Exponential Temperature Dependence of Young's Modulus for Several Oxides

Wachtman, J. B.; Tefft, Wayne E.; Lam, D. G.; Apstein, C. S.

doi:10.1103/physrev.122.1754

Cited by 464 publications

(191 citation statements)

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“…The derivative with respect to temperature of any elastic constant tends towards zero approaching absolute zero [128], while a linear dependence of Young's modulus with respect to temperature has been observed for many crystalline solids at high temperatures [128]. A simple linear fit has been used by several researchers for the temperature dependence of elastic moduli, as the deviation from linear variation with temperature is small except at low temperatures [129].…”

Section: Young's Bulk and Shear Modulimentioning

confidence: 99%

“…However, this fit can lead to a slight over-estimation of the room temperature Young's modulus from intermediate or high temperature data. The Wachtman equation has been shown to accurately describe the temperature dependence of Young's modulusprovided the variation in Poisson's ratio with temperature is small-or bulk modulus, across a broad range of temperature for various non-metallic crystals and polycrystalline ceramics [128,130]:…”

Section: Young's Bulk and Shear Modulimentioning

confidence: 99%

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A review of the processing, composition, and temperature-dependent mechanical and thermal properties of dielectric technical ceramics

et al. 2011

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The current review uses the material requirements of a new space propulsion device, the Variable Specific Impulse Magnetoplasma Rocket (VASIMR ® ) as a basis for presenting the temperature dependent properties of a range of dielectric ceramics, but data presented could be used in the engineering design of any ceramic component with complementary material requirements. A material is required for the gas containment tube (GCT) of VASIMR ® to allow it to operate at higher power levels. The GCT's operating conditions place severe constraints on the choice of material. A dielectric is required with a high thermal conductivity, low dielectric loss factor, and high thermal shock resistance. There is a lack of a representative set of temperature-dependent material property data for materials considered for this application and these are required for accurate thermo-structural modelling. This modelling would facilitate the selection of an optimum material for this component. The goal of this paper is to determine the best material property data values for use in the materials selection and design of such components. A review of both experimentally and theoretically-determined temperature-dependent & room temperature properties of several materials has been undertaken. Data extracted are presented by property. Properties reviewed are density, Young's, bulk and shear moduli, Poisson's ratio, tensile, flexural and compressive strength, thermal conductivity, specific heat capacity, thermal expansion coefficient and the factors affecting maximum service temperature. Materials reviewed are alumina, aluminium nitride, beryllia, fused quartz, sialon and silicon nitride.

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Section: Young's Bulk and Shear Modulimentioning

confidence: 99%

Section: Young's Bulk and Shear Modulimentioning

confidence: 99%

A review of the processing, composition, and temperature-dependent mechanical and thermal properties of dielectric technical ceramics

et al. 2011

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“…However, since the elastic modulus of the individual phases are not available at elevated temperatures, the effective modulus is used here. The results of measurement and data from Fukuhara and Sanpei (1993) are plotted in figure 3 along with the model by Wachtman et al (1961) …”

Section: Coupling Of Phase and Flow Stress Modelsmentioning

confidence: 99%

A model for Ti–6Al–4V microstructure evolution for arbitrary temperature changes

Murgau

Pederson

Lindgren

2012

Modelling Simul. Mater. Sci. Eng.

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This thesis is devoted to microstructure modelling of Ti-6Al-4V. The microstructure and the mechanical properties of titanium alloys are highly dependent on the temperature history experienced by the material. The developed microstructure model accounts for thermal driving forces and is applicable for general temperature histories. It has been applied to study wire feed additive manufacturing processes that induce repetitive heating and cooling cycles. The microstructure model adopts internal state variables to represent the microstructure through microstructure constituents' fractions in finite element simulation. This makes it possible to apply the model efficiently for large computational models of general thermomechanical processes. The model is calibrated and validated versus literature data. It is applied to Gas Tungsten Arc Welding -also known as Tungsten Inert Gas welding-wire feed additive manufacturing process. Four quantities are calculated in the model: the volume fraction of phase, consisting of Widmanstätten , grain boundary , and martensite . The phase transformations during cooling are modelled based on diffusional theory described by a Johnson-Mehl-AvramiKolmogorov formulation, except for diffusionless martensite formation where the Koistinen-Marburger equation is used. A parabolic growth rate equation is used for the to transformation upon heating. An added variable, structure size indicator of Widmanstätten , has also been implemented and calibrated. It is written in a simple Arrhenius format. The microstructure model is applied to in finite element simulation of wire feed additive manufacturing. Finally, coupling with a physically based constitutive model enables a comprehensive and predictive model of the properties that evolve during processing.

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“…13 The third law of thermodynamics requires that the derivative of any elastic constant with respect to the temperature must approach zero as the temperature approaches absolute zero. Combining this criterion with the observed linear relationship at higher temperatures, Wachtman et al 14 where B 0 is the bulk modulus at absolute zero, T is the temperature, and b 1 and T 0 are arbitrary constants. Theoretical justification for the equation of Wachtman et al was suggested by Anderson.…”

Section: Introductionmentioning

confidence: 99%

The temperature dependence of the isothermal bulk modulus at 1bar pressure

Garai

Laugier²

2007

Journal of Applied Physics

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It is well established that the product of the volume coefficient of thermal expansion and the bulk modulus is nearly constant at temperatures higher than the Debye temperature. Using this approximation allows predicting the values of the bulk modulus. The derived analytical solution for the temperature dependence of the isothermal bulk modulus has been applied to ten substances. The good correlations to the experiments indicate that the expression may be useful for substances for which bulk modulus data are lacking.

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Exponential Temperature Dependence of Young's Modulus for Several Oxides

Cited by 464 publications

References 10 publications

A review of the processing, composition, and temperature-dependent mechanical and thermal properties of dielectric technical ceramics

A review of the processing, composition, and temperature-dependent mechanical and thermal properties of dielectric technical ceramics

A model for Ti–6Al–4V microstructure evolution for arbitrary temperature changes

The temperature dependence of the isothermal bulk modulus at 1bar pressure

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