Elastic Constitutive Relationship of Metallic Materials Containing Grain Shape

The grain shape and orientation distribution of metal sheets at mesoscales are usually irregular, which has an impact on the elastic properties of metal materials. A grain shape function (GSF) is constructed to represent the shape of grains. The expansion coefficient of GSF on the basis of the Wigner D function is called the shape coefficient. In this paper, we study the influence of average grain shape on the elastic constitutive relation of orthogonal polycrystalline materials, and obtain a new expression of the elastic constitutive relation of polycrystalline materials containing grain shape effects. The seven string method is proposed to fit the shape of irregular grains. Experiments show that the GSF can better describe the shape of irregular grains. Using the microscopic images of the grains, we carried out the experimental measurement of micro and macrostrain at grain scale. The experimental results show that the grain shape parameter (slenderness ratio) is consistent with the theoretical results of the material macroscopic mechanical properties.