Transient Dynamic Stress Intensity Factors Research Articles

Thermal shock fracture in a cracked strip: Incorporating convective heat transfer between lateral surfaces and ambient environment

This paper presents a comprehensive analysis of transient temperature and thermal stress around a thermal insulated crack in a finite thermoelastic strip subjected to thermal shock based on the dual-phase-lag (DPL) heat conduction. A detailed investigation of the effect of convective heat exchange between the lateral surfaces of the strip and the ambient environment is conducted. By employing integral transform technique, the thermoelastic crack problem is reduced to a set of singular integral equations, and solutions for the transient temperature distribution and dynamic stress intensity factors (SIFs) at the crack tips are then obtained. Numerical results reveal a considerable temperature gradient near the heating surface when both the high convective heat transfer coefficient and thin strip are involved. Consequently, the SIFs in such scenarios where cracks are located close to the heating surface are significantly larger compared to those calculated by neglecting the convective heat loss. Furthermore, during the initial period following a thermal shock, the SIFs may exhibit higher magnitudes than the steady-state values. These findings emphasize the importance of accounting for the influence of convective heat exchange with the ambient environment in material design and optimization to enhance fracture resistance under transient thermal loading.

Mixed-mode computation of the transient dynamic stress intensity factor for multiple interface cracks

In this paper, the transient dynamic stress intensity factors are estimated for multiple cracks which are located at the interface between a nonhomogeneous elastic half-plane and an elastic half-plane. The material properties of the nonhomogeneous half-plane vary continuously in the y-direction. First, Laplace and Fourier transforms are applied to reduce the mixed boundary value problem to a system of singular integral equations with Cauchy kernels which are solved numerically. By numerical Laplace inversion technique, the dislocation density on the crack faces is obtained and then transient dynamic stress intensity factors at crack tips have been determined. For validity and accuracy of the method, the results are compared with other references and very good agreement is shown. The influences of nonhomogeneity parameters, crack length, the variation in time and the interaction between of cracks on the transient dynamic stress intensity factors are studied. It is observed that the mode I stress intensity factors decrease regularly with increasing the FG constant and the results are briefly discussed.

Transient Dynamic Stress Intensity Factor of FGM Plates Using the State Space and MLPG Methods

In this paper, a new effective method named state-space is extended and utilized to analyze FGM dynamic fracture problems, discretized by the meshless local Petrov–Galerkin method. Both the moving least square and the direct method have been applied to estimate the shape function and to impose the essential boundary conditions. The visibility criterion is used to simulate the displacement and stress field around the crack tip. Normalized dynamic stress intensity factors are calculated using the path-independent integral, J*, which is formulated for the non-homogeneous material. Two methods commonly used in solving such discretized problems, namely, the central difference method and the Newmark method, are compared with the proposed method. Both homogeneous and non-homogeneous (FGM) center-cracked plates under uniform tensile impact load are used to examine the accuracy and the computational time of the new method. The results of the implementation of these methods are compared with existent solutions. The results show that the state-space method saves substantial computational time for a given accuracy. The center-cracked plate made of FGM with two different material gradations (along and normal to the crack length) and four different FGM zones under the effect of uniform tensile impact load are considered, and the dynamic stress intensity factors are studied under the influence of various non-homogeneity ratios.

Analysis of transient dynamic fracture parameters of cracked functionally graded composites by improved meshfree methods

In this paper, computation and analysis for transient dynamic stress intensity factors (DSIFs) of two-dimensional fracture problems of functionally graded materials (FGMs) by extended meshfree methods are described. The extended moving Kriging based meshfree method (X-MK) is introduced and compared with recently developed extended meshfree radial point interpolation method (X-RPIM) in the dynamical fracture context of FGM models. Moreover, in the present study, the X-MK is improved by introducing three new different types of correlation function that fully eliminate the user parameter for MK shape functions. The standard basis functions are used as the enrichment for asymptotic near crack tip fields to accurately capture the singularities at the crack tip and the Heaviside function is used to enrich the displacement discontinuity along the crack faces. We apply the dynamic form of non-homogenous interaction integral in conjunction with the asymptotic near crack tip field to extract the DSIFs. The DSIFs obtained from the proposed methods are further compared with reference solutions derived from other existing methods, including analytical method, (extended-) finite element method, boundary element method, and scaled boundary finite element method.

Dynamic stationary crack analysis of isotropic solids and anisotropic composites by enhanced local enriched consecutive-interpolation elements

The recently developed local enriched consecutive-interpolation 4-node quadrilateral element (XCQ4) is extended to study transient dynamic stress intensity factors (DSIFs) for isotropic solids and anisotropic composite materials containing stationary cracks. The XCQ4 involves both nodal values and averaged nodal gradients as interpolation conditions to smooth the distribution of unknown variables. The possible physical properties of enriched nodes in consecutive-interpolation procedure (CIP) would be thought as non-locality feature, which could improve the accuracy of results and eliminate the non-smooth stresses among inter-elements. In XCQ4, the crack is determined by level set function and enriched by Heaviside and crack-tip enrichment functions with special anisotropic enriched crack-tip functions. Time-dependent discrete equations for dynamic cracks are solved by Newmark time integration scheme at each time step without considering the effects of velocity-based global damping matrix. The proposed method is verified through a series of numerical examples of transient fracture in both isotropic and anisotropic materials. Numerical DSIFs are compared with reference solutions available in literature. The behavior of dynamic response is explored in specimens with complex configuration under step and sine loads.

Transient dynamic fracture analysis by an extended meshfree method with different crack-tip enrichments

Investigation of transient dynamic stress intensity factors (DSIFs) of two-dimensional fracture problems of isotropic solids and orthotropic composites by an extended meshfree method is described. We adopt the recently developed extended meshfree radial point interpolation method (X-RPIM), which combines either the standard branch functions or the new linear ramp function associated with Heaviside functions to capture crack-tip behaviors. It is the first time the linear ramp function integrating into meshfree X-RPIM has been presented in a dynamical fracture context. We are particularly interested in exploring insight into the behaviors of DSIFs under dynamic impact loadings (e.g., step, blast and sine loading types) using our meshfree method. For some of these problems numerical examples have been performed using the new ramp functions, and the obtained results of DSIFs have also been compared with those using the standard enrichment functions under which the two schemes have the same setting. In each case it is found that the numerical solutions delivered using the X-RPIM associated with the ramp enrichments are in good agreement with those with the standard functions. The paper first describes formulations and then provides verification of our developed approach through a series of numerical examples in transient dynamic fracture for both solids and orthotropic composites. Illustration of scattered elastic stress waves propagating in the cracked body is depicted to take an insight look at the behavior of dynamic response.

Transient dynamic stress intensity factors around three stacked parallel cracks in an infinite medium during passage of an impact normal stress

Transient dynamic stresses around three stacked parallel cracks in an infinite elastic plate are estimated for an incident impact stress wave impinging normal to the cracks. Using Fourier and Laplace transform techniques, the boundary conditions are reduced to six simultaneous integral equations in the Laplace domain. The differences in the displacements inside the cracks are expanded in a series of functions that have zero value outside the cracks. The Schmidt method is used to solve the unknown coefficients in the series such that the conditions inside the cracks are satisfied. The stress intensity factors are defined in the Laplace domain, and these are inverted using the numerical method. The stress intensity factors are calculated numerically for some crack configurations.

OS1302 2個のき裂の動的応力拡大係数に及ぼすモーメント応力の影響について

OS1302 2個のき裂の動的応力拡大係数に及ぼすモーメント応力の影響について

Effect of Couple-Stresses on the Transient Dynamic Stress Intensity Factors for a Crack in an Infinite Elastic Medium Under an Impact Stress Wave

This study applies linearized couple-stress theory to evaluate the dynamic stresses around a crack in an infinite elastic medium that is subjected to an incoming shock stress wave impinging normal to the crack. The boundary conditions with respect to the crack are reduced to dual integral equations using a Fourier transform in the Laplace domain. To solve these equations, the differences in the displacement and rotation at the crack are expanded by a series of functions that are zero-valued outside the crack in the Laplace domain.

Anti-plane transient analysis of planes with multiple cracks

In this paper, the transient dynamic stress intensity factor is determined for multiple curved cracks under impact loading. The dislocation method has rarely been applied to the problems involving dynamic loading. The transient response of Volterra-type dislocation in a plane is obtained by means of the Cagniard-de Hoop method. The distributed dislocation technique is used to construct integral equations for an infinite isotropic plane weakened by cracks. These 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 determine stress intensity factors for multiple smooth cracks. Numerical results are obtained to validate the formulation and illustrate its capabilities.

Calculation of transient dynamic stress intensity factors at bimaterial interface cracks using a SBFEM-based frequency-domain approach

A frequency-domain approach based on the semi-analytical scaled boundary finite element method (SBFEM) was developed to calculate dynamic stress intensity factors (DSIFs) at bimaterial interface cracks subjected to transient loading. Because the stress solutions of the SBFEM in the frequency domain are analytical in the radial direction, and the complex stress singularity at the bimaterial interface crack tip is explicitly represented in the stress solutions, the mixed-mode DSIFs were calculated directly by definition. The complex frequency-response functions of DSIFs were then used by the fast Fourier transform (FFT) and the inverse FFT to calculate time histories of DSIFs. A benchmark example was modelled. Good results were obtained by modelling the example with a small number of degrees of freedom due to the semi-analytical nature of the SBFEM.

Transient dynamic stress intensity factors around two rectangular cracks in a nonhomogeneous interfacial layer between two dissimilar elastic half-spaces under impact load

Transient dynamic stresses around two rectangular cracks in a nonhomogeneous interfacial layer sandwiched between two dissimilar elastic half-spaces are examined. The material properties vary continuously in the layer within a range from those of the upper half-space to those of the lower half-space. An incoming shock stress wave impinges perpendicular on the crack surfaces. In order to solve the problem, the interfacial layer is divided into several homogeneous layers that have different material properties. Application of Laplace and Fourier transforms reduces the problem to the solution of a pair of dual integral equations. To solve the equations, the differences in the crack surface displacements are expanded into a series of functions that vanish outside the crack. The unknown coefficients in the series are solved using the Schmidt method. The stress intensity factors are defined in the Laplace transform domain and these are inverted numerically in physical space. Numerical calculations are carried out for composite materials made of a ceramic half-space and a steel half-space.

S15 2個の長方形き裂を有する不均質層で接合される異材半無限体の衝撃応答問題(SS(5)「渥美光」記念セッション)

S15 2個の長方形き裂を有する不均質層で接合される異材半無限体の衝撃応答問題(SS(5)「渥美光」記念セッション)

Effects of material gradients on transient dynamic mode-III stress intensity factors in a FGM

This paper presents a transient dynamic crack analysis for a functionally graded material (FGM) by using a hypersingular time-domain boundary integral equation method. The spatial variations of the material parameters of the FGM are described by an exponential law. A numerical solution procedure is developed for solving the hypersingular time-domain traction BIE. To avoid the use of time-dependent Green’s functions which are not available for general FGM, a convolution quadrature formula is adopted for approximating the temporal convolution, while a Galerkin method is applied for the spatial discretization of the hypersingular time-domain traction BIE. Numerical results for the transient dynamic stress intensity factors for a finite crack in an infinite and linear elastic FGM subjected to an impact anti-plane crack-face loading are presented and discussed. The effects of the material gradients of the FGM on the transient dynamic stress intensity factors and their dynamic overshoot over the corresponding static stress intensity factors are analyzed.

Yoffe–type moving crack in a functionally graded piezoelectric material

In this paper, the problem of a functionally graded piezoelectric material (FGPM) with a constantvelocity Yoffetype moving crack is considered. The strip is assumed to be under an antiplane mechani...

Transient dynamic stress intensity factors around a crack in a nonhomogeneous interfacial layer between two dissimilar elastic half-planes

Dynamic stresses around a crack in a nonhomogeneous interfacial layer between two dissimilar elastic half-planes are obtained. The material constants vary continuously in the layer. An incoming shock stress wave impinges on the crack at right angles to the crack faces. In order to solve the problem, the interfacial layer is divided into several homogeneous layers that have different material properties. The boundary conditions are reduced to dual integral equations using the Fourier–Laplace transform technique. The equations are solved by expanding the differences of the crack faces in a series in the Laplace transform domain. The unknown coefficients in the series are determined using the Schmidt method. The stress intensity factors in the transform domain are inverted numerically in physical space. Using these numerical results, the stress intensity factors for a very thin layer can be estimated.

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

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.

Dynamic response of planar interface crack between viscoelastic bodies

In this paper, the transient dynamic stress intensity factor (SIF) is determined for an interface crack between two dissimilar half-infinite isotropic viscoelastic bodies under transient loading. An anti-plane step loading is assumed to act suddenly on the surface of interface crack of finite length. The stress field incurred near the crack tip is analyzed. The dynamic SIF during a small time-interval is evaluated in the numerical example given, and the effects of the viscoelastic material parameters on dynamic SIF are analyzed.

Dynamic SIF of interface crack between two dissimilar viscoelastic bodies under impact loading

In this paper, the transient dynamic stress intensity factor (SIF) is determined for an interface crack between two dissimilar half-infinite isotropic viscoelastic bodies under impact loading. An anti-plane step loading is assumed to act suddenly on the surface of interface crack of finite length. The stress field incurred near the crack tip is analyzed. The integral transformation method and singular integral equation approach are used to get the solution. By virtue of the integral transformation method, the viscoelastic mixed boundary problem is reduced to a set of dual integral equations of crack open displacement function in the transformation domain. The dual integral equations can be further transformed into the first kind of Cauchy-type singular integral equation (SIE) by introduction of crack dislocation density function. A piecewise continuous function approach is adopted to get the numerical solution of SIE. Finally, numerical inverse integral transformation is performed and the dynamic SIF in transformation domain is recovered to that in time domain. The dynamic SIF during a small time-interval is evaluated, and the effects of the viscoelastic material parameters on dynamic SIF are analyzed.

Impact response of a finite crack in an orthotropic piezoelectric ceramic

The transient dynamic stress intensity factor and dynamic energy release rate were determined for a cracked piezoelectric ceramic under normal impact in this study. A plane step pulse strikes the crack and stress wave diffraction takes place. Laplace and Fourier transforms are employed to reduce the transient problem to the solution of a pair of dual integral equations in the Laplace transform plane. The solution of the dual integral equations is then expressed in terms of a Fredholm integral equation of the second kind. A numerical Laplace inversion technique is used to compute the values of the dynamic stress intensity factor and the dynamic energy release rate for some piezoelectric ceramics, and the results are graphed to display the electroelastic interactions.