Generalized beam theory applied to shear stiffness

There is no consensus of opinion on the correct expressions for shear stiffness, even in the apparently simple case of rectangular sections made from homogeneous isotropic material. A general beam theory has been proposed which is applicable to all regular prismatic systems. This has been used to find the appropriate beam-like flexibilities for trusses. The same approach can be used for normal beams, giving values for the shear stiffnesses of various cross-sections as particular results of a general theory embracing torsion, binding, extension and shear of regular prismatic systems.     

Microstructural effects on shear instability and shear band spacing

A constitutive relation that accounts for the thermally activated dislocation motion and microstructure interaction is used to study the stability of a homogeneous solution of equations governing the simple shearing deformations of a thermoviscoplastic body. An instability criterion and an upper bound for the growth rate of the infinitesimal deformations superimposed on the homogeneous solution are derived. By adopting Wright and Ockendon's postulate, i.e., the wavelength of the dominant instability mode with the maximum growth rate determines the minimum spacing between shear bands, the shear band spacing is computed. The effect of the initial dislocation density, the nominal strain-rate, and parameters describing the initial thermal activation and the initial microstructure interaction on the shear band spacing are delineated.     

A three-dimensional rectangular crack subjected to shear loading

In this paper a solution is derived to treat the three-dimensional elastostatic problem of a narrow rectangular crack embedded in an infinite elastic medium and subjected to equal and opposite shear stress distribution across its faces. Employing two-dimensional integral transforms and assuming a plane-strain solution across the width of the crack, the stress field ahead of the crack length is reduced to the solution of an integral equation of Fredholm type. A numerical solution of the integral equation and the corresponding mode II stress-intensity factor is obtained for several crack dimensions and Poisson's ratios of the material.     

Dynamic meshless method applied to nonlocal crack problems

The dynamic meshless methods for local and nonlocal field theories are formulated in this paper. Application to two crack problems is presented. The meshless method of local theory gives solution that is in good agreement with the classical analytical crack tip solution, while the nonlocal theory yields a solution without stress singularity at the crack tip. The numerical results also show the embedded nonlocal nature of meshless methods.     

Maximum-energy-release-rate criterion applied to a tension-compression specimen with crack

The title problem is studied by using the explicit asymptetic analysis presented in the accompanying paper. The asymptotic analysis indicates that the very basic problem is a semi-infinite L-shaped crack governed by a single integral equation. This equation is discretized to a system of complex algebraic equations and solved by a standard HARWELL subroutine. It is found that the maximum-energy-release-rate criterion has two branches, one for tensile loads and one for compressive loads. Our numerical results indicate that the maximum energy-release rate is always associated with maximum K ₁ and K ₂=0, where K ₁ and K ₂ are the stress-intensity factors at the fractured tip. Thus, the well-known K-G relation valid for crack-parallel propagation also holds for non-crack-parallel propagations. This conclusion is, however, purely numerical.Supported by U.S. Army Research Office-Durham under Grant DAAG-29-76-G-0272.     

A new instability mechanism applied to the compressible Couette-flow

A new possible instability mechanism for a compressible Newtonian fluid is presented. This phenomenon has been found in the case of an isothermal creeping plane Couette-flow. The instability stems from the density dependence of the material properties of the fluid in the above-described kinematics.     

Singular integral equations in Hilbert space applied to crack problems

Crack problems are solved by application of a system of singular integral equations in Hilbert space. The method consists of replacing the singular integral equation by a system of linear algebraic equations for the values of the unknown function at specially chosen points within the range of integration. Obtained is a solution for a nonsymmetric cross-shaped crack in an infinite and isotropic solid subjected to a constant pressure, the symmetric configuration being a special case.     

Finite-part integral and boundary element method to solve flat crack problems

Using the Somigliana formula and the concepts of finite-part integral, a set of hypersingular integral equations to solve the arbitrary fiat crack in three-dimensional elasticity is derived and its numerical method is then proposed by combining the finitepart integral method with boundary element method. In order to verify the method, several numerical examples are carried out. The results of the displacement discontinuities of the crack surface and the stress intensity factors at the crack front are in good agrernent with the' theoretical solutions.     

Balanced and unbalanced patching of cracked lap joints using weighted adhesive plate element

First order shear deformation theory is applied to analyze the behavior of one-side (unbalanced) and two-side (balanced) patched lap joints containing initial through cracks. The joints are made of adherends bonded together by adhesives. An adhesive interface plate element is introduced; it consists of an adhesive layer weighted by influence of the adherend. The thin adhesive layer is assumed to behave elastically and modelled as a simple tension-shear spring. The mathematical model contains layers of adherend and weighted adhesive layer.Finite elements are employed to model the adherend with an 8-node isoparametric plate element and interface layer with a 16-node plate element. Numerical results are obtained for one-side and two-side patches the width of which could be narrower or wider than the crack length. The former leads to bulging and possible peeling while the latter provides better bonding. Stresses and crack-tip stress intensity factors are calculated for different patch thickness. Effectiveness of the weighted adhesive layer model is exhibited by comparing the present results with those found in previous work where the adhesive is modelled as an individual layer.     

On the response to point forces suddenly applied to a semi-infinite crack

The solution to the title problem is presented in detail for the case of anti-plane deformation and compared with the more restricted solution available for the plane problem. When instantaneous point forces are applied to the crack's faces the stress ahead of the crack shows a delta-function singularity. It is shown that this result could be derived from a result first obtained by Friedlander.     

Application of differential-integral equation to elliptical crack problem under shear load

Stress intensity factors for an elliptical crack under shear loading are investigated. The differential-integral equation is applied to solve the problem. It is found that, if the integrated function takes the form of (1 − (x/a)² − (y/b)²)^1/2 x^m yⁿ, a and b being the major and minor axis of the ellipse, the relevant differential-integral equation can be evaluated. Using this property, the boundary value problems are solved for the shear loading in the form of power function. Finally, results are presented for twelve particular example problems.     

Energy dissipation due to frictional shake-down on a closed crack subjected to shear

The behaviour of a horizontal crack, subjected to cyclic shear and normal compressive stresses, is investigated with the aim of studying the shake-down and alternating plasticity phenomena. The analysis is carried out by means of the displacement discontinuity numerical method, conveniently modified so as to simulate the development of frictional stresses on the crack surfaces. The assumptions that the crack does not propagate and that the material behaves elastically are made. The critical values of the physical and geometrical parameters which determine the occurrence of frictional shake-down or alternating plasticity are identified. An evaluation of the amount of energy dissipated because of alternating plasticity is also provided.

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Sommario Nel presente articolo viene esaminato il comportamento di una fessura orizzontale soggetta a taglio ciclico e a sforzo normale di compressione. L'analisi è condotta mediante il metodo della Discontinuità di Spostamento, opportunamente modificato in modo da simulare lo sviluppo di sforzi di attrito sulle superfici della fessura. Vengono ricavati i valori critici dei parametri fisici e geometrici che determinano la comparsa del fenomeno dello shake-down. Viene infine valutata la quantità di energia dissipata in ogni ciclo di applicazione del taglio.

     

Limitation on crack speed for a strip-craze model applied to PMMA

A strip-craze model is proposed to study crack propagation in polymers. A nonlinear differential equation is derived to govern the dynamic process of crack propagation. The viscous feature of the material in the craze zone is taken into account by means of an experimentally determined relationship between the craze stress and crack speed. By fitting experimental data of PMMA into the model, some parameters including the strip-craze length are deduced. A non-singular stress is introduced to control the crack propagation with a strip craze at its tip. Variations of the crack length and the crack speed with time are computed and their dependence on the non-singular stress is investigated. For PMMA, three stages of crack propagation are identified in terms of initial non-singular stress σ_ns0. When σ_ns0<60 MPa, the crack speed mm/s and the crack is basically stationary; when 60 <σ_ns0<95 MPa, then mm/s the crack is in slow propagation; when σ_ns0>95 MPa, then mm/s and the crack is in rapid propagation. The proposed model is applicable only in slow crack propagation.     

D-c electric-potential method applied to thermal/mechanical fatigue crack growth

The paper describes a d-c electric potential system for measuring crack length under thermal/mechanical fatigue-crack-growth (TMFCG) test conditions. A programmable d-c current supply and precision multimeter produce reliable electric-potential readings. H.H. Johnson's formula is used to calculate crack length from electric potential for the center-crack-tensionM(T) geometry. Calibration constants for the formula are determined from an initial optical crack-length measurement. The resolution of the system is 1.0 microvolt which corresponds to a crack extension of approximately 0.002 mm for the center-crack-tension geometry using a current of 10.00 amps. Good crack-length accuracy and low data scatter are achieved by taking special precautions to minimize or eliminate errors in potential measurement due to thermal effects. Material resistivity changes are identified as the cause of short and long term changes in the measured electric potential for uncracked specimens. Crack-length accuracy is discussed in terms of short-term scatter and longterm drift.     

Flow instability and shear localization in a drilling mud

To have a better knowledge of problems occurring with drilling fluids in complex wells, we carried out a detailed rheological analysis of a typical drilling mud at low shear rates using both conventional rheometry and MRI velocimetry. We show the existence of a viscosity bifurcation effect: Below a critical stress value, the mud tends to completely stop flowing, whereas beyond this critical stress, it reaches an apparent shear rate larger than a finite (critical) value, and no stable flows can be obtained between this critical shear rate value and zero. These results are confirmed by MRI velocity profiles, which exhibit a slope break at the interface between the solid and the liquid phases inside the Couette geometry. Moreover, this viscosity bifurcation is a transient phenomenon, the progressive development of which can be observed by MRI. A further examination of MRI data shows that, in the transient regime, the shear rate does not vary monotonously in the rheometer gap and is particularly large along the outer (rough) cylinder, which might be at the origin of the development of a region of constant shear rate in the apparent flow curve.     

Energy domain integral applied to solve center and double-edge crack problems in three-dimensions

A three-dimensional Boundary Element Method (BEM) implementation of the energy domain integral for the numerical computation of the crack energy release rate is presented in this paper. The domain expression of the energy release rate is naturally compatible with the BEM, since stresses, strains and derivatives of displacements at internal points can be evaluated using the appropriate boundary integral equations. The pointwise crack energy release rate is evaluated along the three-dimensional crack front over a cylindrical domains that surround a segment of the crack front. The accuracy of the implementation is demonstrated by solving several problems, which include geometries containing straight as well as curved crack fronts.     

Non-linear based time reversal acoustic applied to crack detection: Simulations and experiments

In non-destructive evaluation, non-linear elastic wave spectroscopy (NEWS) methods represent powerful tools to explore damaged zones in a sample. The combination of these methods with time reversal (TR) process can be used to either increase the stress on the retrofocusing position or to retrofocuse elastic waves on the defect, when only the non-linear components of the received signal are time reversed. In this paper, we propose two different approaches to detect cracks in metallic samples in coupling NEWS methods and TR process. The first one, NEWS-TR, is defined by sending back only the non-linear components which are preliminary time reversed. Two different techniques to filter non-linear components have been numerically studied: classical harmonic filter and pulse inversion. In these two cases, performances of retrofocusing on different defect positions are analyzed and compared. The second approach, TR-NEWS, consists in measuring the non-linear signature on the focal spot. An experimental study of parametric interaction between two reversed signals (f₁ and f₂) is led. Measurements of components at f₂-f₁ and f₂+f₁ around a crack are performed and discussed.     

Stability of an intersonic shear crack to a perturbation of its edge

A weight function matrix is developed for obtaining the stress singularity coefficients at the edge of a plane crack, moving uniformly at an intersonic speed while subjected to arbitrary shear loading. This is then utilised for deriving, to first order, the perturbations of these coefficients associated with a small spatially and temporally varying perturbation of its edge. The perturbation solution is employed, in conjunction with a simple fracture criterion, to investigate the stability of a uniformly moving intersonic crack, subjected to following loads.