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The present work investigates the problem of a cylindrical crack in a functionally graded cylinder under thermal impact by using the non-Fourier heat conduction model. The theoretical derivation is performed by methods of Fourier integral transform, Laplace transform, and Cauchy singular integral equation. The concept of heat flux intensity factor...
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Cracks always form at the interface of discrepant materials in composite structures, which influence thermal performances of the structures under transient thermal loadings remarkably. The heat concentration around a cylindrical interface crack in a bilayered composite tube has not been resolved in literature and thus is investigated in this paper...
Citations
... Hu and Chen [9] employed the dual-phase-lag theory to analyze transient heat conduction in a cracked half-plane, highlighting the theory's enhanced capability to accurately capture the thermal behaviors around the crack compared to classical models. Fu et al. [10] focused on non-Fourier heat conduction in a functionally graded cylinder containing a cylindrical crack, revealing that non-Fourier effects have a significant influence on heat flux and temperature fields, especially in materials with graded properties. Wen et al. [11] presented a peridynamic model for non-Fourier heat transfer in orthotropic plates with uninsulated cracks. ...
... Materials 2024, 17, x FOR PEER REVIEW 2 of 13 capture the thermal behaviors around the crack compared to classical models. Fu et al. [10] focused on non-Fourier heat conduction in a functionally graded cylinder containing a cylindrical crack, revealing that non-Fourier effects have a significant influence on heat flux and temperature fields, especially in materials with graded properties. Wen et al. [11] presented a peridynamic model for non-Fourier heat transfer in orthotropic plates with uninsulated cracks. ...
... (ω, y, s) = Ae γ 1 y + Be −γ 1 y −h ≤ y ≤ 0 capture the thermal behaviors around the crack compared to classical models. Fu et al. [10] focused on non-Fourier heat conduction in a functionally graded cylinder containing a cylindrical crack, revealing that non-Fourier effects have a significant influence on heat flux and temperature fields, especially in materials with graded properties. Wen et al. [11] presented a peridynamic model for non-Fourier heat transfer in orthotropic plates with uninsulated cracks. ...
This paper explores the thermal behavior of multiple interface cracks situated between a half-plane and a thermal coating layer when subjected to transient thermal loading. The temperature distribution is analyzed using the hyperbolic heat conduction theory. In this model, cracks are represented as arrays of thermal dislocations, with densities calculated via Fourier and Laplace transformations. The methodology involves determining the temperature gradient within the uncracked region, and these calculations contribute to formulating a singular integral equation specific to the crack problem. This equation is subsequently utilized to ascertain the dislocation densities at the crack surface, which facilitates the estimation of temperature gradient intensity factors for the interface cracks experiencing transient thermal loading. This paper further explores how the relaxation time, loading parameters, and crack dimensions impact the temperature gradient intensity factors. The results can be used in fracture analysis of structures operating at high temperatures and can also assist in the selection and design of coating materials for specific applications, to minimize the damage caused by temperature loading.
... FGMs feature inhomogeneous constituents and microstructures, which result in spatial gradation in the material properties [1]. Pressure vessels and thermal barrier components are only two examples of the many uses for them because of their unique ability to withstand fracture brought on by mechanical and thermal loads [2]. ...
In the present work, we implement a graded finite element analysis to solve the axisymmetric 2D hyperbolic heat conduction equation in a finite hollow cylinder made of functionally graded materials using quadratic Lagrangian shape functions. The graded FE method is verified, and the simple rule of the mixture with power-law volume fraction is found to enhance the effective thermal properties’ gradation along the radial direction, including the thermal relaxation time. The effects of the Vernotte numbers and material distributions on temperature waves are investigated in depth, and the results are discussed for Fourier and non-Fourier heat conductions, and homogeneous and inhomogeneous material distributions. The homogeneous cylinder wall made of SUS304 shows faster temperature wave velocity in comparison to the ceramic-rich cylinder wall, which demonstrates the slowest one. Furthermore, the temperature profiles along the radial direction when n = 2 and n = 5 are almost the same in all Ve numbers, and by increasing the Ve numbers, the temperature waves move slower in all the material distributions. Finally, by tuning the material distribution which affects the thermal relaxation time, the desirable results for temperature distribution can be achieved.
... With the development of computing technology, numerical methods exhibit great advantages. The transient interaction energy integral method (IEIM) is a direct, numerical method to extract the fracture parameters at the crack tip, such as the mixed-mode stress intensity factors [41][42][43], T-stress [44][45][46], and heat flux intensity factor [47,48]. Guo et al. [46,49] and Zhang et al. [14,27,28] obtained the transient, thermal fracture parameters via IEIM, respectively. ...
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.
... The thermal relaxation time is needed to account for the acceleration of heat flow. For thermal fracture problems, the hyperbolic heat conduction theory has been used by many researchers [16][17][18][19][20][21][22][23][24]. Babaei and Chen [16] investigated hyperbolic heat conduction in a functionally graded hollow cylinder. ...
... Then, they [19] investigated partially insulated cracks under thermal shock. The non-Fourier heat conduction model was used by Fu et al. [20] to investigate the problem of a cylindrical crack under thermal shock in a functionally graded cylinder, and obtaine the heat flux intensity factor. Wang and Li [21] analyzed the thermal shock resistance of a plate subjected to a sudden change in temperature within the framework of C-V theory. ...
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.
... The thermoelastic study of cylindrical cracks under static thermal loadings was conducted by Itou [40]. Recently, Fu et al. [41] analyzed the disturbed temperature field of a FG cylinder containing a cylindrical crack. ...
... The Gauss-Jacobi integration formulas in [31] can be adopted to solve Equations (41) and (38) numerically as ...
... Table 1 lists properties of all the material. It should be mentioned that the accurate value of phase lag of the carbon fiber reinforced composite cannot be found in experimental tests, and it is assumed according to Ref. [41]. Phase lag of heat flux is in the order of picoseconds for most of metals due to the phonon-electron coupling effect. ...
Cracks always form at the interface of discrepant materials in composite structures, which influence thermal performances of the structures under transient thermal loadings remarkably. The heat concentration around a cylindrical interface crack in a bilayered composite tube has not been resolved in literature and thus is investigated in this paper based on the singular integral equation method. The time variable in the two-dimensional temperature governing equation, derived from the non-Fourier theory, is eliminated using the Laplace transformation technique and then solved exactly in the Laplacian domain by the employment of a superposition method. The heat concentration degree caused by the interface crack is judged quantitatively with the employment of heat flux intensity factor. After restoring the results in the time domain using a numerical Laplace inversion technique, the effects of thermal resistance of crack, liner material, and crack length on the results are analyzed with a numerical case study. It is found that heat flux intensity factor is material-dependent, and steel is the best liner material among the three potential materials used for sustaining transiently high temperature loadings.
In this paper, the transient temperature response of a cracked plate under thermal shock is investigated. To eliminate the problems caused by the assumption of infinite heat propagation speed, the non-Fourier heat transfer theory is adopted. A peridynamic model is developed to consider the non-Fourier effect, the orthotropy of thermal conductivity, and the crack thermal resistance. This model avoids the spatial derivative and is efficient to analyze the problems with discontinuities. Based on the Kapitza thermal resistance model, a thermal resistance bond is proposed to deal with the uninsulated crack. The explicit and implicit discrete schemes of peridynamic formulation are presented to solve the temperature field. The model is verified by the analytical solution and excellent agreements are obtained. For the non-Fourier phenomenon observed in bismuth, numerical examples are presented for analyzing the effects of crack thermal resistance, crack orientation angle, and multi-crack distribution on non-Fourier heat transfer.
Cracks have a significant effect on heat transfer in composites, yet the influence of oblique cracks on the temperature response of composites has not been fully investigated under strong transient thermal shock, in which the heat propagation velocity cannot be assumed to be infinite. In this work, the dual-phase-lagging heat transfer model is employed to capture the transient temperature response. By imposing different boundary conditions on the crack surface, an extended boundary correction algorithm has been derived to avoid the problem of non-convergence when dealing with large and small angle cracks. The effects of crack orientation angle and interaction between cracks on dual-phase-lagging heat conduction in orthotropic materials are analyzed at the macroscale. For the two-dimensional representative volume element (RVE) of fiber reinforced composite material, the influence of the multi-crack distribution on dual-phase-lagging heat conduction at the mesoscale is further discussed in detail.
This paper investigates the problem of a 2-D plate containing internal cracks at arbitrary angles to the heating surface under thermal shock. The finite difference method is applied to solve the temperature distribution and a difference scheme of the oblique crack is developed. For the first time, a non-Fourier heat transfer analysis method of a 2-D plate with inner cracks at arbitrary direction angles is established. Specifically, for a strip with an inner crack paralleling to the surface, numerical results are compared with the analytical solutions by rotating the boundary, and perfect agreement is obtained. Numerical experiments are further presented to investigate the influence of crack orientation angle and multi-crack distribution on non-Fourier heat conduction.
Non-Fourier thermal and solutal transport in non-Newtonian power law rheological fluid is model via conservations laws under boundary layer approximations. The correlations for thermo-physical properties of pure, power law fluid and hybrid nano-structures are solved numerically with approximated conservations laws. The finite element method (FEM) is used for simulations purpose. The convergence is ensured and mesh-free analysis is performed. Iterative processes are done under computational tolerance 10⁻⁵. Relaxation phenomenon plays a significant role in controlling thermal and solutal boundary layer thickness. The impact of Joule heating can be minimized via thermal relaxation time. The impact of heat generation of temperature is similar to the impact of constructive chemical reaction on solutal transport.
