Analysis of dynamic stress intensity factors of three-point bend specimen containing crack

A new formula is obtained to calculate dynamic stress intensity factors of the three-point bending specimen containing a single edge crack in this study. Firstly, the weight function for three-point bending specimen containing a single edge crack is derived from a general weight function form and two reference stress intensity factors, the coefficients of the weight function are given. Secondly, the history and distribution of dynamic stresses in uncracked three-point bending specimen are derived based on the vibration theory. Finally, the dynamic stress intensity factors equations for three-pointing specimen with a single edge crack subjected to impact loadings are obtained by the weight function method. The obtained formula is verified by the comparison with the numerical results of the finite element method (FEM). Good agreements have been achieved. The law of dynamic stress intensity factors of the three-point bending specimen under impact loadings varing with crack depths and loading rates is studied.     

The influence of elastic waves on dynamic stress intensity factors (two-dimensional problems)

Summary In this paper, an indirect boundary integral equation method for the solution of dynamic crack problems is presented. The Laplace transform method is used to derive the fundamental solutions for the opening mode (mode I) and the sliding mode (mode II) displacement discontinuity. Accurate dynamic stress intensity factorsK _N (t) (N=I,II) resulting from different time-dependent loads on the crack surface are obtained. The specific influences of the various elastic waves on the stress intensity factors can be clearly seen from the results.On leave Central-South University of Technology Changsha, P.R. China     

Analysis of dynamic stress intensity factors of thick-walled cylinder under internal impulsive pressure

Dynamic stress intensity factors are evaluated for thick-walled cylinder with a radial edge crack under internal impulsive pressure. Firstly, the equation for stress intensity factors under static uniform pressure is used as the reference case, and then the weight function for a thick-walled cylinder containing a radial edge crack can be worked out. Secondly, the dynamic stresses in uncracked thick-walled cylinders are solved under internal impulsive pressure by using mode shape function method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary condi- tions, and the history and distribution of dynamic stresses in thick-walled cylinders are derived in terms of Fourier-Bessel series. Finally, the dynamic stress intensity factor equations for thick-walled cylinder containing a radial edge crack sub- jected to internal impulsive pressure are given by dynamic weight function method. The finite element method is utilized to verify the results of numerical examples, showing the validity and feasibility of the proposed method.     

Convolution of the impact three-dimensional elasto-dynamics and dynamic stress intensity factor for an elliptic cracks

This paper presents a formulation for three-dimensional elastodynamics with an elliptic crack based on the Laplace and Fourier transforms and the convolution theorem. The dynamic stress intensity factor for the crack is determined by solving a Fredholm integral equation of the first kind. The results of this paper are very close to those given by the two-dimensional dual integral equation method. The project supported by the National Natural Science Foundation of China (K19672007)     

Determination of the dynamic stress intensity factorsK I d andK II d,for a mixed-mode propagating crack

In this paper, the dynamic propagation problem of a mixed-mode crack was studied by means of the experimental method of caustics. The initial curve and caustic equations were derived under the mixed-mode dynamic condition. A multi-point measurement method for determining the dynamic stress intensity factors,K _I ^d , andK _II ^d , and the position of the crack tip was developed. Several other methods were adopted to check this method, and showed that it has a good precision. Finally, the dynamic propagating process of a mixed-mode crack in the three-point bending beam specimen was investigated with our method.     

Determining stress intensity factors in orthotropic composites from far-field measured temperatures

We demonstrate the ability to determine stress intensity factors in orthotropic materials directly from measured temperatures away from the crack and using far-field expressions for the stresses. This is advantageous, recognizing that recorded thermoelastic data can be very unreliable near the tip of a crack. In addition to singular terms that govern in the immediate vicinity of the crack tip, the present series expressions for the stresses contain higher-order finite terms. Little measured input information is needed and data acquisition positions can be selected largely at the user's discretion.     

Numerical simulation of stress intensity factors via the thermoelastic technique

The purpose of this study is to investigate the accuracy of the least squares method for finding the in-plane stress intensity factorsK _I andK _II using thermoelastic data from isotropic materials. To fully understand the idealized condition ofK _I andK _II calculated from thermoelastic experiments, the total stress field calculated from finite element analysis is used to take the place of data obtained from real thermoelastic experiments. In the finite element analysis, theJ-integral is also calculated to compare with (K _I ² +K _II ² )/E evaluated by the least squares method. The stress fields near the crack tip are dominated by the two stress intensity factors; however, the edge effect will cause inaccuracy of the thermoelastic data near the crack tip. Furthermore, the scan area of thermoelastic experiments cannot be too small. Therefore, we suggest that three or four terms of stress function be included in the least squares method for evaluating stress intensity factors via the thermoelastic technique. In the idealized condition, the error can be smaller than 3 percent from our numerical simulations. If only ther ^–1/2 term (K _I andK _II ) is included in the least squares method, even in the idealized case the error can be up to 20 percent.     

Dynamic stress intensity factors of multiple cracks in a functionally graded orthotropic half-plane

In the present paper dynamic stress intensity factor and strain energy density factor of multiple cracks in the functionally graded orthotropic half-plane under time-harmonic loading are investigated. By utilizing the Fourier transformation technique the stress fields are obtained for a functionally graded orthotropic half-plane containing a Volterra screw dislocation. The variations of the material properties are assumed to be exponential forms which the equilibrium has an analytical solution. The dislocation solution is utilized to formulate integral equation for the half-plane weakened by multiple smooth cracks under anti-plane deformation. The integral equations are of Cauchy singular type at the location of dislocation which are solved numerically to obtain the dislocation density on the faces of the cracks. The dislocation densities are employed to determined stress intensity factor and strain energy density factors (SEDFs) for multiple smooth cracks under anti-plane deformation. Numerical examples are provided to show the effects of material properties and the crack configuration on the dynamic stress intensity factors and SEDFs of the functionally graded orthotropic half-plane with multiple curved cracks.     

Mode III stress intensity factors in an interfacial crack in dissimilar bonded materials

The antiplane shear deformation problem of two edge-bonded dissimilar isotropic wedges is considered. In the case when the sum of the two apex angles is equal to 2π, the problem reduces to that of two edge-bonded dissimilar materials with an interfacial crack subjected to concentrated antiplane shear tractions on the crack faces. An explicit expression is extracted for the stress intensity factor at the crack tip. In the special cases of different combinations of the apex angles, the obtained expression for the stress intensity factor may be simplified and relations of a simpler form are given for the stress intensity factor. It is shown that the stress intensity factor is dependent on the material properties as well as the geometry and loading. However, in special cases of equal apex angles as well as the case of similar materials the dependency of the stress intensity factor on the material properties disappears.     

Computing lower and upper bounds on stress intensity factors in bimaterials

This paper presents a finite element approach for finding complementary bounds of stress intensity factors (SIFs) in bimaterials. The SIF is formulated as an explicit computable linear function of displacements by means of the two-point extrapolation method. An appropriate and computable form of the SIF plays a crucial role in the dual problem involved in the computing procedure of both lower and upper bounds. In our discussions, computable forms of stress intensity factors, K₀ and K_r, are derived, which are related to the energy release rate, and the ratio of the open mode and shear mode SIFs, respectively. Based on a posteriori finite element error estimation, a bounding procedure is used to compute the bounds on the two stress intensity factors. Finally, bounds on the SIFs in a bimaterial interface crack problem are provided to verify the procedure.     

Residual stress field and reduction of stress intensity factors in cold-worked holes

Closed-form and semi-analytical solutions are obtained for the residual stress distributions in a plate caused by pressure acting on a central circular hole, representing the cold-work process. The material is elastic–perfectly plastic. Both Tresca and von Mises yield criteria are used and the corresponding residual stress distributions are compared. The relation between the dimension of the plastic zone and the value of internal pressure is presented. The relation between the magnitude of the residual stresses and the remote uniform tensile stress required to open symmetrical radial cracks is also presented. The reduction of the stress intensity factors of cracked open and riveted holes as a function of the internal pressure applied (or mandrel radial displacement) is investigated using numerical models for both an elastic–perfectly plastic material and for an Al 2024-T3 Alclad aluminum alloy.     

3D dynamic stress intensity factors at three rectangular cracks in an infinite elastic medium subjected to a time-harmonic stress wave

Summary Dynamic stresses around three coplanar cracks in an infinite elastic medium are determined in the paper. Two of the cracks are equal, rectangular and symmetrically situated on either side of the centrally located rectangular crack. Time-harmonic normal traction acts on each surface of the three cracks. To solve the problem, two kind of solutions are superposed: one is a solution for a rectangular crack in an infinite elastic medium, and the other one is that for two rectangular cracks in an infinite elastic medium. The unknown coefficients in the combined solution are determined by applying the boundary conditions at the surfaces of the cracks. Finally, stress intensity factors are calculated numerically for several crack configurations. Received 14 July 1998; accepted for publication 2 December 1998     

A fractional differential constitutive model for dynamic stress intensity factors of an anti-plane crack in viscoelastic materials

Fractional differential constitutive relationships are introduced to depict the history of dynamic stress inten- sity factors （DSIFs） for a semi-infinite crack in infinite viscoelastic material subjected to anti-plane shear impact load. The basic equations which govern the anti-plane deformation behavior are converted to a fractional wave-like equation. By utilizing Laplace and Fourier integral transforms, the fractional wave-like equation is cast into an ordinary differential equation （ODE）. The unknown function in the solution of ODE is obtained by applying Fourier transform directly to the boundary conditions of fractional wave-like equation in Laplace domain instead of solving dual integral equations. Analytical solutions of DSIFs in Laplace domain are derived by Wiener-Hopf technique and the numerical solutions of DSIFs in time domain are obtained by Talbot algorithm. The effects of four parameters α, β, b1, b2 of the fractional dif- ferential constitutive model on DSIFs are discussed. The numerical results show that the present fractional differential constitutive model can well describe the behavior of DSIFs of anti-plane fracture in viscoelastic materials, and the model is also compatible with solutions of DSIFs of anti-plane fracture in elastic materials.     

A study on stress intensity factors and singular stress fields of three-dimensional interface crack

By using the finite-part integral concepts and limit technique, the hypersingular integrodifferential equations of three-dimensional (3D) planar interface crack were obtained; then the dominant-part analysis of 2D hypersingular integral was further used to investigate the stress fields near the crack front theoretically, and the accurate formulae were obtained for the singular stress fields and the complex stress intensity factors. After that, a numerical method is proposed to solve the hypersingular integrodifferential equations of 3D planar interface crack, and the problem of elliptical planar crack is then considered to show the application of the method. The numerical results obtained are satisfactory. Project supported by the Foundation of Solid Mechanics Open Research Laboratory of State Education Commission at Tongji University and the National Natural Science Foundation.     

3D dynamic stress intensity factors around two parallel square cracks in an infinite elastic medium under impact load

Summary  Transient stresses around two parallel cracks in an infinite elastic medium are investigated in the present paper. The shape of the cracks is assumed to be square. Incoming shock stress waves impinge upon the two cracks normal to tzheir surfaces. The mixed boundary value equations with respect to stresses and displacements are reduced to two sets of dual integral equations in the Laplace transform domain using the Fourier transform technique. These equations are solved by expanding the differences in the crack surface displacements in a double series of a function that is equal to zero outside the cracks. Unknown coefficients in the series are calculated using the Schmidt method. Stress intensity factors defined in the Laplace transform domain are inverted numerically to the physical space. Numerical calculations are carried out for transient dynamic stress intensity factors under the assumption that the shape of the upper crack is identical to that of the lower crack. Received 2 February 2000; accepted for publication 10 May 2000     

Analysis of interlaminar stress and nonlinear dynamic response for composite laminated plates with interfacial damage

By considering the effect of interfacial damage and using the variation principle, three-dimensional nonlinear dynamic governing equations of the laminated plates with interfacial damage are derived based on the general sixdegrees-of-freedom plate theory towards the accurate stress analysis. The solutions of interlaminar stress and nonlinear dynamic response for a simply supported laminated plate with interfacial damage are obtained by using the finite difference method, and the results are validated by comparison with the solution of nonlinear finite element method. In numerical calculations, the effects of interfacial damage on the stress in the interface and the nonlinear dynamic response of laminated plates are discussed.     

Interface crack-tip generalized stress field and stress intensity factors in transversely isotropic piezoelectric bimaterials

Transversely isotropic piezoelectric (TIP) bimaterials with an impermeable interface crack have been classified [Int. J. Frac. 119 (2003) L41] into two classes corresponding to the vanishing of the two singularity parameters or κ. It is shown in the present paper that the related eigenvalue problems for either =0 or κ=0 are not degenerate. The crack-tip generalized stress fields are obtained subsequently. A new definition of crack-tip intensity factors is presented for interface cracks in practical TIP bimaterial of practical interest. Such defined intensity factors are real numbers, which dominate the maximum crack-tip stress singularity and do not generate any phase angle change under any dimension system transformation for physical quantities.     

Stress state in the vicinity of an inclined elliptical defect and stress intensity factors for biaxial loading of a plate

The problem of determining the stress state of a plate with an inclined elliptical notch under biaxial loading is considered. The Kolosov-Muskhelishvili method is used to obtain an expression for the stress near the vertex of an inclined ellipse, whose particular case are expressions for the stress in the case of an inclined crack. The stress intensity factors K _I and K _II were determined experimentally by holographic interferometry in the case of extension of a plate with an inclined crack-like defect. The calculation results are compared with experimental data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 118–127, January–February, 2009.     

Photoelastic determination of dynamic crack-tip stresses in an anisotropic plate

The paper outlines a technique of determining the dynamic stress-intensity factors (SIFs) in structurally anisotropic composites from photoelastic measurement data. A composite is considered a linear elastic, homogeneous, orthotropic body. An equation is derived that relates the fringe order with the SIFs and the far-field stresses at the tip of a crack, which is parallel to the orthotropy axis __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 5, pp. 95–103, May 2006.