Transient Thermal Stress Intensity Factors Research Articles

A peridynamic model based on generalized thermoelastic theory in a plate with oblique cracks

In this paper, a peridynamic model based on generalized thermoelastic theory is derived by irreversible thermodynamics. This model avoids the spatial derivative and can be easily applied to generalized thermoelastic problems with discontinuities. The transient temperature response is captured using the non-Fourier CattaneoVernotte (C-V) model. The interaction integral is employed to calculate the transient thermal stress intensity factors (TSIFs). Numerical examples are presented for analyzing the effects of crack orientation angle and multi-crack distribution on transient thermoelastic response. And the crack propagation behavior under non-Fourier thermal shock is further discussed in detail. It is found that with the increase of the angle between inner crack and heating boundary, the sensitivity of mode-I TSIFs to the non-Fourier effect increases, while the sensitivity of mode-II TSIFs to the non-Fourier effect decreases. This peridynamic model may be useful for understanding the crack behaviors of thermal protection materials under thermal shock.

Research on the on-line fracture assessment of cracked primary loop pipes in NPPs

The cracked pipes usually need to be replaced or conservatively evaluated in the Nuclear Power Plants (NPPs). There is still a lack of effective methods for a real-time crack propagation and safety evaluation based on massive monitoring transient data. In order to ensure the safe and economic operation of the NPPs, the authors have developed an on-line fracture assessment technology in this paper. The calculation method of total stress suitable for on-line monitoring data, optimizing the calculation method of transient thermal stress and stress intensity factor (SIF) based on the influence function method are discussed. Then, the on-line software for the primary loop hot-leg pipe which is based on the research results is developed. In this paper, an on-line safety assessment method based on the monitoring data which can meet the requirements of the in-service inspection code (RSE-M Code) is given. The influence function is proposed to be established at a fixed time interval which will make the computational complexity reduced significantly. By the parallel calculation method and the characteristics of the algorithm, the origin algorithm along the time axis is optimized to an algorithm that can be calculated to obtain the target parameters at each time point within the specified attenuation time range of the influence function. Then the calculation efficiency is significantly improved. By compiling the data and calculation methods in the code, the calculation method of SIF suitable for on-line monitoring is obtained, and the reliability is also verified by the analyzed case. Based on the technical results obtained from the research and the requirements in the RSE-M Code, the re-development is carried out in the general commercial software platform. The software is developed, and it is demonstrated that it has sufficient analysis accuracy.

Coupled thermoelastic fracture analysis of a cracked fiber reinforced composite hollow cylinder by fractional Cattaneo-Vernotte models

Coupled thermoelastic fracture problem of a fiber reinforced composite hollow cylinder containing an embedded circumferential crack is investigated in the present paper based on generalized fractional Cattaneo-Vernotte heat conduction models. The temperature and stress fields are obtained by solving the coupled partial differential equations, and then corresponding thermal axial stress with minus sign is applied to the crack surface to form a mode I crack problem. Integral transform techniques are employed to reduce the mixed boundary value problem to a series of singular integral equations. The effects of different fractional Cattaneo-Vernotte models, fractional order, convective heat transfer coefficient, volume fraction, and thermodynamic coupling coefficient on the transient temperature and thermal stress intensity factors are analyzed. The results show that each physical parameter has a significant effect on the responses, which is important to make predictions regarding the stability of crack growth, thermal fatigue life etc.

Investigation of the thermomechanical behavior of nonhomogeneous, layered materials with mixed-mode cracks subjected to rapid thermal shock loading

For mixed-mode, thermal shock crack problems with thermal lagging behaviors, it is difficult to obtain the transient thermal stress intensity factors (TSIFs). This paper aims to develop a method combining the Newmark method and the transient interaction energy integral method (IEIM) to extract the transient, mixed-mode TSIFs of nonhomogeneous, layered materials with mixed-mode cracks. The transient temperature field obtained by non-Fourier heat conduction theory is discretized in the spatial and temporal domains through the finite element method (FEM) and Newmark method, respectively. The effect of the continuity of thermomechanical parameters at the dual interface on the transient, mixed-mode TSIFs of nonhomogeneous, layered materials is discussed, then the fracture resistance of nonhomogeneous, layered materials is evaluated. Moreover, the maximum hoop stress criterion is utilized to obtain the crack growth angle and the equivalent, transient TSIFs of nonhomogeneous, layered materials. The influences of the interface on crack growth angle and equivalent transient TSIFs of nonhomogeneous layered materials are also studied. The present work is beneficial for the thermal design of nonhomogeneous, layered materials with mixed-mode cracks subjected to rapid thermal shock loading.

Analysis of Thermal Fracture for Nonhomogeneous Materials Plate with Multiple Cracks

In this paper, the transient interaction integral method (IEIM) is established to obtain the transient thermal stress intensity factors (TSIFs) in order to study the fracture problems of nonhomogeneous materials under thermal shock loading. The transient temperature field is evaluated by using the finite difference method and the finite element method. The TSIFs of nonhomogeneous materials with multiple cracks are analysed, then the mixed-mode TSIFs of nonhomogeneous materials with different positions are discussed. The results of this study have shown that the current approach is applicable to obtain fracture parameters of nonhomogeneous materials with multiple cracks efficiently, which can be used as a significant reference for the engineering application of nonhomogeneous materials.

Fracture analysis of a non-homogeneous coating structure with dual interfaces under thermal shock

To solve the thermal fracture problem of non-homogeneous coating structure (NCS) with dual interfaces under strong transient thermal loading, this paper proposes a method to extract fracture parameters by combining the Newmark method and the transient interaction energy integral method (IEIM). The strong transient temperature and the transient thermal stress intensity factors (TSIFs) of NCS with dual interfaces under strong transient thermal load can be obtained through the proposed method. The interfaces are divided into an ideal interface, weak interface, and strong interface according to the continuity of the material parameters of NCS at the interface. Firstly, the influences of Young's modulus, thermal relaxation time, thermal expansion coefficient, and density continuity on TSIFs at strong and weak interfaces are studied. Then, the crack growth laws under thermal shock at the strong and weak interfaces are analyzed. Finally, according to the influence of the coating thickness on TSIFs, the optimal thickness ratio of the dual interface structure ranging is selected to minimize the likelihood of thermal fracture. This work can be used for the thermal design, evaluation, and engineering applications of NCS.

Investigation of the fracture problem of functionally graded materials with an inclined crack under strong transient thermal loading

In this paper, a special method for solving transient thermal stress intensity factors (TSIFs) in functionally graded materials (FGMs) with inclined cracks under strong, transient thermal shock loading is established based on the hyperbolic heat conduction equation. First, the Newmark method is employed to obtain the strong transient temperature field of FGMs containing inclined cracks. Then, the transient interaction energy integral method (IEIM) is used to solve the TSIFs for inclined cracks. In addition, the influences of the distribution patterns of the thermal relaxation parameter, the crack length and the crack angle on the TSIFs, and the crack growth angle are investigated. Moreover, we discuss the difference between using the hyperbolic heat conduction theory and the classical, Fourier heat conduction theory in calculating the TSIFs of FGMs with inclined cracks. The results show that the present, combined IEIM-Newmark method can be used to solve strong transient thermal shock crack problems with high efficiency. This work can be used for the thermal design, evaluation, and engineering applications of FGM structures.

Non-fourier thermal fracture analysis of a griffith interface crack in orthotropic functionally graded coating/substrate structure

Serving as thermal barrier coatings in the harsh environment, functionally graded materials are usually subject to the extremely high temperature gradient, under which circumstance the classical Fourier's law breaks down and the non-Fourier effect becomes pronounced. The configuration of an orthotropic functionally graded coating bonded to the homogenous substrate containing a Griffith interface crack is considered in this work. The dual-phase-lag heat conduction theory is adopted to analyze the transient heat conduction and the resulting thermal stress intensity factors of the coating/substrate structure. The governing partial differential equations subjected to the complex thermal/mechanical boundary conditions are solved by the integral transform coupled with singular integral equations. A good agreement is achieved between the transient thermal stress intensity factors in the present work and steady-state values from previous literature. The influence of the thermal lags, nonhomogeneous parameters, and the thicknesses of two layers on the thermomechanical responses are investigated.

Thermal shock resistance of ceramic foam sandwich structures: Theoretical calculation and finite element simulation

In this paper, the thermal shock resistance of a ceramic foam sandwich (CFS) slab is studied. Two typical thermal shock conditions are considered, i.e., the hot shock and the cold shock. Variations of transient temperature and thermal stress fields with thermal shock time and position are derived. The transient thermal stress intensity factor (SIF) of the thermally induced embedded and edge crack are detected by the developed theoretical model. Simultaneously, the corresponding thermal shock simulation of CFS slab is performed based on finite element (FE) analysis. The results between the presented theoretical model and FE analysis exhibit excellent agreement. Furthermore, the effects of the faceplate thickness and the relative density of the foam core on the thermal shock resistance of CFS slab under hot shock are discussed. Constructive suggestions for the structural optimization design of CFS structures are provided. The study demonstrates the asymmetric fracture behavior under the asymmetric hot shock, and determines the position of the danger zone. Notably, the variations of the influence degree of foam core density on the thermal shock resistance of the CFS slab under cold shock are indicated. The Crack propagation behaviors are investigated and the corresponding crack growth trajectories are provided from the fracture mechanics criterion.

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.

Meshless fracture analysis of 3D planar cracks with generalized thermo-mechanical stress intensity factors

This paper implements three dimensional meshless local Petrov–Galerkin method in the linear elastic fracture mechanics analyses of isotropic functionally graded and homogeneous materials under different thermo-mechanical loads. Energy equation based on Lord–Shulman non-Fourier heat conduction law coupled with equation of motion is applied to evaluate the effect of theoretical and realistic relaxation times on transient thermal stress intensity factors along 3D thorough or semielliptical cracks under thermo-mechanical shock. A new coordinate transform method with linear weight function is introduced to evaluate stress intensity factors by generalized interaction integral method based on incompatibility formulation. Simple linear test function is introduced, which is approximated via compatible radial basis functions and leads in eliminating internal boundary integrals of meshless method and reducing computational time. Shape functions are constructed in every Gauss point by determining the closest domain point method in preprocessing. Parametric studies are carried out in order to determine suitable radial basis functions shape parameters and penalty method parameter. Reasonable accuracy and the small number of used points are the main advantages of this method over finite element method.

Coupling effects of dual-phase-lag heat conduction and property difference on thermal shock fracture of coating/substrate structures

This paper firstly studies the heat conduction in a coating/substrate structure subjected to a sudden cooling on the coating surface based on the dual-phase-lag heat conduction model. Then the thermally induced surface cracking problem is solved and the thermal stress intensity factor at the crack tip is evaluated. It is found that the coupling effects of the thermal properties (such as coefficients of thermal conductivity and diffusivity, and phase lags of heat flux and temperature gradient) on the thermoelastic behavior can be predicted by two introduced factors. Besides, the numerical examples reveal that the thermal stress intensity factor decreases with the ratio of substrate elasticity modulus to coating elasticity modulus. Especially if the ratio is greater than 1, namely the substrate is harder than the coating, the peak value of transient thermal stress intensity factor may decrease with the crack length.

A numerical method for the thermal-shock crack problems of nonhomogeneous materials with inclusions based on an interaction energy integral method

Nonhomogeneous materials, especially for particulate composites, usually contain defects such as voids and debonding introduced during manufacturing process. Due to existence of defects, nonhomogeneous materials are prone to fracture failure under thermal shock loading. This paper aims to develop a set of methods for analysing the thermal-shock crack problems of nonhomogeneous material plates (NMPs) with inclusions. A modified domain-independent interaction energy integral method (IEIM) is developed to obtain the mixed-mode transient thermal stress intensity factors (TSIFs). Then the IEIM, the extended finite element method (XFEM) and the finite difference method (FDM) are combined together to address a thermal-shock crack problem of a NMP with an inclusion. With the methods, the influences of the inclusion on the transient mixed-mode TSIFs are investigated. The results show that the present method can be applied to solve the thermal shock crack problem effectively. Furthermore, the relations between the mixed-mode TSIFs and model parameters including material constants as well as locations of the inclusion are established. It is found that the thermal expansion coefficient and Young’s modulus of the inclusion affect the mixed-mode TSIFs in a dominant manner in comparison with other factors such as the specific heat, heat conductivity and density of the inclusion affect the TSIFs slightly. Specifically, the critical normalized distance, beyond which the influence of the inclusion on the mixed-mode TSIFs is negligible, is revealed. The present work will be significant for fracture mechanics analysis and design of nonhomogeneous materials with inclusions.

Transient thermal stress intensity factors for a circumferential crack in a hollow cylinder based on generalized fractional heat conduction

A generalized fractional heat conduction theory is applied to investigate the transient thermal fracture problem of a hollow cylinder with an embedded or surface circumferential crack. Integral transform technique is used to solve an associated initial-boundary value problem. Explicit temperature field and thermal stresses are given in the Laplace transform domain for a circumferentially cracked hollow cylinder subjected to thermal shock at the inner surface and with an insulated outer surface. Numerical results in the time domain are obtained by using numerical inversion of the Laplace transform. Transient thermal stresses induced by a crack are determined and thermal stress intensity factors at the crack front are calculated. The effects of fractional order, phase lag of heat flux on the transient temperature field, thermal stresses and thermal stress intensity factors are illustrated graphically for internal and surface cracks. The obtained results based on non-Fourier law of fractional heat conduction are compared with those using the classical Fourier law and hyperbolic heat conduction models, respectively.

Transient Thermoelastic Analysis of a Solid Cylinder Containing a Circumferential Crack Using the C–V Heat Conduction Model

This article presents the transient thermoelastic analysis in a long solid cylinder with a circumferential crack using the C–V heat conduction theory. The outer surface of the cylinder is subjected to a sudden temperature change. The Laplace transform technique is adopted to solve the one-dimensional hyperbolic heat conduction equation, and the axial thermal stress is obtained for the un-cracked cylinder in the Laplace domain. Then this axial thermal stress with a minus sign is applied to the crack surface to form a mixed boundary value problem in the cylindrical coordinate system. A singular integral equation is derived by applying the Fourier and Hankel transforms to solve the mode I crack problem. The transient thermal stress intensity factors are obtained by solving the singular integral equation numerically. The influences of thermal relaxation time, crack geometry, and Biot's number upon transient temperature distributions, axial stress fields, and stress intensity factors are analyzed.

Investigation Methods for Thermal Shock Crack Problems of Functionally Graded Materials–Part II: Combined Analytical-Numerical Method

Fractures phenomena can be often found in functionally graded materials (FGMs) subjected to thermal shock loadings. This paper aims to develop a set of analytical-numerical methods for analyzing the mixed-mode thermal shock crack problems of a functionally graded plate (FGP). First, a domain-independent interaction energy integral method is developed for obtaining the mixed-mode transient thermal stress intensity factors (TSIFs). A perturbation method is adopted to obtain the transient temperature field. Then an analytical-numerical method combining the interaction energy integral method, a perturbation method, and the finite element method is developed to solve the present crack problem. Particularly, the influences of the materials parameters, crack length, and crack angle on the TSIFs and the crack growth angle are investigated. The results show that the present analytical-numerical method can be used to solve the thermal shock crack problem with high efficiency. The present work will be significant for the fracture mechanics analysis and design of FGM structures.

Investigation Methods for Thermal Shock Crack Problems of Functionally Graded Materials–Part I: Analytical Method

In most published papers, in order to obtain the analytical solution of the crack problems in functionally graded materials (FGMs), the thermomechanical properties of FGMs are usually assumed to be very particular functions and, hence, may not be physically realizable for many actual material combinations. Very few analytical methods can be used to solve the thermal shock crack problem of an FGM cylindrical shell or plate with general thermomechanical properties. In this article, a set of analytical methods is proposed for the thermal shock crack problem of an FGM plate or cylindrical shell with general thermomechanical properties. The crack problem of a cylindrical shell is modeled by a plate on an elastic foundation. Greatly different from previous studies, a set of analytical methods using both the perturbation method and a piecewise model are developed to obtain the transient temperature field and thermal stress intensity factor (TSIF). The perturbation method is applied to deal with the general thermal properties and the piecewise model is used to deal with the general mechanical properties. In the analytical procedure, integral transform, the residue theorem, and the theory of singular integral equation are used. Several representative examples are considered to check the capability of the present method. The transient thermal shock behavior of a ZrO2/Ti-6Al-4 V FGM plate with a surface crack and a Rene 41-Zirconia FGM cylindrical shell with a circumferential crack are analyzed.

Fracture analysis of a nonhomogeneous coating/substrate system with an interface under thermal shock

The work is devoted to establish a model for the interface problem of a nonhomogeneous coating/substrate system. In the model, according to the distribution of material properties, three types of interface problems are considered: (i) The material properties and their derivatives are continuous on the interface; (ii) the material properties are continuous, but their derivatives are discontinuous on the interface; and (iii) the material properties as well as their derivatives are discontinuous on the interface. In order to solve the complex interface problems, a transient interaction energy integral method (IEIM) is developed in this paper. The transient thermal stress intensity factors are evaluated using the IEIM combined with the finite element method and the finite difference method. The influences of the interface discontinuity and the geometric parameters on the transient TSIFs are investigated. Particularly, the crack growth behavior with different interface discontinuities is discussed.

Transient thermal cracking of a brittle half space medium with a semi-elliptical surface crack

The paper conducts the cracking study of a brittle half space medium with a semi-elliptical surface crack. The transient thermal stress intensity factors are obtained and are graphically presented. Effects of thermal shock time, crack size, and crack shape on the crack growth and thermal shock resistance behavior of the medium are investigated in details. A thermal shock resistance analysis methodology is established, allowing us to study the fracture strength of brittle media subjected to thermal shock.

Fracture of a Finite Medium with a Circular Internal Crack under Hyperbolic Heat Conduction-Prescribed Crack Face Temperature

This paper studies the fracture mechanics of a thermoelastic material layer with an internal crack subjecting to a prescribed temperature. The hyperbolic heat conduction theory is used and the transient thermal stress intensity factor is obtained. Comparisons of the results from the non-Fourier model and the Fourier model are made. The results demonstrate that the non-Fourier effect has a strong effect on the transient thermal stress around the crack tip. Thermal stress intensity factor predicted by the hyperbolic heat conduction model is considerably high then that predicted by the classical Fourier.