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Chapter 3
Numerical Modeling of Orthogonal Micro-Cutting
3.1 Numerical modeling of micro-cutting process
In recent years, FEA has become the
main tool for simulating orthogonal micro-cutting processes since its first use
in 1970’s. Since then there has been a tremendous increase in the use of FEA in
modeling micro-cutting. A concise literature review of historical developments
along with major research work in machining processes using FEA has been
presented by Soo [92] and Mackerle [93-94].
Fig. 3.1 shows two different time integration techniques i.e.
explicit and implicit used in numerical modeling and simulation of
micro-cutting processes. The implicit method solves a set of finite element
equations by performing iterations until a convergence criterion is achieved
for each time step increment. On the other hand, the explicit approach determines
the solution to the set of finite element equations by using a central difference
method (CDM) to integrate the equations of motion through time. Researchers
used both implicit and explicit methods in the numerical simulation of cutting processes.
They also elaborated on the use of implicit or explicit techniques [95-98]. In
general, a review of literature shows that the simulation of micro-cutting uses
various numerical formulations, they are:
·
Lagrangian formulation,
·
Eulerian formulation,
·
Arbitrary Lagrangian-Eulerian (ALE) formulation, and
·
Smoothed Particle Hydrodynamics (SPH) formulation.
With the rapid growth of various
commercial frameworks, modeling of the cutting process can be readily achieved
to understand complex phenomena of micro-cutting. Until late 1990, numerous
researchers used their own codes. However of late, the use of commercially
available software packages have increased dramatically, which includes NIKE-2D,
FORGE2, ANSYS, LS-DYNA, DEFORM, ABAQUS, MSC.MARC, and AdvantEdge.
Literature review reveals that
micro-cutting processes can be simulated using various finite element
formulations such as Lagrangian [97-100], Eulerian [101], Arbitrary
Lagrangian-Eulerian (ALE) [102-104], and Smoothed Particle Hydrodynamics (SPH)
[105-109] within these commercial software frameworks. Evidently, choosing a
suitable finite element formulation to simulate micro-cutting in two- or three-dimensions
can be difficult as each one has its own pros and cons, as summarized in Fig 3.1. Based on the above review, in
the present work, structural-thermal coupled simulations have been performed
using Lagrangian formulation to study microcrack and gross fracture phenomenon,
whereas the SPH formulation has been used to model the workpiece microstructure
within LS-DYNA framework.
3.2 FEA simulation of micro-cutting using Lagrangian formulation
3.3 Microstructure modeling using SPH formulation
3.4 Summary