angular frequency     

Piezoelectric wafer active sensor embedded ultrasonics in beams and plates

In this paper we present the results of a systematic theoretical and experimental investigation of the fundamental aspects of using piezoelectric wafe active sensors (PWASs) to achieve embedded ultrasonics in thin-gage beam and plate structures. This investigation opens the path for systematic application of PWASs forin situ health monitoring. After a comprehensive review of the literature, we present the principles of embedded PWASs and their interaction with the host structure. We give a brief review of the Lamb wave principles with emphasis on the understanding the particle motion wave speed/group velocity dispersion. Finite element modeling and experiments on thin-gage beam and plate specimens are presented and analyzed. The axial (S ₀) and flexural (A ₀) wave propagation patterns are simulated and experimentally measured. The group-velocity dispersion curves are validated. The use of the pulse-echo ultrasonic technique with embedded PWASs is illustrated using both finite element simulation and experiments. The importance of using high-frequency waves optimally tuned to the sensor-structure interaction is demonstrated. In conclusion, we discuss the extension of these results toin situ structural health monitoring using embedded ultrasonics.