Elasto-plastic Properties Of Sheet Metals With Effects Of Microstructures And Their Measurements

Sheet metal is widely used in materials processing engineering. Sheet metal is considered as polycrystalline aggregate of tiny crystallites in the meso-scale. Crystalline grain is anisotropic, therefore the elastic and plastic properties of polycrystalline is not only dependent on single crystal, but also related to the orientation distribution of crystallites, which is expressed by orientation distribution function(ODF).ODF can be expanded under Wigner D-bases, and its coefficients are defined as texture coefficients. The relationship between orientation distribution of crystallites and the elastic and plastic properties of polycrystalline is specifically researched in this paper.The elastic constitutive of polycrystalline is closely related with the grain orientation distribution, so the texture coefficients describing the orientation distribution can be included in the elastic constitutive. In this paper, we make use of Clebsch-Gordan expression to deduce general expressions of elastic constitutive for anisotropic hexagonal poly-crystal. The expressions do not relied on any physical models, and contain linear form of texture coefficients. Then we give an ultrasonic measurement method to determine texture coefficients of the expressions that we deduced. We also introduce a method to measure the texture coefficients of orthorhombic cubic sheets, and take uniaxial tensile tests for aluminum and steel sheets to determine their elastic modulus and texture coefficients.The research on plastic nature of sheet metal in this paper focuses on the relationship between the earing in deep drawing and the orientation distribution of crystallites. Choosing Hill yield function to be plastic potential function, we obtain the relationship between coefficients of Hill yield function and earing in the plane stress and plane strain states respectively, then making use of the relationship between Hill yield function coefficients and texture coefficients we obtain the relationship between the earing and texture coefficients. The expressions have the same form with the expressions deduced by texture coefficients' own nature, and the deep drawing test of aluminum indicated that the expressions are in line with the results of the test. Hill yield criterion depends only on the quadratic terms of yield stress, we further find out the yield functions considering the three items of stress, and give the relationship between the coefficients and texture coefficients.Finally, we measured the r-value of steel plates in plastic deformation process by uniaxial tensile experiments. By utilizing the relationship between r-value and texture coefficients, we obtain the evolution of texture coefficients.