Thermal Shock Fracture Research Articles

Phase-field modeling of thermal shock fracture in functionally graded materials

In this paper, the thermo-elastic fracture problems of functionally graded materials (FGMs) are thoroughly investigated based on a modified phase field model. In this model, the material constants and fracture toughness vary along a specified direction, the thermal conductivity and stiffness constants in the damaged regions are degraded by the phase-field variable, and the crack evolution is driven by the variation of elastic energy induced by the thermo-mechanical loading. Therefore, the temperature, mechanical and damage fields are coupled with each other. The validation of the present approach has been checked by comparing the present results with the analytical, numerical, and experimental results in literature. The examples of thermo-elastic tensile fracture and thermal shock cracking of FGMs are performed to investigate the influence of material heterogeneity and external thermal loading. Furthermore, the experimental phenomenon of crack deflection in FGMs has been captured by the present simulations. The present study provides a guidance for understanding the fracture mechanism, material design and safety assessment of FGM structures in engineering practice.

Mechanisms and experimental study of directional thermal shock fracture of granite under bidirectional horizontal loading

The study of the mechanism of thermal shock directional fracture of rocks under bidirectional horizontal stress is important for the application of directional thermal shock fracture technology. With the engineering background of the thick igneous roof overlying the coal seam, we conducted high temperature thermal shock directional fracture tests on granite under different horizontal loads to investigate the fracture mechanism. The results show that during the directional thermal shock of granite, the heating rate of borehole surrounding rock experienced three stages of rapid increase, rapid decrease and slowly decrease. AE tests were used to characterize the typical features of rocks during thermal shock fracture: the appearance of macrocracks in the specimen was accompanied by sharp increases in the cumulative AE count and the sudden drops in b-value. The experimental results show that thermal shock can create macroscopic directional fractures within the rock. Within a certain range of horizontal stress difference, the expansion direction of thermal shock cracks could be released locally from geological stress control, i.e. expanding along the direction of the minimum horizontal dominant stress. This provides completely new thinking for the cutting of hard roof and the directional fracturing of rock. In addition, directional thermal shock caused modifications in the distribution of stress in borehole surrounding rocks. We have established a model for stress distribution around the borehole rock and given the calculation formula for the initiation stress of the rock. The studies provide significant theoretical guidance for the industrial application of directional thermal shock fracturing technology.

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.

Thermal Shock Fracture of Functionally Graded Materials Based on the Phase-Field Fracture Method

Thermal Shock Fracture of Functionally Graded Materials Based on the Phase-Field Fracture Method

Thermal shock fracture of honeycomb-based porous thermoelectric materials with non-Fourier heat conduction

Compared with dense thermoelectric materials (TEMs), the auxetic honeycomb porous TEMs can enhance mechanical performance and energy conversion efficiency. The Fourier heat conduction law becomes unavailable due to the thermal wave speed in the porous TEMs is limited. Considering the non-Fourier law, this paper analyzes the thermal shock fracture characteristics of the porous TEMs bonded to an elastic substrate. A theoretical model for the effects of non-Fourier heat conduction, thickness of TME, shape and dimensions of honeycomb cell on strength failure and fracture failure is proposed. The analysis demonstrates that the maximum thermal stresses in the porous TEMs are underestimated without considering the non-Fourier heat conduction. The stress level in the auxetic honeycomb-based TEMs is much smaller than that in the traditional honeycomb TEMs with the positive Poisson's ratio architecture. It is found that a thicker TEM, a bigger relative density and a larger length ratio of the horizontal to the inclined strut can result in a smaller thermal stress. Based on the strength and fracture criterions, the envelope of safety angle between the horizontal and the inclined strut is identified. The simplified expressions of the safety angle envelope versus the applied thermal load are given.

Memory effects on the thermal fracture behavior of cracked plates via fractional heat conduction models

Studies have shown that fractional derivatives have important memory effect on the thermal shock fracture of structures. In the present work, four generalized fractional models are applied to investigate the thermal fracture problem of cracked plates. Laplace transform and finite sine transform are employed to obtain transient temperature and thermal stresses. Stress intensity factors around the crack tips are evaluated through the weight function method for edge and center cracks. Numerical results show that memory effects on the thermoelastic fields are different with different fractional derivative definition and fractional orders, and the effects will vary accordingly with crack geometry parameters.

A peridynamic model for coupled thermo-mechanical-oxygenic analysis of C/C composites with SiC coating

The oxidation induced by coating cracking is a general failure mode of high-temperature composites such as C/C and C/SiC. However, this failure mode has not been fully investigated due to the lack of a method suitable for both crack simulation and oxidation interface capture. In this paper, a coupled thermo-mechanical-oxygenic peridynamic model is proposed for SiC-coated C/C composites in an oxidizing environment. The ordinary state-based peridynamics is extended to plane strain thermoelastic problems for orthotropic media to calculate the crack distribution. Cracks in the coating are modeled as oxygen diffusion channels and the peridynamic oxidation equation is developed to simulate the oxidation of the C/C substrate. Furthermore, the peridynamic non-Fourier heat transfer equation is employed to consider the finite thermal propagation speed and the model is validated by experimental results. Numerical examples are presented to investigate the oxidation failure after thermal shock, non-Fourier thermal shock fracture, and stress oxidation failure of SiC-coated C/C composites.

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.

Numerical Analysis of Thermal Shock Cracking Behaviors of Ceramics Based on the Force-Heat Equivalence Energy Density Principle

Thermal shock is one of the main causes for the fracture of ceramic materials due to their inherent brittleness. Aiming to explore the mechanism of thermal shock cracking behavior of ceramics under different thermal shock conditions, a novel temperature-dependent failure criterion of thermal shock fracture of the ceramic materials was deduced based on the force-heat equivalence energy density principle. Combining this failure criterion and the finite element method, the thermal shock cracking behaviors of the thin circular and rectangular ceramic slabs under different thermal shock initial temperature were simulated. Results show that the morphology, periodicity, hierarchy, and number of thermal shock cracks obtained by numerical simulation are in good agreement with the experimental results. These essential characteristics verify the validity of the temperature-dependent failure criterion for thermal shock fracture. Furthermore, the strain energy of tension produced by thermal shock is proved to be the dominated mechanism for thermal shock-induced fracture.

Thermal shock damage assessment of a BNW/SiO2 ceramic: Insight from temperature-dependent material properties

The high-temperature service performance of nearly fully dense 20 wt% BNW/SiO2 ceramic was systematically investigated. The oxidation damage and strength degradation of the whiskers combined with the surface microstructures of the samples predominantly influence the flexural strength from RT to 1000 °C. In previous work, the temperature dependence of the material properties is invariably ignored when evaluating thermal stress crack initiation and propagation behaviour. In this work, modified thermal shock models that include temperature-dependent material properties were established based on thermal-shock fracture (TSF) theory and thermal-shock damage (TSD) theory. Then, the thermal shock resistance (TSR) of the BNW/SiO2 ceramic was evaluated by preforming a water quenching test. The modified models could better explain the TSR behaviour of the ceramic, indicating that considering the temperature-dependent material properties will reveal the thermal shock damage mechanism more precisely.

Size effect on heat conduction and associate thermal fracture behavior of thin ceramic plates

Thermal barrier materials used in gas-turbine engines and aerospace vehicles have to resist large thermal gradients or high heat fluxes. The existence of high temperature gradient results in nonlocal effect of heat conduction, especially in very small time and space scale, the size effect of heat conduction is significant. In this work, a nonlocal dual-phase-lag heat conduction model is adopted to analyze the thermal shock fracture problem of thin cracked plates under sudden thermal shock. By using Laplace transform and inverse transform, the temperature field and the thermal stress field are obtained first. Then through the principle of superposition, the formulation results in a mode I crack problem. In the numerical part, the effects of different heat conduction models, thermal nonlocal parameters, and crack geometry parameters on the transient responses are discussed. By comparison analysis, the results show that taking the size effect into account is crucial in the assessment of thermal shock fracture of ceramic plates at micro/nano scale. The stress intensity factor first increases and then decreases with the increase of crack geometry parameters, indicating that the cracked plate exhibits crack growth resistance behaviour.

EFFECT OF PORE COMPOSITION ON THERMAL SHOCK RESISTANCE OF POROUS CERAMICS

Porous alumina ceramics with different pore composition (intrinsic pores and extrinsic pores) were prepared by gel injection molding process combined with pore forming technology and effects of intergranular pores and extrinsic pores on thermal shock fracture resistance and thermal shock damage resistance were studied. The results show that, when the solid phase content or total porosity is the same, the porous ceramic material with extrinsic pores has higher damage tolerance, thermal shock critical temperature difference (ΔTc) and residual strength retention rate. A ratio parameter (KIC/E) for evaluating the thermal shock stability of materials is deduction. The larger the ratio is, the better the thermal shock resistance of materials.

Thermal Shock Behavior of a Soda Lime Glass Treated by Ion Exchange

In this work, we have submitted a soda lime glass to thermochemical treatment by ion exchange in order to introduce compressive stresses in their surface. Subsequently, we studied the hot-cold thermal shock resistance of ion-exchange reinforced glass. A potassium ion from the molten salt bath replaces the sodium ion of the glass surface by a superficial diffusion process. We have determined the potassium diffusion profile by two techniques: X-ray fluorescence spectroscopy XRF and X-rays microanalysis coupled with Scattering Electronic Microscopy. In addition, for the same purpose, we used X-ray fluorescence spectroscopy. Then, we determined by micro-indentation the profile of the compressive stresses induced in the glass surface by the exchange of Na+ ions by larger ones of K+. The compressive stress profile induced by chemical tempering depends on potassium ion concentration. It reaches a maximum value of 988 MPa for a treatment done during 50 hours at 480°C. We have subjected the glass specimens treated by ion exchange to a hot-cold thermal shock technique; we realized the cooling by air jet at room temperature. The heat transfer coefficient was about 600 W/m2 °C (Biot number β = 0.3). We have determined the residual strengths of the ion exchange treated and thermal shocked specimens by a three-point bending test. The strength is improved; it passes from 90 MPa of the as received glass to 380 MPa for the chemically treated glass. We noticed that the critical temperature difference ΔTc, which caused the thermal shock fracture, depends on the glass samples states. Consequently, because of the thermochemical treatment, ΔTc has shifted to higher temperatures. Its value was 254°C for raw glass and reached 455°C for the case of reinforced glass by ion exchange at 480°C during 50 hours. The thermochemical ion exchange treatment improve the glass thermal shock resistance.

Thermal shock fracture associated with a unified fractional heat conduction

Recently, a unified fractional heat conduction model is newly proposed, which is a further improvement of the fractional thermoelasticity theory. It would be interesting to know how the newly developed fractional derivative definitions affects the thermal fracture behavior when some defects such as cracks exist in the medium. This work is aimed at analyzing the thermal fracture problem of an elastic half-space and strip with an insulated Griffith crack based on the unified fractional heat conduction model. Fourier and Laplace transforms are employed to solve the mixed boundary problem associated with a time-fractional partial differential equation. Temperature and stress intensity factors are evaluated by solving a system of singular integral equations. Effects of different fractional derivatives and different parameters on the thermoelastic fields are analyzed. A comparison of the temperature and stress intensity factors between the present model and the Fourier model is made. Numerical results show that different fractional definitions have different memory effects on the transient responses, and the effects of fractional definitions on the responses will vary accordingly with the parameter values.

Simulation of the thermal shock cracking behaviors of ceramics under water quenching for 3-dimension conditions

To overcome the limitations of widely used criteria, maximum principal stress and maximum tension stress, in simulating and evaluating thermal shock resistance of ceramics for 3-dimension (3D) problems, a temperature-dependent critical fracture energy density criterion was proposed based on the force-heat equivalence energy density principle for the 3D thermal shock fracture problems of ceramic materials in this paper. Taking advantage of the criterion and finite element method, the thermal shock behavior of water quenching of cuboid Al2O3 specimens with different temperature differences were simulated. The crack patterns of the simulation results were shown to be approximated in the experiments. Especially the essential features, the longitudinal main crack and crack branches, are embodied well in the simulation results. However, the thermal shock cracks obtained by using the criteria, maximum principal stress and maximum tension stress, failed to meet the experiments. The effects of water entry posture on thermal shock crack features revealed in the results confirm the efficiency of the criterion in 3D conditions of thermal shock fracture in this paper. Finally, the maximum temperature gradient, not maximum temperature difference, was found to be the main controlling factor which caused the fracture energy density to reach a critical value to produce thermal shock crack.

Fracture Considerations for the Thermal Shock Resistance of Porous Ceramic Materials

The influence factors of thermal shock resistance of porous ceramic materials are analysed from the point of stress criterion and energy criterion. Results show that material properties, relative density and initial crack have important effects to thermal shock fracture of porous ceramic materials. In energy criterion, the total elastic energy is given. The driving force for crack propagation is provided by the elastic energy stored at fracture. When the elastic energy stored in porous ceramic materials is larger than the fracture energy, the crack will propagate. The relationship between crack length and initial crack length is given. In addition, the reason why the thermal shock resistance of porous ceramic materials is larger than dense ceramics is explained.

Effects of microstructures of foam core on the thermal shock strength of ceramic foam sandwich structures

The effects of microstructures of foam core on the thermal shock strength of the sandwich slabs are investigated by macro-micro analysis. Each slab has two ceramic matrix composite (CMC) face sheets and an open-cell ceramic foam core. Asymmetric thermal shock fracture is evaluated at the macro continuum level. The position of the danger zone varying with the thickness of face sheets is determined. The finite element (FE) model based on the 3D Voronoi tessellations consists of a local micro-scale region surrounding the crack tip. For a calculated stress intensity factor in the macro model, the displacements along the boundary of the local model are calculated based on linear elastic fracture mechanics. The thermal shock strength of the sandwich structure is found to be dominated by the cell regularity, the cross-sectional shape of the cell struts and the relative density of foam core. The physical mechanisms responsible for those results are identified. The effective methods to improve the thermal shock resistance of the sandwich structures with ceramic foam core are proposed.

Effects of Microstructures of Foam Core on the Thermal Shock Strength of Ceramic Foam Sandwich Structures

The effects of microstructures of foam core on the thermal shock strength of the sandwich slabs are investigated by macro-micro analysis. Each slab has two ceramic matrix composite (CMC) face sheets and an open-cell ceramic foam core. Asymmetric thermal shock fracture is evaluated at the macro continuum level. The position of the danger zone varying with the thickness of face sheets is determined. The finite element (FE) model based on 3D Voronoi tessellations consists of a local micro-scale region surrounding the crack tip. For a calculated stress intensity factor in macro model, the displacements along the boundary of the local model are calculated based on linear elastic fracture mechanics. The thermal shock strength of the sandwich structure is found to be dominated by the cell regularity, the cross-sectional shape of the cell struts and the relative density of foam core. The physical mechanisms responsible for those results are identified. The effective methods to improve the thermal shock resistance of the sandwich structures with ceramic foam core are proposed.

Thermal shock fracture of a crack in a functionally gradient half-space based on the memory-dependent heat conduction model

In the present study, we consider a thermoelastic half-space made of a functionally gradient material with an insulated crack, which is subjected to a thermal impact. The memory-dependent heat conduction model is adopted for analysis. By using the Fourier and Laplace transforms, the thermoelastic problem is formulated in terms of singular integral equations which can be solved numerically. Effects of the time delay, kernel function, and nonhomogeneity parameters on the temperature and stress intensity factor are analyzed. Our results are also compared with those based on the Fourier and CV heat conduction models, which can be viewed as two special cases of the present model. In conclusion, the memory-dependent derivative and nonhomogeneity parameters play an essential role in controlling the heat transfer process.

Thermal shock resistance of sodalime glass eroded by sandblasting

This is a study of the effect of sandblasting of glass on its thermal shock resistance. A soda-lime flat glass was first eroded on both faces by sandblasting. The mass of the projected sand was the only varying experimental parameter considered. Other usual parameters such as the angle of particle impact, the speed, and the sand grain size were kept constant. The particle’s impacts on the glass surface generated various superficial defects (microcracks, craters, and scaling) that scatter the incident light and reduce the optical transmission and mechanical strength. The obtained eroded specimens were then submitted to thermal shock. The critical temperature differences causing their fracture were determined. The effect of the presence of superficial artificial defects introduced by sandblasting on the glass thermal shock resistance is discussed. The results showed that the most damaged glass specimens are the least resistant to thermal shock. The surface critical defects created by sandblasting are the initiators of the critical thermal shock fracture. The transient thermal stresses propagate instantly these defects.