Thermally coupled constitutive relations of thermoelastic materials and determination of their material constants based on digital image correlation with a laser engraved speckle pattern

Thermally coupled constitutive relations are the key to the study of coupled thermal stress problems of materials. However, theoretical studies on thermally coupled constitutive relations are not perfect due to limitations in experimental data and analytical difficulties. In this paper, thermally coupled constitutive relations of thermoelastic materials are obtained using a strain energy function proposed here. A high temperature measuring system is designed and a digital image correlation (DIC) method is used to obtain mechanical properties of magnesium alloy with high temperature. A novel laser engraving technique is applied to create speckle patterns on surfaces of magnesium alloy specimens. Material constants are determined by experimental results with a data fitting approach that uses planar stress and strain fields. The equivalent Young's modulus, Poisson's ratio, and coefficient of thermal expansion of a material are theoretically derived as a function of temperature. Deformations of magnesium alloy tensile specimens with different temperatures are theoretically obtained based on thermally coupled constitutive relations and compared with experimental results.