Metal cutting or machining is a process in which a thin layer or metal, the chip, is removed by a wedge-shaped tool from a large body. Metal cutting processes are present in big industries (automotive, aerospace, home appliance, etc.) that manufacture big products, but also high tech industries where small piece but high precision is needed. The importance of machining is such that, it is the most common manufacturing processes for producing parts and obtaining specified geometrical dimensions and surface finish, its cost represent 15% of the value of all manufactured products in all industrialized countries. Cutting is a complex physical phenomena in which friction, adiabatic shear bands, excessive heating, large strains and high rate strains are present. Tool geometry, rake angle and cutting speed play an important role in chip morphology, cutting forces, energy consumption and tool wear. The study of metal cutting is difficult from an experimental point of view, because of the high speed at which it takes place under industrial machining conditions (experiments are difficult to carry out), the small scale of the phenomena which are to be observed, the continuous development of tool and workpiece materials and the continuous development of tool geometries, among others reasons. Simulation of machining processes in which the workpiece material is highly deformed on metal cutting is a major challenge of the finite element method (FEM). The principal problem in using a conventional FE model with langrangian mesh is mesh distortion in the high deformation. Traditional Langrangian approaches such as FEM cannot resolve the large deformations very well. Element distortion has been always matter of concern which limited the analysis to incipient chip formation in some studies. Instead, FEM with an Eulerian formulation require the knowledge of the chip geometry in advance, which, undoubtedly, restricts the range of cutting conditions capable of being analyzed. Furthermore serrated and discontinuous chip formation cannot be simulated.
The main objective of this work is precisely to contribute to solve some of the problems described above through the extension of the Particle Finite Element Method (PFEM) to thermo-mechanical problems in solid mechanics which involve large strains and rotations, multiple contacts and generation of new surfaces, with the main focus in the numerical simulation of metal cutting process. In this work, we exploit the particle and lagrangian nature of PFEM and the advantages of finite element discretization to simulate the different chip shapes (continuous and serrated) that appear when cutting materials like steel and titanium at different cutting speeds. The new ingredients of PFEM are focused on the insertion and remotion of particles, the use of constrained Delaunay triangulation and a novel transfer operator of the internal variables.
The remotion and insertion of particles circumvents the difficulties associated to element distortion, allowing the separation of chip and workpiece without using a physical or geometrical criterion. The constrained Delaunay improves mass conservation and the chip shape through the simulation, and the transfer allows us to minimize the error due to numerical diffusion.