Research On Large Deformation Constitutive Relationship Based On Cylindrical Shaft Torsion Test

Material parameters in large deformation constitutive relationship can be defined by simple test. In the dissertation, within the framework of the principles of continuum mechanics, large deformation elastoviscoplastic constitutive relationships are defined by torsion test with cylinder specimens. First of all, the stress-strain curve of plastic material for cylinder torsion test is discussed. Then, deformation and motion laws of cylinder specimens for torsion are researched and several spins are given; representation of plastic rigidity function h is derived from large deformation constitutive equation of cylinder specimen for torsion. Finally, in order to discuss adaptability of constitutive relationship given in the paper, simple shear problem is analyzed and elastoviscoplastic stress response is derived by adopting the torsion constitutive relationship. These works are introduced as follows:1. The deformation geometric theory and motion theory for large deformation problem is analyzed, then several stress defining are given; the objective principles that is needful in constitutive theory are introduced; based on objective principle, constitutive relationships for small deformation is generalized to large deformation problem; general formulas of constitutive relationships for large elastic deformation and general formulas of constitutive relationships for isotropic hardening materials in large elastoviscoplastic deformation with Mises yield condition are reduced.2. According to plat surface hypothesis and no axial deformation hypothesis, formulas of real shear stress and real shear strain for torsion deformation are derived based on curve of torque-corner (Mn-φ) for torsion test with cylinder specimens; the deformation geometric laws and motion laws for cylinder specimen is analyzed by using tensor and matrix form; deformation rate d and several common spins for torsion problem is given under not only right-anglecoordinate but also cylinder coordinate; objective stress tensors (Cauchy stress and Kirchhoff stress) for torsion are developed.3. Representations of several objective stress rates are derived for torsion test with cylinder specimens; material stress rate and objective stress rates are illustrated by rigidly revolving cylinder shaft for torsion, in order to explain that only objective stress rates can represent true stress state; representation of plastic rigidity function h is developed by large deformation constitutive equation of cylinder specimen for torsion and general large deformation constitutive relationship is given on the basis of torsion test; it is explained theoretically by deformation laws of cylinder shaft for torsion that objective stress rates have no influence on plastic rigidity function h if large deformation constitutive relationship is defined by torsion test.4. For simple shear problem, the deformation laws and motion laws and stress are analyzed by using matrix form and Jaumann rate and Green—Naghdi rate with Kirchhoff stress r are derived; elastic stress response in simple shear problem is given by applying Jaumann rate and Green—Naghdi rate with Kirchhoff stress r to large deformation elastic converse constitutive equation; the numerical results show that the oscillating stress response is homologous to Jaumann stress rate and purely increasing stress response is homologous to Green —Naghdi stress rate; on the base of the torsion elastoviscoplastic constitutive equation obtained in the paper, large deformation elastoviscoplastic constitutive relationship for simple shear problem is developed by adopting Jaumann rate and Green—Naghdi rate with Kirchhoff stress r and the corresponding stress response is given; it is illustrated theoretically that elastoviscoplastic stress responses for the two torsion elastoviscoplastic constitutive equation with Jaumann rate and Green—Naghdi rate should be resemble.