bluuebunny/crossref_metadata_2025 huggingface dataset:
Nondestructive Evaluation of the J and M Integrals
Authors: King R. B. , Herrmann G.
Published: July 2009

The usefulness of two conservation integrals, the so-called J and M integrals, in fracture mechanics is reviewed. A method for experimental evaluation of these quantities by direct determination of the values of their integrands at various points along a contour is presented, and contrasted with “compliance” methods which have been used to evaluate J. This technique has been applied to three different specimen configurations, and the experimental results compare favorably with theoretical predictions.
The Study of Sluice Gate and Sharp-Crested Weir Through Hodograph Transformations
Authors: Han T. Y. , Chow W. L.
Published: July 2009

The problems of sluice gate and sharp crested weir were studied through hodograph transformations. Numerical calculations of the stream function in terms of hodograph variables were carried out after the hodographs were transformed into rectangles. Results were compared with the available experimental data and other results of calculations. Favorable agreement in all cases substantiated the fact that the method of hodograph transformation is effective in dealing with these problems strongly influenced by gravitation.
On the Characterization of Strain-Hardening in Plasticity
Authors: Casey J. , Naghdi P. M.
Published: July 2009

In the context of a purely mechanical, rate-type theory of elastic-plastic materials and utilizing a strain space formulation introduced in [1], this paper is concerned mainly with developments pertaining to strain-hardening behavior consisting of three distinct types of material response, namely, hardening, softening, and perfectly plastic behavior. It is shown that such strain-hardening behavior may be characterized by a rate-independent quotient of quantities occurring in the loading criteria of strain space and the corresponding loading conditions of stress space. With the use of special constitutive equations, the predictive capability of the results obtained are illustrated for strain-hardening response and saturation hardening in a uniaxial tension test.
Constitutive Equations of Elastoplastic Materials With Anisotropic Hardening and Elastic-Plastic Transition
Authors: Hashiguchi K.
Published: July 2009

Constitutive equations of elastoplastic materials with anisotropic hardening and elastic-plastic transition are presented by introducing three similar surfaces, i.e., a loading surface on which a current stress exists, a subyield surface limiting a size of the loading surface and a distinct-yield surface representing a fully plastic state. The assumption of similarity of these surfaces leads the derived equations to remarkably simple forms. Also a more general rule of the kinematic hardening for the distinct-yield surface is incorporated into the constitutive equations. While they seem to be applicable to various materials, special constitutive equations of metals, for example, are derived from them and are compared with experimental data on a cyclic uniaxial loading of aluminum. A close correlation between theory and experiment is observed in this comparison.
The Effect of Crack-Tip Plasticity on the Determination of Dynamic Stress-Intensity Factors by the Optical Method of Caustics
Authors: Rosakis A. J. , Freund L. B.
Published: July 2009

The shadow spots which are obtained in using the optical method of caustics to experimentally determine dynamic stress-intensity factors are usually interpreted on the basis of a static elastic crack model. In this paper, an attempt is made to include both crack-tip plasticity and inertial effects in the analysis underlying the use of the method in reflection. For dynamic crack propagation in the two-dimensional tensile mode which is accompanied by a Dugdale-Barenblatt line plastic zone, the predicted caustic curves and corresponding initial curves are studied within the framework of plane stress and small scale yielding conditions. These curves are found to have geometrical features which are quite different from those for purely elastic crack growth. Estimates are made of the range of system parameters for which plasticity and inertia effects should be included in data analysis when using the method of caustics. For example, it is found that the error introduced through the neglect of plasticity effects in the analysis of data will be small as long as the distance from the crack tip to the initial curve ahead of the tip is more than about twice the plastic zone size. Also, it is found that the error introduced through the neglect of inertial effects will be small as long as the crack speed is less than about 20 percent of the longitudinal wave speed.
A Micromechanical Description of Granular Material Behavior
Authors: Christoffersen J. , Mehrabadi M. M. , Nemat-Nasser S.
Published: July 2009

Considered is a sample of cohesionless granular material, in which the individual granules are regarded rigid, and which is subjected to overall macroscopic average stresses. On the basis of the principle of virtual work, and by an examination of the manner by which adjacent granules transmit forces through their contacts, a general representation is established for the macroscopic stresses in terms of the volume average of the (tensorial) product of the contact forces and the vectors which connect the centroids of adjacent contacting granules. Then the corresponding kinematics is examined and the overall macroscopic deformation rate and spin tensors are developed in terms of the volume average of relevant microscopic kinematical variables. As an illustration of the application of the general expressions developed, two explicit macroscopic results are deduced: (1) a dilatancy equation which both qualitatively and quantitatively seems to be in accord with experimental observation, and (2) a noncoaxiality equation which seems to support the vertex plasticity model. Since the development is based on a microstructural consideration, all material coefficients entering the results have well-defined physical interpretations.
Vibration of Thick Rectangular Plates of Bimodulus Composite Material
Authors: Bert C. W. , Reddy J. N. , Chao W. C. , Reddy V. S.
Published: July 2009

A finite-element analysis is carried out for small-amplitude free vibration of laminated, anisotropic, rectangular plates having arbitrary boundary conditions, finite thickness shear moduli, rotatory inertia, and bimodulus action (different elastic properties depending upon whether the fiber-direction strain is tensile or compressive). The element has five degrees of freedom, three displacements and two slope functions, per node. An exact closed-form solution is also presented for the special case of freely supported single-layer orthotropic and two-layer, cross-ply plates. This solution provides a benchmark to evaluate the validity of the finite-element analysis. Both solutions are compared with numerical results existing in the literature for special cases (all for ordinary, not bimodulus, materials), and good agreement is obtained.
Nonlinear Theory for Flexural Motions of Thin Elastic Plate—Part 1: Higher-Order Theory
Authors: Sugimoto N.
Published: July 2009

This paper develops a comprehensive higher-order theory for flexural motions of a thin elastic plate, in which the effect of finite thickness of the plate and that of small but finite deformation are taken into account. Based on the theory of nonlinear elasticity for a homogeneous and isotropic solid, the nonlinear equations for the flexural motions coupled with the extensional motions are systematically derived by the moment asymptotic expansion method. Denoting by ε the ratio of the thickness of the plate to a characteristic wavelength of flexural motions, an order of characteristic deflection is assumed to be ε2 and that of a characteristic strain ε3. The displacement and stress components are sought consistently up to the next higher-order terms than those in the classical theory.
Reexamination of Stability of a Two-Dimensional Finite Panel Exposed to an Incompressible Flow
Authors: Matsuzaki Y.
Published: July 2009

Stability of a flat or buckled panel exposed to an incompressible flow has been reanalyzed as the analyses on this problem by other investigators have errors in the fluid forces used. The deflection of the panel in an oscillatory motion is assumed in such a way that there occurs no change in the fluid volume in a control surface enclosing the panel. The nonlinear equation of motion of the panel on a continuous elastic spring is solved by using the Galerkin method and the generalized fluid forces which are derived in the author’s previous paper. The stability of the flat and buckled configuration in static equilibrium is examined against small disturbances. Existence of the limit cycle oscillation is studied by applying the harmonic balance method. Numerical results are compared with those of the analysis on a two-dimensional finite elastic channel conveying an almost incompressible flow.
On Stress-Strain Relations Suitable for Cyclic and Other Loading
Authors: Drucker D. C. , Palgen L.
Published: July 2009

The analysis and design of pressure vessels and other structures subjected to cyclic loading and occasional large overloads requires stress-strain relations sufficiently simple to be usable with computer programs and yet adequate to describe the essential aspects of the response of the material. One such form with two quite different options is proposed for the time-independent domain which avoids the difficulties of earlier approaches. It has the kinematic hardening attributes needed for reversal of loading, allows for cyclic hardening or softening, gives zero mean stress as the asymptotic response to cyclic straining between fixed limits of strain, and reduces to a J2 stress-hardening form for radial or proportional loading so that it can model both cyclic and other loading to a good first approximation.
Stable Phase of Ductile Fracture in Two and Three Dimensions, Final Stretch Model
Authors: Wnuk M. P.
Published: July 2009

Analysis given here is based on the final stretch concept employed in conjunction with a line plasticity model as suggested by the author in 1972 [6] and in this Journal in 1974 [8]. Its objective is to provide the equations governing quasi-static extension of a tensile crack contained in either partially or in a fully yielded specimen. Differential equations defining the apparent material resistance developed during the early stages of a ductile fracture process are derived from a requirement that the “essential work of fracture” dissipated in a small volume immediately ahead of the crack front, or equivalently, the “final stretch,” remains invariant in the process of ductile tear. The model suggests a certain near-tip distribution of displacements associated with a quasi-static Mode I crack such that the resulting strains are logarithmically singular at the crack tip. In contrast to the earlier work on this subject, here we impose no restrictions on the amount of plasticity which precedes the onset of crack growth and which accompanies spread of stable ductile fracture up to the point of global failure. The final results, which are illustrated in the diagrams of J-resistance curves, are analogous to the data obtained by other researchers on the basis of the incremental plasticity theory. Similarities between the present results and the solutions due to Hutchinson, Paris, and coworkers as well as the most recent data obtained by Shih and coworkers, are pointed out.
Energy-Release Rate and Crack Kinking Under Combined Loading
Authors: Hayashi K. , Nemat-Nasser S.
Published: July 2009

Based on the maximum energy-release-rate criterion, kinking from a straight crack is investigated under the plane strain condition. Solutions are obtained by the method that models a kink as a continuous distribution of edge dislocations. The energy-release rate is expressed as a quadratic form of the stress-intensity factors that exist prior to the onset of kinking, and the coefficients of this quadratic form are tabulated for various values of the kink angle. The examination of the results shows that Irwin’s formula for the energy-release rate remains valid for any kink angle provided that the stress-intensity factors in the formula are taken equal to those existing at the tip of a vanishingly small kink.
Elastodynamic Stress-Intensity Factors for a Crack Near a Free Surface
Authors: Achenbach J. D. , Brind R. J.
Published: July 2009

Elastodynamic Mode I and Mode II stress-intensity factors are presented for a subsurface crack in an elastic half space. The plane of the crack is normal to the surface of the half space. The half space is subjected to normal and tangential time-harmonic surface tractions. Numerical results show the variation of KI and KII at both crack tips, with the dimensionless frequency and the ratio a/b, where a and b are the distances to the surface from the near and the far crack tips, respectively. The results are compared with corresponding results for a crack in an unbounded solid.
Contact Pressures on Closely Conforming Elastic Bodies
Authors: Paul B. , Hashemi J.
Published: July 2009

A numerical method is developed for the determination of the contact pressure that arises when two elastic bodies with closely conforming non-Hertzian frictionless surfaces are pressed together. The method is a generalization of that recently developed by the authors for the case of antiformal contact, and includes a technique for automatically generating meshes that overlay the changing (load-dependent) contact patches. The method has been implemented in a computer program called CONFORM, and has been applied to problems of wheel and rail contact. The results have been verified by comparison with those generated by an independent program for the special case of relatively light wheel loading, where the contact is known a priori to be essentially counterformal. The results given herein for a relatively heavy (but realistic) wheel loading on the throat of the flange represent the first known solution for conformal contact between a railroad wheel and rail.
Finite Elements Based Upon Mindlin Plate Theory With Particular Reference to the Four-Node Bilinear Isoparametric Element
Authors: Hughes T. J. R. , Tezduyar T. E.
Published: July 2009

Concepts useful for the development of Mindlin plate elements are explored. Interpolatory schemes and nodal patterns which are ideal according to the proposed criteria are found to be somewhat more complicated than desirable for practical applications. However, these ideas are found to be useful as starting points in the development of simpler elements. This is illustrated by the derivation of a new four-node bilinear quadrilateral which achieves good accuracy without ostensible defect.
Response of Periodic Systems to a Moving Load
Authors: Jezequel L.
Published: July 2009

The motion of a beam or a plate resting on an elastic foundation and subjected to a moving load has been studied by numerous authors. But the extension of these studies to the case of periodic structures is difficult. In this paper, a method allowing the calculation at low numerical cost of periodically supported beams subjected to a moving force, is proposed. The interpretation of this method on the basis of the free-wave propagation equations in periodic structures has led to the definition of the predominant, so-called “primary,” critical speeds. Individual examples were used to test the method. It was also possible to define the limits of a Winkler continuous model in representing the support reactions.
On the Space of Stress Invariants
Authors: Stokes V. K.
Published: July 2009

The representation of stress through its three invariants I1,I2, and I3 has been examined. It has been shown that all possible states of stress are mapped into a connected region of the space of stress invariants that is bounded by two surfaces which meet in a cusp on a curve which corresponds to states of isotropic stress. All other states of stress for which two principal stresses are equal, lie on this surface. The I1 axis corresponds to one-dimensional states of stress. Two-dimensional stresses are represented by a connected region of the I1–I2 plane. The negative half of the I2 axis corresponds to pure shear. The positive half of the I2 axis, and the I3 axis, do not correspond to any states of stress. The representation of yield surfaces in this space has also been considered.
Application of the Reissner Method to a Timoshenko Beam
Authors: Rao J. S. , Kulkarni S. V. , Subrahmanyam K. B.
Published: July 2009

The Reissner and the potential energy methods have been applied to a Timoshenko beam vibrating in flexure. Frequency equations are developed using shape functions for bending moment, shearing force, deflection, and slope in series form through the Ritz process. Natural frequencies and mode shapes are obtained and comparison is made between the results of the two approaches from which it is observed that the Reissner method indicates a quicker convergence and gives better mode shapes.
On the Mean Reynolds Equation in the Presence of Surface Roughness: Squeeze-Film Bearing
Authors: Phan-Thien N.
Published: July 2009

The mean Reynolds equation in the presence of surface roughness is derived using the techniques developed by Keller. This mean equation is nonlocal in the sense that the mean pressure at all points in the flow field has some effect on the mean pressure at any particular point. The performance of a two-dimensional squeeze film bearing with homogeneous surface roughness is considered next showing that the load is enhanced by a factor of 1 + ε2a2S/h2, where εa is the amplitude of the roughness, h is the film thickness, and S varies between −3 〈m2〉, for parallel surface roughness, to 6 〈m2〉 for transverse surface roughness. Here, the bearing surfaces are described by εam1 and h + εam2 and m = m2 − m1.
The Exact Solutions of Some Stefan Problems With Prescribed Heat Flux
Authors: Tao L. N.
Published: July 2009

The Stefan problem of a semi-infinite material with arbitrarily prescribed initial and flux conditions is studied. When the surface temperature is initially different from the freezing temperature, there exists a presolidification or a premelting period prior to the occurrence of a phase change. The exact solutions for both periods, before and after the appearance of a phase change, are established. This indicates that the initial condition of the Stefan problem with a prescribed heat flux at the surface cannot be assumed to be constant. Possibilities of similarity solutions of the problem are also examined. A similarity solution exists only when the heat flux is proportional to t−1/2 and the initial and boundary conditions satisfy an inequality. The solidification of a supercooled liquid is also investigated. The exact solution is obtained.
The Effective Elastic Moduli of Porous Granular Rocks
Authors: Digby P. J.
Published: July 2009

A porous granular rock is modeled by an aggregate of identical, randomly stacked, spherical particles. Contacting particles are initially bonded together across small areas. A theory is developed for the deformation of two such spherical particles under equal and opposite forces acting through the line joining their centers. The theory is used to calculate the effective elastic moduli of the medium. The dependence of the derived elastic wave speeds on the confining pressure and adhesion radius of the contacting particles is then predicted.
The Continuous Damage Theory of Brittle Materials, Part 1: General Theory
Authors: Krajcinovic D. , Fonseka G. U.
Published: July 2009

The paper focuses on the establishment of the damage law consistent with the adopted physical interpretation of the damage. The model is developed within the framework of the general thermodynamics theory. In addition, the model incorporates a rigorous mathematical description of the damage growth kinematics including both cleavage and slip modes.
An Educational Elasticity Problem With Friction, Part 1: Loading, and Unloading for Weak Friction
Authors: Dundurs John , Comninou Maria
Published: July 2009

The paper treats an elasticity problem with friction that can be solved in closed form. It involves an unbounded solid with a semi-infinite cut. The solid is compressed in a direction perpendicular to the cut, but the cut is induced to separate and slip locally by applying a concentrated force at the tip of the cut. The first part deals with the initial loading phase and includes unloading for weak friction.
Fatigue Failure Criteria for Unidirectional Fiber Composites
Authors: Hashin Z.
Published: July 2009

Three-dimensional fatigue failure criteria for unidirectional fiber composites under states of cyclic stress are established in terms of quadratic stress polynomials which are expressed in terms of the transversely isotropic invariants of the cyclic stress. Two distinct fatigue failure modes, fiber mode, and matrix mode, are modeled separately. Material information needed for the failure criteria are the S-N curves for single stress components. A preliminary approach to incorporate scatter into the failure criteria is presented.
Mode Interaction of Axially Stiffened Cylindrical Shells: Effects of Stringer Axial Stiffness, Torsional Rigidity, and Eccentricity
Authors: Hui David , Tennyson R. C. , Hansen J. S.
Published: July 2009

This paper deals with the effect of stringer axial stiffness, torsional rigidity, and eccentricity on the panel initial postbuckling behavior and mode interaction of axially stiffened cylindrical shells. As far as the local panel mode is concerned, the cylinder is taken to be integrally stiffened and the postbuckling redistribution of the axial load-carrying capacity between the skin and stringers is investigated. It is found that although the buckling analysis is more or less identical to previous analyses, there are significant changes in the quartic term of the potential energy of the local mode and hence, the imperfection-sensitivity of the structure is altered. These changes are due to the interaction between the stringers and the skin in the postbuckling analysis. In addition, to assess the effect of a nonlinear prebuckling state resulting from the presence of local imperfections, Koiter’s theory of amplitude modulation of the local mode is applied to an example problem of interest.
Mechanics of Ice-Lifting From a Flat Surface Through Penetration With a Sharp Blade
Authors: Huang N. C.
Published: July 2009

This paper is concerned with the mechanism of ice-lifting from a flat surface through penetration of the interface by means of a sharp blade. We first considered a static case in which the lifted ice was treated as an elastic Timoshenko beam of the cantilever type. The principle of the balance of energy was used in formulating the problem. Our objective was to find the relationship between the applied thrust and the length of the crack at the interface. Special attention has been focused on the instability phenomenon associated with crack propagation. An experimental program has been conducted for comparing the measured critical thrust for instability with the theoretical predictions. The static problem was then generalized to the case of dynamic loading where the sharp blade penetrated the interface through the action of an impact. In the dynamic case, the speed of the blade was found to decrease continuously when time increases. Our interest was to determine the relationship between the applied impulse and the maximum length of the crack generated at the interface.
Dynamic Behavior of Continuous Cantilevered Pipes Conveying Fluid Near Critical Velocities
Authors: Rousselet J. , Herrmann G.
Published: July 2009

The plane motion of a cantilevered pipe conveying fluid is examined when the flow velocity is in the neighborhood of that generating flutter. In contrast to previous studies, the flow velocity is not prescribed as a constant, but is determined from the laws of motion. We are thus led to a system of two nonlinear partial differential equations which are coupled through the nonlinear terms. The solution is found by the use of the Krylov-Bogoliubov averaging method and the results are discussed indicating the effect of nonlinearities.
Parametric Instability of a Rotating Shaft Due to Pulsating Torque
Authors: Unger A. , Brull M. A.
Published: July 2009

The torque transmitted by a shaft is usually a pulsating one. This torque may under certain conditions cause transverse parametric oscillations of the shaft leading to its failure. In this paper, an analytical numerical investigation is presented to determine the stability regions of the shaft due to a pulsating torque applied at its ends. The present work deals with three types of parametric instabilities. Unstable regions bounded by oscillatory motions characterized by period T and by period 2T and combination resonance. The results indicate that the most common and dangerous parametric instabilities arise as a result of combination resonance.
Amplitude Incremental Variational Principle for Nonlinear Vibration of Elastic Systems
Authors: Lau S. L. , Cheung Y. K.
Published: July 2009

The incremental method has been widely used in various types of nonlinear analysis, however, so far it has received little attention in the analysis of periodic nonlinear vibrations. In this paper, an amplitude incremental variational principle for nonlinear vibrations of elastic systems is derived. Based on this principle various approximate procedures can be adapted to the incremental formulation. The linear solution for the system is used as the starting point of the solution procedure and the amplitude is then increased incrementally. Within each incremental step, only a set of linear equations has to be solved to obtain the data for the next stage. To show the effectiveness of the present method, some typical examples of nonlinear free vibrations of plates and shallow shells are computed. Comparison with analytical results calculated by using elliptic integral confirms that excellent accuracy can be achieved. The technique is applicable to highly nonlinear problems as well as problems with only weak nonlinearity.
On Plastic Strain in Porous Materials
Authors: Carroll M. M. , Schatz J. F. , Yamada S. E.
Published: July 2009

The formulation of continuum theories for inelastic response usually involves the definition of plastic strains or plastic strain increments. For solid materials, these are usually defined in terms of the residual deformation resulting from a loading-unloading stress cycle. For porous materials, the residual deformation may involve both irreversible and reversible deformation mechanisms in the solid matrix. We treat the special case of hydrostatic response of dry or fluid-saturated isotropic porous materials and we show that a particular definition of the plastic volume strain increment isolates the irreversible deformation mechanism, thereby making it perhaps the most useful definition for theoretical purposes.
Elasticity Solution for a Multilayered Transversely Isotropic Circular Cylindrical Shell
Authors: Chandrashekhara K. , Gopalakrishnan P.
Published: July 2009

An elasticity solution has been obtained for a long multilayered cylindrical shell of transversely isotropic layers subjected to axisymmetric radial load following Lekhnitskii’s stress function method. Numerical results are presented for a two layered shell for different ratios of thickness-to-outer radius and for different ratios of the moduli of elasticity in the radial direction of the layers. The results obtained from this analysis have been compared with those obtained from the multilayered shell theory of Ambartsumian.
Large Deflection of a Fluid-Filled Spherical Shell Under a Point Load
Authors: Taber L. A.
Published: July 2009

Large deflection of a fluid-filled spherical shell under a concentrated load was studied analytically and experimentally. The analysis involves a strain energy approach based on thin shell theory for moderately large rotation. Load and fluid pressure from tests on rubber shells filled with water show good agreement with computed results for deflection as large as 60 percent of the radius of the shell. Deflection less than 20 percent of the radius is dominated by bending while larger deflection is governed mainly by stretching due to the displaced fluid.
Edge Effects in Laminated Composite Plates
Authors: Dong S. B. , Goetschel D. B.
Published: July 2009

The attenuation of self-equilibrated edge stress states into the interior of a laminated plate composed of an arbitrary number of bonded, elastic, anisotropic layers is investigated in the context of Saint-Venant’s principle using the exponential decay results of Toupin, Knowles, and Horgan. To model the plate’s behavior, a semianalytical method is used with finite element interpolations over the thickness and exponential decay into the plate’s interior. The formulation leads to a second-order algebraic eigensystem whose eigenvalues are the characteristic inverse decay lengths, and corresponding right eigenvectors depict the displacement distributions of self-equilibrated traction states. Orthogonality relations between these right and left eigenvectors of the adjoint system are established. An eigenvector expansion for representing arbitrary self-equilibrated edge tractions is then presented. This approach is useful in revealing the interlaminar effects and their decay rates in a laminated composite plate under plane strain. Two examples are provided where the interlaminar phenomena due to eigenstates of self-equilibrated edge stress are illustrated.
A Simple and Effective Pipe Elbow Element—Interaction Effects
Authors: Bathe K. J. , Almeida C. A.
Published: July 2009

Our elbow element presented in an earlier communication is enhanced to account for interaction effects between elbows and rigid flanges, elbows of different curvatures, and elbows joining straight pipe sections. The interaction effects are modeled by including the appropriate additional strain terms in the stiffness matrix formulation and by using a penalty procedure to enforce the continuity of the derivatives in the pipe skin radial displacements. The enhancement in the formulation has been implemented and the results of various sample analyses are presented.
Membrane Locking and Reduced Integration for Curved Elements
Authors: Stolarski H. , Belytschko T.
Published: July 2009

The behavior of a curved beam element is studied by comparison to an analytic solution. In the curved beam element, curvature effects are incorporated through a “shallow-shell” type theory. It is shown that when low-order, inplane displacement fields are used for the element, the curvature terms increase the bending stiffness due to contributions from the membrane strains; this is called “membrane locking.” Reduced integration yields a bending stiffness, which is in better agreement with the analytic value, and yet it retains the bending-membrane coupling, which is characteristic of curved elements. The results of the analysis are verified by several numerical examples.
Dynamic Instability in Ice-Lifting From a Flat Road Surface Through Penetration With a Sharp Blade
Authors: Huang N. C.
Published: July 2009

This paper is concerned with the problem of dynamic instability during ice-lifting from a flat surface through penetration of the interface by means of a sharp blade. The blade is subjected to a horizontal impulsive load and a constant horizontal thrust, both applied suddenly and simultaneously. The principle of the balance of energy is used to analyze the deformation of the ice associated with the crack propagation along the interface. In our formulation, the effect of wave propagation in the ice is neglected. However, the inertia force due to the acceleration of the blade is included. The motion of the blade is investigated by the numerical solution of a complex, nonlinear, initial value problem. It is found that under a given horizontal thrust, if the initial velocity of the blade is sufficiently small, the motion of the blade may stop. However, if the initial velocity of the blade is sufficiently large, the motion of the blade is always forward and the crack can propagate indefinitely along the interface.
A Modified Strain-Energy Density Criterion Applied to Crack Propagation
Authors: Theocaris P. S. , Andrianopoulos N. P.
Published: July 2009

An exact solution is presented to the problem of the crack-initiation direction by applying the minimum strain-energy density criterion in the case of a slant crack loaded uniaxially. The exact expressions of stresses, obtained from Muskhelishvili’s complex functions, are used in evaluating strain energy. Although the position of direction of the minimum density (ϑm) was accepted as the probable direction of the next kink of a propagating crack, the mean value of the strain-energy density is also introduced, instead of its minimum value, in the role of the critical quantity for crack initiation. Interesting results were derived for the behavior of this quantity concerning the phenomenon of bifurcation. The ratio of the mean-energy densities above and below the expected path of propagation is introduced as a second factor influencing the exact value of angle ϑm of propagation.
The 〈111〉 Elliptic Inclusion in an Anisotropic Solid of Cubic Symmetry
Authors: Yang H. C. , Chou Y. T.
Published: July 2009

This paper deals with a generalized plane problem in which a uniform stress-free strain transformation takes place in the region of an elliptic cyclinder (the inclusion) oriented in the 〈111〉 direction in an anisotropic solid of cubic symmetry. Closed-form solutions for the elastic fields and the strain energies are presented. The perturbation of an otherwise uniform stress field due to a 〈111〉 elliptic inhomogeneity is also treated including two extreme cases, elliptic cavities and rigid inhomogeneities.
Dynamic Propagation of a Kinked or Bifurcated Crack in Antiplane Strain
Authors: Burgers P.
Published: July 2009

An initially unloaded, semi-infinite, stationary crack is assumed to kink or bifurcate at time t=0 and the new crack tip(s) propagate out along a straight line at a constant velocity vCT. A Green’s function, consisting of a dislocation whose Burgers vector is growing linearly with time, that is suddenly emitted from the tip of a stress-free semi-infinite crack and propagates out along the kinked crack line at constant velocity u, is used to form a Cauchy singular integral equation. This equation is solved using standard numerical techniques and the stress-intensity factor is obtained as a function of crack-tip speed vCT and kink angle δ. The bifurcation case is treated in a similar manner. Finally, some conclusions concerning crack initiation and propagation are drawn.
Unconventional Internal Cracks, Part 2: Method of Generating Simple Cracks
Authors: Wu C. H.
Published: July 2009

The meaning of the word crack is extended to include holes with cusps of vanishing cusp angle. A crack is said to be simple if the associated elasticity problem has a closed-form solution. Many classes of simple cracks are constructed and solved in this two-part paper. In particular, a method of constructing very sharp cusps is described. These cusps possess not only a zero slope (zero cusp angle) but a vanishing curvature as well. In fact, a crack may be constructed in such a way that the first N derivatives are all zero.
On the Solutions to Forced Motions of Rectangular Composite Plates
Authors: Reddy J. N.
Published: July 2009

For two different lamination schemes, under appropriate boundary conditions and sinusoidal distribution of the transverse load, the exact form of the spatial variation of the solution is obtained, and the problem is reduced to the solution of a system of ordinary differential equations in time, which are integrated numerically using Newmark’s direct integration method. Numerical results for deflections and stresses are presented showing the effect of plate side-to-thickness ratio, aspect ratio, material orthotropy, and lamination scheme. The results presented herein should be of interest to composite-structure designers, and to experimentalists and numerical analysts in verifying their results.
On the Instability of Rotating Shafts Due to Internal Damping
Authors: Bucciarelli L. L.
Published: July 2009

Internal damping in rotating shafts can lead to dynamic instability — the unbounded growth over time of the off-axis displacement of the spinning shaft in whirl. In analyzing this phenomenon, some authors have phrased the instability criterion in terms of energies dissipated through internal and external damping. One such study has claimed that instability ensues when the rate of work done by internal damping equals that done by external damping. This analysis shows that this criterion is wrong and explains why it fails. It also provides a clear picture of how internal forces can act to produce instability by coupling the motion of spin with motion in whirl.
Extended Kane’s Equations for Nonholonomic Variable Mass System
Authors: Ge Z.-M. , Cheng Y.-H.
Published: July 2009

An extension of Kane’s equations of motion for nonholonomic variable mass systems is presented. As an illustrative example, equations of motion are formulated for a rocket car.
Two-Dimensional Theory of Incompressible Flow Over Inlets
Authors: Huang M. K.
Published: July 2009

On the basis of the assumption of incompressible inviscid fluid, a linearized solution has been derived for the two-dimensional flow over an inlet of general form. The theory can be used to estimate the external drag of the inlets with sharp lips at subsonic speeds.
Theory of Maximum Tensile Stresses in the Solidifying Shell of a Constrained Rectangular Casting
Authors: Tien R. H. , Richmond O.
Published: July 2009

A theoretical model is derived for determining the stresses that develop during the early stages of solidification in flat-sided ingot molds. The model requires flatness of the solidifying skin and is strictly valid only up to the time when an air gap begins to form at the corners. Here it is argued that the model continues to provide a valid estimate of the maximum stresses in the central portion of the flat sides, where mold contact is maintained long after the first appearance of an air gap at the corners. This argument is supported by the fact that the lateral contraction of this portion is inhibited both by mold friciton and by tensile forces transmitted through the contracted corners from adjacent faces of the skin. Specific calculations are made for low-carbon steel by using physical property data from the literature. The maximum tensile stresses occur at the outer face and have values between 500-1500 psi, depending on the cooling rate. The theory is believed to be relevant to the interpretation of “center-line” cracking.
A Numerical Analysis of the Hydraulic Bulging of Circular Disks Into Axisymmetric Dies
Authors: Nakamachi E. , Takezono S. , Sowerby R.
Published: July 2009

The hydraulic bulging of peripherally clamped, thin, circular disks into axisymmetric dies is studied by means of an incremental finite element method, based on membrane shell theory and formulated to account for finite strains and rotations. The material is treated as an isotropic, elastic-plastic solid obeying the von Mises yield criterion and plastic-potential flow law. The analysis was first performed for a flat-bottomed die, assuming Coulomb friction between the material and the die base. Experimental data were gathered from aluminium disks deformed into a die having a flat, thick glass base. The glass permitted a continuous assessment of the deformation profile and the contact boundary between the aluminium and the glass, using Moire´ topography. The agreement between the experimental observations and theoretical predictions is good.
Boundary-Layer Effects in Composite Laminates: Part 1—Free-Edge Stress Singularities
Authors: Wang S. S. , Choi I.
Published: July 2009

A study of boundary-layer stress singularities in multilayered fiber-reinforced composite laminates is presented. Based on Lekhnitskii’s stress potentials and the theory of anisotropic elasticity, formulation of the problem leads to a pair of coupled governing partial differential equations (P.D.E.’s). An eigenfunction expansion method is developed to obtain the homogeneous solution for the governing P.D.E. ’s. The order or strength of boundary-layer stress singularity is determined by solving the transcendental characteristic equation obtained from the homogeneous solution for the problem. Numerical examples of the singular strength (or singular eigenvalues) of boundary-layer stresses are given for angle-ply and cross-ply composites as well as the cases of more general composite lamination.
Boundary-Layer Effects in Composite Laminates: Part 2—Free-Edge Stress Solutions and Basic Characteristics
Authors: Wang S. S. , Choi I.
Published: July 2009

Boundary-layer effects in composite laminates are considered. Based on the theory of anisotropic elasticity and Lekhnitskii’s complex-variable stress function formulation, the exact laminate elasticity solution is derived for the problem. The solution contains the exact boundary-layer stress singularity and higher-order terms in eigenfunction series. Convergence and accuracy of the solution are studied, and present results are compared with existing approximate numerical solutions. For illustrative purposes, the complete solution for a symmetric [45/−45 / −45/45] graphite-epoxy composite is presented to elucidate fundamental characteristics of the boundary-layer effects. Detailed stress distributions in the boundary-layer region are determined. Boundary-layer stress intensity factors are introduced to characterize the singular edge-stress field. Physical significance of the parameters is discussed in the realm of fracture initiation and failure modes in the laminate boundary region.
On the Stability of Waves in a Thin Orthotropic Spinning Disk
Authors: Nowinski J. L.
Published: July 2009

A system of two ordinary coupled differential equations with periodic coefficients of the Mathieu type for two temporal perturbation parameters is derived. A closed-form solution of the system in terms of elementary functions is found and discussed. A condition for the wave stability involving the coefficients of anisotropy is established. Illustration involves a specific range of these coefficients.
Bifurcations in Three-Dimensional Motions of Articulated Tubes, Part 1: Linear Systems and Symmetry
Authors: Bajaj A. K. , Sethna P. R.
Published: July 2009

Three-dimensional motions of a two-segment articulated tube system carrying a fluid and having rotational symmetry about the vertical axis are examined for bifurcating periodic solutions. As the flow rate through the tubes is increased past a critical value, the downward vertical position of equilibrium gets unstable and bifurcates into two qualitatively different kinds of periodic motions. The mathematical problem is more general than that occurring in the Hopf bifurcations and the method of analysis used is the method of Alternate Problems. Since physical systems invariably have some asymmetry, the analysis takes into account these symmetry-breaking perturbations. In Part 1 of this two-part paper, symmetry properties of the system and the linear stability are discussed.
Bifurcations in Three-Dimensional Motions of Articulated Tubes, Part 2: Nonlinear Analysis
Authors: Bajaj A. K. , Sethna P. R.
Published: July 2009

The equations of motion of the two-segment articulated tube system, discussed in Part 1, are analyzed for bifurcating periodic solutions near critical flow velocities. In addition to the flow parameter, the system depends on four other parameters. Depending on the values of these parameters the system exhibits a wide variety of behavior. This behavior is studied in detail in several specific cases.
Strong Stability of Impulsively Initiated Couette Flow for Both Axisymmetric and Nonaxisymmetric Disturbances
Authors: Chen J.-C. , Neitzel G. P.
Published: July 2009

A viscous, incompressible fluid is enclosed between two infinitely long coaxial cylinders. The entire system is assumed to be rotating initially as a rigid body with angular velocity Ω. At time t = 0, the outer cylinder is impulsively stopped. The resulting unsteady Couette flow is subject to centrifugal instabilities. Energy theory (strong stability) calculations have been performed for both axisymmetric and nonaxisymmetric disturbances to verify that the most dangerous mode is axisymmetric. The results include global stability bounds, lower bounds on the onset time, and/or upper bounds on the decay times, and are compared to previous marginal stability results for the same basic state.
Experiment and Analysis of Instability of Tube Rows Subject to Liquid Crossflow
Authors: Chen S. S. , Jendrzejczyk J. A.
Published: July 2009

A tube array subjected to crossflow may become unstable by either one or both of the two basic mechanisms: velocity mechanism and displacement mechanism. An experimental and analytical study of tube rows in liquid crossflow is performed to verify the existence and transition between the two mechanisms at the intermediate values of mass-damping parameter. Experimental data and analytical results are found to be in good agreement.
Plasticity Analysis of Laminated Composite Plates
Authors: Bahei-El-Din Y. A. , Dvorak G. J.
Published: July 2009

Elastic-plastic behavior of symmetric metal-matrix composite laminates is analyzed for the case of in-plane mechanical loading. The overall response of the laminate at each instant is derived from the elastic-plastic deformation of the individual fibrous layers, and from their mutual constraints. Constitutive equations of the laminated plates are presented in terms of initial yield conditions, hardening rules, and instantaneous compliances. Local stresses, hardening parameters, and strains are found in each lamina and in the fiber and matrix phases within each lamina. Specific results are obtained with the continuum model of elastic-plastic fibrous composites [1] which has been recently developed by the authors. Comparisons of analytical results with experimental measurements are made for certain laminated plates.
Approximate Analytical Model of Anchor Pull-Out Test
Authors: Miller G. R. , Keer L. M.
Published: July 2009

The two-dimensional problem of a rigid, unbonded plate embedded in an infinite medium with cracks emanating from the edges of the plate is solved with loading conditions approximating those found in pull-out testing and other engineering applications. The analysis employs the Green’s function approach of Lo, which leads to a singular integral equation that is solved numerically. Stress intensity factors are presented for several combinations of load geometry, crack length, and crack extension angle. These results are used to predict qualitively the crack propagation behavior under the assumptions of linear-elastic fracture mechanics.