Abstract
Extensive studies have shown that engineering materials, including metals and their oxides, will present different mechanical properties in tension or compression; however, this difference is generally neglected due to the complexity of the analysis. In this study, we theoretically analyze the thermal stress of a metal bar with a bimodular effect. First, the common strain suppression method is used to obtain a one-dimensional thermal stress expression. As a contrast with the one-dimensional solution, a two-dimensional thermoelasticity solution is also derived, based on the classical Duhamel theorem concerning body force analogy. Results indicate an important phenomenon that the linear temperature rise mode will produce thermal stress in a bimodular metal bar, whereas there is no thermal stress in the case of singular modulus. If the equilibrium relation is needed to be satisfied, the variation trend between different moduli and different thermal expansion coefficients in tension and compression should be opposite. In addition, the amplitude of stress variation, from the maximum tensile stress to the maximum compressive stress, increases dramatically. There exists an inevitable link between one- and two-dimensional solutions. These results are helpful to the refined analysis and measurements of the thermophysical properties of metals and their oxides.
Highlights
In the classical Theory of Elasticity by Timoshenko and Goodier [1], the theoretical analysis for thermal stress began with problems of boundary force that we all are familiar with, that is, a bar with uniform thickness is subjected to a temperature change
The thermal stress problem of bimodular metal bars is theoretically analyzed under three different temperature rises modes, and the one-dimensional solution based on the strain suppression method and the two-dimensional thermoelasticity solution based on body force analogy is obtained
The results indicate that the introduction of the bimodular effect, as well as different thermal expansion coefficients, will bring forth obvious changes for the thermal stress
Summary
In the classical Theory of Elasticity by Timoshenko and Goodier [1], the theoretical analysis for thermal stress began with problems of boundary force that we all are familiar with, that is, a bar with uniform thickness is subjected to a temperature change. We devote ourselves to the theoretical analysis of thermal stress of a bar with a bimodular effect. Wen et al [25] presented a two-dimensional thermoelasticity solution for a bimodular beam under the combined action of thermal and mechanical loads. The potential change of thermal expansion coefficients in the case of the bimodular effect of materials has not been considered, this seems to be insufficient for refined analysis and further theoretical study. This study is devoted to the attainment of one-dimensional and two-dimensional thermal stress solutions of a bimodular bar under different temperature rise modes, the external temperature field is regarded as steady, and does not change with time [1,20].
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