Damage Implementation of Nonlocal Ductile Damage Model and Its Application in Orthogonal Cutting Process.
Year: Sept. 2008- Feb. 2011.
In the present work, a general framework for a nonlocal damage model based on the implicit gradient damage model is developed and implemented using finite element method. Continuum damage models describe the changes of material stiffness and strength, caused by the evolution of defects, in the framework of continuum mechanics. In many materials, a fast evolution of defects leads to stress strain laws with softening, which creates serious mathematical and numerical problems. The reason for this is the observed dependency of the obtained results with mesh size and orientation, especially in the neighborhood of localized damage area. The finite element simulations of material instability problems converge to meaningful results upon further refinement of the finite element mesh. To avoid pathological localisation and mesh dependence and to incorporate length scale effects due to microstructure evolution, the damage growth is driven by a nonlocal variable via a second order partial differential equation. This implicit gradient formulation introduces an additional partial differential equation of the Helmholtz type, which is solved in a coupled fashion with the standard equilibrium equation. Implementing this coupled problem in a finite element program for small deformations follows standard routines: elaboration of the weak form of the governing equations, linearization and discretization. The system of equations is incorporated in a full Newton-Raphson incremental iterative solution strategy. This thesis covers a study on using nonlocal damage model in simulation of orthogonal metal cutting by finite element method. The numerical examples presented in the following thesis have a twofold purpose: to illustrate the effectiveness of the proposed nonlocal implicit gradient formulation in attenuating the mesh dependency, in cutting simulation involving damage localization due to formation of primary shear band, and propose a reliable separation criteria for orthogonal metal cutting. To focus on effectiveness of the proposed nonlocal implicit gradient formulation on the cutting simulation, a simple finite element model under plane strain deformation will be used to investigate the mechanics of cutting from the incipient stage.The use of nonlocal gradient damage models in cutting simulation analysis provides consistent and reliable FEM simulation. The use of nonlocal damage aims to obtain a clearer figure about the reliability of the separation criteria for orthogonal metal cutting.
Keywords:Nonlocal Damage, Finite Element Method, Length Scale, Shear Band, Localization, Separation Criterion, Orthogonal Cutting.