Thermal Stress Intensity Factors Research Articles

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.

Thermal shock resistance enhancement of auxetic honeycomb layer considering multi-cracking and temperature-dependent material properties

This paper assesses the thermal shock behaviors of the auxetic honeycomb layer (HL) through consideration of crack propagation and new crack initiation. All material properties are temperature-dependent. To calculate the thermal stress field with no crack, the finite difference approach is used. On this basis, a theoretical model for thermal stress intensity factor and thermal stress between cracks is developed. The model combines the equivalent fracture toughness and equivalent tensile fracture strength as the failure criteria. The critical temperature for crack propagation and new crack initiation in the HL is determined. The results reveal that the thermal shock resistance (TSR) of the HL is overestimated if the temperature-dependent material properties (TDMPs) are not taken into account. Multiple cracking can dramatically improve the TSR of the HL. Compared to the non-auxetic HL, the TSR of the auxetic HL is significantly enhanced. Furthermore, the HL with lower relative density generally possesses higher TSR, and the corresponding physical mechanisms are revealed.

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.

Schmidt method to study the disturbance of steady-state heat flows by an arbitrary oriented crack in bonded functionally graded strips

This article aims to investigate the impact of a partially insulated crack on vertical and horizontal components of heat flow. The crack is arbitrary oriented and its center is located at the interface of bonded finitely thick functionally graded strips. Employing the integral transformation, the thermoelastic equations are reduced to a set of singular integral equations. The unknown variables of these equations are the jump in temperature and displacements across the crack surfaces. Representing the unknowns as a series of Jacobi polynomials, the solutions of the singular integral equations are obtained by employing the Schmidt method which further helps to determine the analytical forms of crack tip heat flux intensity factors (HFIFs) and thermal stress intensity factors (TSIFs). The results of the present study are also validated for a particular case.To quantify the strength of heat flow components, the crack tip HFIFs and TSIFs as a function of crack angle, crack insulation parameter, strips’ width, and non-homogeneity parameters’ ratio are demonstrated pictorially.

Thermal stress intensity factor solutions for reactor pressure vessel nozzles

To ensure the safety margin of a reactor pressure vessel (RPV) under normal operating conditions, it is regulated through the pressure-temperature (P-T) limit curve. The stress intensity factor (SIF) obtained by the internal pressure and thermal load should be obtained through crack analysis of the nozzle corner crack in advance to generate the P-T limit curve for the nozzle. In the ASME code Section XI, Appendix G, the SIF via the internal pressure for the nozzle corner crack is expressed as a function of the cooling or heating rate, and the wall thickness, however, the SIF via the thermal load is presented as a polynomial format based on the stress linearization analysis results. Inevitably, the SIF can only be obtained through finite element (FE) analysis. In this paper, simple prediction equations of the SIF via the thermal load under, cool-down and heat-up conditions are presented. For the Korean standard nuclear power plant, three geometric variables were set and 72 cases of RPV models were made, and then the heat transfer analysis and thermal stress analysis were performed sequentially. Based on the FE results, simple engineering solutions predicting the value of thermal SIF under cool-down and heat-up conditions are suggested.

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.

Three-dimensional thermal fracture analysis of piezoelectric material by extended finite element methods

The effect of poling direction and thermal fracture analysis of penny-shaped crack (PSC) in piezoelectric material (PM) exposed to a uniform temperature and steady-state heat flow is presented using the XFEM approach. The intrinsic coupling, thermo-electro-mechanical under thermal shocks are studied and thermal stress intensity factors (TSIFs), and electrical displacement intensity factors (EDIF) are evaluated using the strain energy-based, thermal interaction integral. The discontinuous crack surfaces are treated as adiabatic and electrically impermeable. The discontinuity in both the temperature gradient and electrical field displacement over the crack surface is enriched using the Heaviside enrichment function. The fracture parameters, TSIFs, and EDIF of penny-shaped crack are a function of applied temperature fields and the thermo-electro-mechanical properties of piezoelectric material are studied. Further, the effect of poling direction, and in-plane and out-plane offset of crack position, and the inclined crack on the TSIFs and EDIF are presented. The comparison of both analytical and numerical results of the intended formulation showed excellent accuracy which has been verified on benchmark problems. The results are quite useful for the design of the sensors, transducers, and actuators in heat transfer applications.

Mechanism of Crack Initiation and Propagation of Re-Entrant Auxetic Honeycombs Under Thermal Shock

Abstract Thermal shock multiple cracking behaviors of re-entrant auxetic honeycombs with a negative Poisson’s ratio are investigated, and the crack initiation and propagation behavior are discussed. An effective macro continuum model is developed to detect the effects of cracking density and microstructures of auxetic honeycombs on the thermal stress and intensity. The microscale tensile stresses in the struts ahead of the crack as functions of the corresponding thermal stress intensity factor (SIF) at the macroscale are evaluated by employing a macro–micro model. Then, a lower-bound method is proposed to assess the critical thermal load of auxetic honeycombs by combining the macro-micro model and the macro continuum model. A significant increase in both transient thermal stress and intensity as the growing cell-wall angle is demonstrated. Results for the maximum thermal SIF as well as the maximum tensile stress in the middle of cracks are calculated as functions of crack density and length. With the identical SIF, the microscale tensile stresses ahead of the crack in honeycombs with smaller cell-wall angles are greater than that in mediums with larger angles due to the more significant crack tip opening displacement. Critical thermal load prediction reveals that the honeycombs with smaller cell-wall angles generally possess more excellent thermal shock resistance. Also, the varying failure modes of different auxetic honeycomb strips under specific thermal load are predicted. The corresponding mechanisms of crack initiation and propagation are revealed.

Non-Fourier thermal shock resistance and transient thermal fracture of magneto-electro-elastic composite with a penny-shaped crack

Magneto-electro-elastic composite with a penny-shaped crack is analyzed. The exact solution of temperature field based on non-Fourier heat conduction is derived by the method of standard separation of variables. The thermal stress, electrical displacement and magnetic induction in the transversely isotropic andaxis-symmetric magneto-electro-elasticcylinder are evaluated by Hankel transform technique. The thermal stress, electrical displacement and magnetic induction intensity factors at the tip of penny-shaped crack are obtained by Abel type integral equation. The influence of the thermal relaxation time, crack length, characteristic length of materials and magneto-electro-thermo-elastic coupling on intensity factors are analyzed. Thermal shock resistance of MEE cylinder is evaluated by associating the stress based failure criterion and fracture mechanics based failure criterion.

Transient non-Fourier thermoelastic fracture analysis of a cracked orthotropic functionally graded strip

In this work, the fracture problem of an orthotropic functionally graded strip containing an internal crack parallel to its surfaces subjected to thermal shocks is examined. To eliminate the paradox of infinite heat propagation speed and take the microstructural interactions of thermal energy carriers into account, the non-Fourier, dual-phase-lag theory is employed to investigate the transient heat conduction and the associated thermal stresses response. By utilizing Laplace transform and Fourier transform, the thermoelastic problems are finally reduced to the Cauchy-type singular integral equations, which are solved by the Lobatto–Chebyshev technique numerically. The temperature field and thermal stress intensity factors are evaluated by the numerical inversion of Laplace transform to illustrate the effects of two thermal lags and nonhomogeneous parameters. The results show the fracture risks accompanied by the dual-phase-lag heat conduction can be higher than the classical analysis and it would be more conservative to consider non-Fourier effects in designing the orthotropic functionally graded materials.

Evaluation of stress intensity factors under thermal effect employing domain integral method and ordinary state based peridynamic theory

In this article, several thermoelastic benchmark cases are studied within the framework of ordinary state based peridynamic theory (OSPD). By using OSPD, the limitations of geometrical discontinuity in fracture analysis can be overcome. Meanwhile, double nodes can also be avoided during crack definition. A domain integral method with thermal effect is applied in calculating the thermal stress intensity factors (TSIFs). Meanwhile, peridynamic differential operators are utilized to rewrite the spatial derivatives in the domain integral. Numerical investigations of TSIFs in the single and mixed-mode crack scenarios are provided respectively, and verified by the reference solutions. Good agreements between OSPD and the reference solutions show high performance and capability of the proposed method in thermoelastic fracture analysis.

Enhanced fatigue performance of auxetic honeycomb/substrate structures under thermal cycling

This paper studies the fatigue behavior of auxetic honeycomb layer/substrate structures due to interfacial delamination damage. First, the interfacial thermal stress and cyclic interfacial thermal stress intensity factor (ITSIF) at the free ends of the structure are determined in terms of the thermal shock time, relative density, aspect ratio, and internal cell angle of the honeycomb. Then, a theoretical model for the service life analysis of the structures is established based on Paris's law. The results show that the auxetic structures have a lower ITSIF level and a longer service life compared with those of the non-auxetic structures. Another interesting finding is that a reduction in the relative density of the honeycomb layer will increase the service life of the structures. This confirms the significance of applying auxetic materials in re-usable structures for thermal protection purposes. This research is the first attempt to evaluate the service life of the auxetic honeycomb layer/substrate structures under thermal cycling.

Temperature, thermal flux and thermal stress distribution around an elliptic cavity with temperature-dependent material properties

Temperature is an important factor affecting the physical and chemical properties of materials, especially when the temperature changes significantly, such as in the process of heat conduction. The corresponding changes of material properties greatly complicate the distribution of temperature and thermal stress, and make it much more difficult to accurately solve the thermal-elastic field. Using the generalized complex variable method, the thermal-elastic problem of an elliptic cavity embedded in an infinite medium has been analyzed in this paper, with the temperature dependence of thermal conductivity, elastic modulus and thermal expansion coefficient fully accounted for. The temperature, thermal flux and thermoelastic fields have been obtained analytically. The analytical and numerical results show that thermal flux solution is consistent with the temperature independent case, while the temperature and thermal stress solutions are much more complicated. When the elliptical cavity degenerates into a crack, Mode I thermal stress intensity factor K1 has a tiny negative value, which indicates that thermal flux can actually close the crack slightly. In addition, both K1 and K2 vary nonlinearly with remote thermal loads, and depend on 3/2,5/2 and 7/2 power of crack length. These results provide a powerful tool for the failure and reliability analysis of temperature dependent materials.

Crack growth behavior and thermal shock resistance of ceramic sandwich structures with an auxetic honeycomb core

This paper developed a thermal–mechanical analysis model to describe the thermal shock behavior of ceramic sandwich structures (CSSs) with an auxetic honeycomb core. The transient temperature distribution and the associated thermal stress field of CSSs subjected to a thermal shock were determined. The crack growth behavior was discussed based on the thermal stress intensity factor (TSIF), crack location, face-sheet thickness, and internal cell orientation of the honewycomb core in detail. The results revealed that the auxetic and non-auxetic honeycomb cores have the similar temperature distribution profile however the auxetic honeycomb core can substantially reduce the overall thermal stress level. Furthermore, by equating the maximum TSIF and equivalent fracture toughness, the critical temperature for which the honeycomb core can sustain without failure was obtained. The results showed that CSSs with auxetic honeycomb core possessed a higher thermal shock resistance than that of non-auxetic. This research work was the first attempt to identify the the thermal shock resistance of CSSs with an auxetic honeycomb core. The results would provide fresh insight into the design and selection of CSSs applied in an extreme temperature environments.

Thermoviscoelastic fracture analysis of a cracked orthotropic fiber reinforced composite strip by the dual-phase-lag theory

Fiber-reinforced polymer composites have gained tremendous popularities in various engineering applications due to their superior mechanical performances. This work is devoted to investigating the transient thermomechanical responses of an orthotropic fiber-reinforced strip containing a crack aligned along the fiber direction. The non-Fourier, dual-phase-lag theory is employed to account for the finite time required to complete the process of transporting heat and building local thermal equilibrium in composites, while the Generalized Maxwell viscoelastic model is utilized to characterize the constitutive law of the polymeric matrix and the fibers are treated to be elastic. By using Laplace transform and Fourier transform, the mixed, boundary-value problems are finally reduced to the Cauchy-type singular integral equations, which are solved by the Lobatto-Chebyshev technique numerically. The temperatures and thermal stress intensity factors in the time domain are evaluated through the numerical inversion of Laplace transform. Numerical results are displayed graphically based on graphite fiber reinforced epoxy composite, and detailed comparisons are made to investigate the effects of thermal lags, viscoelastic properties, and fiber volume fractions on the thermoviscoelastic responses.

Fracture Analysis of Griffith Interface Crack in Fine-Grained Piezoelectric Coating/Substrate under Thermal Loading

Coating often plays a role in monitoring and protecting substrates in engineering applications. Interface cracks between the coating and the substrate can lead to crack growth under the action of external loading and will cause device failure. In this paper, the behavior of a fine-grained piezoelectric coating/substrate with a Griffith interface crack under steady-state thermal loading is studied. The temperature field, displacement field, and electric field of the coupling of thermal and electromechanical problems are constructed via integral transformation and the principle of superposition. Thus, problems are transformed into a system of singular integral equations, and the expressions of thermal intensity factor, thermal stress intensity factor, and electric displacement intensity factor are obtained. We used a numerical calculation and a system of singular equations to obtain the relationship of strength factor with material parameters, coating thickness, and crack size.

Effect of Temperature on the Mechanical Properties of Carbon Composites

The purpose of this research is to investigate and analyze the effect of temperature on the mechanical properties of carbon composites, aluminum foam, and carbon nanotube reinforced aluminum foam. For this analysis, fatigue behavior of aluminum foam has been discussed, and interlaminar shear stress between single-walled carbon nanotube reinforced aluminum foam and multiwalled carbon nanotube reinforced aluminum foam has been compared. The comparison has shown that the interlaminar shear stress within the interface of single-walled carbon nanotube and aluminum foam is higher than that within the interface of multiwalled carbon nanotube and aluminum foam. Hence, the probability of stress concentration and crack initiation within the interface of single-walled carbon nanotube and aluminum foam is higher than that within the interface of multiwalled carbon nanotube and aluminum foam. Furthermore, thermal fatigue lives of different single-walled carbon nanotube reinforced matrix nanocomposites have been evaluated. Additionally, interaction between carbon and molten aluminum has been analyzed. Finally, a new relation for the thermal interlaminar shear stress intensity factor to predict the crack initiation sites on fiber/matrix interface has been introduced.

Annular crack in a thermoelastic half-space

The purpose of this article is to analytically investigate the three-dimensional thermoelastic fields in a semi-infinite medium weakened by an annular crack. The crack faces are exposed to a prescribed temperature load and the external surface of the medium is kept at the reference temperature. The problem is formulated as a three-part mixed boundary value problem and is treated through Goodier’s thermoelastic potential and the Boussinesq harmonic functions. The Hankel transform method is employed to convert this problem into triple integral equations and a system of coupled ones. Using some integral relations and the Gegenbauer addition formula, the set of triple integral equations is ultimately reduced to an infinite system of linear algebraic equations. Closed-form formulas for various quantities of physical interest are derived and expressed in terms of the solution of the obtained infinite algebraic system. Moreover, the combined mechanical and thermal loading conditions are also considered. Numerical results for thermoelastic fields and mixed-mode thermal stress intensity factors are shown graphically to analyze their dependence on the radii and depth of the crack. Results for the thermoelastic problem of an infinite medium containing an annular crack are also obtained as a special case of this study.

Crack initiation and propagation mechanism of Al2O3-DBC substrate during thermal cycling test

For high power density modules, improving the reliability and the fatigue lifetime is a real challenge. The direct bonding copper (DBC) substrate is really critical for a suitable and reliable packaging integration, conduct detailed thermo-mechanical analysis and failure mechanism study causes for concern. In this paper, we thoroughly study the failure process of Al2O3-DBC substrate during thermal cycling from −55 °C to 150 °C by experimental, theoretical and finite element numerical methods. The failure phenomenon of DBC substrates were observed by scanning acoustic microscopic. The cross-section sample was tested by microscope and scanning electron microscope to further determine the crack initiation and propagation process and mechanism. It can be found that the crack deviated from original crack direction with a certain angle and propagated into ceramic. After a certain length of crack growth, the crack propagated along the direction parallel to interface and finally caused substrate completely broke. Based on experimental results, we established failure mode of DBC substrate during thermal cycling test, applied interface stress intensity factor K to build interface crack propagation and deflection criterion of DBC substrate, and calculated the interface thermal stress intensity factor for DBC substrate by both theoretical and numerical methods. The analyzed results agreed well with the experimental observations.