Local and non-local thermomechanical modeling and finite-element simulation of high-speed cutting
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Date
2010-11-25
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Abstract
High-speed cutting is an important and widely-used process in modern production engineering.
Considering the fundamental non-linear nature of this thermomechanical process, the finiteelement
method is the numerical simulation tool of choice. In this context, a realistic numerical
simulation of cutting processes places high demands on accuracy and efficiency. Since large
deformation and deformation localization are involved, continual remeshing and mesh adaptation
are required. In the context of a finite-element analysis, localized deformation patterns,
as observed in experimental observations, can be modeled using thermo-viscoplastic material
models including in particular the effect of thermal softening and in general damage as well.
As is well-known, such softening effects result in a loss of solution uniqueness, resulting in socalled
pathological mesh-dependence of the simulation results. In the last ten to fifteen years,
a number of extensions to classical local modeling of softening, damage and failure have been
proposed in order to account for the inherently non-local character of many processes contributing
to such failure. For example, in the case of ductile failure in metal-matrix composites as
based on void development, the process of void coalescence leading to failure is inherently
non-local. From the mathematical / numerical point of view, many non-local models have the
additional benefit of regularizing the boundary-value problem and alleviating mesh dependence.
On this basis, the intention of the work presented in the following is to develop a general finite
element framework to model and simulate the process of metal cutting and related processes.
Here, we deal with two key issues. To resolve the complex deformation patterns, observed in
context of metal cutting, we develop an adaptive finite element framework, based on a combination
of error estimation and refinement indication. Further, we present an extended thermodynamic
framework, with a general non-local description of several thermodynamic quantities.
In this context we also discuss the effect of ductile damage. In the context of standard isochoric
plasticity, the influence of hydrostatic pressure on the development of ductile damage is usually
accounted for in an indirect fashion, by defining, e.g., a pressure-dependent formulation for the
rate of damage. In contrast, the current work is based on both hydrostatic stress- and deviatoric
stress-driven inelastic deformation, damage, and failure. The former drives for example
primarily microvoid development, while the latter is related to micro-shear-band or microcrack
development. The extended non-local description allows the modeling of lengthscale-effects,
in general, but also the additional benefit of further reduction of mesh dependence is important
and will be discussed.
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Keywords
finite element simulation, adaptive, damage, non-local, high-speed cutting