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Effect of machining parameters and heat treatment on the residual stress distribution in titanium alloy IMI-834
Journal of Materials Processing Technology 139 (2003) 628–634
Effect of machining parameters and heat treatment on the residual stress distribution in titanium alloy IMI-834 B.R. Sridhar∗ , G. Devananda, K. Ramachandra, Ramaraja Bhat Gas Turbine Research Establishment, Bangalore 560 093, India
Abstract The residual stress variation in titanium alloy IMI-834 as a function of depth following milling at different feeds, speeds and depths of cut was determined by a strain-gauge technique involving blind-hole drilling. The residual stresses were found to be compressive in nature and to be dependent upon the milling parameters. Heat treatment was found to relieve the residual stresses, the degree of stress relief being found to increase with increase in temperature. Optimum temperatures were determined at which significant relaxation occurred without adversely affecting the microstructure and mechanical behaviour of the material. © 2003 Elsevier B.V. All rights reserved. Keywords: IMI-834; Strain-gauge technique; Residual stress
1. Introduction IMI-834 is a near-␣ titanium alloy with the nominal composition Ti–5.8Al–4.5Sn–4Zr–0.7Nb–0.5Mo–0.40Si–0.06C. This is a creep resistant alloy with a service temperature up to 600 ◦ C and is primarily intended for gas turbine aero-engine applications such as discs, rings and blades. Residual stresses play an important role in determining the fatigue life of a component. This calls for relieving these stresses in such cases where an adverse effect is seen on the fatigue life. This paper highlights the variation in the magnitude and distribution of residual stresses locked up in the material following a milling operation at different speeds, feeds and depths of cut. The effects of varying temperature in relieving these stresses have also been discussed in the paper. Residual stresses were measured by the standard straingauge technique involving blind-hole drilling [1–7]. The method calls for the use of a strain-gauge rosette of the size 25 mm × 25 mm (shown schematically in Fig. 1) supplied by Micro-measurement Group, USA [5]. If ε1 , ε2 and ε3 are the values of the relieved strain noted from strain gauges 1, 2 and 3, respectively, of the strain gauge rosette used during blind-hole drilling, the principal residual stresses σ max and σ min are calculated as below:
σmax
ε3 + ε1 = − 4A
σmin
ε3 + ε1 + = 4A
tan 2α =
(ε3 − ε1 )2 + (ε3 + ε1 − 2ε2 )2 4B
(1)
(ε3 − ε1 )2 + (ε3 + ε1 − 2ε2 )2 4B
(2)
ε3 + ε1 − 2ε2 ε3 − ε 1
(3)
where A=−
(1 + ν)¯a 2E
and
B=−
b¯ 2E
(4)
in which α is the angle made by σ max with respect to gauge 1, ν the Poisson’s ratio of the material and a¯ and b¯ are the uniform stress coefficients determined by Schajer by finite element studies, and available as a function of Z/D (hole depth/hole diameter). The residual stresses in the cutting direction (σ c ) and normal direction (σ n ) were calculated using the expressions: σc + σn = σmax + σmin
(5)
σc − σn = (σmax − σmin ) cos 2θ
(6)
where θ is the angle made by σ c with σ max .
2. Experimental procedures ∗ Corresponding author. E-mail address: [email protected] (B.R. Sridhar).
0924-0136/03/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0924-0136(03)00612-5
Hot-rolled, solution-treated and ground pickled 50 mm diameter bars were machined into 38 mm × 25 mm × 15 mm
B.R. Sridhar et al. / Journal of Materials Processing Technology 139 (2003) 628–634
629
An air turbine assembly was used to drill a blind hole at the centre of the strain-gauge rosette (Fig. 1) used in the experiment. Drilling was carried out at incremental depths and at each depth the relieved strains, ε1 , ε2 and ε3 (of the strain gauges 1, 2 and 3 from the strain-gauge rosette) were noted. These strains were used in the evaluation of residual stresses by the use of Eqs. (1)–(6).
3. Results Figs. 2–9 present plots of the residual stress distribution as functions of depth below the surface for different milling parameters employed in the present study. Negative values of the maximum and minimum residual stresses indicate that the residual stresses were compressive in nature. The maximum stresses in the cutting and normal directions were found to be at a depth of about 0.1 mm below the surface. 3.1. Effect of feed (constant v and d) Fig. 1. Strain-gauge rosette arrangement for measuring residual stresses.
rectangular test-pieces. In order to remove the residual stresses induced during the fabrication of specimens, the test-pieces were stress relieved by keeping them at 600 ◦ C for 1 h in a vacuum furnace followed by an argon gas quench. The machining operations were carried out on FN-2V HMT milling lathe, 5 HP capacity, using a T Max K-20 face milling cutter of 50 mm diameter and four TN-35-M titanium nitride coated inserts (TPAN-1603 PPN, WIDIA). Servo Cut ‘S’ 1:20 soluble oil was employed as a cutting fluid. The test-pieces were milled at different milling parameters by varying the speed (v, m/min), feed (f, mm/tooth/rev.) and depth of cut (d, mm) as given in Table 1. Test-pieces milled with the parameters, v = 11 m/min, f = 0.056 mm/tooth/rev., d = 0.25 mm were stress relieved at 400, 500 and 600 ◦ C for 1 h in a vacuum furnace followed by an argon gas quench. Both the machined and heat-treated test-pieces were subjected to residual stress measurement by blind-hole drilling. Table 1 Milling parameters Sl. no.
v (m/min)
f (mm/tooth/rev.)
d (mm)
1 2 3 4 5 6 7 8 9 10
11.00 11.00 56.00 56.00 11.00 11.00 56.00 56.00 35.00 35.00
0.056 0.100 0.056 0.100 0.056 0.100 0.056 0.100 0.075 0.075
0.250 0.250 0.250 0.250 2.000 2.000 2.000 2.000 1.125 1.125
At low speed (11 m/min) the residual stresses were found to decrease with increase of feed (cf. Figs. 2 and 3). However, at high speed (56 m/min) they were found to increase with increase in feed (cf. Figs. 4 and 5; Figs. 8 and 9). The peak residual stress was also observed to slightly shift towards the surface with decrease in feed (cf. Figs. 2 and 3; Figs. 4 and 5; Figs. 6 and 7). 3.2. Effect of cutting velocity (constant f and d) The magnitude of the compressive stresses increased with increase in cutting velocity (cf. Figs. 3 and 5; Figs. 7 and 9). However, the magnitude was found to decrease with increase in cutting velocity at low values of feed and depth of cut (cf. Figs. 2 and 4). Also, with increase in cutting speed, the peak residual stress was found to shift to the surface (Figs. 3 and 5; Figs. 6 and 8). Further, in a few cases the depth of the residually stressed layer increased with increase in the magnitude of the residual stress. 3.3. Effect of depth of cut (constant v and f) The magnitude of the residual stresses decreased with increase in depth of cut (cf. Figs. 2 and 6; Figs. 3 and 7; Figs. 4 and 8; Figs. 5 and 9). The peak residual stress was found to shift slightly towards the surface with increase in depth of cut. No obvious trend was seen pertaining to the depth of the residually stressed layer. 3.4. Effect of heat treatment Figs. 10–12 reveal the effect of heat treatment at different temperatures (400–600 ◦ C) on the magnitude and distribution of the residual stresses. It was found that the magnitude as well as the depth of the residually stressed layer decreased
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Fig. 2. Variation of residual stresses due to vertical face milling as a function of depth. IMI-834; cutting speed, 11 m/min; feed, 0.056 mm/tooth/rev.; depth of cut, 0.25 mm.
with increase in temperature. The degree of relaxation was 60% at 400 ◦ C, 75% at 500 ◦ C and 90% at 600 ◦ C. The relaxation rate was very high in the initial 0.25 mm of depth but thereafter it decreased, the degree of relaxation being almost linear with depth (Figs. 13 and 14).
4. Discussion The results obtained for IMI-834 subsequent to a milling operation were consistent with those obtained for titanium alloys, IMI-318 (Ti–6Al–4V) and IMI-685 (Ti–6Al–5Zr–0.5Mo–0.25Si) in the machined and polished condition [6]. Shift of the peak residual stress to the surface indicated an increase in the degree of cold work [8,9]. How-
Fig. 3. Variation of residual stresses due to vertical face milling as a function of depth. IMI-834; cutting speed, 11 m/min; feed, 0.1 mm/tooth/rev.; depth of cut, 0.25 mm.
ever, this is contradicted by a decrease in the peak residual stress, which is also supposed to increase with increase in the level of cold work in the surface layers [8,9]. These indicate that the milling parameters such as speed, feed and depth of cut have a role to play in determining the extent of cold work during a machining operation. The effect of the machining parameters on the resulting residual stress and other response variables has been studied theoretically by different authors [10,11]. Accordingly, the dependence of the residual stresses on the milling parameters could be explained by the following linear equation: σ = b0 + b1 v + b2 f + b3 d
(7)
In Eq. (7), coefficients b0 , b1 , b2 and b3 can be determined by experimental data relating the residual stresses to the milling parameters. As per this equation the residual stresses vary
Fig. 4. Variation of residual stresses due to vertical face milling as a function of depth. IMI-834; speed, 56 m/min; feed, 0.056 mm/tooth/rev.; depth of cut, 0.25 mm.
B.R. Sridhar et al. / Journal of Materials Processing Technology 139 (2003) 628–634
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Fig. 5. Variation of residual stresses due to vertical face milling as a function of depth. IMI-834; cutting speed, 56 m/min; feed, 0.1 mm/tooth/rev.; depth of cut, 0.25 mm.
linearly with respect to any parameter provided that there is constancy of the other two. For example, at the same f and d the magnitude of residual stress increases or decreases, respectively, with increase or decrease of v. However, as explained earlier and as per the residual stress data presented in Table 2, this trend was not shown consistently. This indicated that the milling parameters, in addition to acting independently, are likely to interact with each other in determining the residual stress state of the material. Adding some interactive terms [10,11], Eq. (7) could be modified as: σ = b0 + b1 v + b2 f + b3 d + b4 vf + b5 vd + b6 fd + b7 vfd (8)
Fig. 6. Variation of residual stresses for vertical face milling as a function of depth. IMI-834; cutting speed, 11 m/min; feed, 0.056/tooth/rev.; depth of cut, 2.0 mm.
Eq. (8) was solved using the generated data for the residual stresses in the cutting (σ ct ) and normal (σ nt ) directions and relationships were obtained as given below: σct = −1784.2 + 24.9v + 17392.6f + 438.1d − 393vf − 3.4vd − 4593.8fd + 69.7vfd
(9)
σnt = −1782.5 + 18.5v + 16221.1f + 389.8d − 293.9vf − vd − 3797fd + 38.6vfd
(10)
The residual stresses in the cutting and normal directions were evaluated using Eqs. (9) and (10), being highlighted
Fig. 7. Variation of residual stresses due to vertical face milling as a function of depth. IMI-834; cutting speed, 11 m/min; feed, 0.1 mm/tooth/rev.; depth of cut, 2.0 mm.
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Fig. 8. Variation of residual stresses due to vertical face milling as a function of depth. IMI-834; cutting speed, 56 m/min; feed, 0.056 mm/tooth/rev.; depth of cut, 2.0 mm.
in Tables 3 and 4. Experimental and calculated values were found to match reasonably with minimal errors. Residual stress relaxation in titanium was found to start at about 280 ◦ C [12]. Stress relaxations have been associated with the onset of micro-plastic deformations resulting in the rearrangement/annihilation of dislocations [13]. Any processes such as precipitations can adversely affect these phenomena and reduce the relaxation rates. Relaxations observed at 400, 500 and 600 ◦ C in IMI-834 were consistent with the generally observed trend. Titanium alloy IMI-834 is similar to titanium alloy IMI-685 that was found to be prone to silicide precipitation [14]. The increase in stress relaxation with increase in temperature indicated that no deleterious precipitations such as silicides occurred
Fig. 9. Variation of residual stresses due to vertical face milling as a function of depth. IMI-834; cutting speed, 56 m/min; feed, 0.1 mm/tooth/rev.; depth of cut, 2.0 mm.
Fig. 10. Variation of residual stresses for vertical face milling: cutting speed, 11 m/min; feed, 0.056/tooth/rev.; depth of cut, 0.25 mm. Stress relieved at 400 ◦ C.
Fig. 11. Variation of residual stresses for vertical face milling: cutting speed, 11 m/min; feed, 0.056 mm/tooth/rev.; depth of cut, 0.25 mm. Stress relieved at 500 ◦ C.
Fig. 12. Variation of residual stresses for vertical face milling: cutting speed, 11 m/min; feed, 0.056 mm/tooth/rev.; depth of cut, 0.25 mm. Stress relieved at 600 ◦ C.
B.R. Sridhar et al. / Journal of Materials Processing Technology 139 (2003) 628–634
Fig. 13. Variation of residual stress in the cutting direction, σ c for vertical face milling as a function of depth at different temperatures cutting speed, 11 m/min; feed, 0.056 mm/tooth/rev.; depth of cut, 0.25 mm.
633
Fig. 14. Variation of the relaxation of residual stress in the cutting direction, σ c as a function of depth at different temperatures.
Table 2 Peak residual stresses for different milling parameters Sl. no.
v (m/min)
f (mm/tooth/rev.)
d (mm)
σ c (MPa)
σ n (MPa)
1a 2a 3b 4b 1c 5c 8d 4d 1e 7e 6f 4f
11.00 56.00 11.00 56.00 11.00 11.00 56.00 56.00 11.00 11.00 56.00 56.00
0.056 0.056 0.100 0.100 0.056 0.100 0.056 0.100 0.056 0.056 0.100 0.100
0.250 0.250 2.000 2.000 0.250 0.250 2.000 2.000 0.250 2.000 0.250 2.000
−738.72 −604.02 −174.31 −502.44 −738.72 −205.93 −238.17 −502.44 −738.72 −412.49 −815.57 −502.44
−806.04 −701.04 −198.56 −429.74 −806.04 −271.82 −274.53 −429.74 −806.04 −473.09 −730.30 −429.74
With increase in v at low f and d, the peak residual stresses have decreased. With increase in v at high f and d, the peak residual stresses have increased. c With increase in f at low v and d, the peak residual stresses have decreased. d With increase in f at high v and d, the peak residual stresses have increased. e With increase in d at low v and f, the peak residual stresses have decreased. f With increase in d at high v and f, the peak residual stresses have decreased. a
b
Table 3 Peak residual stresses (σ c ) in the cutting directiona,b Sl. no.
v (m/min)
f (mm/tooth/rev.)
d (mm)
σ c (MPa)
σ ct (MPa)
(σc − σct ) (MPa)
(σc − σct )2 (MPa)2
1 2 3 4 5 6 7 8 9 10
11.00 11.00 56.00 56.00 11.00 11.00 56.00 56.00 35.00 35.00
0.056 0.100 0.056 0.100 0.056 0.100 0.056 0.100 0.075 0.075
0.250 0.250 0.250 0.250 2.000 2.000 2.000 2.000 1.125 1.125
−738.72 −205.93 −604.02 −815.57 −412.49 −174.31 −238.17 −502.44 −445.93 −410.81
−732.12 −199.15 −597.58 −808.19 −405.93 −167.61 −231.79 −495.43 −463.61 −463.61
−6.60 −6.78 −6.44 −7.37 −6.56 −6.70 −6.37 −7.00 −17.68 −52.80
43.56 45.97 41.47 54.32 43.03 44.89 40.58 49.00 312.58 2787.84
a b
Sum of squared error = 3463.24. σct = −1784.2 + 24.9v + 17392.6f + 438.1d − 393vf − 3.4vd − 4593.8fd + 69.7vfd.
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Table 4 Peak residual stresses (σ n ) in the normal directiona,b Sl. no.
v (m/min)
f (mm/tooth/rev.)
d (mm)
σn
σ nt (MPa)
1 2 3 4 5 6 7 8 9 10
11.00 11.00 56.00 56.00 11.00 11.00 56.00 56.00 35.00 35.00
0.056 0.100 0.056 0.100 0.056 0.100 0.056 0.100 0.075 0.075
0.250 0.250 0.250 0.250 2.000 2.000 2.000 2.000 1.125 1.125
−806.04 −271.82 −701.04 −730.30 −473.09 −198.56 −274.53 −429.74 −471.91 −480.70
−804.18 −269.82 −699.30 −727.86 −471.28 −196.63 −272.94 −427.60 −496.46 −496.46
a b
(σn − σnt ) (MPa) −1.85 −1.99 −1.73 −2.44 −1.81 −1.93 −1.59 −2.14 24.55 15.76
(σn − σnt )2 (MPa)2 3.42 3.96 2.99 5.95 3.28 3.72 2.53 4.58 602.70 248.38
Sum of squared error = 881.51. σnt = −1782.5 + 18.5v + 16221.1f + 389.8d − 293.9vf − vd − 3797fd + 38.6vfd.
at the stress relieving temperatures employed. Greater relaxation at the surface compared to the core (Fig. 14) could be attributed to the effect of greater residual stress gradients at the surface than at the core [11,15]. Major contribution to the overall stress relaxation appeared to originate from the initial 200 to 300 m of the surface layers.
Acknowledgements
5. Conclusions
[1] J. Mathar, Trans. ASME 56 (4) (1934) 249–254. [2] R.A. Kelsey, Proc. Soc. Exp. Stress Anal. 14 (1) (1956) 181–194. [3] R.J. Rendler, I. Vigness, Proc. Soc. Exp. Stress Anal. 23 (2) (1966) 577–586. [4] G.S. Schajer, J. Eng. Mater. Technol. 110 (4) (1988) 338–349. [5] Technical Bulletin 304-F and Instruction Manual for RS-200-01 Milling Guide, Measurements Group Inc., Raleigh, USA, 1988. [6] B.R. Sridhar, W.G. Nafde, K.A. Padmanabhan, J. Mater. Sci. 27 (1992) 5783–5788. [7] Annual Book of ASTM Standards, E 837-45, ASTM, Philadelphia, 1987, pp. 991–997. [8] B.R. Sridhar, K. Ramachandra, K.A. Padmanabhan, J. Mater. Sci. 31 (1996) 4381–4385. [9] H. Wohlfarht, in: H.O. Fuchs (Ed.), Proceedings of the Second International Conference on Shot Peening (ICSP-2), American Shot Peening Society, New Jersey, 1984, pp. 306–315. [10] E. Harrington Jr., Industrial Quality Control 21 (10) (1965) 494–498. [11] G. Derringer, R. Suich, J. Qual. Technol. 12 (4) (1980) 214–219. [12] O. Vohringer, T. Hirsch, E. Macherauch, Titanium science and technology, in: G. Luetjering, W. Zwicker, W. Bunk (Eds.), Fifth International Conference on Titanium, Deutsche Gesellschaft fur Metallkunde E.V., vol. 4, Oberusel, 1984, pp. 2203–2210. [13] O. Vohringer, Advances in Surface Treatment Technology, Applications. [14] D.F. Neal, P.A. Blenkinsop, Titanium and Titanium Alloys, in: J.C. Williams, A. Belov (Eds.), Proceedings of Third International Conference on Titanium, vol. 3, Plenum Press, New York, 1982, pp. 2003–2014. [15] A.L. Esquivel, R. Evans, Exp. Mech. 8 (1968) 496.
1. Residual stresses due to the milling operations for the milling parameters employed were compressive in nature. 2. The variation in the magnitudes of the residual stresses did not reveal any definite trend with respect to the milling parameters. 3. A linear relationship could not explain the variation of the residual stresses with respect to the milling parameters, but a polynomial relationship involving both linear and interactive terms could explain the variations with reasonable accuracy. 4. Stress relieving treatments led to the relaxation of residual stresses almost linearly with depth from the surface. 5. The relaxation rates increased with increasing temperature and did not reveal any evidence for deleterious precipitation such as of silicides. 6. The greater relaxation rates at the surface compared to the core could be attributed to the steeper residual stress gradients at the surface than at the core. 7. The major contribution to the overall stress relaxation appeared to originate from the surface layers.
The authors express their sincere thanks to the Director, GTRE, for extending facilities and giving encouragement throughout the course of the present work. References
Effect of machining parameters and heat treatment on the residual stress distribution in titanium alloy IMI-834 B.R. Sridhar∗ , G. Devananda, K. Ramachandra, Ramaraja Bhat Gas Turbine Research Establishment, Bangalore 560 093, India
Abstract The residual stress variation in titanium alloy IMI-834 as a function of depth following milling at different feeds, speeds and depths of cut was determined by a strain-gauge technique involving blind-hole drilling. The residual stresses were found to be compressive in nature and to be dependent upon the milling parameters. Heat treatment was found to relieve the residual stresses, the degree of stress relief being found to increase with increase in temperature. Optimum temperatures were determined at which significant relaxation occurred without adversely affecting the microstructure and mechanical behaviour of the material. © 2003 Elsevier B.V. All rights reserved. Keywords: IMI-834; Strain-gauge technique; Residual stress
1. Introduction IMI-834 is a near-␣ titanium alloy with the nominal composition Ti–5.8Al–4.5Sn–4Zr–0.7Nb–0.5Mo–0.40Si–0.06C. This is a creep resistant alloy with a service temperature up to 600 ◦ C and is primarily intended for gas turbine aero-engine applications such as discs, rings and blades. Residual stresses play an important role in determining the fatigue life of a component. This calls for relieving these stresses in such cases where an adverse effect is seen on the fatigue life. This paper highlights the variation in the magnitude and distribution of residual stresses locked up in the material following a milling operation at different speeds, feeds and depths of cut. The effects of varying temperature in relieving these stresses have also been discussed in the paper. Residual stresses were measured by the standard straingauge technique involving blind-hole drilling [1–7]. The method calls for the use of a strain-gauge rosette of the size 25 mm × 25 mm (shown schematically in Fig. 1) supplied by Micro-measurement Group, USA [5]. If ε1 , ε2 and ε3 are the values of the relieved strain noted from strain gauges 1, 2 and 3, respectively, of the strain gauge rosette used during blind-hole drilling, the principal residual stresses σ max and σ min are calculated as below:
σmax
ε3 + ε1 = − 4A
σmin
ε3 + ε1 + = 4A
tan 2α =
(ε3 − ε1 )2 + (ε3 + ε1 − 2ε2 )2 4B
(1)
(ε3 − ε1 )2 + (ε3 + ε1 − 2ε2 )2 4B
(2)
ε3 + ε1 − 2ε2 ε3 − ε 1
(3)
where A=−
(1 + ν)¯a 2E
and
B=−
b¯ 2E
(4)
in which α is the angle made by σ max with respect to gauge 1, ν the Poisson’s ratio of the material and a¯ and b¯ are the uniform stress coefficients determined by Schajer by finite element studies, and available as a function of Z/D (hole depth/hole diameter). The residual stresses in the cutting direction (σ c ) and normal direction (σ n ) were calculated using the expressions: σc + σn = σmax + σmin
(5)
σc − σn = (σmax − σmin ) cos 2θ
(6)
where θ is the angle made by σ c with σ max .
2. Experimental procedures ∗ Corresponding author. E-mail address: [email protected] (B.R. Sridhar).
0924-0136/03/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0924-0136(03)00612-5
Hot-rolled, solution-treated and ground pickled 50 mm diameter bars were machined into 38 mm × 25 mm × 15 mm
B.R. Sridhar et al. / Journal of Materials Processing Technology 139 (2003) 628–634
629
An air turbine assembly was used to drill a blind hole at the centre of the strain-gauge rosette (Fig. 1) used in the experiment. Drilling was carried out at incremental depths and at each depth the relieved strains, ε1 , ε2 and ε3 (of the strain gauges 1, 2 and 3 from the strain-gauge rosette) were noted. These strains were used in the evaluation of residual stresses by the use of Eqs. (1)–(6).
3. Results Figs. 2–9 present plots of the residual stress distribution as functions of depth below the surface for different milling parameters employed in the present study. Negative values of the maximum and minimum residual stresses indicate that the residual stresses were compressive in nature. The maximum stresses in the cutting and normal directions were found to be at a depth of about 0.1 mm below the surface. 3.1. Effect of feed (constant v and d) Fig. 1. Strain-gauge rosette arrangement for measuring residual stresses.
rectangular test-pieces. In order to remove the residual stresses induced during the fabrication of specimens, the test-pieces were stress relieved by keeping them at 600 ◦ C for 1 h in a vacuum furnace followed by an argon gas quench. The machining operations were carried out on FN-2V HMT milling lathe, 5 HP capacity, using a T Max K-20 face milling cutter of 50 mm diameter and four TN-35-M titanium nitride coated inserts (TPAN-1603 PPN, WIDIA). Servo Cut ‘S’ 1:20 soluble oil was employed as a cutting fluid. The test-pieces were milled at different milling parameters by varying the speed (v, m/min), feed (f, mm/tooth/rev.) and depth of cut (d, mm) as given in Table 1. Test-pieces milled with the parameters, v = 11 m/min, f = 0.056 mm/tooth/rev., d = 0.25 mm were stress relieved at 400, 500 and 600 ◦ C for 1 h in a vacuum furnace followed by an argon gas quench. Both the machined and heat-treated test-pieces were subjected to residual stress measurement by blind-hole drilling. Table 1 Milling parameters Sl. no.
v (m/min)
f (mm/tooth/rev.)
d (mm)
1 2 3 4 5 6 7 8 9 10
11.00 11.00 56.00 56.00 11.00 11.00 56.00 56.00 35.00 35.00
0.056 0.100 0.056 0.100 0.056 0.100 0.056 0.100 0.075 0.075
0.250 0.250 0.250 0.250 2.000 2.000 2.000 2.000 1.125 1.125
At low speed (11 m/min) the residual stresses were found to decrease with increase of feed (cf. Figs. 2 and 3). However, at high speed (56 m/min) they were found to increase with increase in feed (cf. Figs. 4 and 5; Figs. 8 and 9). The peak residual stress was also observed to slightly shift towards the surface with decrease in feed (cf. Figs. 2 and 3; Figs. 4 and 5; Figs. 6 and 7). 3.2. Effect of cutting velocity (constant f and d) The magnitude of the compressive stresses increased with increase in cutting velocity (cf. Figs. 3 and 5; Figs. 7 and 9). However, the magnitude was found to decrease with increase in cutting velocity at low values of feed and depth of cut (cf. Figs. 2 and 4). Also, with increase in cutting speed, the peak residual stress was found to shift to the surface (Figs. 3 and 5; Figs. 6 and 8). Further, in a few cases the depth of the residually stressed layer increased with increase in the magnitude of the residual stress. 3.3. Effect of depth of cut (constant v and f) The magnitude of the residual stresses decreased with increase in depth of cut (cf. Figs. 2 and 6; Figs. 3 and 7; Figs. 4 and 8; Figs. 5 and 9). The peak residual stress was found to shift slightly towards the surface with increase in depth of cut. No obvious trend was seen pertaining to the depth of the residually stressed layer. 3.4. Effect of heat treatment Figs. 10–12 reveal the effect of heat treatment at different temperatures (400–600 ◦ C) on the magnitude and distribution of the residual stresses. It was found that the magnitude as well as the depth of the residually stressed layer decreased
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Fig. 2. Variation of residual stresses due to vertical face milling as a function of depth. IMI-834; cutting speed, 11 m/min; feed, 0.056 mm/tooth/rev.; depth of cut, 0.25 mm.
with increase in temperature. The degree of relaxation was 60% at 400 ◦ C, 75% at 500 ◦ C and 90% at 600 ◦ C. The relaxation rate was very high in the initial 0.25 mm of depth but thereafter it decreased, the degree of relaxation being almost linear with depth (Figs. 13 and 14).
4. Discussion The results obtained for IMI-834 subsequent to a milling operation were consistent with those obtained for titanium alloys, IMI-318 (Ti–6Al–4V) and IMI-685 (Ti–6Al–5Zr–0.5Mo–0.25Si) in the machined and polished condition [6]. Shift of the peak residual stress to the surface indicated an increase in the degree of cold work [8,9]. How-
Fig. 3. Variation of residual stresses due to vertical face milling as a function of depth. IMI-834; cutting speed, 11 m/min; feed, 0.1 mm/tooth/rev.; depth of cut, 0.25 mm.
ever, this is contradicted by a decrease in the peak residual stress, which is also supposed to increase with increase in the level of cold work in the surface layers [8,9]. These indicate that the milling parameters such as speed, feed and depth of cut have a role to play in determining the extent of cold work during a machining operation. The effect of the machining parameters on the resulting residual stress and other response variables has been studied theoretically by different authors [10,11]. Accordingly, the dependence of the residual stresses on the milling parameters could be explained by the following linear equation: σ = b0 + b1 v + b2 f + b3 d
(7)
In Eq. (7), coefficients b0 , b1 , b2 and b3 can be determined by experimental data relating the residual stresses to the milling parameters. As per this equation the residual stresses vary
Fig. 4. Variation of residual stresses due to vertical face milling as a function of depth. IMI-834; speed, 56 m/min; feed, 0.056 mm/tooth/rev.; depth of cut, 0.25 mm.
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Fig. 5. Variation of residual stresses due to vertical face milling as a function of depth. IMI-834; cutting speed, 56 m/min; feed, 0.1 mm/tooth/rev.; depth of cut, 0.25 mm.
linearly with respect to any parameter provided that there is constancy of the other two. For example, at the same f and d the magnitude of residual stress increases or decreases, respectively, with increase or decrease of v. However, as explained earlier and as per the residual stress data presented in Table 2, this trend was not shown consistently. This indicated that the milling parameters, in addition to acting independently, are likely to interact with each other in determining the residual stress state of the material. Adding some interactive terms [10,11], Eq. (7) could be modified as: σ = b0 + b1 v + b2 f + b3 d + b4 vf + b5 vd + b6 fd + b7 vfd (8)
Fig. 6. Variation of residual stresses for vertical face milling as a function of depth. IMI-834; cutting speed, 11 m/min; feed, 0.056/tooth/rev.; depth of cut, 2.0 mm.
Eq. (8) was solved using the generated data for the residual stresses in the cutting (σ ct ) and normal (σ nt ) directions and relationships were obtained as given below: σct = −1784.2 + 24.9v + 17392.6f + 438.1d − 393vf − 3.4vd − 4593.8fd + 69.7vfd
(9)
σnt = −1782.5 + 18.5v + 16221.1f + 389.8d − 293.9vf − vd − 3797fd + 38.6vfd
(10)
The residual stresses in the cutting and normal directions were evaluated using Eqs. (9) and (10), being highlighted
Fig. 7. Variation of residual stresses due to vertical face milling as a function of depth. IMI-834; cutting speed, 11 m/min; feed, 0.1 mm/tooth/rev.; depth of cut, 2.0 mm.
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Fig. 8. Variation of residual stresses due to vertical face milling as a function of depth. IMI-834; cutting speed, 56 m/min; feed, 0.056 mm/tooth/rev.; depth of cut, 2.0 mm.
in Tables 3 and 4. Experimental and calculated values were found to match reasonably with minimal errors. Residual stress relaxation in titanium was found to start at about 280 ◦ C [12]. Stress relaxations have been associated with the onset of micro-plastic deformations resulting in the rearrangement/annihilation of dislocations [13]. Any processes such as precipitations can adversely affect these phenomena and reduce the relaxation rates. Relaxations observed at 400, 500 and 600 ◦ C in IMI-834 were consistent with the generally observed trend. Titanium alloy IMI-834 is similar to titanium alloy IMI-685 that was found to be prone to silicide precipitation [14]. The increase in stress relaxation with increase in temperature indicated that no deleterious precipitations such as silicides occurred
Fig. 9. Variation of residual stresses due to vertical face milling as a function of depth. IMI-834; cutting speed, 56 m/min; feed, 0.1 mm/tooth/rev.; depth of cut, 2.0 mm.
Fig. 10. Variation of residual stresses for vertical face milling: cutting speed, 11 m/min; feed, 0.056/tooth/rev.; depth of cut, 0.25 mm. Stress relieved at 400 ◦ C.
Fig. 11. Variation of residual stresses for vertical face milling: cutting speed, 11 m/min; feed, 0.056 mm/tooth/rev.; depth of cut, 0.25 mm. Stress relieved at 500 ◦ C.
Fig. 12. Variation of residual stresses for vertical face milling: cutting speed, 11 m/min; feed, 0.056 mm/tooth/rev.; depth of cut, 0.25 mm. Stress relieved at 600 ◦ C.
B.R. Sridhar et al. / Journal of Materials Processing Technology 139 (2003) 628–634
Fig. 13. Variation of residual stress in the cutting direction, σ c for vertical face milling as a function of depth at different temperatures cutting speed, 11 m/min; feed, 0.056 mm/tooth/rev.; depth of cut, 0.25 mm.
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Fig. 14. Variation of the relaxation of residual stress in the cutting direction, σ c as a function of depth at different temperatures.
Table 2 Peak residual stresses for different milling parameters Sl. no.
v (m/min)
f (mm/tooth/rev.)
d (mm)
σ c (MPa)
σ n (MPa)
1a 2a 3b 4b 1c 5c 8d 4d 1e 7e 6f 4f
11.00 56.00 11.00 56.00 11.00 11.00 56.00 56.00 11.00 11.00 56.00 56.00
0.056 0.056 0.100 0.100 0.056 0.100 0.056 0.100 0.056 0.056 0.100 0.100
0.250 0.250 2.000 2.000 0.250 0.250 2.000 2.000 0.250 2.000 0.250 2.000
−738.72 −604.02 −174.31 −502.44 −738.72 −205.93 −238.17 −502.44 −738.72 −412.49 −815.57 −502.44
−806.04 −701.04 −198.56 −429.74 −806.04 −271.82 −274.53 −429.74 −806.04 −473.09 −730.30 −429.74
With increase in v at low f and d, the peak residual stresses have decreased. With increase in v at high f and d, the peak residual stresses have increased. c With increase in f at low v and d, the peak residual stresses have decreased. d With increase in f at high v and d, the peak residual stresses have increased. e With increase in d at low v and f, the peak residual stresses have decreased. f With increase in d at high v and f, the peak residual stresses have decreased. a
b
Table 3 Peak residual stresses (σ c ) in the cutting directiona,b Sl. no.
v (m/min)
f (mm/tooth/rev.)
d (mm)
σ c (MPa)
σ ct (MPa)
(σc − σct ) (MPa)
(σc − σct )2 (MPa)2
1 2 3 4 5 6 7 8 9 10
11.00 11.00 56.00 56.00 11.00 11.00 56.00 56.00 35.00 35.00
0.056 0.100 0.056 0.100 0.056 0.100 0.056 0.100 0.075 0.075
0.250 0.250 0.250 0.250 2.000 2.000 2.000 2.000 1.125 1.125
−738.72 −205.93 −604.02 −815.57 −412.49 −174.31 −238.17 −502.44 −445.93 −410.81
−732.12 −199.15 −597.58 −808.19 −405.93 −167.61 −231.79 −495.43 −463.61 −463.61
−6.60 −6.78 −6.44 −7.37 −6.56 −6.70 −6.37 −7.00 −17.68 −52.80
43.56 45.97 41.47 54.32 43.03 44.89 40.58 49.00 312.58 2787.84
a b
Sum of squared error = 3463.24. σct = −1784.2 + 24.9v + 17392.6f + 438.1d − 393vf − 3.4vd − 4593.8fd + 69.7vfd.
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Table 4 Peak residual stresses (σ n ) in the normal directiona,b Sl. no.
v (m/min)
f (mm/tooth/rev.)
d (mm)
σn
σ nt (MPa)
1 2 3 4 5 6 7 8 9 10
11.00 11.00 56.00 56.00 11.00 11.00 56.00 56.00 35.00 35.00
0.056 0.100 0.056 0.100 0.056 0.100 0.056 0.100 0.075 0.075
0.250 0.250 0.250 0.250 2.000 2.000 2.000 2.000 1.125 1.125
−806.04 −271.82 −701.04 −730.30 −473.09 −198.56 −274.53 −429.74 −471.91 −480.70
−804.18 −269.82 −699.30 −727.86 −471.28 −196.63 −272.94 −427.60 −496.46 −496.46
a b
(σn − σnt ) (MPa) −1.85 −1.99 −1.73 −2.44 −1.81 −1.93 −1.59 −2.14 24.55 15.76
(σn − σnt )2 (MPa)2 3.42 3.96 2.99 5.95 3.28 3.72 2.53 4.58 602.70 248.38
Sum of squared error = 881.51. σnt = −1782.5 + 18.5v + 16221.1f + 389.8d − 293.9vf − vd − 3797fd + 38.6vfd.
at the stress relieving temperatures employed. Greater relaxation at the surface compared to the core (Fig. 14) could be attributed to the effect of greater residual stress gradients at the surface than at the core [11,15]. Major contribution to the overall stress relaxation appeared to originate from the initial 200 to 300 m of the surface layers.
Acknowledgements
5. Conclusions
[1] J. Mathar, Trans. ASME 56 (4) (1934) 249–254. [2] R.A. Kelsey, Proc. Soc. Exp. Stress Anal. 14 (1) (1956) 181–194. [3] R.J. Rendler, I. Vigness, Proc. Soc. Exp. Stress Anal. 23 (2) (1966) 577–586. [4] G.S. Schajer, J. Eng. Mater. Technol. 110 (4) (1988) 338–349. [5] Technical Bulletin 304-F and Instruction Manual for RS-200-01 Milling Guide, Measurements Group Inc., Raleigh, USA, 1988. [6] B.R. Sridhar, W.G. Nafde, K.A. Padmanabhan, J. Mater. Sci. 27 (1992) 5783–5788. [7] Annual Book of ASTM Standards, E 837-45, ASTM, Philadelphia, 1987, pp. 991–997. [8] B.R. Sridhar, K. Ramachandra, K.A. Padmanabhan, J. Mater. Sci. 31 (1996) 4381–4385. [9] H. Wohlfarht, in: H.O. Fuchs (Ed.), Proceedings of the Second International Conference on Shot Peening (ICSP-2), American Shot Peening Society, New Jersey, 1984, pp. 306–315. [10] E. Harrington Jr., Industrial Quality Control 21 (10) (1965) 494–498. [11] G. Derringer, R. Suich, J. Qual. Technol. 12 (4) (1980) 214–219. [12] O. Vohringer, T. Hirsch, E. Macherauch, Titanium science and technology, in: G. Luetjering, W. Zwicker, W. Bunk (Eds.), Fifth International Conference on Titanium, Deutsche Gesellschaft fur Metallkunde E.V., vol. 4, Oberusel, 1984, pp. 2203–2210. [13] O. Vohringer, Advances in Surface Treatment Technology, Applications. [14] D.F. Neal, P.A. Blenkinsop, Titanium and Titanium Alloys, in: J.C. Williams, A. Belov (Eds.), Proceedings of Third International Conference on Titanium, vol. 3, Plenum Press, New York, 1982, pp. 2003–2014. [15] A.L. Esquivel, R. Evans, Exp. Mech. 8 (1968) 496.
1. Residual stresses due to the milling operations for the milling parameters employed were compressive in nature. 2. The variation in the magnitudes of the residual stresses did not reveal any definite trend with respect to the milling parameters. 3. A linear relationship could not explain the variation of the residual stresses with respect to the milling parameters, but a polynomial relationship involving both linear and interactive terms could explain the variations with reasonable accuracy. 4. Stress relieving treatments led to the relaxation of residual stresses almost linearly with depth from the surface. 5. The relaxation rates increased with increasing temperature and did not reveal any evidence for deleterious precipitation such as of silicides. 6. The greater relaxation rates at the surface compared to the core could be attributed to the steeper residual stress gradients at the surface than at the core. 7. The major contribution to the overall stress relaxation appeared to originate from the surface layers.
The authors express their sincere thanks to the Director, GTRE, for extending facilities and giving encouragement throughout the course of the present work. References