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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.

Theoretical Study on Thermal Stresses of Metal Bars with Different Moduli in Tension and Compression