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Deformation Mechanics Associated with Formation of Ultra-Fine Grained Chips in Machining

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The deformation field associated with chip formation in plane strain (2-D) machining has been simulated using the finite element method (FEM), with the objective of developing 2-D machining as an experimental technique for studying very large strain deformation phenomena. The principal machining parameters are the tool rake angle, cutting velocity and the friction at the tool-chip interface while the deformation field parameters are strain, strain rate and temperature. The relation between rake angle and the shear strain in the deformation zone is studied for the low-speed cutting of lead. This correspondence is validated by comparison with measurements of the deformation parameters made by applying a Particle Image Velocimetry (PIV) technique to high-speed photographic image sequences of the deformation. It is shown that plastic strains in the range of 1-15 can be realized in a controlled manner by appropriate choice of the rake angle. The unique capabilities offered by 2-D machining for studying micro-and nano-mechanics of large strain deformation, and the creation of ultra-fine grained materials are highlighted in the context of these results.
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Deformation Mechanics Associated with Formation of Ultra-Fine
Grained Chips in Machining
Michael Sevier1,a, Seongeyl Lee2,b, M. Ravi Shankar2,c, Henry T.Y. Yang1,d,
Srinivasan Chandrasekar2,e, and W. Dale Compton2,f
1Department of Mechanical Engineering, University of California Santa Barbara
Santa Barbara, CA 93106, USA
2School of Industrial Engineering, Purdue University
West Lafayette, IN 47907-2023, USA
asevier@engineering.ucsb.edu, blee128@ecn.purdue.edu, cshankarr@ecn.purdue.edu,
dhenry.yang@chancellor.ucsb.edu, echandy@ecn.purdue.edu, fdcompton@ecn.purdue.edu
Keywords: Machining, large strain deformation, ultra fine grained materials, finite elements.
Abstract. The deformation field associated with chip formation in plane strain (2-D) machining has
been simulated using the finite element method (FEM), with the objective of developing 2-D
machining as an experimental technique for studying very large strain deformation phenomena. The
principal machining parameters are the tool rake angle, cutting velocity and the friction at the tool-
chip interface while the deformation field parameters are strain, strain rate and temperature. The
relation between rake angle and the shear strain in the deformation zone is studied for the low-speed
cutting of lead. This correspondence is validated by comparison with measurements of the
deformation parameters made by applying a Particle Image Velocimetry (PIV) technique to high-
speed photographic image sequences of the deformation. It is shown that plastic strains in the range
of 1-15 can be realized in a controlled manner by appropriate choice of the rake angle. The unique
capabilities offered by 2-D machining for studying micro- and nano- mechanics of large strain
deformation, and the creation of ultra-fine grained materials are highlighted in the context of these
results.
Introduction
Ultra-fine grained (UFG) materials are often harder, stronger and more wear-resistant than their
coarse grained counterparts [1]. Recent developments in fabrication of UFG materials have focused
on the use of large strain or severe plastic deformation as a method for achieving microstructure
refinement in metals and alloys. The case has also been made recently for chip formation by
machining as a low-cost method for manufacture of UFG materials [2]. Furthermore, since chip
formation involves the introduction of large shear strains (>>1) in a single pass, it offers a simple
framework for studying effects of large strain deformation in a variety of materials.
Plane strain (2-D) machining. The geometry of machining in its simplest manifestation, i.e.
plane strain machining (Fig. 1), is characterized by a sharp, wedge-shaped tool that removes a
preset depth of material (ao) by moving in a direction perpendicular to its cutting edge [3, 4]. Chip
formation occurs by concentrated shear within a narrow deformation zone often idealized as the
“shear plane” [4-6]. Most of the grain refinement associated with the formation of the UFG chips
can be attributed to the large shear strains imposed in this deformation zone.
The deformation field in plane strain machining is uniquely determined by the tool rake angle
(
α
) and undeformed chip thickness (ao). In the shear plane model, the shear strain (γ) may be
obtained from Eqs. 1 and 2; it is immediately apparent that this strain can be readily varied by
modifying the tool rake angle (
α
).
cos
sin cos( )
α
γ
φ
φα
= (1)
cos cos
tan
1sin1sin
co
oc
co
oc
Va
Va
Va
Va
α
α
φ
α
α
==
−−
(2)
In machining, unlike say Equal Channel Angular Extrusion (ECAE), the deformation characteristics
are not defined a priori; for the same rake angle (
α
), different materials can be strained to different
values of strain depending on the associated shear angle (
φ
). Additionally, the friction at the tool-
chip interface influences the shear strain. Therefore, it is essential that the relationship between the
geometry of the machining and the associated shear strain be determined in order to successfully
adapt plane strain machining as a viable large strain deformation technique. Once this is modeled, it
will be possible to impose any arbitrary value of shear strain in the chip by suitably defining the
machining parameters. It has been demonstrated elsewhere [7], that for certain combinations of
machining parameters and, consequently, different shear strains (2-15), a range of ultra-fine grained
and nanoscale microstructures are created in the chip. In particular, a switch-over from elongated
sub-grain to nanoscale equi-axed grain structures, with a significant fraction of high-angle grain
boundaries, is observed at the higher levels of strain. This switch over, which typically occurs at a
critical value of strain, is controllable in various alloys by varying the deformation conditions and
has not been realized in a single stage of deformation in any of the usual SPD processes. Again,
effective modeling would enable control of the chip microstructures by predicting the requisite
machining parameters required to produce pre-determined UFG morphologies.
It may be noted that the shear plane model is essentially an upper-bound analysis of the chip
formation process and does not provide any details regarding the geometry of the deformation zone.
Therefore, a finite element model has been developed in the present study to characterize the details
of the deformation zone, in particular the strains associated with the formation of the UFG chips.
Background: Experimental characterization of the deformation zone
While the deformation zone is often idealized as planar, experimental observations have shown this
zone to be fan shaped with finite width and thickness [5, 6]. In situ characterization of material flow
in the deformation zone using a high speed imaging system and Particle Image Velocimetry (PIV),
has been recently used to estimate the velocity and strain fields [3]. Some typical results from this
experiment shown in Fig. 2 confirm the deformation to be spread over a zone of finite width.
Furthermore, the cumulative strain imposed in the chip is seen to be different in different materials
for the same tool rake angle. These observations highlight the need for modeling of the chip
Workpiece
deformation zone
V0
α
φ
a0
ac
Tool
Chip
Fig. 1: Schematic of plane strain (2-D)
machining.
Vc
formation process in order to relate machining parameters (rake angle, velocity, friction) to
deformation field parameters (strain, strain rate, temperature).
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
Points along trajectory ABCE
Cumulative shear strain
A
L6061-T6
Lead
Copper
BDC
(a) (b)
Fig. 2: Deformation field parameters determined using high speed imaging and PIV analysis (a)
shear strain distribution and (b) cumulative shear strain at various points along a trajectory ABCD
for various materials. Vo= 10mm/sec, rake angle = +10° and undeformed chip thickness = 100
μ
m.
Finite Element Model of chip formation
The application of the finite element method to simulate the machining process has to date
primarily focused on understanding the characteristics of the workpiece [8-12]. The present analysis
is devoted almost exclusively to characterizing the deformation field associated with chip
formation. When modeling a process involving large deformation such as chip formation, it is
imperative to minimize the mesh distortion. Initial attempts used a series of steps, each involving
slight tool advancement followed by manual remeshing [11-13]. Other studies have used a
predefined “parting line”, to create artificial separation along a line of nodes ahead of the tool tip
resulting in a chip being formed [8]. More recently, adaptive meshing has come to the forefront as
method to continuously redistribute the elements during severe deformation in order to preserve the
integrity of the mesh [14].
An important aspect in modeling of machining is the interaction between the tool rake face and
the chip [15]. The friction at this interface has a significant effect on the chip morphology and the
shear strain associated with chip formation. In some models, a constant coefficient of friction is
assumed along the length of the rake face while in others, the tool-chip contact region is
decomposed into a “sticking” region near the tool tip and a “sliding” region away from the tool tip
[8]. Here, for the sake of simplicity, a constant value is assigned for friction at the chip-tool
interface.
A dynamic analysis of plane strain, low-speed cutting of lead is carried out in the present study
using ABAQUS/Explicit. In this model (Fig. 3), the lead workpiece is constrained vertically but is
imparted with a horizontal velocity towards a fixed cutting tool. The mesh itself is adaptive, with an
Eulerian boundary prescribed on the left and right sides of the mesh. These represent an “inflow”
and “outflow” region for which the material moves through at a prescribed cutting velocity of
10mm/s. The top and bottom of the workpiece are both sliding boundaries, the top eventually
deforming into a chip during the progression of the simulation. The undeformed chip thickness is
set at 100 microns while the total height of the workpiece is 2 mm. The radius of the tool cutting
edge is assumed to be 10 microns, which is sufficiently small to represent typical experimental
conditions.
Mechanical properties characteristic of lead are taken as: Young’s Modulus of 10 GPa, Poisson’s
ratio of 0.45, and yield strength of 10 MPa [16]. The workpiece material is assumed to be elastic-
Points along trajectory ABCD
perfectly plastic. The coefficient of friction between the tool and the workpiece is assumed to be a
constant, with a value of 0.5 for a simulation of dry cutting and 0.2 for simulation of lubricated
(wet) cutting. The simulations were carried out for tool rake angles between -30º and +30º at 5º
increments.
(a) (b)
Fig. 3: The finite element mesh for cutting with a +10 degree rake angle tool (a) undeformed (b)
after chip formation.
Results
The results of the finite element simulation with the +10 degree rake angle tool (Fig. 4a) show that
the shear strains in chip formation are introduced over a finite deformation zone, similar to what has
been recorded in the high speed images of the machining process. Fig. 4b, which presents the
cumulative strain across the deformation zone, confirms that this zone has a small width.
Furthermore, the cumulative shear strain is seen to reach a steady state value of ~ 2.2 in the chip.
It is of interest to compare the finite element simulation results for the shear strain with
corresponding values estimated using the shear plane model. For this comparison, a representative
value for the shear strain in the chip for each simulation was estimated by evaluating the average
shear strain in the chip. These values are plotted along with the analytic results from Eqs. 1 and 2 in
Fig. 5. It can be seen from Fig. 4 that the shear strain results from the finite element simulation
compare favorably against the shear plane model. Furthermore, the value of the shear strain is seen
to increase with decreasing rake angle, i.e., as the rake angle becomes more negative or less
positive. This observation is consistent again with the prediction of the shear plane model of a
monotonic increase in the value of the shear strain with decreasing rake angle. The shear strain is
seen to be greater when the friction at the tool-chip interface is higher. Lastly, shear strain values as
high as 11 are predicted by the simulation for dry cutting of lead with a -25 degree rake angle tool.
This is similar to measured values of strain reported by Swaminathan et.al. [7]. These results also
demonstrate the powerful capability afforded by the FE simulation in predicting the deformation
(e.g., strain) as a function of machining parameters (e.g., rake angle).
The simulation results suggest that friction plays a prominent role in determining the shear strain
associated with chip formation, especially when machining with negative rake angle tools. This
effect may be attributed to a significant elevation in the stress state of the system in the primary
deformation zone with negative rake tools vis-à-vis positive rake angles. In these situations, the
friction forces the chip material adjacent to the rake face to “stick” to this face, causing the
surrounding material to bypass the “stuck” material by plastically flowing around it. This “stuck”
region of “dead metal” allows material to build up ahead of the tool tip. This effect has also been
observed in experiments [3] and we note the congruence of the model and the experimental results
in this regard. Under dry cutting conditions, for rake angles less than -25º, the FE simulation
predicts infeasibility of chip formation; instead the work material piles up ahead of the tool tip. This
rake angle can be identified as the critical rake angle below which no chip formation is possible.
Such a lack of chip formation has indeed been observed in experiments carried out in our group.
(a) (b)
Fig. 4: Deformation field in dry machining of lead with a +10 degree rake angle tool (a) shear strain
distribution and (b) cumulative shear strain along AB.
Finally, we note close similarity between the experimentally determined variation in cumulative
shear strain and that predicted by this model (Figs. 2b and 4b). The shearing of the material across a
narrow deformation zone, as seen in these figures, would indicate a progressive grain refinement
process that is distributed over this deformation zone. The result is the formation of ultra-fine
grained microstructures in the chip. Transmission Electron Microscopy (TEM) observations of the
deformation zone carried out in Al6061-T6 appear to support this hypothesis.
Concluding Remarks
The finite element model presented here is an important element in modeling the mechanics of large
strain deformation leading to the formation of ultra-fine grained chip microstructures. In showing
that the shear strains in the deformation zone can be varied over a significant range by varying the
tool rake angle-an input parameter- a key step has been taken in relating the machining parameters
(e.g., velocity, rake angle, friction) to the deformation field parameters (e.g., strain, strain rate,
temperature). Such a correlation is necessary for establishing machining as an experimental
framework in which to study the manifold effects of large strain deformation on microstructure and
properties of materials. Comparison of shear strains estimated using the model with direct
measurement of strains made in the deformation zone, have shown more than reasonable
agreement, with further validation studies in progress. Earlier TEM studies of the microstructure of
machining chips have confirmed the occurrence of nanoscale and ultra-fine grained microstructures,
and their dependence on the deformation field. By accurately modeling the mechanics of
deformation and the associated strains, and incorporating microstructure-based models, it will likely
be possible to predict the right combinations of parameters required to fabricate UFG materials of
A
B
A
B
Fig. 5: Variation of cumulative shear strain with
rake angle for dry and lubricated cutting as
determined from the FE simulation. Also shown in
the figure are analytical estimates for the strain
made using the shear plane model (Eqs. 1 and 2)
suitable grain sizes and grain morphologies by machining. The mechanics of microstructure
evolution at different length scales could also be elucidated.
Acknowledgments
We would like to acknowledge NSF grant CMS-0200509 and Department of Energy grant
4000031768 (via UT-Batelle) that supported this work. We are very grateful to Dr Ken Chong (NSF
Program Director for Mechanics and Materials) for his personal interest in and encouragement of
this work.
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