Research Journal of Applied Sciences, Engineering and Technology 2(8): 749-756, 2010
ISSN: 2040-7467
© M axwell Scientific Organization, 2010
Submitted date: October 16, 2010
Accepted date: November 05, 2010
Published date: December 10, 2010
Study of Residual Stress Tensors in High-Speed Milled Specimens of
Aluminium Alloys Using a Method of Indent Pairs
1
C.A . Mammana, 1 F.V. Díaz, 2 A.P.M. Guidobono and 3 R.E. Bolm aro
Departamento de Ingeniería Electrom ecánica - Departamento de Ingeniería Industrial,
Facultad Regional Rafaela, Universidad Tecnológica Nacional, Bvd Roca 989,
2300 Rafaela, Argentina
2
División Metrología D imensional, Centro Reg ional Rosario (INT I) Ocampo y Esm eralda,
2000 Rosario, Argentina
3
Instituto de Física Rosario (CO NIC ET - UN R) B vd 27 de Febrero 210 bis,
2000 Rosario, Argentina
1
Abstract: From data obtained using a method of indent pairs it was possible to analyse different residual stress
states generated in high-speed milled specimens of AA 6082-T6 and AA 7075-T6 aluminium alloys. The
present method integrates a special device of indentation into a universal measuring machine, allowing the
introduction of elongated indents to significantly reduce the absolute error of measurement. Diverse protoc ols
for operations of high-speed face milling allow us to compare residual stress tensors inherent to climb and
conventional cutting zones. Through an exha ustive analysis of the Mohr’s circles correspo nding to those zones,
a relationship was detected, which expre sses the sensitivity of both alloys to develop surface residual stresses.
Key words: Aluminium alloys, climb cutting, conventional cutting, high speed milling, process parameters,
residual stresses
INTRODUCTION
Machining is a manufacturing process that plays an
important role in the econo my of almost every country.
The costs of diverse types of machining can be reduced
increasing the volume of chips cut per unit of time
(Trent, 1991). The fast development of machines and tool
materials has allowed to augment the values of principal
processing parameters, converting the conventional
machining in to H ig h-S peed M achinin g (H SM )
(King, 1985; Sch ulz, 1996). Although each HSM
operation presents a series of technological challenges due
to the great speed of some the components, significant
benefits can be obtained by this type of machining such as
reduced operation time, longer service time of tools and
higher productivity. On the other hand, residual stresses
generated at the surface of a high-speed m achined part
can considerably affect its useful life (Mantle and
Aspinw all, 2001; W ithers, 20 07).
During the last decad es, differe nt exp erimental
techniques have been deve loped and g reatly impro ved in
order to determine with high accuracy the residual
stresses generated in the processing of engineering
materials (Rowlands, 1987; Lu, 1996; Withers and
Bhadeshia, 2001). In the case of machining, two
approaches have been w idely used: X-ray diffraction
technique (Fuh and W u, 1995; M `Saoubi et al., 1999;
Hua et al., 2005) and the hole-drilling method (B ouzid
Saï et al., 2001; Capello, 2005). However, in recent years
different techniques based on instrumented indentation
have been used in order to study different issues of
residual stresses in machining. Warren et al. (2005) used
nanoindentation to perform a study that focused on
understanding the basic relationships between mechanical
behaviour, residual stress, and m icrostructure of the
machined subsurface. Then, Wyatt and Berry (2006)
developed a method o f inden t pairs in order to perform
different studies of residual stresses in high-speed milled
componen ts. More recently, Díaz et al. (2010) studied the
influence of mechanical and thermal mechanisms on the
residual stress generation in high-speed machined
specimens of different aluminium alloys using an
impro ved method of inden t pairs.
In this study, this method of ind ent pairs is used to
carry out a detailed and accurate evaluation of residual
stress tensors inherent to climb and conventional cutting.
For this purpose, different tests of high-speed face milling
were carried out in specimens of AA 6082-T6 and AA
7075-T6 aluminium alloys. It must be noted that through
face milling o perations it is possible to ge nerate machined
regions corresponding to climb and conventional cutting
(Trent, 1991). The above-mentioned tests were performed
Corresponding Author: F.V. Díaz, Departamento de Ingeniería Electromecánica - Departamento de Ingeniería Industrial,
Facultad Regional Rafaela, Universidad Tecnológica Nacional, Bvd Roca 989, 2300 Rafaela, Argentina.
Tel: + 54 3492 432710; Fax: + 54 3492 422880
749
Res. J. Appl. Sci. Eng. Technol., 2(8): 749-756, 2010
Table 1: Chemical compositions and mechanical properties of the evaluated alloys
Alloy
Ch emical co mpo sition (w t %)
--------------------------------------------------------------------------------Mg
Si
Mn
Fe
Cr
Zn
Cu
Al
6082-T6
0.91 0.87
0.58
0.5
0.22
0.2
0.16
balance
7075-T6
2.52 0.2
0.16
0.32
0.17
5.6
1.72
balance
Tab le 2: To ol geo metry
Ra ke a ngle
( (<)
45
an d pro cess pa rameters
Cle aran ce an gle
" (<)
7
En tranc e an gle
P (<)
45
Mechanical properties
--------------------------------------------------------------------------F u (Mpa)
F y0.2 (Mpa)
A (% )
HV 0.5
340
310
11
108
564
506
11
186
Cutting speed
V (m/min )
1000
in a numerically controlled vertical milling machine. The
depth of cut was varied in order to evaluate its effects on
stress tensors. Different Mohr’s circles (Gere, 2001)
corresponding to the climb and conventional cutting zones
were drafted in order to evaluate ex haustively these
effects in both zones. Finally, this evaluation allowed us
to identify a relation ship between the sensitivities of both
alloys to develop residual stresses.
Fee d rate
f (mm /rev)
0.2
Depth of cut
d (mm )
1.00 – 1.25
which have good machinability (curled or easily broken
chips and g ood to excellent finish). AA 6082-T6 is a
relatively new alloy, which is used in structural
applications in the marine and transportation industries as
we ll as for precision machined parts in the automotive
industry. On the other hand, AA 7075-T6 is a structural
alloy widely used for aircraft, aerospace and defence
applications due to its high mechanical resistance/weight
ratio. Table 1 shows both the chemical compositions and
mechanical properties of these alloys. The specimen
shape and dimensions are shown in Fig. 1. Before the
machining tests, the specimens were annealed to remove
residual stresses generated during the manufacturing
operations. The temperature and time corresponding to the
distension procedure were 573 K and 80 min,
respectively. The milling tests were performed with a face
mill of 63 m m in diameter. Five tungsten carbide inserts
(Palbit SEH T 1204 AF FN-A L SM 10) we re incorporated
to the face mill. These inserts were specially designed
for using with different types of aluminium alloys. In
Table 2, both the insert geometry and high-speed
parame ters selected for this work are detailed. The tests of
high-speed face milling were performed in a numerically
controlled vertical milling mach ine (Clever C MM-100).
Figure 2 shows an upper view of the specimen-cutting
tool system. As it can be seen, the processed surface can
be divided in two zones corresponding to climb and
conventional cu tting.
Using the present method of indent pairs it is possible
to evaluate the residual stress state at any point of the
milled surface. Taking into account the above mentioned
study (Díaz et al., 2010 ), two representative points were
selected. Figure 3 shows these points, w hich are located
at the barycentres of the climb and conventional cutting
zones. The elongated indents were introduced at the
corners of two adjacent squares. The coordinates of these
inden ts were m easured b efore and after a distension
treatment, within a temperature range of 20±0.2ºC, using
a measuring machine GSIP MU -314. Finally, the
distension treatment was performed at a temperature of
573 K during 80 m in.
MATERIALS AND METHODS
This study was carried out in the year 2009 at the
Departamen to de Ingeniería Electromecánica and the
Departam ento de Ingeniería Industrial, Facultad Regional
Rafaela, U niversidad T ecno lógica Naciona l.
Experimental work: The m ethod of inde nt pairs consists
in determ ining the change in indent spacing, w hich is
produced when the specimen is subjected to a distension
procedure (Wyatt and Berry, 2006). First, the indent
coordinates are measured before and after the distension
using a Univ ersal M easu rin g M achin e (U M M ) and then,
the components of the residual stress can be evaluated by
classical and/or empirical analysis. It is important to note
that if the distension treatment is performed below the
recrys tallization temp erature (M ao, 20 03), th e
dimensional chan ges at the specimen will be governed
only by the elastic relaxation of the lattice. Therefore, the
com ponents of the residual stress can be obtained from
the strain components using an elastic model
(Timoshe nko and G oodier, 1970).
In this work, sev eral indents are introduced using an
indentator device that is sp ecially integrated to the U M M .
Through this integration it is possible to obtain a great
accu racy in the optical localization of those indents. It is
also possible to introduce elongated indents, from which
the uncertainty of specimen repositioning after the
distension treatment can be reduced. The maximum
abso lute errors corresponding to pyramidal and elongated
indent distances were compared in a previous study
(Díaz et al., 2010); for a nominal distance of 28 mm, the
obtained values were ±1.51 and ±0.26 :m, respectively.
This reduction allowed us to substantially diminish the
abso lute error of stress components, which in turn enabled
to extend the sensitivity of the method below 6% of the
yield stress.
The experimental work was carried out in specimens
of AA 6082-T6 and AA 7075-T6 aluminium alloys,
Residual strain and stress determination: For the points
A and B in F ig. 3 it is possible to determine norm al strain
com ponents in three directions. Two of these,
corresponding to the components g x and g y , are
orthogonal. The direction of the other com ponent, g 4 5 ,
750
Res. J. Appl. Sci. Eng. Technol., 2(8): 749-756, 2010
Fig. 1: Test specimen. The units are in mm and the thickness is 4 mm
Fig. 2: Diagram of the face milling operation
corresponds to the bisector of the angle formed by the
directions inherent in g x and g y . These compo nents of
residual strain can be expressed as:
Fig. 3: Barycentres of climb and conventional cutting zones
Besides, through the compon ents g x , g y and ( xy , it is
possible to express the normal and shear com ponents
associated to an arbitrary direction (Gere, 200 1):
(1)
whe re lx and l’x are the mean values of the horizontal sides
of the square (Fig. 3), and ly and l’y are the mean values of
the vertical sides, for both cases before and after the
distension, respectively. In addition, the distances l4 5 and
l’4 5 correspond to the diago nal of the mentioned square,
also before and after the distension, respectively.
Then, the shear strain com ponent ( xy can be obtained
from the no rmal com ponen ts using (Ge re, 2001):
(3)
whe re 2 is the angle formed by the arbitrary direction and
the axis y = 0 (Fig. 3).
As mentioned above, if the distension procedu re is
performed below the recrystallization temperature, the
dimensional change of the evaluated surface will be
caused by the elastic relaxation o f the lattice. Therefore,
if the evaluated surface is considered to be under planestress conditions (Timoshenko and Goodier, 1970), the
(2)
751
Res. J. Appl. Sci. Eng. Technol., 2(8): 749-756, 2010
infinitesimal element w hose axes were rotated an angle 2
with respect to the reference ax es (Gere, 20 01). In
addition, the different point at each circle relates to the
reference direction (2 = 0 in F ig. 3).
M ohr’s circles correspon ding to the bary centre of
climb cutting zone (point A) are show n in Fig . 4a. It is
worth noting that in this zone the Vy component of cutting
speed and feed rate have the same directions. By
comparing the circles, it is obvio us that the normal
stresses in alloy 6082-T6 are lower (more compressive)
than those corresponding to alloy 7075-T6. In addition,
alloy 6082-T6 shows higher sensitivity when the depth of
cut is incre ase d. Figure 4b show s M ohr’s circles
corresponding to the baryce ntre of conventional cutting
zone (point B). In this zone, the Vy com ponent and feed
rate have opposite directions. Altho ugh this circle
arrangement is similar to that of point A, all circles
associated to point B are slightly shifted to the left, which
means that normal stresses are more comp ressive in the
region corresponding to conventional cutting. It occurs
that this type of cutting is so light at the beginning that
each insert slides on the specimen surface until sufficient
pressure is built up and it begin s to cut. This introduces a
small additional increase in local plastic deformation of
the machined surface, which does not occur in the case of
climb cutting (Trent, 1991).
Figure 5 shows the F p component of the normal
stress, which corresponds to a principal direction, as a
function of the depth of cut for both tested alloys. It
shou ld be no ted that the principal directions are those
associated to the normal components with the maximum
and minim um values (G ere, 2001). In o ur case, F p
corresponds to the most compressive component. It can be
observed that the different gradients corroborate each
alloy has a singular way of changing when the depth of
cut is increased. For each alloy, the stress increment does
not depe nd on the evaluated barycentre. Moreover, the
differences betw een the values correspo nding to these
barycentres would no t be dependent neither on the alloy
type nor on the value of depth o f cut. Table 3 reports the
increm ents of F p due to the variation of depth of cut. It
must be noted th at all increments are negative. In
addition, the values are similar on both barycentres. From
Table 3, it is possible to express a relationship between
the increments corresponding to both alloys:
residual stress components for the case of a homogeneou s,
isotropic and linear-elastic material can be expressed as:
(4)
whe re k 1 = E / ( 1 - L² ), k 2 = L · k 1 , E is the longitudinal
elastic mod ulus, G is the shear elastic modulus and L is
the Poisson’s ratio. It is possible to assert that the residual
stress state at a point of the ev aluated surface is
com pletely defined by the components F x , F y , and J x y .
How ever, it could be necessary to evaluate residual stress
com ponents associated to other directions. The normal
and tangential components in an arbitrary direction 2 can
be obtained through (G ere, 2001):
(5)
It is worth noting that these components show a
continuous variation in function of the angle 2. In
addition, these can be represented using a graphical
format known as Mohr’s circle (Timoshenko and
Goo dier, 1970). This graphical representation is very
useful because it allows visualizing the relationships
between normal and shear com ponents co rrespo nding to
different orientations. Moreover, this representation also
enables to appreciate c learly the intervals of variation of
each com ponent.
Furthermore, the errors inherent in residual strain and
stress com ponents were obtained fro m the absolute error
corresponding to indent distances using the equation
of the probable absolute error (Bevington and
Robinson, 2002). The values corresponding to these
components were ±0.001% and ±0.9 MPa, respectively.
RESULTS AND DISCUSSION
It is possible to evaluate different Mohr’s circles for
each significant point of the studied surfaces in order to
clearly comp rehend the different residual stress states
generated by H SM . As mentioned above, two
representative points situated at the barycentres of the
conventional and climb cutting zones were selected
(points A and B in Fig. 3). Mohr’s circles corresponding
to these points are shown in Fig. 4. It is important to note
that orthogonal coordinates at each point represent the
values of residual stress components corresponding to an
Tab le 3: P rincip al stres s incr eme nts
(MP a)
Alloy
6082-T6
7075-T6
752
----------------------------------------------------------Po int A
Po int B
- 7.23
- 6.82
- 3.32
- 3.36
Res. J. Appl. Sci. Eng. Technol., 2(8): 749-756, 2010
Fig. 4: Mohr’s circles corresponding to the barycentres (a) A and (b) B
Fig. 5: Principal stress corresponding to the barycentres A and B
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Res. J. Appl. Sci. Eng. Technol., 2(8): 749-756, 2010
temperature increm ents. Figure 6 show s the effe cts
associated to the principal stress increments. From
climb to conventional cutting zone, the principal
s t r e s s c ha nge s a re simila r i n b o th a l lo y s
because the cutting force
increm ents are low (the mechanical effect prevails). On
the other hand, when the depth of cut is modified, higher
cutting force increm ents m ake p ossible the manifestation
of the thermal effect. Finally, it is possible to expect the
surface temperature increments, related to the change in
depth of cut, responding to a relationship similar to that
obtained for p rincipal stress increme nts.
CONCLUSION
Fig. 6: Effects associated to the principal stress increments
The measurement procedure carried out in this work
allowed a comp lete evaluation of the residual stress
components in representative points of different machined
surfaces, which correspond to zones of climb and
conventional cutting. This evaluation included the
residual stress compo nents associated to arbitrary
directions, which made possible to comprehend the
complete variation of the normal and shear componen ts.
The normal co mpon ents are distributed in reduced ranges
around small values, and they are also compressive. On
the other hand, the tangential componen t values are
concentrated in reduced ran ges around zero .
The sensitivity of the present method e nabled to
detect a small difference between the residual stresses
associated to climb and conventional cutting zone s. This
difference would be related to the influence of the relative
orientation of the vectors Vy and f on the generation of
local plastic strain. Regarding the principal components of
residual stress, it was observed that each alloy has a
singular way of changing when the depth of cut is
increased. In addition, alloy 6082-T6 showed larger
susceptibility to be stressed. Th e difference in the
susceptibility between both alloys could be quantified by
a relationship associated to the stress tensors. This
relationship is the same for climb and conventional
cutting zone s. Finally, this susceptibility difference would
be due to the differenc es in the thermal flow from the
cutting primary zone to specimen surface, which is always
highe r for the case of alloy 6082-T6.
which would qu antify the sensitivity difference to the
chan ge in depth of cut when the values corresponding to
F p are evaluated. This relationship is similar to
(Díaz et al., 2010 ):
which was obtained in a previous work , for the stress
component perpendicular to the feed direction, when the
barycentres of entire surfaces generated by HSM were
evaluated. It is important to note that the present
relationship corresponds to the stress tensors because the
associated direction s are not the sa me fo r both alloys.
The difference on sensitivity between both alloys,
which is similar in both evaluated regions, could be
explained from thermal effects generated in the cutting
zone. First, it is possible to expect the the rmal energy in
the cutting primary zone to be similar for both alloys
because the machin ability difference between them could
com pensate the small difference in cutting forces (higher
for alloy 7075-T6) (Díaz et al., 2010). It must be noted
that alloy 6082-T6 is m ore difficult to machine because
the magnesium it contains is essentially tied up w ith
silicon to fo rm hard M g2 Si particles (Kamiya and
Yakou, 2008). Secondly, the fraction of the energy
generated in the cu tting prim ary zo ne that enters in the
machined surface will always be higher for alloy 6082T6, which basically responds to the difference on thermal
conductivity between both alloys (K 6 0 8 2 /K 7 0 7 5 = 1.3) (Özel
and Zeren, 2004). Due to this thermal effect, stresses are
always more compressive for alloy 6082-T6. When the
depth of cut is increased, the change in cutting forces is
similar for both alloys (Díaz et al., 2010). Therefore, the
difference between the principal stress inc reme nts would
respond to a precise difference between surface
ACKNOWLEDGMENT
The authors w ish to express their sincere thanks to
Eduardo Cravero and Silvio Acosta for their assistance
during HSM test pha se. Th is work was supported by the
Departam ento de Ingeniería Electromecánica and the
Departam ento de Ing eniería Industrial, Facultad Regional
Rafaela, U niversidad T ecno lógica Naciona l.
754
Res. J. Appl. Sci. Eng. Technol., 2(8): 749-756, 2010
NOMENCLATURE
A
d
E
f
G
HV0.5
k1, k2
K
lx , l’x
ly , l’y
l4 5 , l’4 5
V
Vx
Vy
"
(
( xy
( x'y'
gx
g x'
gy
g45
2
L
Fx
F x'
Fy
Fp
Fu
F y0.2
J xy
J x'y'
P
REFERENCES
elongation (% )
depth of cut (mm)
longitudinal elastic mo dulus (G Pa)
feed rate (mm/rev)
transverse elastic modulus (G Pa)
Vickers micro-hardn ess (test load: 500 gf)
elastic constants
thermal con ductivity (w/( mAK ))
mean values of the horizontal sides of the square,
before and after the stress-relieving, respectively
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mean values of the vertica l sides of the squa re,
before and after the stress- relieving, respectively
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length of the square diag onal, before and after the
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cutting speed (m/min)
cutting speed component at the x directio n
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cutting speed comp onent at the y directio n
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clearance angle (deg)
rake angle (deg)
tangential deformation component
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