Transient 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.

Non-Fourier thermoelastic interaction of two collinear cracks in a functionally graded layer

Designed with a predetermined composition profile, functionally graded materials receive much attention in serving as the thermal barrier coating to resist severe thermal loading. By means of the dual-phase-lag theory, the non-Fourier effect is considered in establishing the theoretical thermoelastic model of the cracked layer under sudden thermal shocks. The novelty of the present work lies in revealing the interaction effects of two collinear Griffith cracks embedded in a functionally graded layer on the transient temperature and thermal stress fields under harsh conditions. Via employing the Fourier sine and cosine transforms, coupled with the Laplace transform, the dynamic mixed mode crack problem is transformed into a group of Cauchy-type singular integral equations. Numerical calculations are implemented to evaluate the transient temperature and stress intensity factors. The influences of the crack spacing, the nonhomogeneous parameters, and the thermal lags on the thermal and stress concentrations are explored. The results indicate that both mode I and II thermal stress intensity factors of the outer crack tips are noticeably higher than those of the inner crack tips, even up to 71% and 128%, respectively. A larger fracture risk may occur with the closer two adjacent cracks.

Thermo-mechanical analysis of a FGM plate subjected to thermal shock – A new numerical approach considering real time temperature dependent material properties

Abstract In present the study, sudden cooling, in other words thermal shock, is applied to a plate that is originally a functionally graded material (FGM). The flat plate is assumed to have an edge crack on it. Hence a numerical couple-field analysis is performed on the plate. The FGM is a combination of Ni and Al2O3. The thermal and mechanical properties of the FGM are assumed to depend on temperature variation. The mixing percentages of the Ni and Al2O3 throughout the plate are considered to vary (i) linearly, (ii) quadratically and (iii) in half-order. In order to solve the problem, a new subroutine depending on temperature is written using APDL (ANSYS Parametric Design Language) codes. Three values of the heat transfer coefficient are applied to the initially heated plate. As a result, the transient temperature variation and stress intensity factor are presented to show the thermo-mechanical relation of the plate. The material properties changing with temperature results in more reliable temperature values. Increasing the heat transfer coefficient results in better cooling and in a lesser amount of time to reach ambient air temperature.

Effect of cladding thickness on brittle fracture prevention of the base wall of reactor pressure vessel

In case of a loss of coolant accident, the cooling water is injected into the downcomer of reactor pressure vessel (RPV) and produces a pressurized thermal shock (PTS). Considering that the current cladding thickness is small, thermal shock and neutron irradiation are easy to cause brittle fracture of base material. The transient stress intensity factors of the crack tips at the base-cladding interface are obtained by the interaction integral method. Since the test of the crack propagation on the cladding-base interface is quite difficult and dangerous, the allowable internal pressure values obtained from the K-T curves are verified by XFEM in the thermo-mechanical coupling fields. By increasing the cladding thickness, the resulting temperature fields are compared with each other to demonstrate the different embrittlement effects caused by thermal shock. Then the elastic-plastic fracture mechanics (EPFM) method and the linear elastic interaction integral method are used to study the structural integrity at relatively low and high nil-ductility reference temperatures respectively. Furthermore, the influence of the crack size on the ultimate bearing capacity of the structure is quantitatively analyzed for various thicknesses of cladding and base wall. The size effect of crack decreases obviously with the increase of cladding thickness.

Non-classical hygrothermal fracture behavior of a hollow cylinder with a circumferential crack

By extending the classical Fourier heat conduction law and Fick diffusion law, a hyperbolic hygrothermal coupled model is newly proposed to investigate the fracture problem of a hollow cylinder containing a circumferential crack. The cylindrical system is subjected to a hygrothermal shock at the inner surface, and its outer surface is insulated and damp-proof. The integral transform technique and decoupling technique are used to solve the hygrothermal and mechanical boundary problem. Finally, the effects of hygrothermal coupling, thermal and moisture relaxation time on the transient temperature, moisture, hygrothermal stress and stress intensity factors are calculated. It is found that the hyperbolic model gives more conservative results than the parabolic model for the safety design of structures against fracture under hygrothermal loads.

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.

Dual-phase-lagging heat conduction and associated thermal shock fracture of sandwich composite plates

This paper studies a penny-shaped crack at the middle of a symmetric sandwich structure and is under a sudden temperature gradient on the crack faces. The temperature field of the structure and the stress intensity factor (SIF) at the crack tip are derived based on the dual-phase-lag non-Fourier heat conduction theory. Two specific factors are identified to predict the coupling effects of the thermal property differences between the skin and the core (including the differences in thermal conductivity, thermal diffusivity, heat flux lag and temperature gradient lag) on the thermoelastic behavior. If the coefficient of thermal expansion (CoTE) of the skins is greater than that of the core, the peak value of transient SIF increases. If the CoTE of the skins is smaller than that of the core, the transient SIF is scarcely influenced. The results are useful for the designs and applications of sandwich structures work under thermal shock.

Thermo-mechanical shock fracture analysis by meshless method

Different types of mechanical and thermal shock loads are considered to investigate transient stress intensity factors of two/three dimensional cracked specimens via meshless method with linear test function. Steady state and transient analyses show that the method is reliable. The effect of crack length, density and Lord-Shulman relaxation time on stress intensity factors are studied. Results represent the different effect of crack length on mechanical and thermal stress intensity factors. Various theoretical and real values of relaxation time are used to show how thermal stress intensity factor curves change when modified Fourier heat conduction law is employed compared with classical Fourier law. Additionally, the effect of specimen size on non-Fourier thermal stress intensity factor curves is investigated. We observed that using a functionally graded material instead of a composite coated substrate reduces local mean and peak values of transient thermal stress intensity factors.

Investigation of the thermal-elastic problem in cracked semi-infinite FGM under thermal shock using hyperbolic heat conduction theory

In this paper, a thermoelastic analytical model is established for a functionally graded half-plane containing a crack under a thermal shock in the framework of hyperbolic heat conduction theory. The moduli of functionally graded materials (FGMs) are assumed to vary exponentially with the coordinates. By employing the Fourier transform and Laplace transform, coupled with singular integral equations, the governing partial differential equations under mixed, thermo-mechanical boundary conditions are solved numerically. For both the temperature distribution and transient stress intensity factors (SIFs) in FGMs, the results of hyperbolic heat conduction model are significantly different than those of Fourier’s Law, which should be considered carefully in designing FGMs.

Elasto-hydrodynamics of quasicrystals with a crack under sudden impacts

ABSTRACTIn this paper, a mode-III crack in one-dimensional (1D) hexagonal quasicrystals subjected to anti-plane impact loading is analyzed. The elasto-hydrodynamics of quasicrystals is adopted, where the phonon field obeys wave equation, and the phason field obeys diffusion equation. By introducing a new auxiliary function, the coupled wave-diffusion equations are converted to a single higher-order partial differential equation. With the aid of the Laplace transform, an associated mixed initial-boundary value problem is reduced to two sets of dual integral equations, and then transformed into two coupled Fredholm integral equations of the second kind. Numerical results of transient phonon and phason stress intensity factors and crack-centre displacement jump are obtained through the numerical inversion of the Laplace transform and are presented graphically to show the influences of the phason.

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 Stress Intensity Factors of Functionally Graded Hollow Cylinders with Internal Circumferential Cracks

In this paper, transient thermomechanical stress intensity factors for functionally graded cylinders with complete internal circumferential cracks are obtained using the weight function method. The finite difference method is used to calculate the time dependent temperature distribution and thermal stresses along the cylinder thickness. Furthermore, finite element analysis is performed to determine the weight function coefficients and to investigate the accuracy of the predicted stress intensity factors from the weight functions. Variation of the stress intensity factors with time and effects of the material gradation on the results are investigated, as well. It is shown that the proposed technique can be used to accurately predict transient thermomechanical stress intensity factors for functionally graded cylinders with arbitrary material gradation.

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.

Non-Fourier thermoelastic behavior of a hollow cylinder with an embedded or edge circumferential crack

In this paper, the non-Fourier heat conduction theory is used to investigate the facture behavior of a hollow cylinder containing an embedded or edge circumferential crack under convective heat transfer boundary conditions. By neglecting the thermo-elastic coupling and inertial effects, the one-dimensional temperature field and the axial thermal stress for an un-cracked hollow cylinder are obtained in the Laplace domain. Then a mode I crack problem is formulated in the cylindrical system by using the superposition method. Integral transform technique is employed to reduce this mixed boundary value problem to a singular integral equation, which is solved numerically with the Gauss–Jacobi quadrature formulas. Finally, the effects of phase lag of heat flux, Biot’s number, and crack geometry on the transient temperature field, axial stress, and stress intensity factors are analyzed. It is found that the C–V heat conduction model gives more conservative results than the Fourier model for the structure safe design against fracture under thermal loading.

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.

Transient thermal cracking associated with non-classical heat conduction in cylindrical coordinate system

This paper studies the fracture behavior of a thermoelastic cylinder subjected to a sudden temperature change on its outer surface within the framework of non-classical heat conduction. The heat conduction equation is solved by separation of variable technique. Closed form solution for the temperature field and the associated thermal stress are established. The critical parameter governing the level of the transient thermal stress is identified. Exact expression for the transient stress intensity factor is obtained for a crack in the cylinder. The difference between the non-classical solutions and the classical solution are discussed. It is found that the traditional classical heat conduction considerably underestimates the transient thermal stress and thermal stress intensity factor.