Generation of segmental chips in metal cutting modeled with the PFEM

Abstract

The Particle Finite Element Method, a lagrangian finite element method based on a continuous Delaunay retriangulation of the domain, is used to study machining of Ti6Al4V. In this work the method is revised and applied to study the influence of the cutting speed on the cutting force and the chip formation process. A parametric methodology for the detection and treatment of the rigid tool contact is presented. The adaptive insertion and removal of particles are developed and employed in order to sidestep the difficulties associated with mesh distortion, shear localization as well as for resolving the fine-scale features of the solution. The performance of PFEM is studied with a set of different two-dimensional orthogonal cutting tests. It is shown that, despite its Lagrangian nature, the proposed combined finite element-particle method is well suited for large deformation metal cutting problems with continuous chip and serrated chip formation.B J. M. Carbonell

Dislocation Density Based Flow Stress Model Applied to the PFEM Simulation of Orthogonal Cutting Processes of Ti-6Al-4V

“…Here, χ is the fraction of mechanical energy spent on vacancy generation, Q v f is the activation energy of vacancy formation, ζ is the neutralization effect by vacancy emiting and absorbing jogs, c j is the concentration of jogs, Ω 0 is the atomic volume, D vm is the diffusivity of vacancies andṪ is the time derivative of the temperature field. The coupled solution of the system of ordinary differential equations (ODE) of Equations (9) and (21) is carried out at elementary level with a Newton-Raphson iterative scheme, a similar solution scheme to coupled equations is presented in References [27,31,32]. The coupled solution of Equations Given the new value ofε p and ε p , and the old value X d , X s , X g , ρ i , g and c v .…”

“…An implicit PFEM was used with an updated Lagrangian formulation accounting for large deformation, large strains, thermal coupling strains, heat transfer due to conduction, heat generation due to plasticity and heat generation due to friction [26,27]. A staggered/fractional step approach called isothermal split method [80][81][82] was used to couple the mechanical and thermal problem.…”

“…The methods supported by a mesh include the Multi-material Eulerian Method (MMEM) [13,14], the Volume of Solid (VOS) [15], and the Material Point Method (MPM) or Point in Cell (PiC) method [16,17]. Among the particles/meshless methods applied to metal cutting we found: the Smoothed Particle Hydrodynamics (SPH) [18,19], the Finite Point Method (FPM) [20], the Constrained Natural Element Method (CNEM) [21], the Discrete Element Method (DEM) [22], the Maximum Entropy MeshFree method [23], the stabilized optimal transportation meshfree method (OTM) [24], and the Particle Finite Element Method (PFEM) [25][26][27][28]. Most of these new methods are applied using similar simplified models.…”

“…There are several references [25][26][27][28] that present the capabilities of the PFEM as a numerical tool to model large deformations surpassing the problems of mesh distortions and diffusion of state variables that are typical in FEM simulations. Also, PFEM includes capabilities to deal with thermo-mechanical coupling, contact and friction, treatment of the incompressibility constraint due to plasticity.…”

“…Therefore, it is preferable to use models which are related to the physics of the deformation because the range of validity out of the experimental calibration range is larger compared to phenomenological models. There is evidence of this better behavior when the dislocation density (DD) constitutive model was used to model metal cutting with SANMAC 316L stainless steel in References [27,31,32]. A physically based Voyiadjis-Abed model including the hardening due to dynamic strain aging is presented in References [33,34], it is expected that including the dynamics strain aging in the numerical modeling of metal cutting process will increase the accuracy of the results.…”