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Elastic modulus plays a key role in the application of porous metallic materials. However, to the best of our knowledge, few attempts have been made to model the simultaneous dependence of elastic modulus on temperature and porosity for metallic materials. The present article contributes to a rational temperature-porosity-dependent elastic modulus model for metallic materials with all parameters having definite physical significance. The model can well predict the elastic moduli of porous metallic materials, from extremely low temperature to ultrahigh temperature, and from dense material to about 0.9 porosity, with reference to an easy-to-access elastic modulus. In a special case, when intrinsic elastic modulus [M] = 2 and critical porosity P C = 1, a phenomenological parameter-free predictive model can be obtained. The model can be applied when the matrix Poisson ratio is 0.1 < v < 0.4 for Young’s modulus and 0.17 < v < 0.27 for shear modulus, which covers most metallic porous materials.

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. [ABSTRACT FROM AUTHOR]

In this study, we report a theoretical model for the temperature and size dependent surface energy of metallic nanomaterials. The model is verified by making a comparison with the available simulation and experimental data. Reasonable agreement has been observed between these results. This study reveals that the decrease of surface energy at high temperatures is caused by cohesive energy weakening and bond expansion. With the same nanomaterial size, the sequence of size effects on the surface energy from weak to strong is thin films, nanowires, and nanoparticles. In particular, this work can provide a theoretical basis for the prediction of size dependent surface energy of metallic nanomaterials at different temperatures, which can help in the understanding of the mechanical and thermodynamic properties of metal surfaces. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a temperature‐dependent model for predicting the tensile strength of 2D woven fiber reinforced ceramic matrix composites. The model takes into account the combined effects of temperature, temperature‐dependent residual thermal stress, temperature‐dependent matrix strength, and fibers strength on the tensile strength of composites. To verify the model, the tensile strengths of 2D woven fiber reinforced ceramic matrix composites available are predicted at different temperatures. The model predictions agree well with the experimental data. This work could provide a practical technical means for predicting the temperature‐dependent tensile strength of 2D woven fiber reinforced ceramic matrix composites and uncovering the dominated mechanisms leading to the change of tensile strength and their evolution with temperature. [ABSTRACT FROM AUTHOR]

Based on a limited energy storage viewpoint proposed by our team, it is assumed that there is a maximum constant value for the maximum storage of energy per unit volume when dislocation slip starts in a metal. A temperature-dependent critical resolved shear stress (CRSS) model without any fitting parameters is developed for metals in a pure shear mode. The CRSSs of Cu, Cu–Au, Cu–Co and Cu–Au–Co in the pure shear mode are predicted, and are in excellent agreement with the experimental results. This work offers an approach to predict the temperature-dependent CRSS for metals in the pure shear mode. [ABSTRACT FROM PUBLISHER]

In this paper, based on the Griffith fracture theory, the slow crack growth theory and the temperature-dependent fracture surface energy model, a temperature and test rate dependent fracture strength model for zirconia and alumina single crystal fibers was established. As a comparison, the other one based on the temperature-dependent free surface energy was also deduced and discussed. These models were verified by comparison with the experimental data of the two types of ceramic single crystal fibers. Good agreement between the model predictions and the experimental data was obtained. Moreover, based on the present model and the existing material parameters, the influencing factor analysis for these ceramic single crystal fibers were systematically conducted. Some new findings regarding their high temperature fracture strengths were provided for the first time. [ABSTRACT FROM AUTHOR]

Tensile strength is a key mechanical property of fibers used as sustainable reinforcements for advanced fiberreinforced composites. This study aims to conduct experimental investigation on the fracture strength of bamboo fibers of different dimensions subjected to longitudinal tensile loading. The statistical distributions of the fracture strength in bamboo fibers are correlated with the effects of fiber length and diameter variation. These are described according to Weibull statistics, which exhibit the random nature of fiber strength. The Weibull function parameters used for strength prediction are obtained from the test specimens. A comparison of predicted results and experimental data is presented to assess the accuracy of using weak-link scaling. Furthermore, the findings of this study also indicate that fiber strength statistics dominate size dependence of tensile strength. [ABSTRACT FROM AUTHOR]

In this study, a temperature‐dependent bulk modulus model without any adjustable parameters for solids single crystals is developed based on an equivalent relation between deformation energy and heat energy. This model uncovers the quantitative relation between the temperature‐dependent bulk modulus, heat capacity, boiling point, enthalpy of solid‐state phase transition, enthalpy of fusion, enthalpy of vaporization, and volume coefficient of thermal expansion. As examples, the temperature‐dependent adiabatic bulk moduli of α‐Al2O3, MgO, Si, Ti, SrF2, CaF2, and MgF2 are predicted, and are in good agreement with the available experimental results. This study provides a new and practical method to quantitatively characterize the temperature‐dependent bulk modulus of solid single crystals. A temperature‐dependent bulk modulus model without any adjustable parameters is developed for solids single crystals. The quantitative relation between the temperature‐dependent bulk modulus and heat capacity, boiling point, enthalpy of solid‐state phase transition, enthalpy of fusion, enthalpy of vaporization, and volume coefficient of thermal expansion is found. This study can help to quantitatively characterize their temperature‐dependent bulk modulus. [ABSTRACT FROM AUTHOR]

Based on fracture mechanics theory and a temperature-dependent interfacial shear strength model established by the authors, this paper develops a temperature-dependent theoretical model for the non-steady state first matrix cracking stress of fiber ceramic matrix composites. The model unifies the combined effects of temperature, crack length and thermal residual stress on the first matrix cracking stress into a single theory. The model predictions for the first matrix cracking stress of silicon carbide fiber reinforced zircon matrix composite agree well with the experimental results. Compared with the classical models proposed by Danchaivijit and Shetty, Thouless and Evans, and Marshall et al., our model has obvious advantages from the aspects of applicability, convenience and accuracy. Moreover, the analysis of influencing factors for the first matrix cracking stress is conducted systematically. Some new insights into improving the first matrix cracking stress of fiber ceramic matrix composites are obtained. [ABSTRACT FROM AUTHOR]

Knowledge of vacancy formation energy (VFE) for metallic materials at different temperatures is of fundamental importance. In the present study, following Brook's method and cohesive energy theory, two temperature dependent VFE models of metallic materials are developed based on our previous studies. The developed models are validated using the available experimental and simulation results. Agreement is good between model predictions and corresponding available experimental and simulation results. This study indicates that the VFE firstly remains approximately constant and then goes down almost linearly with increase of temperature. Furthermore, this work can provide simple and effective methods to calculate VFE of metallic materials at different temperatures, and can help understand the fundamental mechanisms which control the decrease of VFE at high temperatures. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a theoretical model for predicting the longitudinal tensile strength of unidirectional fiber reinforced polymer (FRP) composites at different temperatures is established. This model considers the combined effects of temperature, matrix strength, fiber size, fiber volume fraction, and the fiber strength scatter on the tensile strength of unidirectional FRP composites. The model is verified by comparison with available experimental data of carbon fiber and glass fiber reinforced polymer composites at different temperatures. The agreement between the theoretical model and experimental results is found to be satisfactory, which indicates the applicability and reasonability of the model. Particularly, the model has advantages compared with Curtin's model, Gao-Reifsnider's (G-R's) model and Subramanian-Reifsnider's (S-R's) model from the aspects of accuracy and convenience. Furthermore, the influencing factor analysis for unidirectional FRP composites regarding their temperature dependent tensile strength was systematically conducted, which provide better understanding on the strength control mechanism and material design. [ABSTRACT FROM AUTHOR]

In this study, a thermal shock resistance model over a wide range of cooling environment temperatures for fiber reinforced brittle matrix composites is developed. The model takes into account the combined effects of cooling environment temperature and temperature-dependent material parameters. The critical temperature difference causing matrix cracking of SiC fiber reinforced reaction bonded Si 3 N 4 composite and Nicalon fiber reinforced borosilicate composite are predicted over a wide range of cooling environment temperatures. The results show that the thermal shock resistance of composites is strongly dependent on the cooling environment temperature. Moreover, the quantitative influences of matrix Young's modulus, thermal expansion coefficient of matrix, and interfacial shear stress on thermal shock resistance with increase of cooling environment temperature are studied in detail. And some insights into improving the thermal shock resistance of fiber reinforced brittle matrix composites are obtained. [ABSTRACT FROM AUTHOR]

A model of temperature dependent shear modulus and Young's modulus in bulk metallic glasses is established. The inherent relationship between the glass transition temperatures, the Debye temperature and shear modulus of bulk metallic glasses is revealed. The temperature dependent shear modulus can be predicted by our model without any fitting parameter. The model is presented based on a critical energy density criterion for plastic yielding which is derived from fundamental thermodynamics. This critical energy density consists of two parts: the heat added to the system and the input of mechanical energy, which are not completely equivalent. The agreement between theoretical results and experimental results is striking. And it is found that the temperature dependent Young's modulus could also be predicted pretty well by our model. [ABSTRACT FROM AUTHOR]

In this study, the temperature-dependent antiphase boundary energy is established from a view of energy conservation. Subsequently, a theoretical model for yield strength anomaly of Ni-base superalloys at elevated temperature is developed on the basis of pre-existing yield strength model and traditional precipitation strengthening theories. The model is verified at different temperatures by comparison with experimental data of several Ni-base superalloys. The excellent agreement between predictions and experiments shows a good prediction ability of this model. This study provides a quantitatively theoretical characterization method for yield strength anomaly of Ni-base superalloys at elevated temperature. [ABSTRACT FROM AUTHOR]

In this work, we proposed a novel temperature dependent yield strength model for metallic materials which has no fitting parameters. The temperature dependent yield strength at arbitrary temperatures can be predicted. And a critical yield energy density with material yield is introduced, which comprises the distortional strain energy, potential energy and kinetic energy of atomic motion. A kind of quantitative relationship between the yield strength, temperature, elastic modulus and Poisson’s ratio is presented. The agreement between theory and experiment is of good satisfaction. Moreover, a temperature dependent yield strength model considering the precipitation strengthening is introduced to predict the yield stress of precipitation strengthened superalloy. Based on the proposed temperature dependent model, a new temperature and strain rate dependent yield strength is established. The good agreement between theory and experiment is found at the temperatures and strain rates considered. [ABSTRACT FROM AUTHOR]

The tensile properties of superalloy GH4033 have been evaluated at temperatures ranging from room temperature to 1000 °C. Fracture surfaces and precipitation were observed using a field-emission scanning electron microscope (FE-SEM). The alloy mainly consisted of γ ’ precipitate particles homogeneously dispersed in the γ matrix interior. The effects of dynamic strain aging and precipitation on the strength were verified. A temperature-dependent yield strength model was developed to describe the temperature and precipitation effects on the alloy's yield behaviour. The model is able to consider the effect of precipitation strengthening on the yield strength. The yield behaviour of the precipitation-strengthened superalloy was demonstrated to be adequately predictable over a wide range of temperatures. Note that this model reflects the quantitative relationship between the yield strength of the precipitation-strengthened superalloy and the temperature, the elastic modulus, the specific heat capacity at constant pressure, Poisson's ratio, the precipitate particle size and the volume fraction of the particles. [ABSTRACT FROM AUTHOR]

This study aims to characterize the size and shape dependent melting temperature of nanomaterials. Considering that surface atoms and interior atoms affect the melting of materials in different manners, we thus define an equivalent relationship between the contribution of surface atoms and interior atoms. Based on this definition, a criterion of melting is proposed through introducing a critical energy storage density of melting, the sum of the contribution of surface atoms and the interior atoms. According to the proposed criterion, a new theoretical model without any adjustable parameters is developed to characterize the size effect of melting temperatures of nanomaterials. The model predictions are in good agreement with the available experimental data or molecular dynamics simulations. This model uncovers the quantitative relationship between the melting temperature, size, atomic diameter and shape of nanomaterials. In addition, this model is extended to predict the size dependent glass transition temperatures of polymers. This study can help to better understand and characterize the size dependent melting temperatures of nanomaterials, as well as the size dependent glass transition temperatures of polymers.