Finite element analysis of the effect of cutting speeds on the orthogonal machining process of AA 6082 (T6) alloy.
Sekar, K.S. Vijay ; Kumar, M. Pradeep
Introduction
Metal cutting process is a complex phenomenon yet to be fully
understood and analyzed. The last five decades has seen many researchers
providing detailed insights into the cutting process. In this context
the advent of the Finite element method has witnessed a spurt in its
usage to interpret the mechanics of the orthogonal cutting process.
Chandrakanth [1] used FEM to analyze the orthogonal cutting process.
Movahhedy [2] used an arbitrary Lagrangian - Eulerian FEM method to
interpret the metal cutting process. Halil [3] studied the effect of
different commercial FE codes on the orthogonal cutting process. Ozel
and Zeren [4] used an explicit ALE method to study the simulation of
AISI 1045 steel. Childs [5] worked on materials subjected to a range of
thermal softening and strain hardening and studied their FE simulations.
Mamalis [6] reported the simulation results of high speed hard turning.
The results of these studies have revolutionized the concept of the
manufacturing process and have helped improve the quality of the tooling
standards. The prediction of critical variables like cutting force,
stress, strain, strain rate and temperature has resulted in creating a
process of maximum efficiency with minimum operating inputs and reduced
cost. The accuracy of the FEM predictions is squarely dependent on the
choice of Flow stress models [7, 8, 9] used to represent the
constitutive behavior of the work material. The J-C and Z-A flow stress
models have been considered in this research work to model and predict
the orthogonal cutting mechanics of AA6082 (T6) alloy material with two
cutting speeds. Jaspers [10] has done quality work with AA 6082 (T6)
alloy with analytical and experimental studies .The FEM investigations
in this work provide more insights into the cutting behavior of AA 6082
(T6) alloy .
Flow stress models
The instantaneous stress required for plastic deformation of the
work material is defined as the Flow stress of a material. It depends on
strain, strain rate, temperature and microstructure. A variety of
methods have been used to determine flow stress data of materials.
Shatla [11] conducted two dimensional orthogonal slot milling
experiments to determine flow stress data. Sartkulvanich [12] used
orthogonal slot milling in conjunction with quick stop tests to
determine the flow stress data through a program called OXCUT. Fang [13]
presented a sensitivity analysis of the flow stress of 18 materials
based on the J-C model. Umbrello [14] explicitly stated the influence of
five different set of material constants of the J-C model to describe
the behavior of AISI 316 L steel. Anurag [15] suggested that strain rate
history significantly affects the flow stress of materials. Ozel and
Karpat [16] used evolutionary computational methods to identify the
constitutive model parameters and hence find out the deformation
behavior of work materials during high strain rate conditions.
Jasper's and Dautzenberg [17] utilized the Split Hopkinson's
test to calculate the flow stress data in metal cutting. Guo [18]
studied an integral J-C model to characterize the material behavior.
Baker [19] used a generic flow stress law to study the influence of
cutting speed on the cutting force and chip formation process. The FEM
results depend on the selection of the appropriate Flow stress model.
The J-C model and the Z-A models have been selected in the present work
to predict the orthogonal cutting behavior of AA 6082 (T6).
Johnson-Cook Model
The Johnson and Cook model [7] is given in equation (1).The work
material flow stress is depicted as a product of strain, strain rate and
temperature effects which induce work hardening, strain rate hardening
and thermal softening respectively.
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (1)
Where [sigma] is the Von-Mises flow stress; [epsilon], the
equivalent plastic strain; [epsilon]', the strain rate;
[[epsilon]'.sub.o], the reference plastic strain rate; T, the
temperature of the work material; [T.sub.melt], the melting temperature
of the work material; and [T.sub.room] , the room temperature.
Coefficient A is the yield strength, B, the hardening modulus, C, the
strain rate sensitivity coefficient; n, the hardening coefficient and m
is the thermal softening coefficient. The strain rate [epsilon]' is
normalized with a reference strain rate [[epsilon]'.sub.o]. The
temperature term in the model reduces the flow stress to zero at the
melting temperature of the alloy leaving the material model devoid of
any temperature effect. The J-C Model suggests that the slope of the
flow stress curve is independently affected by the three terms given in
each bracket and there is an influence of strain on the temperature of
this model due to adiabatic deformation at high strain rates [10].
Zerilli-Armstrong Model
The Zerilli and Armstrong model [8] is given in equation (2).
[sigma] = [[C.sub.0] + [C.sub.2] ([[epsilon].sup.n]) exp
[-[C.sub.3] T + [C.sub.4] T ln ([[epsilon]'.sup.n])] (2)
Where [sigma] is the flow stress, [C.sub.0], [C.sub.2], [C.sub.3]
and [C.sub.4] and n are material constants and T is the absolute
temperature. The strain hardening exponent 'n' is assumed to
be 0.5 for all f.c.c. materials. [C.sub.0] is the stress component that
accounts for the solute and the original dislocation density on the flow
stress. It also represents the stress related to the slip band stress
concentrations at grain boundaries needed for transmission of plastic
flow between the poly crystal grains. The flow stress model is based on
the theory of dislocation mechanics and crystal structure of materials
and distinguishes between the b.c.c and f.c.c lattice structures.
Zerilli and Armstrong assume the flow stress dependence on strain to be
influenced by strain rate and temperature for f.c.c crystals unlike
b.c.c crystals. The material constants for the J-C and Z-A models for AA
6082(T6) are given in Table 1.
Orthogonal cutting experiments
A tube of AA 6082 (T6) material was machined on a Lathe Machine
tool without any coolant. A coated carbide commercial insert with a rake
angle of--5[degrees] and a clearance angle of 5[degrees] was used as the
tool material. A Kistler [type 9257 B] three-component piezo electric
dynamometer was used to measure the cutting force. The chip thickness
was measured and the shear angle calculated from known empirical
formulae. Table 2 shows the experimental set -up parameters for the
orthogonal cutting process.
Finite element modeling and simulation
The FEM code DEFORM--2D[TM], which is based on an updated
Lagrangian formulation for large plastic deformation analysis was used
to perform the Finite element modeling and simulation. The geometry of
the work material was assumed as plastic with dimensions of 10 mm length
and 1.5 mm width and meshed with 5500 four noded quadrilateral elements.
The tool material was modeled as rigid and meshed with 250 elements.
Figure 1 shows the boundary conditions for the FEM model. The
experimental cutting conditions were used in the simulations and the
chip formation process treated as plastic flow. The chip separation
criterion was based on continuous re-meshing. The Flow stress curve was
plotted with the data calculated from the J-C and Z-A models. This is
provided as input to the preprocessor of the FE code. The post processor
plots the parameters like cutting force, chip thickness and shear angle
for the two cutting speeds. These results were compared against the
experimental values and the percentage of error for both the material
models analyzed. The FEM results for effective stress, strain, strain
rate and temperature at the two cutting speeds and the various feed
rates were analyzed.
[FIGURE 1 OMITTED]
Results and Discussion
Cutting Forces
Figures 2 (a) and 2 (b) show the comparison for FEM predicted
cutting forces with the Experimental values for cutting speeds of 34
m/min and 82 m/min respectively. The cutting forces for the J-C and Z-A
model give values significantly lower than the Experimental values for
both the speeds. At a cutting speed of 34 m/min the J-C model predicts
within a deviation of 28 % at higher feed rates of 0.205 and 0.26 mm/rev
and 44% at lower feed rates of 0.102 and 0.159 mm/rev. The Z-A model
gives better results at lower feed rates with deviations under 39% while
giving slightly higher deviation of 33% at higher feed rates. At a
cutting speed of 82 m/min, the J-C model is slightly better than the Z-A
model at higher feed rates where the error is within 16% and above 22%
for the Z-A model. At lower feed rates the deviation is 30-42% for the
J-C model and 33-46% for the Z-A model. The flow stress values
calculated from the J-C and Z-A models are lower than the experimental
values for AA 6082 (T6), which resulted in lower cutting forces and high
percentage error for both the cutting speeds. Jasper's [10]
compared the theoretical and experimental cutting forces for AA 6082
(T6) alloy in his research work and produced a similar result. The FEM
results with J-C model at a cutting speed of 82 m/min produced better
results than the values at a cutting speed of 34 m/min and the
predictions matched experiments better than the Z-A model for the
undertaken cutting conditions.
[FIGURE 2 OMITTED]
Chip thickness and Shear angle measurements
Figures 3(a) and 3 (b) show the values of chip thickness as
calculated from Experiments and predicted by FE simulations with J-C and
Z-A models. At a cutting speed of 34 m/min, the J-C model predicted
within deviations of 22% at intermediate feed rates of 0.159 and 0.205
mm/rev and 2% at lower and higher feed rates of 0.102 and 0.26 mm/rev.
The deviations with the Z-A model were under16 % at intermediate feed
rates and lower than 37% at low and high feed rates. At a cutting speed
of 82 m/min the J-C model predicts the chip thickness within a deviation
of 5% at intermediate feed rates and within 15% at lower and higher feed
rates. The Z-A model in contrast gives a deviation of 17-28 % at
intermediate feed rates and 5-54% at the low and high feed rate values.
The geometry of the chips generated by the two models at the two cutting
speeds was comparable to the experiments. The J-C model predicted the
chip parameters better than the Z-A model at a cutting speed of 82
m/min.
Figures 4(a) and 4(b) shows the comparison of shear angle values
for the Experiments and the J-C and Z-A models. At a cutting speed of 34
m/min the J-C model produced deviations of 2-39 % and the Z-A model
3-50% across the feed rates suggesting the inability to predict the
cutting process at lower cutting speeds. At a cutting speed of 82 m/min
the values predicted by both the flow stress models are in close
agreement with the experimental values. The J-C model gives a better
approximation of the shear angle within an error percentage of 0.2-2%.
The Z-A model predictions are slightly on the higher side with a
deviation of 2-9 % across all feed rates. At a feed rate of 0.102 mm/rev
both the models estimate the shear angle with marginal deviations from
the experiments. The error percentage shows an increasing trend for the
Z-A model as the feed rate increases from 0.159-0.26 mm/rev suggesting
its inadequacy in high feed rate predictions. The J-C model predicts the
shear angle better than the Z-A model for a cutting speed of 82 m/min.
[FIGURE 3 a-b OMITTED]
[FIGURE 4 a-b OMITTED]
Effective stress distribution
Figures 5 (a), 5(b), 5(c) and 5(d) show the FEM contours for
effective stress distribution for the J-C and Z-A models for cutting
speeds of 34 m/min and 82 m/min at a feed rate of 0.159 mm/rev. The J-C
and Z-A stress contours for a cutting speed of 82 m/min shows better
stress distribution in the shear plane than the contours for a cutting
speed of 34 m/min. The maximum stress values for the J-C and Z-A models
at a cutting speed of 34 m/min were 667 MPa and 692 MPa. At a cutting
speed of 82 m/min the maximum stress value of 683 MPa and 712 MPa was
achieved at the secondary deformation zone near to the sticking region
by the J-C and Z-A models respectively. The stress values decreased at
the primary deformation zone to 598 MPa and 623 MPa for the J-C and Z-A
models at 82 m/min and to 583 MPa and 606 MPa at a cutting speed of 34
m/min for both the models. The effective stress values predicted by both
the models for both cutting speeds are lesser than the theoretical
stress values [10], though the nature of stress distribution achieved by
both the cutting speeds and models was consistent with the principles of
orthogonal metal cutting. The lower stress predictions by both the
models are the result of thermal softening and work hardening effects at
the shear plane. The stress distributions for higher feed rates of 0.205
and 0.26 mm/rev gives better approximations with the J-C model than the
Z-A model for both the cutting speeds. The Z-A model for a cutting speed
of 82 m/min gives a marginally better result for the stress distribution
at a feed rate of 0.102 mm/rev. The J-C model appears more suitable to
predict the stress pattern of AA6082 (T6) alloy at a higher cutting
speed of 82 m/min.
[FIGURE 5 a-b OMITTED]
[FIGURE 5 c-d OMITTED]
Effective strain distribution
Figures 6 (a), 6 (b), 6(c) and 6(d) show the FEM contours for
effective strain for the J-C and Z-A models for cutting speeds of 34
m/min and 82 m/min at feed rate of 0.159 mm/rev. The maximum strain
values at a cutting speed of 34 m/min were 2.34 at the chip-tool
interface and 3.29 at the primary deformation zone for the J-C and Z-A
models. The values at the primary deformation zone were 0.877 and
1.24.At a cutting speed of 82 m/min the J-C and Z-A models estimated the
maximum strain values of 2.51 and 2.90 at the chip-tool interface
indicating the severity of the material deformation at this secondary
deformation zone. The values at the primary deformation zone were 0.942
and 1.09 for the J-C and Z-A models. The effective strain contours
reveal the nature of work hardening and residual deformation in the chip
and the work piece. The effective strain values at 82 m/min for both the
models are consistent with experiments. The strain values decreased
gradually from the primary shear zone to the uncut work piece. The J-C
model strain contours across the primary and secondary deformation zones
are evenly distributed while the Z-A model shows higher strain in the
same region. The J-C and Z-A model contour at 82 m/min predicted values
within 2% and 6 % of the experiments across all feed rates while the
values were within 22% and 26 % at a cutting speed of 34 m/min. The
results suggest that the J-C model predicts the strain distribution of
AA 6082(T6) alloy better than the Z-A model for both the cutting speeds
and the strain contours at 82 m/min match the experiments better than
the values at 34 m/min.
[FIGURE 6 a-b OMITTED]
[FIGURE 6 c-d OMITTED]
Effective strain rate distribution
Figures 7(a), 7(b), 7(c) and 7(d) show the FEM contours for
effective strain rate distribution for the J-C and Z-A models for
cutting speeds of 34 m/min and 82 m/min at feed rate of 0.159 mm/rev. At
a cutting speed of 34 m/min the J-C and Z-A models estimate maximum
values of 3090 [s.sup.-1] and 3550 [s.sup.-1] respectively at the
tool-chip interface. The values at 82 m/min were much higher and
appropriate at 7410 [s.sup.-1] and 6990 [s.sup.-1] for both the models.
The strain rate contours reveal high values at the shear plane and tool
tip region. The predicted strain rate values for both the models are
similar at feed rates between 0.159 and 0.26 mm/rev, but show a marked
difference at a low feed rate of 0.102 mm /rev under the given cutting
conditions. It is evident that higher stress is required to deform the
material plastically due to the effect of strain hardening. The FEM
results for strain rate are consistent with the experimental results of
Jaspers [10].The Split Hopkinson's test apparatus [10, 17, 20, 21,
22, ] and Rastegaev type compression experiments [10, 17] for high and
low strain calculations show the dependence of flow stress on strain
rate. There is a steep fall in the flow curve between a temperature of
200 and 400 ??C due to removal of the T6 temper. The thermal softening
and strain hardening values predicted by the ZA model are incorrect as
found by Jaspers [10, 17]. The predictions at a lower cutting speed of
34 m/min do not represent the cutting mechanics appropriately. The J-C
model at a cutting speed of 82 m/min is marginally better suited to
predict the effective strain rate distribution for the given material
and conditions than the Z-A model.
[FIGURE 7 a-b OMITTED]
[FIGURE 7 c-d OMITTED]
Temperature distribution
Figures 8(a), 8(b), 8(c), 8(d) show the FEM contours for
temperature distribution for the J-C and Z-A model for cutting speeds of
34 and 82 m/min and a feed rate of 0.l59 mm/rev. The maximum temperature
values were 249[degrees]C and 289[degrees]C at a cutting speed of 34
m/min, which is lesser than the experiments. At a cutting speed of 82
m/min the maximum temperature values of 350[degrees]C and 370[degrees]C
are reported at the secondary deformation zone where the effective
strain values are also high. The temperature distribution at the shear
plane with the J-C model gives a value in the range of 150-270[degrees]
C and the Z-A model depicts a value in the range of 158-285[degrees]C
for a cutting speed of 82 m/min, which is marginally higher than the
temperature of AA6082 (T6) alloy, which is around 190[degrees]C[10]. The
corresponding values were in the range of 112[degrees] C-194[degrees]C
and 127[degrees]C--224[degrees]C at a cutting speed of 34 m/min. At both
the cutting speeds, the J-C model approximations for the feed rates of
0.102, 0.205 and 0.26 mm/rev predicted better values than the Z-A model.
At a cutting speed of 82 m/min the temperature values predicted by the
J-C model are marginally better than the values predicted at 34 m/min
though the shear plane temperatures predicted by the J-C model at 34
m/min is in agreement with the experiments [10].
[FIGURE 8 a-b OMITTED]
[FIGURE 8 c-d OMITTED]
Conclusions
The Finite element simulation of the orthogonal machining process
of AA 6082(T6) alloy was compared with the Experiments. The Johnson-Cook
and the Zerilli--Armstrong flow stress models were used to model the
material behavior of AA6082 (T6) alloy. The FEM results for Cutting
force, Chip thickness and Shear angle for cutting speeds of 34 m/min and
82 /min were compared with the Experimental results. The Effective
Stress, Strain, Strain rate and Temperature contours for both the
cutting speeds were analyzed to interpret the cutting process of the
given material.
The FEM results for both the cutting speeds produced low values for
the cutting force due to the reduced flow stress values computed with
the J-C and Z-A models. At a cutting speed of 82 m/min the J-C model
predicts the cutting forces within a deviation of 16% at elevated feed
rates of 0.205 and 0.26 mm/rev while the Z-A model shows slightly higher
deviations up to 22%. The deviations are on the higher side at 28% and
33 % for the two models respectively at a lower cutting speed of 34
m/min. The J-C model predictions at 82 m/min for chip thickness show a
5-15% deviation across all feed rates while Z-A model errors go up to
5-54%. The errors further increase for a cutting speed of 34 m/min for
the J-C model at 1-22% and marginally decrease to 12-37 % for the Z-A
model. The J-C model prediction at 82 m/min for shear angle is closer to
the experiments with errors limited to 2% while the Z-A model predicts
within an error of 9%. The errors in predictions at a cutting speed of
34 m/min are on the higher side at 39 % and 50 % for the two models. The
J-C model at a cutting speed of 82 m/min predicts the cutting forces,
chip thickness and shear angle comparatively better than the Z-A model
at either cutting speeds.
The Effective stress, strain, strain rate and temperature contours
show some consistency in the predictions. The thermal softening and
strain hardening effects oppose the flow stress of the material which
resulted in lower stress predictions. The effective strain contours
revealed the nature of work hardening and residual deformation in the
chip and the work piece. The effective strain rate and temperature
distribution accurately predicted the effects of strain rate hardening
and thermal softening respectively. The effective stress, strain, strain
rate and temperature predictions of the J-C Model for a cutting speed of
82 m/min are better than the results at 34 m/min. The J-C model is
qualitatively superior to the Z-A model in simulating the orthogonal
cutting mechanics of AA 6082 (T6) alloy.
Acknowledgement
The Authors wish to acknowledge the contribution of the Central
workshop of the Mechanical Department at the College of Engineering,
Anna University, Chennai, India, for providing the infrastructure for
the experimental work.
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K.S. Vijay Sekar (1) and M. Pradeep Kumar (2)
(1) Asst. Professor, Department of Mechanical Engineering, SSN
College of Engineering, Chennai, India, E-mail: vijaysekarks@ssn.edu.in
(2) Asst. Professor, Department of Mechanical Engineering, CEG,
Anna University, Chennai, India
Table 1: Material constants for the J-C Model and Z-A Model for
AA 6082 (T6) [10].
Constants J-C Model Constant Z-A Model
A (MPa) 428.5 [C.sub.0] (MPa) 0
B (MPa) 327.7 [C.sub.1] (MPa) --
C 0.00747 [C.sub.2] (MPa) 3551.4
n 1.008 [C.sub.3] ([K.sup.-1] 0.00341
m 1.31 [C.sub.4] (K.sup.-1 0.000057
[T.sub.melt] K (855 n 0.5
Table 2: Experimental set up parameters.
Work material Tube of AA 6082 (T6) alloy
Work dimensions (mm x mm) 250 x 80 (length x outer diameter)
Tube thickness (mm) 2.5
Tool material Coated carbide insert
Cutting Speeds (m/min) 34 and 82
Feed rates (mm/rev) 0.102, 0.159, 0.205, 0.26
Cutting conditions Without coolant
