Effective thermal expansion of heterogeneous materials with application to low temperature environments

Nadeau, J. C.; Ferrari, Mauro

doi:10.1016/s0167-6636(03)00009-7

Cited by 15 publications

(10 citation statements)

References 32 publications

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“…Ito等人 [22] , McCartney等人 [23] 早期建立了可以预测层合复合材料热膨胀系数的细观力学和层合板理论. Nadeau等人 [24] 采用细观力学的方法理论建立了预测两相复合材料线热膨胀系数的方法. Wakashima 等人 [25] 理论设计及实验制备了可实现负和零膨胀的玻璃纤层合板.…”

Section: 石英具有极小热膨胀系数但这些材料的负、低热膨胀效应只能保持在要么很低要么很高的狭窄温度unclassified

Development of designing lightweight composites and structures for tailorable thermal expansion

Wei¹,

Pei²

2016

Chin. Sci. Bull.

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Section: 石英具有极小热膨胀系数但这些材料的负、低热膨胀效应只能保持在要么很低要么很高的狭窄温度unclassified

Development of designing lightweight composites and structures for tailorable thermal expansion

Wei¹,

Pei²

2016

Chin. Sci. Bull.

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“…Being more general, the framework accounts for more phenomena than does linear thermoelasticity. Thus, within the broader framework, Nadeau and Ferrari (2004) showed theoretically that the presence of a superimposed local eigenstrain field can induce anisotropy in the overall thermal expansion response in an otherwise macroscopically isotropic composite of isotropic constituents. They also drew a parallel between their findings and a "most surprising" thermal expansion anisotropy experimentally observed in a polycrystal, one explanation for which could be the presence of residual stresses .…”

Section: Introductionmentioning

confidence: 99%

Effects of superimposed eigenstrains on the overall thermoelastic moduli of composites

Boussaa

2017

Mechanics of Materials

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This study investigates the effects that an initial local eigenstrain field, when superimposed on the thermal eigenstrain field, has on the overall thermal expansion coefficients and heat capacities of thermoelastic composites. The study can also be seen as an investigation into how a local residual stress field affects these overall moduli, as initial eigenstrains are generally a source of residual stresses. The approach taken is thermodynamic. Expressions that include the superimposed eigenstrain field are developed for the overall moduli within the framework of small strain thermoelasticity with temperature dependent materials. These expressions, which are written in terms of the concentration tensors and residual fields (stress and strain fields given rise to by the eigenstrains under zero overall stress and strain, respectively), contain correction terms that are absent in the expressions developed within linear thermoelasticity. Taking into account the temperature dependence of the constituent moduli is shown to be essential to capture the effects of the superimposed eigenstrain field. A Ti-6Al-4V/ZrO2 composite is investigated for which the correction terms are found to be negligible for the heat capacities but significant for the thermal expansion coefficients. This suggests that, for applications with large temperature changes, using the linear-thermoelasticity-based expressions can affect the accuracy of the estimates of the overall moduli, and therefore the accuracy of thermostructural analyses of composite structures. The proposed expressions can be of use to estimate the overall thermoelastic moduli in contexts in which the strains remain small, temperature changes are large, and superimposed eigenstrains may be present.

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“…For most materials, this is known as material softening. Thermal expansion coefficient and thermal conductivity of FGMs are also varied with position; several experimental contributions have been published on this matter, see e.g., [17,18]. The coefficient of thermal expansion of materials can also vary with temperature changes [19].…”

Section: Introductionmentioning

confidence: 99%

Axisymmetric and One-Dimensional Thermoelastic Fields of Radially Graded Bodies

Mohammadi

2015

Journal of Thermal Stresses

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In this paper, both Young's modulus and Poisson's ratio along with thermal expansion coefficient are allowed to vary across the radius in a solid ring and a curved beam. Effects of non-constant Poisson's ratio on the thermoelastic field in these graded axisymmetric and one-dimensional problems are studied. A governing differential equation in terms of stress function is obtained for general axisymmetric and onedimensional problems. Two linearly independent solutions in terms of hypergeometric functions are then attained to calculate the stresses and the strains. Using Green's function method, a form of a solution for the stress functions in terms of integral equations for a curved beam and a solid ring are obtained. Specifically, closed form solutions for the stress functions, when Young's modulus and Poisson's ratio are expressed as power law functions across the radius, are calculated. The results show that the effect of varying Poisson's ratio upon the thermal stresses is considerable for the solid ring. In addition, a non-constant Poisson's ratio has significant influences on the thermal strain field in solid rings. The effect of varying Poisson's ratio upon the thermal stresses is negligible for the curved beam. However, non-constant Poisson's ratios have substantial effects on the thermal strain field in curved beams. Finally, the effects of varying Poisson's ratio on the thermal stresses in thick solid rings and curved beams are also investigated.

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Effective thermal expansion of heterogeneous materials with application to low temperature environments

Cited by 15 publications

References 32 publications

Development of designing lightweight composites and structures for tailorable thermal expansion

Development of designing lightweight composites and structures for tailorable thermal expansion

Effects of superimposed eigenstrains on the overall thermoelastic moduli of composites

Axisymmetric and One-Dimensional Thermoelastic Fields of Radially Graded Bodies

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