A study of stationary crack-tip deformation fields in thin sheets by computer vision

The in-plane deformation fields near a stationary crack tip for thin, single edge-notched (SEN) specimens, made from Plexiglas, 3003 aluminum alloy and 304 stainless steel, have been successfully obtained by using computer vision. Results from the study indicate that (a) in-plane deformations ranging from elastic to fully plastic can be obtained accurately by the method, (b) for U, and , the size of the HRR dominant zone is much smaller than forV and , respectively. Since these results are in agreement with recent analytical work, suggesting that higher order terms will be needed to accurately predict trends in the data, it is clear that the region where the first term in the asymptotic solution is dominant is dependent on the component of the deformation field being studied, (c) the HRR solution can be used to quantity only in regions where theplastic strains strongly dominate the elastic strain components (i.e., when ); forV, the HRR zone appears to extend somewhat beyond this region, (d) the displacement componentU does not have the HRR singularity anywhere within the measurement region for either 3003 aluminum or 304 SS. However, the displacement componentV agrees with the HRR slope up to the plastic-zone boundary in 3003 aluminum ( ) and over most of the region where measurements were obtained ( ) in 304 SS and (e) the effects of end conditions must be included in any finite-element model of typical SEN specimen geometries to accurately calculate theJ integral and the crack-tip fields.Paper was presented at the 1992 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 8–11.     

Generalized diagonalization of matrices over quaternion field

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Transient response of a finite crack in an orthotropic strip under the in-plane shear impact

The transient response of a central crack in an orthotropic strip under the in-plane shear impact loading is studied by using the dual integral equation method proposed by Copson and Sih. The general formula for the shear stress intensity factor near the crack tip is derived. Numerical results of with in various cases are obtained by solving the second kind Fredholm integral equation and by performing the inverse Laplace transform.     

A Numerical Study of the Applicability of the Shear Compression Specimen to Parabolic Hardening Materials

This paper addresses quasi-static loading of the shear compression specimen (SCS), that has been especially developed to investigate the shear response of materials at various strain rates. Previous work [4, 5] addressed bi-linear hardening materials, whereas the present work concerns parabolic hardening materials. The investigation is done numerically using three-dimensional elastoplastic finite element simulations. The analyses show that the averaged von Mises stress ( ) and strain ( ) on a mid-section of the gauge reflect accurately the prescribed parabolic hardening model. A method for finding the parabolic hardening coefficients and reducing the measured load, P, and displacement, d, into equivalent stress and strain is introduced and tested. A very good agreement is observed, thus confirming the potential of the technique for large strain testing of parabolic hardening materials.     

Unsteady flow in an annulus between two concentric rotating spheres

An analysis is presented for the unsteady laminar flow of an incompressible Newtonian fluid in an annulus between two concentric spheres rotating about a common axis of symmetry. A solution of the Navier-Stokes equations is obtained by employing an iterative technique. The solution is valid for small values of Reynolds numbers and acceleration parameters of the spheres. In applying the results of this analysis to a rotationally accelerating sphere, a virtual moment of intertia is introduced to account for the local inertia of the fluid.Nomenclature R _i radius of the inner sphere - R _o radius of the outer sphere - radial coordinate - r dimensionless radial coordinate, - meridional coordinate - azimuthal coordinate - time - t dimensionless time, - Re _i instantaneous Reynolds number of the inner sphere, _i R _k ² / - Re _o instantaneous Reynolds number of the outer sphere, _o R _o ² / - radial velocity component - V _r dimensionless radial velocity component, - meridional velocity component - V dimensionless meridional velocity component, - azimuthal velocity component - V dimensionless azimuthal velocity component, - viscous torque - T dimensionless viscous torque, - viscous torque at surface of inner sphere - T _i dimensionless viscous torque at surface of inner sphere, - viscous torque at surface of outer sphere - T _o dimensionless viscous torque at surface of outer sphere, - externally applied torque on inner sphere - T _p,i dimensionless applied torque on inner sphere, - moment of inertia of inner sphere - Z _i dimensionless moment of inertia of inner sphere, - virtual moment of inertia of inner sphere - Z _i,v dimensionless virtual moment of inertia of inner sphere, - virtual moment of inertia of outer sphere - _i instantaneous angular velocity of the inner sphere - _o instantaneous angular velocity of the outer sphere - density of fluid - viscosity of fluid - kinematic viscosity of fluid,/ - radius ratio,R _i/R _o - swirl function, - dimensionless swirl function, - stream function - dimensionless stream function, - _i acceleration parameter for the inner sphere, - _o acceleration parameter for the outer sphere, - shear stress - _r dimensionless shear stress,      

About a condition for blow up of solutions of cauchy problem for a wave equation

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A technique for evaluation of three-dimensional behavior in turbulent boundary layers using computer augmented hydrogen bubble-wire flow visualization

A system is described which allows the recreation of the three-dimensional motion and deformation of a single hydrogen bubble time-line in time and space. By digitally interfacing dualview video sequences of a bubble time-line with a computer-aided display system, the Lagrangian motion of the bubble-line can be displayed in any viewing perspective desired. The u and v velocity history of the bubble-line can be rapidly established and displayed for any spanwise location on the recreated pattern. The application of the system to the study of turbulent boundary layer structure in the near-wall region is demonstrated.List of Symbols Reynolds number based on momentum thickness u /v - t⁺ nondimensional time - u shear velocity - u local streamwise velocity, x-direction - u ⁺ nondimensional streamwise velocity - v local normal velocity, -direction - x ⁺ nondimensional coordinate in streamwise direction - ⁺ nondimensional coordinate normal to wall - ₊ ^wire wire nondimensional location of hydrogen bubble-wire normal to wall - z ⁺ nondimensional spanwise coordinate - momentum thickness - v kinematic viscosity - _W wall shear stress     

Grundzüge einer Stabilitätstheorie für elastische Systeme unter nichtkonservativer Belastung

Zusammenfassung Um den Einfluß von nichtkonservativen Kräften zu erfassen, muß die Stabilitätstheorie nichtkonservativer elastischer Systeme auf dem Prinzip der virtuellen Verrückung aufgebaut werden, das von genügender Allgemeinheit ist. Als mathematische Methode steht nach Klärung von Konvergenzfragen das Galerkinsche Verfahren zur Verfügung, das dem ursprünglichen Problem der Stabilität elastischer Systeme das Problem der Stabilität der Bewegung eines mechanischen Systems von unendlich vielen Freiheitsgraden als gleichwertig zuordnet und die Algebraisierung des Stabilitätsproblems erlaubt. Damit wird die Ljapunowsche Theorie anwendbar. Als Wichtigstes ist die Berechtigung der Linearisierung zu untersuchen, wozu der Einfluß der Dämpfung festzustellen ist. Es ergibt sich, daß bei Berücksichtigung von Dämpfung die Stabilität stets asymptotisch ist, so daß die Linesarisierung gerechtfertigt wird. Darüber hinaus zeigt es sich, daß die Struktur der Matrizen und von entscheidender Bedeutung für die Zuständigkeit eines der in Frage kommenden Stabilitätskriterien ist: Ist symmetrisch und eine beliebige positive Diagonalmatrix bzw. schiefsymmetrisch, oder symmetrisierbar bzw. unsymmetrisch und noch gleichzeitig (die Dämpfungskoeffizienten alle gleich), so wirkt in diesen Fällen die Dämpfung günstig, und die Stabilitätskriterien des ungedämpften Vorganges, das statische bzw. das kinetische, bleiben daher hinreichend. Man darf dann auch ohne Dämpfung rechnen. Ist dagegen unsymmetrisch und eine positive Diagonalmatrix mit verschiedenen Elementen, so darf in solch einem Fall nicht ohne Dämpfung gerechnet werden, weil gegenüber dem ungedämpften Vorgang ein Sprung in den Stabilitätsbedingungen auftritt, durch welchen das Ergebnis der Rechnung ohne Dämpfung in Frage gestellt wird.     

The extended Jordan's lemma and the relation between laplace transform and fourier transform

I.IntroductionItiswell4n0wnthatthecontourintergrationofcomp1exvariableftinctioncanmakealotintegrationveryconvenient.Jordan'slemmahasaveryimportantstatusintheonec0mplexvariableintegration,anditisveryusefulforavarityofintegration.Withthetheoryoffunctionsofo…     

Interval stochastic matrices: A combinatorial lemma and the computation of invariant measures of dynamical systems

The concept of an interval stochastic matrix is introduced. We prove a combinatorial theorem which describes the network flow associated with an interval matrix. The semi-invariant vectors of are characterized in terms of eigenvectors with unit eigenvalue of stochastic matrices . These results are then applied to the approximation and machine computation of invariant measures of dynamical systems.Funded under Australian Research Council Grant A 8913 2609.     

The flow regime in the turbulent near wake of a hemisphere

The work presented is a wind tunnel study of the near wake region behind a hemisphere immersed in three different turbulent boundary layers. In particular, the effect of different boundary layer profiles on the generation and distribution of near wake vorticity and on the mean recirculation region is examined. Visualization of the flow around a hemisphere has been undertaken, using models in a water channel, in order to obtain qualitative information concerning the wake structure.List of symbols C _p pressure coefficient, - D diameter of hemisphere - n vortex shedding frequency - p pressure on model surface - p ₀ static pressure - Re Reynolds number, - St Strouhal number, - U, V, W local mean velocity components - mean freestream velocity inX direction - U ^* shear velocity, - u, v, w velocity fluctuations inX, Y andZ directions - X Cartesian coordinate in longitudinal direction - Y Cartesian coordinate in lateral direction - Z Cartesian coordinate in direction perpendicular to the wall - it* boundary layer displacement thickness, - diameter of model surface roughness - elevation angleI - O boundary layer momentum thickness, - _w wall shearing stress - dynamic viscosity of fluid - density of fluid - streamfunction - _x longitudinal component of vorticity, - _y lateral component of vorticity, - _z vertical component of vorticity, This paper was presented at the Ninth symposium on turbulence, University of Missouri-Rolla, October 1–3, 1984     

Modelling of the pressure-velocity correlation in turbulence diffusion

Most current computations of trubulent flows with second-moment closure adopt the diffusion models which neglect the effect of pressure-velocity correlation. In the present paper the importance of this correlation effect is elucidated the neglect of this effect accounts for some major defects in the wide application of the second-moment closures. Through the relation between and , established by Lumley, we propose here a new turbulence diffusion model which takes into consideration the pressure effect. Applications of this new model in the computation of shearless turbulence mixing layer and plane and round-jet flows show that the spreading rate of these flows can be satisfactorily captured.     

The compression LS estimate of regression coefficient in multivariate linear model

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Pseudo-molecular dynamics study of grain boundary segregation

The segregation of bismuth atoms on the [101] tilt copper grain boundaries Σ3 ( ) 70.53°, Σ33 ( ) 58.99°, Σ11 ( ) 50.48° and Σ9 ( ) 38.94° has been studied by pseudo-molecular dynamics using the empiricalN-body potentials. The relationship between bismuth segregation and grain boundary structure has been discussed in detail. The subject supported by the Chinese Academy of Sciences and National Natural Science Foundation of China     

Druckabhängigkeit der Viskosität einiger Polyolefinschmelzen

Zusammenfassung Es wird die Druckabhängigkeit des nicht -Newtonschen Fließverhältens von Polyolefinschmelzen (Hochdruck-, Niederdruck-,Phillips-Polyäthylen und Polypropylen) experimentell untersucht und gefunden, daß der durch Gl. [1] definierte Druckkoeffizient mit zunehmender Deformationsgeschwindigkeit kleiner wird und dabei die (im einzelnen in der Tabelle 1 angeführten) Werte annimmt. Der Druckkoeffizient der Polyolefinschmelzen ist ebenso wie für vieleNewtonsche Flüssigkeiten bis 2000 kp cm^–2 unabhängig vom Druck, er wird mit zunehmender Temperatur kleiner und nimmt mit zunehmender Verzweigung zu. Die Meßergebnisse werden mit Hilfe eines Aufweitungsvolumens interpretiert. Es wird gezeigt, daß eine Deutung des Fließverhaltens von Polyäthylen durch das freie Volumen allein nicht möglich ist.

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Summary The influence of pressure of the non-Newtonian flow behaviour of polyolefin melts (Low- and High density Polyethylene,Phillips-Polyethylene and Polypropylene) was investigated. The results are: the coefficient of pressure as defined by eq. [1], decreases with increasing shear rate and reaches the values given in table 1 . The pressure coefficient of polyolefin melts does not depend on pressure up to 2000 kp cm^–2. As observed with manyNewtonian fluids, decreases with increasing temperature and increases with the degree of branching. The experimental results are explained by means of a so called volume of expansion. It has been shown that it is impossible to explain the flow behaviour of polyethylene exclusively with the free volume.

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Für die Diskussion und Förderung dieser Arbeit danke ich Herrn Professor Dr.K.-H. Hellwege und Herrn Dr.W. Knappe.     

Plane stress dynamic fields near a propagating crack-tip in a power-law material

Based on the plastic-dynamic equations, the asymptotic behaviour of the near-tip fields for a plane stress tensile crack propagating in a power-law material has been studied in this paper. It is shown that the stress and strain singularities are, respectively, of the order and , whereA is a constant which is related to the size of plastic region,r is the distance to the crack tip,n is the power-law exponent. Projects sponsored by the National Science Foundation.     

Experimental simulation of matrix cracking and debonding in a model brittle matrix composite

A model composite material system was designed to simulate typical damage mechanisms in unidirectional fiber reinforced brittle matrix composites. Experiments were performed at low to high quasistatic, macroscopic loading rates . At all loading rates reversal of the transverse strain was observed and was correlated to matrix cracking and debonding. The optical method of coherent gradient sensing (CGS) was used to obtain qualitative information regarding the stress fields and to observe the progression of damage. It was found that the sequence of damage formation (damage path) depended on the macroscopic loading rate. At lower loading rates periodic matrix cracks developed; minimal debonding of the reinforcement-matrix interface occurred only much later in the experiment. At higher loading rates extensive debonding followed propagation of the initial matrix crack, and periodic cracking was not observed. Several features of the material response of the model material system were also observed in a previously studied unidirectional ceramic matrix composite.     

On the continuum modelling of porous media containing fluid: a molecular viewpoint with particular attention to scale

Mass conservation and linear momentum balance relations for a porous body and any fluid therein, valid at any given length scale in excess of nearest-neighbour molecular separations, are established in terms of local weighted averages of molecular quantities. The mass density field for the porous body at a given scale is used to identify its boundary at this scale, and a porosity field is defined for any pair of distinct length scales. Specific care is paid to the interpretation of the stress tensor associated with each of the body and fluid at macroscopic scales, and of the force per unit volume each exerts on the other. Consequences for the usual microscopic and macroscopic viewpoints are explored.Nomenclature material system; Section 2.1. - porous body (example of a material system); Sections 2.1, 3.1, 4.1 - fluid body (example of a material system); Sections 2.1, 3.1, 4.1 - weighting function; Sections 2.1, 2.3 - ,h weighting function corresponding to spherical averaging regions of radius and boundary mollifying layer of thicknessh; Section 3.2 - Euclidean space; Section 2.1 - V space of all displacements between pairs of points in; Section 2.1 - mass density field corresponding to; (2.3)₁ - ^P , ^f mass density fields for , ; (4.1) - P momentum density field corresponding to; (2.3)₂ - v velocity field corresponding to; (2.4) - S _r (X) interior of sphere of radiusr with centre at pointx; (3.3) - boundary ofany region - region in which ^p > 0 with = ,h; (3.1) - subset of whose points lie at least+h from boundary of ; (3.4) - abbreviated versions of ; Section 3.2, Remark 4 - strict interior of ; (3.7) - analogues of for fluid system ; Section 3.2 - general version of corresponding to any choice of weighting function; (4.6) - interfacial region at scale; (3.8) - ₀ scale of nearest-neighbour separations in ; Section 3.2. Remark 1 - porosity field at scales ( ₁; ₂); (3.9) - pore space at scales ( ₁; ₂); (3.12)     

Behaviour of the Reynolds stress on rough walls

Quadrant analysis is used to study the contributions, associated to the four quadrants of the (u,v) plane, to the production of the turbulent shear stress on rough walls. The measurements are described for a fully developed turbulent flow between two rough plates with varying the parameterλ _z(span/height ratio of roughness elements). The application of this technique indicates that the (Q ₂) events (ejections) and (Q ₄) events (sweeps) cause an intense production of the Reynolds stress —ρ as compared with the (Q ₁) and (Q ₃) quadrants. The (Q ₂) contribution to the Reynolds stress depends on the geometry factorλ _z. Variation of the parameterλ _zaffects the distributions of and forH⩽3, whereH is a particular threshold. Comparison with boundary layer flow shows that the region 0.2⩽y/h⩽0.7 is characterized by a Reynolds stress production, independent of the flow nature. The third moment of the longitudinal velocity fluctuations is found to be sensitive to the surface roughness.     

Der selbsterregte unsymmetrische Kreisel

Zusammenfassung Wir können alle bisherigen Erkenntnisse über die Selbsterregung des unsymmetrischen Kreisels dahin zusammenfassen, daß — abgesehen von den trivialen Fällen der Drehungen um jede der drei Hauptachsen und abgesehen von den permanenten Drehungen um beliebige Achsen — zu jeder achsenfesten zeitunabhängigen Selbsterregung achsenbewegliche Drehungen gehören, wie wir solche in Ziff. 2 bis 7 untersucht haben; ferner daß es, wieder abgesehen von jenen trivialen Fällen, nur den einzigen Typ der achsenfesten zeitabhängigen Selbsterregung von Ziff. 9 gibt, welche eine achsenfeste zeitabhängige Drehung zu beeinflussen, wenn auch weder zu erzeugen noch zu vernichten vermag; endlich daß der Momentvektor der Selbsterregung, welcher eine beliebige achsenfeste Drehung erzeugen oder vernichten oder in beliebiger Weise beeinflussen soll, im allgemeinen (also abgesehen von den trivialen Fällen und von dem Fall in Ziff. 9) zeitabhängig in einer körperfesten Ebene wandern muß. Die achsenbeweglichen Drehungen, welche von achsenfester zeitunabhängiger Selbsterregung erzeugt oder unterhalten werden, sind je nach der Lage (und Größe) des Momentes der Selbsterregung periodisch hinsichtlich der Bewegung des Drehvektors im Kreisel oder asymptotisch mit unbeschränkt wachsendem Drehvektor oder asymptotisch mit einem Drehvektor , der sich einem permanenten Drehvektor (von endlichem Betrag) annähert (oder auch sich von ihm entfernt).