Theoretical predictions on temperature-dependent strength for MAX phases

MAX phases have great application potential in high-temperature fields due to their unique combination of ceramic and metallic properties. In this work, a physics-based theoretical model is developed for the prediction of temperature-dependent strength of MAX phases, based on the force-heat equivalence energy principle. The quantitative relationship between the strength, Young's modulus, temperature, and melting point is revealed by the proposed model. Through the comparison between theoretical predictions of strength and available experimental results from the literature, the model is proved to be efficient in predicting the strength of MAX phases at high temperatures. Since the melting point and Young's modulus of material can be easily obtained, the proposed theoretical model provides a convenient and feasible method for predicting the temperature-dependent strength of MAX phases.     

Temperature dependent first matrix cracking stress model for the unidirectional fiber reinforced ceramic composites

Based on a kind of equivalence between heat energy and fracture energy, assuming that there is a constant maximum storage of energy that includes both heat energy and fracture energy, a new temperature dependent fracture surface energy model is developed. Using the new model and the classical ACK theory, a temperature dependent first matrix cracking stress model is obtained for the fiber reinforced ceramic composites. According to the model, the temperature dependent first matrix cracking stress of materials can be easily predicted using some basic material parameters such as matrix fracture surface energy and Young’s modulus. The model is verified by comparison with experimental data of SiC fiber reinforced reaction-bonded Si₃N₄ composites at different temperatures. Good agreement is obtained between predicted and experimental data of first matrix cracking stress. The dependency of first matrix cracking stress on fracture surface energy and interfacial shear strength is systematically analyzed.     

Temperature-dependent fracture strength of whisker-reinforced ceramic composites: Modeling and factor analysis

In this study, a temperature-dependent fracture strength model for whisker-reinforced ceramic composites was developed. This model considers the strength degradation of both whisker and ceramic matrix at elevated temperatures, as well as the evolution of residual thermal stress with temperature. It was verified by comparison with the available flexural strengths of five types of whisker-reinforced ceramic composites at different temperatures, and good agreement between the model predictions and the experimental data is obtained. Moreover, based on the established model, we systematically analyzed the effects of six influencing factors, including the volume fraction and the aspect ratio of whisker, the Young's modulus of matrix and whisker, the thermal expansion coefficient difference and the stress-free temperature, on the temperature-dependent flexural strengths of whisker-reinforced ceramic composites. Some new insights which could help optimize and improve the temperature-dependent fracture strength of whisker-reinforced ceramic composites are obtained.     

Temperature dependence of Young’s modulus and damping of partially sintered and dense zirconia ceramics

Young’s modulus and damping of partially sintered and almost fully dense zirconia ceramics (tetragonal zirconia polycrystals with 3 mol.% yttria), obtained by firing to different temperatures (range 1000–1400°C), have been determined via impulse excitation, and the evolution of Young’s modulus and damping of partially sintered zirconia with temperature has been monitored from room temperature to 1400°C and back to room temperature. The room-temperature Young’s modulus of the partially sintered materials obeys the Pabst-Gregorová exponential prediction, which is relatively unusual for partially sintered materials. With increasing temperature Young’s modulus decreases, until the original firing temperature is exceeded and sintering (densification) continues, resulting in a steep Young’s modulus increase. During heating and cooling the temperature dependence obeys a master curve with a typical inflection point at approximately 200 °C, the temperature where damping (internal friction) exhibits a maximum. The reasons for this characteristic behavior of doped zirconia are recalled.     

The temperature‐dependent surface energy of ceramic single crystals

Knowledge of the surface energy of ceramic single crystals at elevated temperatures is of fundamental importance. However, it is very hard to obtain this quantity from the existing experiments, simulations, and theories. In the present work, following the Orowan‐Polanyi and Gilman models’ principles, two theoretical models for the temperature‐dependent surface energy of the ceramic single crystals are proposed based on the authors’ previous studies on the temperature‐dependent ideal tensile strength of solids. Thus established models relate the temperature dependence of the surface energy to these of the specific heat at constant pressure, Young's modulus, and coefficient of the linear thermal expansion. The temperature‐dependent surface energies of α‐Al₂O₃ and β‐Si₃N₄ are calculated and agree well with the experimental data. The study shows that the surface energy firstly remains approximately constant and then decreases linearly as temperature increases from 0 K to melting point. However, it has stronger temperature dependence than Young's modulus, that is, surface energy decreases more rapidly with increasing temperature.     

Theoretical prediction of temperature-dependent fracture strength for ultra-high temperature ceramic composites considering the evolution of damage and thermal residual stress

Based on the maximum storage energy density criterion of material fracture, a model of temperature-dependent fracture strength for ultra-high temperature ceramic composites is established. The combined impacts of the evolution of damage and thermal residual stress with temperature are considered. The model predictions are highly consistent with available experimental values. Besides, the critical crack sizes of ZrB₂–30 vol%SiC in air from 1400 to 1600 °C are predicted using the proposed model, which agree well with the total oxidation thickness of the reported literature at 1400 and 1500 °C, and a more reasonable definition of critical crack size at 1600 °C are given. Moreover, the quantitative effect of crack size on the fracture strength is analyzed under different environment temperature, and a useful conclusion is obtained that decreasing crack size is more effective to improve the fracture strength of the composites at low temperatures. This study not only provides a feasible and convenient method to predict the fracture strengths at different temperatures, but also offers a theoretical support for the design of ultra-high temperature ceramic composites.     

Modeling the effect of temperature on first matrix cracking stress and fracture strength of cross-ply fiber reinforced ceramic-matrix composites

In this work, we proposed a temperature-dependent first matrix cracking stress model for cross-ply fiber reinforced ceramic-matrix composites (FRCMCs) first. It takes into account of the effects of interfacial shear stress and residual thermal stress as well as their evolution with temperature. Moreover, in order to characterize the effect of temperature on fracture strength, we defined the critical strain energy density associated with composites fracture, by which and the force-heat equivalence energy density principle, the temperature-dependent fracture strength model for cross-ply FRCMCs was established. The models’ predictions of first matrix cracking stress and fracture strength at different temperatures are in good agreement with experimental results available. This study not only advances our in-depth understanding of the quantitative relationship between temperature and mechanical properties of cross-ply FRCMCs, but also offers a powerful tool to predict the temperature-dependent first matrix cracking stress and fracture strength.     

Young’s modulus evolution during heating,re-sintering and cooling of partially sintered alumina ceramics

The Young modulus of partially and fully sintered alumina ceramics, obtained by firing to different temperatures (range 1200–1600°C), has been determined via impulse excitation, and the evolution of Young’s modulus of partially sintered alumina with temperature has been monitored from room temperature to 1600°C. As expected, the room-temperature Young modulus of the partially sintered materials is lower than all theoretical predictions. With increasing temperature Young’s modulus decreases, until the original firing temperature is exceeded and sintering (densification) continues, resulting in a steep Young’s modulus increase. During heating and cooling the temperature dependence obeys a master curve for alumina, unless the temperature of the original firing is excessively low.     

Temperature dependent fracture toughness model for whisker-reinforced ceramic matrix composites

A temperature dependent fracture toughness model for whisker-reinforced ceramic matrix composites was developed in this study, which considers the effects of matrix fracture toughness, residual thermal stress, crack bridging, crack deflection, and their temperature dependence. Its predicted results were compared with the fracture toughness of six types of whisker-reinforced ceramic matrix composites at different temperatures, and good agreement between predicted results and experimental results is obtained. Furthermore, based on this model, we systematically analyzed the effects of the volume fraction and aspect ratio of whisker, Young's modulus of matrix and whisker, thermal expansion coefficient difference, stress-free temperature, the ratio between the fracture energy of matrix and that of interface, on their temperature dependent fracture toughness for the first time. Finally, insights and suggestions which could help to optimize and improve the composite fracture toughness at different temperatures are provided.     

Analytical model for strength of MAX phases considering high-temperature oxidation and plastic deformation

As a promising high-temperature material, MAX phases have attracted much attention owing to their combined merits of metals and ceramics. In this study, a temperature-dependent analytical model for prediction of the strength of MAX phases considering high-temperature oxidation and plastic deformation was proposed. A relationship among the strength, Young's modulus, strain-hardening exponent, crack size, and temperature was established. The accuracy of the model was verified by a comparison between the model predictions and available experimental data. The proposed analytical model can provide a straightforward and effective way to predict the strength of MAX phases over a wide range of temperatures. Moreover, the quantitative effects of oxidation time, strain-hardening exponent, and Young's modulus on the strength, as well as their evolution with temperature, were analyzed. The findings of this study would be useful for the high-temperature strength prediction and design of MAX phase materials.     

On temperature-dependent interfacial fracture energy/stress intensity factor and matrix cracking in ceramic composites

The first matrix cracking stress is a crucial indicator to appraise the mechanical properties of ceramic-matrix composites, which is the starting point of permanent damage. Based on the classic energy balance method and stress intensity method, two temperature-dependent first matrix cracking stress models of fiber-reinforced ceramic matrix composites are established, respectively. The model established by the energy balance method considers the evolution of interfacial fracture energy with temperature, and the model established by the stress intensity method takes into account the evolution of stress intensity factor with temperature. The predictions of the above models in a wide temperature range are verified using experimental data available in the literature, which shows the rationality and accuracy of the above models. Moreover, on the basis of the energy balance method model, the main factors controlling the first matrix cracking stress at different temperatures are analyzed by the numbers. Finally, in view of the analysis results, some suggestions on how to optimize and enhance the first matrix cracking stress at different temperatures are put forward.     

High temperature stiffening of ferroelastic LaCoO3

The cyclic ferroelastic hysteretic behavior of pure LaCoO₃ perovskite ceramic has been studied at different temperatures in four point bending. The stress-strain deformation behavior of LaCoO₃ was analyzed both in the term of the maximum stress in the cycle and in terms of the temperature used when the cyclic testing was performed. The characteristics of the stress-strain hysteresis loops, such as hysteresis loop area and irreversible strain, as well as effective Young’s modulus, were analyzed, and it was established that both the loading and the temperature history have a significant influence on the mechanical behavior of LaCoO₃. Young’s modulus values are reported to be much higher in the 700–900 °C temperature range as compared to the measurements performed in the RT-400 °C temperature range.     

Thermomechanical properties of Y-substituted SrTiO3 used as re-oxidation stable anode substrate material

Re-oxidation robustness is important to warrant a reliable operation of anode-supported solid oxide fuel cell systems. The current work concentrates on the mechanical properties of re-oxidation stable Y-substituted SrTiO₃ ceramic for the use as anode substrate material. Room temperature micro-indentation yielded Young's modulus and hardness of 160 and 7 GPa, respectively, whereas the temperature-dependent modulus was measured with a resonance-based method up to ∼950 °C. The effective Young's modulus as a function of porosity was measured at room temperature and compared with fracture strength data. The fracture toughness was assessed using a combination of pre-indentation cracks and bending test. Creep rates were measured at 800 and 900 °C in a 3-point bending configuration. Post-test fractographic analysis performed using stereo, confocal and scanning electron microscopy, revealed important information on fracture origins and critical defects in the material. A methodology to assess the mechanical properties of porous materials is suggested.     

Mechanical properties of solid oxide fuel cell glass-ceramic sealants in the system BaO/SrO-MgO-B2O3-SiO2

Planar solid oxide fuel cells (p-SOFCs) require materials that can satisfy the high mechanical demands related to their utilization in stationary and, especially, in mobile applications. Two suitable glass-ceramic sealants based on the system BaO/SrO-MgO-B₂O₃-SiO₂ have been characterized with respect to their mechanical properties such as hardness, Young’s modulus, flexural strength at room and elevated temperature, fracture toughness as well as creep behavior at relevant operation temperatures (800 °C). Fracture toughness was calculated from crack opening displacements (COD) and the results were compared with fracture toughness measured by bending tests of notched bar samples. The mechanical behavior has been discussed regarding different thermal aging times of the glass-ceramics and their microstructural evolution. The glass-ceramics containing SrO revealed a better mechanical behavior than glass-ceramics with BaO. In particular, several superior properties were found in comparison to previously reported materials for this application.     

Ultra-high-temperature mechanical behaviors of two-dimensional carbon fiber reinforced silicon carbide composites: Experiment and modeling

Carbon fiber reinforced silicon carbide (C/SiC) composites are enabling materials for components working in ultra-high-temperature extreme environments. However, their mechanical properties reported in the literature are mainly limited to room and moderate temperatures. In this work, an ultra-high-temperature testing method for the mechanical properties of materials in inert atmosphere is presented based on the induction heating technology. The flexural properties of a 2D plain-weave C/SiC are studied up to 2600 °C in inert atmosphere for the first time. The deformation characteristics and failure mechanisms at elevated temperatures are gained. Theoretical models for the high-temperature Young’s modulus and tensile strength of 2D ceramic matrix composites are then developed based on the mechanical mechanisms revealed in the experiments. The factors contributing to the mechanical behaviors of C/SiC at elevated temperatures are thus characterized quantitatively. The results provide significant understanding of the mechanical behaviors of C/SiC under ultra-high-temperature extreme environment conditions.     

Microstructure and mechanical properties of an alumina–glass low temperature co-fired ceramic

The microstructure and mechanical properties of an alumina–glass low temperature co-fired ceramic (LTCC) have been investigated. The microstructure was studied by using optical microscope, scanning electron microscope, energy spectrum analysis and X-ray diffraction. The Young's modulus, hardness, flexure strength and fracture toughness were measured by three-point bending, indentation and nanoindentation tests. The LTCC can be regarded as a particle-reinforced composite with macroscopically isotropic properties: particles mainly composed of synthetic corundum and matrix mainly of corundum and silica. The particles with irregular shape and an average radius of 0.71 μm are homogeneously dispersed in the matrix. The properties of the individual particle and matrix were successfully measured and further used to obtain the effective properties of the composite by micromechanics methods. The existence of rigid particles improves not only the modulus, hardness and strength but also the fracture toughness of LTCC materials.     

Mechanical and optical property assessment of irradiated SiC with displaced atoms

Explicit method to emulate neutron radiation effects on key ceramic materials is lacking, with most literatures stressing direct comparison between radiation parameters while underestimating the defect-property correlation. Herein, the evolutionary correlation between defects of displaced atoms and properties in 6H-SiC was systematically investigated, aiming to found the basis for performance assessment of neutron irradiated material. The point defect accumulation, defect cluster growth, and homogeneous crystalline-amorphous (c-a) transition were recognized, with different stages of Young’s modulus reduction and optical absorption enhancement accordingly triggered. Specifically, the relaxation process accompanying the c-a transition was believed to induce the final reduction stage of Young’s modulus and account for the conflict between existing research results. Average lattice disorder, regarded as the average density of displaced atoms, was proved to be the success reference in the property assessment approach, paving the way for the extension into high temperature radiation where more defect types coexist.     

Temperature Effect on the Mechanical Properties of Electrospun PU Nanofibers

Polyurethane (PU) nanofibers were prepared from electrospun method. Atomic force microscopy (AFM) was employed to characterize the mechanical properties of electrospun PU nanofibers. The impact of temperature on the mechanical behavior of PU nanofibers was studied using three-point bending test based on AFM. A Young’s modulus of ~?25?GPa was obtained for PU nanofibers with diameter at ~?150?nm at room temperature. With decrease in nanofiber’s diameter, the increasing Young’s modulus can be due to the surface tension effect. The Young’s modulus of the PU nanofiber decreased linearly while the fibrous morphology was maintained with the increase of temperature.     

The effect of concentration of graphene nanoplatelets on mechanical and electrical properties of reduced graphene oxide papers

Macroscopic, freestanding graphene-based paper-like materials are of interest for use as mechanically strong, stiff, and flexible and electrically conductive materials. Chemically reduced graphene oxide paper shows promise for such applications. In this work, we studied the mechanical and electrical properties of a set of paper materials prepared by filtration of homogeneous colloidal suspensions of hydrazine-reduced graphene oxide with different concentrations. Young’s modulus, fracture strength, and fracture strain of each type of sample was determined by tensile tests. The paper sample prepared from the colloidal suspension with the lowest concentration of reduced graphene oxide platelets had the highest modulus and fracture strength and showed the smoothest surface morphology. The electrical conductivity measured by the four-probe measurement method increased as the concentration was increased.     

Numerical prediction of elastic properties for alumina green parts printed by stereolithography process

Stereolithography is a process based on the photopolymerization of a UV-reactive system consisting of ceramic particles dispersion in a curable resin. A key issue of this process is the control of the rigidity of green parts, which are strongly related to UV light exposure. This work is focused on the numerical prediction of green part stiffness according to stereolithography manufacturing parameters. A first macroscopic approach, based on the modelling of ceramic suspension polymerization, makes it possible to establish a relationship between the exposure and the Young's modulus. A second microscopic approach, using a periodic homogenization technique based on the strain energy, is applied to a 2D finite element model to evaluate the effective elastic properties. Numerical results show that macroscopic model is able to provide a Young’s modulus with a good level of accuracy. The modelling results from the microscopic model demonstrate an acceptable convergence with the experimental Young’s modulus.