Thermal Stress Intensity Factors Research Articles

An innovative approach to study the influence of microstructure on thermal shock resistance of porous ceramics

AbstractPorosity is a critical microstructural factor in ceramic materials, influencing their mechanical and thermal properties. However, the detailed mechanisms through which porosity, grain size, and grain boundary fracture energy affect the thermal shock resistance of porous ceramics are still not fully understood. This study introduces a dual‐scale model that integrates these microstructural parameters to predict fracture toughness and thermal shock resistance. Using the single‐edge V‐notch fracture toughness testing principle, we calculate the thermal stress intensity factor and establish its relationship with temperature differentials. The critical temperature differential, which marks the onset of thermal shock damage, is determined when the thermal stress intensity factor reaches the fracture toughness threshold. The model reveals a significant interplay between porosity, grain size, and grain boundary fracture energy, with fine‐grained ceramics (grain size < 10 µm) showing a sharp decrease in fracture toughness as porosity increases, while coarser‐grained ceramics are less affected by porosity. These findings provide a deeper understanding of the microstructural optimization needed to enhance the thermal shock resistance of high‐performance porous ceramics.

Multiple edge cracks in a coated semi-infinite medium due to non-Fourier thermal shock

In this wok, based on the non-Fourier C-V model, the problem for multiple edge cracks is investigated for a coating-substrate pair subjected to a sudden temperature drop at the surface of coating. The temperature and resulting thermal stresses without cracks are obtained by the method of Laplace transform. By numerically solving the singular integral equations, the thermal stress intensity factors (SIFs) are evaluated. The results from the Fourier model and C-V heat conduction model are presented for comparison. Two dimensionless quantities are proposed to account for the coupling effects of heat conduction parameters (i.e., thermal conductivity, thermal diffusivity, and thermal relaxation time). Numerical results are presented for the thermal SIF as a function of normalized quantities such as time, crack depth, material constants and crack spacing. The findings in this work are expected to provide references for maintaining the integrity of the coating-substrate pair in the extreme heat transfer applications.

Transient thermal fracture analysis of a honeycomb layer with a central crack

Auxetic honeycomb materials with negative Poisson’s ratio received rapidly growing attention in recent years owing to their exceptional thermomechanical properties in constructing sandwich composites. The objective of this article is to investigate the transient thermal behavior and fracture risk of a honeycomb layer with a central crack subject to a sudden thermal shock by theoretical modeling. Two different material configurations along both orthogonal directions, as well as the conventional and auxetic hexagonal alumina honeycomb cells, are examined to illustrate their effects on the thermal stress intensity factors. To solve the thermoelastic governing equations subject to complex boundary conditions, the methodology of integral transform with singular integral equation is employed. The numerical results demonstrate that the auxetic honeycombs can reduce the thermal stress intensity factors significantly compared to their conventional counterparts. The ratio of stress intensity factors in auxetic to non-auxetic honeycombs under the same absolute value of the internal cell angle θ decreases monotonically with increasing |θ|. In addition, the effects of the relative density, crack length, and crack position are investigated. Our findings would provide a more comprehensive understanding of the honeycomb’s fracture behaviors and contribute to the material design of the sandwich composites with honeycomb cores.

Transient thermal fracture investigation of a cracked functionally graded layer via Guyer-Krumhansl model

Recent experimental evidence proves the Guyer-Krumhansl (G-K) model’s capability of predicting the nonclassical transient heat transfer process in heterogeneous composites. The objective of this article is to explore the dynamic thermal and fracture behaviors of a cracked orthotropic functionally graded material (FGM) layer subject to abrupt thermal shocks via the G-K equation. The thermal and elastic governing equations determined by the G-K model are transformed into the singular integral equations, which are calculated numerically to assess the non-Fourier transient temperatures and the resultant dynamic thermal stress intensity factors. Parametric comparisons are carried out for the effects of the non-Fourier thermal lagging time and thermal nonlocal length on the transient thermoelastic responses. The findings would benefit the applications of unconventional heat conduction theories and shed light on the scientific understanding of FGM’s fracture behaviors.

Instantaneous thermal fracture behaviors of a bimaterial with a penny-shaped interface crack via generalized fractional heat transfer

In the high-temperature environment, a larger thermal expansion mismatch of a bimaterial leads to pronounced thermal stresses and interface crack growth. In this paper, a generalized fractional heat conduction model is used to determine the instantaneous thermal fracture behaviors of a bimaterial interface crack. An axisymmetric thermoelastic problem is solved with the aid of Goodier's thermoelastic displacement potential and Love's potential functions. A mixed initial-boundary value problem is then converted to a singular integral equation of second kind by using the Hankel and Laplace integral transforms. Numerical results of the intensity factors of heat flux and thermal stresses are evaluated using Stehfest's Laplace inversion scheme. The influence of fractional kernel functions with power and exponential law are analyzed, respectively, for aluminum-steel and steel-epoxy, respectively. The thermal stress intensity factors exhibit more wave-like behaviors based on Riemann-Liouville and Atangana-Baleanu models which is different from Caputo-Fabrizio and the complete diffusion model.

The intrinsic relationship of the thermal stress intensity factor and the temperature difference at the crack surface

The intrinsic relationship of the thermal stress intensity factor and temperature difference between the upper and lower surface of the crack have been studied in this paper. The results show the thermal stress intensity factor is always proportional to the temperature difference between the upper and lower crack surface, and the ratio depends only on material parameters and crack length, but is independent of loading condition. For a finite medium problem, the above conclusion is still valid by simply adding a size related correction factor. When the size of medium is 10 times larger than the crack size, the size related correction factor is less than 1.019, that is, the error is less than 2%. Our conclusion provides a theoretical basis to estimate the localization thermal stress intensity factor simply by measuring the temperature difference of the crack surface.

Modeling of 2D thermo-elastic brittle fracture using smoothed floating node method

This paper presents an extension of the recently developed smoothed floating node method (SFNM) with cohesive zone approach to model crack growth in elastic materials under thermo-elastic loading conditions. The SFNM utilizes floating nodes to accurately model the crack by activating dormant nodes at intersection points of crack path and the corresponding element edges. Through the activation of floating nodes, the cracked element transforms into sub-elements, facilitating separate integration of each sub-element. A smoothing cell-based integration technique is employed to convert the area integral to line integral which mitigates the element distortion issues. The temperature distribution is initially determined across the entire domain, and then imposed as thermal loads in the 2D domain. The thermal stress intensity factor is calculated for both homogeneous and bi-material specimens using the interaction energy integral approach, and the crack propagation is predicted using circumferential stress criterion. The accuracy of the proposed framework is demonstrated with several benchmark problems of fracture mechanics. The develop framework yields comparable results with the available literature with less modeling complexity.

Analytical solutions for the plane thermoelastic problem of a nano-open crack in one-dimensional hexagonal quasicrystal non-periodic plane

As a stable material at high temperatures, the presence of cracks and other defects greatly reduces the performance of quasicrystals (QCs). The plane thermoelastic problem of one-dimensional hexagonal quasicrystals (1DHQ) non-periodic plane containing a nano-open crack is analyzed using surface elasticity theory. The closed form solutions are obtained to describe the thermoelastic field corresponding to the nano-crack by the Fourier integral transformation technique. The analytical solutions of the thermal stress intensity factors (TSIFs) and the strain energy density factor (SEDF) at the crack tip are derived explicitly. The influence of the applied loads, the surface effects and the multi-field coupling effects on the TSIFs and SEDF are discussed. The numerical results reveal that the surface effects have an obvious impact on TSIFs with small applied loads, and the surface effects will inhibit the propagation of nano-open cracks. The research results of this study provide some reliable theoretical references for the development of nano-QCs.

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.

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.

Interfacial thermal damage and fatigue between auxetic honeycomb sandwich and underneath substrate

A general model to evaluate the interfacial thermal damage and predict the fatigue life of the auxetic honeycomb-substrate structure (H-SS) is built. To improve the accuracy, all material parameters in the model are temperature-dependent. The transient temperature field and the associated thermal stresses associated with the temperature changes in the structure are determined by the finite difference method. The interfacial thermal stress intensity factor is employed to characterize the stress concentration behavior. Based on the stress field and the stress concentrations at the interface, interfacial thermal damage evolution and fatigue life prediction of the structure are made. The results show that the auxetic property can significantly enhance the fatigue life of the structure. The fatigue life will be undervalued when the effect of temperature-dependent material properties (TDMPs) is neglected. Furthermore, the influence of TDMPs on the fatigue life of the structure will increase as the absolute value of the internal cell angle increases. This paper provides a comprehensive assessment of the thermal damage and fatigue life of auxetic H-SSs and can serve as a solid theoretical foundation for future applications of related structures in extreme temperature environments.

Coupled crack tip fields under the action of an electric current

Coupled fields of crack tip under the action of electric current is studied by means of theoretical analysis, experimental investigation and numerical simulation. The distribution of electric field, temperature field and thermal stress field near the crack tip is analyzed theoretically when electric current is applied to a metal plate with an edge crack, and the theoretical calculation expression of thermal stress intensity factor is derived. The current treatment process of Al 5052-H32 alloy plate with fatigue crack is investigated by experiment and finite element simulation. The results show that current density and crack length have significant effects on temperature, thermal compressive stress and thermal stress intensity factor near the crack tip. Through the current treatment experiment of Al 5052-H32 alloy plate with fatigue crack, it is found that micro welding is occurred due to temperature concentration and thermal compressive stress around the crack tip. The simulation results also show that there is a high heat flux at the crack tip due to the concentration effect of current flow around. The annular thermal compressive stress caused by temperature gradient is formed around the crack tip to prevent crack propagation and help crack healing. The simulation results are in good agreement with the theoretical and experimental results.

Thermal stress intensity factor of an edge interface crack under arbitrary material combination considering double singular stress fields before and after cracking

Thermal stress intensity factor of an edge interface crack under arbitrary material combination considering double singular stress fields before and after cracking

Thermal shock fracture analysis of auxetic honeycomb layer based on non-Fourier heat conduction

Auxetic honeycomb layer (HL) is a typical metamaterial with a negative Poisson's ratio. In this paper, the thermal shock fracture problem of the auxetic HL is investigated based on non-Fourier heat conduction. The uncracked non-Fourier temperature and thermal stress field are determined by the separation of variables method and the constitutive model of auxetic HL. The corresponding thermal stress intensity factor (TSIF) is obtained in numerical form. Based on the TSIF and the fracture toughness criterion, the critical temperature of auxetic HL is predicted. There is a clear difference between the results based on the non-Fourier and Fourier models. The maximum thermal stress and TSIF of the auxetic HL obtained from the non-Fourier model are both significantly higher than those obtained from the Fourier model. If non-Fourier effects are not taken into account, the critical temperature of the auxetic HL is also overestimated. In addition, the auxetic property can increase the critical temperature of the HL, whether based on the non-Fourier or Fourier model. The results demonstrate the good potential of the auxetic HL in the thermal protection system application.

An interaction energy integral method for an interface crack in nonhomogeneous materials containing complex interfaces under thermal loading

In this study, an interface crack problem of a nonhomogeneous elastic plate subjected to thermal loading is investigated. An interaction energy integral method (IEIM) is derived for obtaining the mixed-mode thermal stress intensity factors (TSIFs) of the interface crack. Compared with the traditional J-integral method, the present IEIM’s advantage is that domain-independence still stands for the thermal interface crack problems. Particularly, when the integral domain intersects other interfaces, the present IEIM can still be proved to be domain-independent. Thus, the present method can be used to deal with the thermal crack problems of nonhomogeneous materials with complex interfaces. Used in conjunction with the extended finite element method (XFEM), the domain-independence of the present IEIM is verified. The numerical results agree well with the analytical ones. Several representative examples of complex interface crack problems in nonhomogeneous materials are analyzed in this study. Numerical results show that the method is effective for the thermal interface crack of nonhomogeneous materials with complex interfaces.

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.

Thermoelastic fracture analysis in orthotropic media using optimized element free Galerkin algorithm

In this work the effectuality of element free Galerkin method (EFGM) have been enhanced by proposing a novel algorithm for modeling discrete cracks in two-dimensional orthotropic media that are subjected to thermoelastic loading. The standard element-free Galerkin method (EFGM) is amended at the approximation level in conjunction with parametric optimization at computational level. The proposed algorithm not only extends the capability of element free Galerkin method for simulating thermoelastic fracture in orthotropic media but additionally it demonstrates a higher degree of computational efficiency and solution accuracy. The proposed algorithm utilizes variable quadrature points from the problem domain for the purpose of numerical integration. A parametric optimization has also been incorporated in the proposed algorithm for minimizing the computational time of simulation. The proposed algorithm is proficient to simulate near tip stress field in both convex and non-convex problem domains. A modified conservative M-integral technique has been used in order to extract the thermal stress intensity factors (SIFs) for the simulated problems. Few static and quasi-static crack problems have been modeled and simulated to illustrate and establish the accuracy and effectiveness of the proposed algorithm. Moreover, two component level problems, having non-convex domains, have also been modeled in order to establish the versatility of proposed algorithm. A good agreement between the obtained results with those of the available reference results establishes the capability and robustness of proposed algorithm for simulating fracture in orthotropic media subjected to thermoelastic loads. Moreover, the proposed EFGM algorithm significantly reduces the computational time which further enhances and augments its modeling prowess.

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.

Weight functions and thermal stress intensity factors for two symmetric non-collinear radial cracks in cylinders

In the present paper, the weight function was derived for a cylinder with two symmetric non-collinear radial cracks. For this purpose, the finite element software ABAQUS was employed to determine the unknown parameters of the weight function considering three reference load conditions. These coefficients are a function of the angle between the cracks and crack relative depth. Green’s function was applied to validate the point-by-point accuracy of the derived weight function. The results were compared with those obtained from finite element analysis, and a good agreement was achieved. Subsequently, the closed-form solution was presented for the stress intensity factors resulting from steady-state thermo-mechanical loading, and it was compared with the finite element results showing good agreement. The results indicated that two symmetric cracks under prescribing temperature to the cylinder surface were the most conservative case in the design phase.