Theoretical And Numerical Characterization Of Anisotropic Plastic Behavior Of Magnesium Alloy Sheets

As the lightest structured metallic materials, the plates of magnesium alloys are more and more widely applied in the fields of aeronautics and space, traffic and trans-portation, electronic products and so on, so many researchers in materials and mechanics attach importance to the theoretical and numerical characterization and application of the anisotropic behavior of plasticity presented by them. In the past more than ten years, sev-eral yielding laws suitable for describing the strength differential effects in tension and compression and plastic anisotropy were presented, the laws given by Cazacu et al for example. Because of a larger amount of material parameters in the laws, their ex-perimental verification and numerical implementation should be conducted deeply. The present work is focused on the development of the finite elastoplastic theory suitable for the yielding law (CPB06) presented by Cazacu et al and the numerical algorithms and program, and provides a base for modelling a variety of forming technology of plates of magnesium alloys in the next step.The following aspects haven been conducted in the work:●On the basis of description of the mechanism for plastic deformation of the HCP metals, the slip and twin systems contributing to the plastic deformation of magne-sium alloys are summarized, further the reasons for the strength differential effects of magnesium alloys are analyzed.●The yielding law (CPB06) presented by Cazacu et al are newly derived, it is indicated that k=±1 is not the global extremal points of the ratio of the tensile and compressive yielding stresses for any exponent a; Several careless mistakes in Cazacu et al are corrected; The conditions in which the expressions of the Lankford coefficients are applicable are indicated.●On the basis of the internal dissipation inequality and the theory of maximum dis-sipation of plasticity, a finite elastoplastic theory described under the R corota-tional frame is developed, which is suitable for the application of the yielding law CPB06; The algorithms for the stress updating and the consistent tangent moduli are derived. These results provide a solid base for the finite element implemen-tation of the yielding law (CPB06) at finite deformations, the assumption of tiny elastic deformation which is usually used in the existing numerical implementation of CPB06 is removed in the present work.●By using the experimental results presented by Wu et al, the effectiveness of the finite elastoplastic theory and numerical algorithms presented in the work is veri-fied. Comparing the numerical results with the experimental observations, it was found that the theory and algorithms presented in the work can simulate well the testing results of uniaxial tension and compression in different sampling directions.The novel aspects of the thesis are presented by the last three points above. The elasto-plastic theory, algorithms and program suitable for the yielding law CPB06 will be the departure point for modelling the forming technologies of the plates of magnesium alloys.