Further studies on dynamic crack branching

The newly derived dynamic-crack-branching criterion with its modifications is verified by the dynamicphotoelastic results of dynamic crack branchings in thinpolycarbonate, single-edged crack-tension specimens. Successful crack branching was observed in four specimens and unsuccessful branching in another. Crack branching consistently occurred when the necessary conditions ofK _I =K _{I b} =3.3 MPa \(\sqrt m\) and the sufficiency condition ofr _o =r _c =0.75 mm were satisfied simultaneously. In the unsuccessful branching test, the necessary condition was not satisfied sinceK _I was always less thanK _{I b} .     

An experimental analysis of displacement field of mixed mode crack

In this paper, the characteristic properties ofv (y-direction displacement) field surrounding the tip of a mixed mode crack are studied. These properties can be used to evaluate the rigid body rotation of the crack tip, theK _I SIF and the ratio ofK _II SIF toK _I.The authors employ a film to record the displacement information based on the technique of moire interferometry with sticking films. By using the data taken from the moire pattern and treating them with the damping least square method, all of the parameters of the crack can be obtained accurately.     

On the dynamics of an elastic body containing a moving crack

It is proved that the energy release rate and the rate of entropy production in the dynamics of an elastic body containing a moving crack are proportional. Moreover, a theorem of the domain of influence type and a uniqueness theorem for solutions to the boundary-initial-value problem of brittle fracture mechanics are proved.     

Photoelastic analysis of the stress field surrounding a fatigue crack

A photelastic analysis was carried out on plane polyester specimens containing a fatigue crack, in order to study the effect of plastic yielding around the crack tip on the elastic stress distribution in the vicinity of the crack. In general, results were in good agreement with values calculated for the case of a sharp-tipped crack. However, very near the crack tip, principal stresses obtained experimentally were slightly lower than calculated stresses, probably due to the bluntness of the fatigue crack. Also lines of constant stress tended to move behind the crack tip, in contrast with the calculated stresses, which occurred further forward over the field of investigation.     

Propagation of an anti-plane moving crack in a functionally graded piezoelectric strip

Summary The propagation of an anti-plane moving crack in a functionally graded piezoelectric strip (FGPS) is studied in this paper. The governing equations for the proposed analysis are solved using Fourier cosine transform. The mixed boundary value problems of the anti-plane moving crack, which is assumed to be either impermeable or permeable, are formulated as dual integral equations. By appropriate transformations, the dual integral equations are reduced to Fredholm integral equations of the second kind. For the impermeable crack, the stress intensity factor (SIF) of the crack in the FGPS depends on both the mechanical and electric loading, whereas, the SIF for the permeable crack depends only on the mechanical loading. The results obtained show that the gradient parameter of the FGPS and the velocity of the crack have significant influence on the dynamic SIF.Support from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. HKU 7081/00E) is acknowledged. Support from the National Natural Science Foundation of China (Project No. 10072041) is also acknowledged.     

Theoretical and experimental studies on the aerodynamic instability of a two-dimensional circular cylinder with a moving attachment

Rain–wind induced vibration of cables in cable-stayed bridges is a worldwide problem of great concern. The effect of the motion of water rivulets on the instability of stay cables has been recognized as one of the mechanisms of this complex phenomenon. In order to investigate how the motion of rivulets affects the unstable vibration of cables without considering the effects of axial flow and axial vortex, a real three-dimensional cable was modeled as a two-dimensional circular cylinder, around which an attachment representing the rivulet can move. This could also be regarded as a new kind of two-dimensional 2-dof dynamic system. This paper studies the aerodynamic instability of the system theoretically and experimentally. Equations governing the motions of the cylinder and the attachment are first established. The Lyapunov stability criterion is applied to the equations of motion to derive the criterion for the unstable balance angle of the attachment. Moreover, a new two-dimensional 2-dof cable model system with a movable attachment is designed and tested in a wind tunnel. Parametric studies are carried out to investigate the effects of major factors such as wind speed, frequency and damping of the dynamic system on the unstable balance angle of the rivulet attachment. Theoretical and experimental results match well. These results may be valuable in elucidating the mechanism of rain–wind induced vibration of stay cables.     

Heat generation at the tip of a moving crack

The high energy concentration at the tip of a moving crack causes irreversible deformations and produces heat as a consequence. The resulting temperatures were calculated by consideration of the crack tip as a moving heat-source of rectangular shape. In brittle materials with very small plastic zones and high crack velocities, these temperatures are predicted to be higher than 1000 K. For the experimental verification of these calculations, a very sensitive radiation thermometer was developed. It registers the intensity of the radiation at four wavelengths. By comparison of these intensities with that of black body radiation, the temperature was determined as 3200 K for glass and 4700 K for quartz.     

Nonlinear stability analysis for a jet moving in a material medium collinearly to an electrostatic field

Analytically, in the second order approximation, the nonlinear internal resonance energy exchange between waves on the surface of a cylindrical incompressible dielectric fluid jet that moves relative to a material medium in the longitudinal electrostatic field is investigated.     

Griffith crack moving in a piezoelectric strip

Summary  The dynamic problem of an impermeable crack of constant length 2a propagating along a piezoelectric ceramic strip is considered under the action of uniform anti-plane shear stress and uniform electric field. The integral transform technique is employed to reduce the mixed-boundary-value problem to a singular integral equation. For the case of a crack moving in the mid-plane, explicit analytic expressions for the electroelastic field and the field intensity factors are obtained, while for an eccentric crack moving along a piezoelectric strip, numerical results are determined via the Lobatto–Chebyshev collocation method for solving a resulting singular integral equation. The results reveal that the electric-displacement intensity factor is independent of the crack velocity, while other field intensity factors depend on the crack velocity when referred to the moving coordinate system. If the crack velocity vanishes, the present results reduce to those for a stationary crack in a piezoelectric strip. In contrast to the results for a stationary crack, applied stress gives rise to a singular electric field and applied electric field results in a singular stress for a moving crack in a piezoelectric strip. Received 14 August 2001; accepted for publication 24 September 2002 The author is indebted to the AAM Reviewers for their helpful suggestions for improving this paper. The work was supported by the National Natural Science Foundation of China under Grant 70272043.     

Simulation and experimental studies of a vibro-impact capsule system driven by an external magnetic field

This paper studies the electromagnetic field used for driving a vibro-impact capsule prototype for small bowel endoscopy. Mathematical models of the electromagnetic field and the capsule system are introduced, and analytical solution of the magnetic force applied on the capsule is derived and verified by experiment. The impact force between the inner mass of the capsule and the capsule body is also compared via numerical simulation and experimental testing. By comparing the capsule’s progressions under different control parameters (e.g. the excitation frequency and duty cycle), the merits of using the vibro-impact propulsion are revealed. Based on the experimental results, the optimised speed of the prototype can achieve up to 3.85 mm/s. It is therefore that the potential feasibility of using the external electromagnetic field for propelling the vibro-impact capsule system is validated.

     

A note on the stress singularity at a non-uniformly moving crack tip

The stress-singularity at a crack tip moving arbitrarily in an elastic plate under plane strain conditions is investigated. By formulating the wave-equations in a polar coordinate system attached to the crack-tip, it is found by an asymptotic analysis that the angle-dependence of the singularity is only dependent on the instantaneous cracktip velocity. This result is used to derive a relation between the dynamic stress-intensity factor and the energyrelease rate.     

Full field analysis of an anti-plane interface crack subjected to dynamic body forces

In this study, the transient full field response of an interface crack between two different media subjected to dynamic body force at one material is investigated. For time t < 0, the bimaterial medium is stress free and at rest. At t = 0, a concentrated anti-plane dynamic point loading is applied at the medium as shown in Fig. 1. The total wave field is due to the effect of this point loading and the scattering of the incident waves by the interface crack. An alternative methodology that is different from the conventional superposition method is used to construct the reflected, refracted and diffracted wave fields. A useful fundamental solution is proposed in this study and the full field solution is determined by superposition of the fundamental solution in the Laplace transform domain. The proposed fundamental problem is the problem of applying an exponentially distributed traction (in the Laplace transform domain) on the interfacial crack faces. The Cagniard–de Hoop method of Laplace inversion is used to obtain the transient solution in time domain. Exact transient closed form solutions for stresses and stress intensity factors are obtained. Numerical results for the time history of stresses and stress intensity factors during the transient process are discussed in detail.     

Perturbed magnetic field of an infinite plate with a centered crack

Deforming a cracked magnetoelastic body in a magnetic field induces a perturbed magnetic field around the crack. The quantitative relationship between this perturbed field and the stress around the crack is crucial in developing a new generation of magnetism-based nondestructive testing technologies. In this paper, an analytical expression of the perturbed magnetic field induced by structural deforma- tion of an infinite ferromagnetic elastic plate containing a centered crack in a weak external magnetic field is obtained by using the linearized magnetoelastic theory and Fourier transform methods. The main finding is that the perturbed magnetic field intensity is proportional to the applied tensile stress, and is dominated by the displacement gradient on the boundary of the magnetoelastic solid. The tangential component of the perturbed magnetic-field intensity near the crack exhibits an antisymmetric distribution along the crack that reverses its direction sharply across its two faces, while the normal component shows a symmetric distribution along the crack with singular points at the crack tips.     

An asymptotic finite-deformation analysis of the elastostatic field near the tip of a crack

Summary This paper contains an asymptotic treatment, consistent with the fully nonlinear equilibrium theory of compressible elastic solids, of the stresses and deformations near the tip of a traction-free crack in a slab of all-around infinite extent under conditions of plane strain. The loading applied at infinity is taken to be one of uniform uniaxial tension at right angles to the faces of the crack. For the particular class of elastic materials considered the tensile stress in large homogeneous uni-axial extension is asymptotic to a continuously adjustable power of the corresponding principal stretch. The asymptotic analysis of the foregoing crack problem is reduced to a nonlinear eigenvalue problem, the solution of which is established in closed form, in terms of elementary functions and a transcendental integral of such functions. This solution involves two arbitrary constants, one of which governs the amplitude of the ensuing elastostatic field near the tip of the crack. A precise estimate of the amplitude parameter, valid at sufficiently small load intensities, is deduced with the aid of a known conservation law. The remaining arbitrary constant, which is left indeterminate by the present lowest-order asymptotic analysis, does not affect the dominant behavior of the field quantities of primary physical interest. II-lustrative numerical results, appropriate to both hardening and softening materials, are presented.

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Zusammenfassung Diese Arbeit betrifft die asymptotische Ermittelung, im Rahmen der nichtlinearen Elastizitätstheorie ebener Verformungen, von den Spannungen und Verschiebungen am Ende eines Schlitzes in einer allseitig unendlich ausgedehnten Scheibe. Die Scheibe ist im Unendlichen durch einen gleichförmigen Zug senkrecht zur Schlitzachse belastet. Die asymptotische Behandlung dieses Problems wird auf ein Eigenwertproblem zurückgeführt, dessen Lösung in geschlossener Form durch elementare Funktionen dargestellt wird. Die gefundene Lösung enthält zwei unbestimmte Konstanten von welchen eine die Amplitude der lokalen Feldsingularitäten bestimmt. Diese Konstante wird für kleine Belastungen streng abgeschätzt auf Grund eines Erhaltungssatzes und mit Hilfe der bekannten Lösung des linearisierten Schlitzproblems.

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The results communicated in this paper were obtained in the course of an investigation supported under Contract N00014-67-A-0094-0020 of the California Institute of Technology with the Office of Naval Research in Washington, D.C.     

Limited permeable crack moving along the interface of a piezoelectric bi-material

A plane problem for a crack moving with a subsonic speed along the interface of two piezoelectric semi-infinite spaces is considered. The crack is assumed to be free from mechanical loading. The limited permeable electric condition with an account of electric traction is adopted at its faces. A uniformly distributed mixed mode mechanical loading and an electric flux are prescribed at infinity. The problem is reduced to the Riemann–Hilbert problem by means of introducing a moving coordinate system and assuming that the electric flux is uniformly distributed along the crack region. An exact solution of this problem is proposed. It permits to find in closed form all necessary electromechanical characteristics at the interface and to formulate the equation for the determination of the electric flux. Analysis of this equation confirms the correctness of the assumption concerning the uniform distribution of the electric flux in the crack region. The values of the electric flux are determined by solving the obtained equation. Thereafter, the stress and electric intensity factors as well as their asymptotic fields at the crack tip are also found. The particular case of a crack moving in a homogeneous piezoelectric material is considered. The values of the electric flux and the fracture parameters are found exactly in a simple form for this case. Also, a numerical analysis is performed for a crack propagating with a subsonic speed between PZT4 and PZT5 materials and for a crack moving in PZT4 material. The electric flux in the crack region, stress and electric intensity factors, crack opening and the energy release rate (ERR) are found as functions of the crack speed, loading and electric permeability of the crack medium. The influence of the electric traction on the crack faces upon the mentioned parameters is demonstrated.     

Remarks on the energy release rate for an antiplane moving crack in couple stress elasticity

This paper is concerned with the steady-state propagation of an antiplane semi-infinite crack in couple stress elastic materials. A distributed loading applied at the crack faces and moving with the same velocity of the crack tip is considered, and the influence of the loading profile variations and microstructural effects on the dynamic energy release rate is investigated. The behavior of both energy release rate and maximum total shear stress when the crack tip speed approaches the critical speed (either that of the shear waves or that of the localized surface waves) is studied. The limit case corresponding to vanishing characteristic scale lengths is addressed both numerically and analytically by means of a comparison with classical elasticity results.     

Further experimental studies on buckling of integrally ring-stiffened cylindrical shells under axial compression

An experimental study of the buckling of closely spaced integrally stiffened cylindrical shells under axial compression was carried out to determine the influence of shell and ring geometry on the applicability of linear theory. Twenty-nine specimens fabricated from 7075-T6 aluminum alloy with different geometries were tested. Test specimens were designed to fail in general instability and under low critical stresses to assure elastic buckling. Agreement of experimental results of the present study, and of those obtained in other studies with linear theory was found to be governed primarily by the ring area parameter, (A ₂ /ah). Values of “linearity,” ? (ratio of experimental buckling load to the predicted one), higher than 80 percent were obtained for (A ₂ /ah)>0.3 and a clear trend towards ?=1 was observed with increasing values of this parameter. Correlation with linear theory was also found to be influenced by ring spacing, (a/h), or rather the combination (a/h) [1+(A ₂ /ah]^?1/2. No significant effect of shell and other ring parameters on the correlation with linear theory could be discerned for the shells tested. By a conservative structural-efficiency criterion it was observed that only for low values of the area parameter, (A ₂ /ah)<≈0.5 ring-stiffened shells are more efficient than equivalent-weight isotropic ones. Highest efficiencies are obtained for (A ₂ /ah)≈0.2.     

A finite element analysis for the temperature field produced by a moving heat source

Using moving mesh finite element method we discuss the temperature field produced by a moving heat source with the variable thermal conductivity and with the raUioative and convective boundary conditions in a wide range of the velocity. The temperature-time relationships at various velocities in the static and moving coordinate systems are studied. The steady-state temperature distributions at various velocities in the moving coordinate systems are given. The temperature field produced by the plastic deformation at the process region (a region very near the crack tip) is also studied, and the results show that the highest temperature at the process region is lower than 1000℃ or 1832℉