Reduction of the mesh size influence on the results of a lagrangian finite element machining mode

Abstract

Mesh dependence of the results of a finite element model are well known in many fields such as in structural design. This problem is however not much addressed in the literature for machining modelling although it is crucial for the quality of the results and the predictive aspect of the model. In this work, an orthogonal cutting model of the titanium alloy Ti6Al4V is exploited. The model formulation is Lagrangian and a damage criterion with eroding elements is used. A strong sensitivity of the results to the size of the elements is observed and the results do not converge when the size of the mesh decreases. To address this issue, a non-local damage criterion that reduces the mesh dependence of the results is introduced. The results show a strong decrease of their dependence to the size of the mesh. The recommendation is to use elements length that is not too far from the size of the grains of the material to avoid a dramatic increase of the computing time for very small elements and the absence of converged results for too large elements.