[SY-E12] Computational generation of the yield surfaces using stress based loading
Ductile fracture in metals proceeds through nucleation, growth and coalescence of microvoids. Determination of the yield surface of a ductile porous material is necessary to simulate onset and evolution of ductile damage in a metal. Since the early work by Gurson where yield function for concentric spherical void inside a spherical RVE was considered, several extensions have emerged. It has been shown that the void shape and anisotropy of the bulk matrix modify the yield function significantly. All these predictions of yield rely on limit analysis of the RVE based on the upper bound theorem and Hill-Mandal homogenization. These models have not accounted for onset of yield through localization of plastic strain.
Recently the competition between localization and uniform yield via the Gurson model has been compared. We have extended this work by performing stress controlled computational homogenization over sub-spaces of the principal stress space, to probe the yield surface of perfectly plastic materials with different void shapes. A special four-noded user element is developed in ABAQUS, that, is tied to a RVE with periodic boundary condition, restrained rigid body rotation and subjected to either macroscopic deformation gradient or Cauchy stress. The macroscopic plastic dissipation rate is monitored to detect yield. As a result, yield due to both uniform plastic deformation and localization are captured. We have compared the results of our computationally determined yield surfaces with the theoretical upper bound estimates. We show that over a significant section of the principal stress sub-space, localization modifies the yield surface. For prolate voids, localization hastens yield while for oblate it is delayed over estimates provided by models based on the upper bound theorem. The comparison gives us a rich insight into the competition between macroscopic yield through uniform proliferation of plasticity and localization.
Recently the competition between localization and uniform yield via the Gurson model has been compared. We have extended this work by performing stress controlled computational homogenization over sub-spaces of the principal stress space, to probe the yield surface of perfectly plastic materials with different void shapes. A special four-noded user element is developed in ABAQUS, that, is tied to a RVE with periodic boundary condition, restrained rigid body rotation and subjected to either macroscopic deformation gradient or Cauchy stress. The macroscopic plastic dissipation rate is monitored to detect yield. As a result, yield due to both uniform plastic deformation and localization are captured. We have compared the results of our computationally determined yield surfaces with the theoretical upper bound estimates. We show that over a significant section of the principal stress sub-space, localization modifies the yield surface. For prolate voids, localization hastens yield while for oblate it is delayed over estimates provided by models based on the upper bound theorem. The comparison gives us a rich insight into the competition between macroscopic yield through uniform proliferation of plasticity and localization.