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The effect of machining-induced residual stresses on the creep characteristics of aluminum alloys
Materials Science & Engineering A 630 (2015) 125–130
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The effect of machining-induced residual stresses on the creep characteristics of aluminum alloys Timothy W. Spence a, Makhlouf M. Makhlouf b,n a b
BAE Systems Electronics and Integrated Solutions, P.O. Box 868, NHQ3-2145, Nashua, NH 03061, USA Department of Mechanical Engineering, Worcester Polytechnic Institute, Worcester, MA 01601, USA
art ic l e i nf o
a b s t r a c t
Article history: Received 15 October 2014 Received in revised form 3 February 2015 Accepted 9 February 2015 Available online 18 February 2015
Precision components, such as those used in optical systems, often experience distortion of their shape during service. This distortion occurs because of residual stresses that are introduced into the surface of the components during machining and lead to creeping of the material when the component is subjected to elevated temperatures for prolonged periods of time. In this paper, a creep model is developed and used to describe how the residual surface stresses created by milling and by fly cutting affect the geometry of an aluminum alloy component as it creeps. The model is verified by applying it to components that are manufactured from two different aluminum alloys; namely 4032-O and 6061-T6; and then it is used to design efficient stress relief schedules for these alloys. Published by Elsevier B.V.
Keywords: Dimensional stability Creep Mathematical modeling Machining-induced residual stress Aluminum alloys
1. Background Dimensional stability of materials is of paramount importance in the fabrication of precision components such as those used in optical systems. Changes in the geometry of these parts over time are unacceptable; particularly if the changes cause the parts to no longer meet the required tolerance. Many sources of dimensional instability have been identified and studied over the years, important among them is residual stresses induced by machining operations; and although stress relief procedures have been developed for many alloys in order to control these stresses, dimensional instability caused by surface stresses due to machining operations has not been thoroughly characterized and a comprehensive understanding of the magnitude of dimensional changes and the kinetics of the strains that develop in the material over time spans and temperature ranges does not exist. Nevertheless, several studies have been performed to characterize the magnitude of residual stress caused by machining operations. Noteworthy among them is an investigation by Brunet [1] in which he characterized the residual stresses induced in an aluminum alloy (7075-T7351) by milling operations. He found that residual stresses always peaked at the surface of the part and that the milling parameters significantly affect the magnitude of the residual stress. For example, he found that up-milling results
in a residual stress that is 100 MPa less in magnitude than down milling, he also found that reducing the cutting speed by 10 times reduces the residual stress by about 200 MPa and reducing the feed speed by 3 times reduces the residual stress by about 150 MPa. Similarly, Field [2] characterized the residual stresses induced in 4340 steel by grinding operations and found that “gentle” grinding produced small compressive stresses at the surface and virtually no internal stresses, while more aggressive grinding produced large tensile stresses at the surface balanced by compressive stresses deeper within the metal's bulk. Also Frommer and Lloyd [3] characterized the residual stresses in heat treated aluminum alloys that have been subjected to different machining operations. They used x-rays to measure the magnitude of surface stresses and acid etching to estimate the depth of the stressed layer. Their findings are summarized in Table 1. Therefore, it is evident that machining operations invariably produce surface stresses in the machined components and that these stresses can range in magnitude from being insignificant to being highly significant. Moreover, the magnitude and sense of these surface stresses depend to a large extent on the machining operation.
2. Development of the model n
Corresponding author. Tel.: þ 1 508 831 5647; fax: þ 1 508 831 5993. E-mail address: [email protected] (M.M. Makhlouf).
http://dx.doi.org/10.1016/j.msea.2015.02.020 0921-5093/Published by Elsevier B.V.
Generally speaking, material that is in a state of sustained stress will creep and there are two unique characteristics to this situation:
126
T.W. Spence, M.M. Makhlouf / Materials Science & Engineering A 630 (2015) 125–130
Table 1 Summary of findings by Frommer and Lloyd related to surface stresses produced by various machining operations. Machining operation
Process details
Stress (MPa)
Depth (mm)
Turning
Flat surface finished with a fine finishing cut (0.038 mm/rev., 0.127 mm depth of cut). Cylindrical surface turned with a rough cut (575 rpm, 0.305 mm/rev., 1.27 mm depth of cut). Surface faced off under conditions that produce chatter marks. Recess made with a flat bottom drill (290 rpm, 0.127 mm/rev.). Flat surface side-milled with a 50.8 long 9.525 diameter end-mill (220 rpm, 0.01 mm/rev., 3.175 mm depth of cut). Flat surface milled with a straddling end-mill (220 rpm, 0.254 mm/rev., 3.175 mm depth of cut).
45 98 282 94 Nil
0.051 0.381 0.610 0.102–0.381 Nil
Nil
Nil
Recessing Surface milling (cutter not enclosed by material)
In Eq. (1), the variables that affect the strain rate ε_ are stress, σ, and absolute temperature, T. The coefficient k, the exponent m, and the activation energy Qc have values that depend on the material and the creep mechanism. A unique condition of creep strain due to residual (not applied) stress in an un-restrained material is that stress is not constant but it is a function of strain, i.e.
Creep strain
Δt
Primary
Δε
σ res ¼ f ðεÞ Given Hooke's Law Secondary
Tertiary
1 E
ε1 ¼ ½σ 1 νðσ 2 þ σ 2 Þ and if
Instantaneous deformation
σ2 ¼ σ3 ¼ 0
Time Fig. 1. Hypothetical creep strain vs. time plot showing (as a dashed line) the region of interest when considering creep induced by residual stresses that are caused by machining operations [10].
1. In general, creep models have a stress term that is raised to an exponent; and for metals, this exponent is larger than unity. Consequently, if a metallic specimen has a non-uniform stress, the more stressed regions will creep at exponentially higher rates than the less stressed regions. 2. As the material strains, the stress level becomes proportionally lower. These two characteristics must be accounted for in any mathematical model that is intended for predicting the dimensional stability of metallic components due to machining residual stresses. The temperature range of interest in this work is 55 1C to þ125 1C. This is known as “the full military temperature range” because it is the service range for a wide variety of military components. The typical magnitude of residual stress caused by machining operations is in the range 100–200 MN/m2 [1–7]. The creep mechanism map for aluminum shows that for this temperature and stress ranges, the operative creep modes are Dislocation Glide and Dislocation Creep [8]. The creep model that is applicable for Dislocation Glide and Dislocation Creep, and also accounts for both stress and temperature is the Power Law [9]. However, the Power Law creep model best represents Secondary Creep; while in this case, the constantly changing stress magnitude (due to creep strain) will keep the creep mode in the Primary Creep regime. Nevertheless, the strains associated with machining residual stresses are small enough and the time spans considered are short enough that a straight line approximation over the range of interest should introduce only a small error into calculations made with the Power Law as shown in Fig. 1. The Power Law Creep equation for crystalline materials [9,11] is given by the following equation: k T
Qc
ε_ ¼ σ m e RT
ð1Þ
then
σ 1 ¼ σ ¼ Eε
ð2Þ
A stress function is then defined with a linear relationship to strain and where the value of stress reduces to zero as strain reaches its final magnitude (εf) as shown in the following equation: ε ð3Þ σ ¼ σ in 1
εf
Substituting Eq. (3) into Eq. (1), and integrating from an initial strain of zero at an initial time of zero, yields an expression that defines strain as a function of initial stress (σin), final strain (εf), stress exponent (m), activation energy (Qc), a constant (k), and time (t) as shown in the following equation: Z ε¼ε Z t¼t Qc σ ε m σ in in dε ¼ ke RT dt ε¼0
εf
t¼0
ε ðm 1Þσ in k RTQ c te þ ðσ in Þ1 m ε ¼ εf f T σ in εf
1 1 m
ð4Þ
It was found that, within the temperature range considered in this work, as the temperature increased, εf also increased. The theoretical maximum creep strain that would be recovered during an isothermal temperature exposure (εf,m) would be in accordance with Hooke's Law (assuming that the initial stress is completely converted to strain), i.e.
εf ;m ¼
σ in E
:
In reality, the theoretical maximum strain is not reached, so an expression is developed to allow predicting εf. The expression includes a material constant, B, and a temperature dependence term, Tn, together with the modulus of elasticity for the material, E, as shown in following equation:
εf ¼ B
σ in E
T n:
ð5Þ
T.W. Spence, M.M. Makhlouf / Materials Science & Engineering A 630 (2015) 125–130
4.1. Measurement of residual stress due to machining
Table 2 Nominal chemical composition of the alloys used. Alloy
Chemical composition
4032 6061
Si
Mg
Cu
Cr
Ni
Zn
Ti
12.2 0.6
1.0 1.0
0.90 0.30
0.10 max 0.20
– 0.9
0.25 max 0.25 max
– 0.15 max
Substituting Eq. (5) into Eq. (4) yields the Creep Model Equation shown as follows:
ε¼B
σ in E
Tn
127
1 1 m Qc BT n ðm 1ÞE k 1m RT þ ðσ Þ te in B E Tnþ1
ð6Þ
Depth-corrected residual stress measurement was performed in accordance with SAE HS-784 [13] in order to assess the magnitude of residual stress in the material after machining. This method uses a series of XRD measurements at increasing depths within the parent material in order to characterize the distribution of residual stress as a function of depth. Depth-corrected residual stress measurements were used because at locations very close to the surface of the coupon, the material relaxes to an extent that can influence the measurements if they were performed with a “surface only” measuring method. A semi-systematic error was determined for the measurements by using a powder metal, zerostress sample that was monitored in accordance with ASTM E915 [14]. This error was determined to be 12.25 MN/m2. Two coupons from each alloy were used for each measurement in order to obtain the average stresses reported in Tables 3–6. The corrected value of stress, which is found just below the surface of the coupon, is highlighted in these Tables.
3. Measurements Coupons made from aluminum alloys 4032-O and 6061-T6 were machined on one side to cause them to curve when they are heated. The magnitude of curvature of these coupons was monitored over an extended period of time at different temperatures. The bimetallic strip model [12] was used to convert these measured curvatures to strains in the machined layer. The creep parameters m, Qc, and k in Eq. (4) were then obtained by fitting the measured strain vs. time and temperature data to curves by means of curve fitting software. The final strain, εf was determined experimentally.
4. Materials and procedures 2.5 15.25 0.15 cm3 coupons that were machined from 4032O and 6061-T6 aluminum alloys that have the nominal chemical composition shown in Table 2 were used. Since the machining operations introduce a stressed layer on all the surfaces of these coupons, the surface layer of the coupons (0.0127–0.0.0152 cm deep1) was removed by etching the coupons for 10 min with a 20% sodium hydroxide solution at 40 1C. The baseline curvature of each coupon was then measured by a CNC vision measuring system2. The etched and measured coupons were then machined on one side by either one of the following operations: (i) Controlled milling; wherein a half inch, 3 flute solid carbide end mill with a 411 rake angle, a 13.71 edge relief angle, and a 9.11 end cutting edge angle was used. The spindle speed was 3000 rpm, the feed rate was 50 cm/min, and the depth of cut was 0.05 cm. Isopropyl alcohol was used as lubricant. (ii) Controlled fly cutting; wherein a single cutting point with a 7.71 back rake angle and a 4.51 end relief angle was used. The spindle speed was 3000 rpm, the feed rate was 75 cm/min, and the depth of cut was 0.05 in. Isopropyl alcohol was used as lubricant. The coupons were heat-treated in a thermal chamber3 with a heating rate of 15 1C/min. Because of the relatively long heat treatment times that were employed, the thermal lag of the coupons during heating and cooling may be ignored without introducing significant errors. The heat treating temperatures were 40 1C, 50 1C, 60 1C, and 85 1C. 1
This thickness was selected based on [5]. 2 Quickvision ELF Pro Inspection System, Mitutoyo Corporation, Kanagawa, Japan. 3 Thermotron Model RA-42-CHV-30-30.
4.2. Measurement of temperature-dependant modulus of elasticity Five specimens from each alloy were used to determine the elevated temperature modulus of elasticity of the coupons. The tensile tests were conducted according to ASTM standard E21 [15] on a Universal Testing machine4 with a ramp rate of 0.127 cm/min. Strain was measured using a high temperature axial extensometer5 that was used until the specimen fractured. The specimens were heated to the test temperature, and tested to fracture in an environment chamber6. Three thermocouples were securely attached to the surface of the specimen inside its reduced section. The measurements were performed after the specimens equilibrated at 25 1C, 60 1C, 85 1C, 125 1C and 175 1C. Table 7 shows the measured elastic modulus vs. temperature for the two alloys.
5. Measurement of coupon curvature As described earlier, curvature of the coupons was measured with a Mitutoyo Quickvision ELF Pro Inspection System. This system utilizes a z-axis camera and an x–y table to perform a series of height measurements that are fit to a diameter. Measurement accuracy values are published by Mitutoyo [16] and are functions of the length of the feature that is being measured. For example the error in measuring 76 cm radius is 70.0018 cm. This error is very small compared to the changes in radius of the coupons, which was on the order of 1.25–25.5 cm.
6. Results, analysis, and discussion The creep parameters m, Qc, and k in Eq. (6) were obtained by fitting the strain vs. time data to curves by means of curve fitting software. Determining these parameters required the raw data (radius of curvature vs. time) to be first converted into strain vs. time data. This was accomplished by means of the simplified version of the bimetallic strip equation given in Eq. (7) [17] where tA and tB are thickness of the stressed and the un-stressed regions respectively, and r1 and r2 are radii of curvature. Eq. (7) is valid 4 Instron model 1332 equipped with an 8500 controller and a 5620 pound load cell. 5 MTS high temperature extensometer model 633.11B-15S/N 173. 6 Instron environment chamber model 3116.
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Table 3 Measured stress distribution in 4032-O coupons that have been milled.
Table 9 Creep parameters for machined 6061-T6 aluminum alloy.
Depth (cm)
Measured stress (MN/m2)
Gradient (MN/m2)
Relaxation (MN/m2)
0.0000 0.0013 0.0025
126.5 7 3.4 177.6 7 3.4 206.17 2.4
59.9 186.4 198.0
59.9 178.9 181.0
Qc (cal/mol)
6907
m
3.583
k Milled
Fly cut
2.717 10 21
7.99 10 22
Table 4 Measured stress distribution in 4032-O coupons that have been fly cut. Depth (cm)
Measured stress (MN/m2)
Gradient (MN/m2)
Relaxation (MN/m2)
0.0000 0.0013 0.0025
31.3 7 3.1 163.3 7 3.4 187.17 3.1
95.9 100.0 183.0
10.1 4.4 5.9
Table 5 Measured stress distribution in 6061-T6 coupons that have been milled. Depth (cm)
Measured stress (MN/m2)
Gradient (MN/m2)
Relaxation (MN/m2)
0.0000 0.0013 0.0025
92.86 7 2.72 143.54 7 2.72 89.80 7 2.72
16.67 146.94 165.99
14.6 141.5 152.7
Table 6 Measured stress distribution in 6061-T6 coupons that have been fly cut. Depth (cm)
Measured stress (MN/m2)
Gradient (MN/m2)
Relaxation (MN/m2)
0.0000 0.0013 0.0025
22.8 72.7 135.072.7 138.1 72.7
68.4 120.7 173.1
186.1 68.7 168.0
Table 7 Modulus of elasticity of 4032-O and 6061-T6 alloys at various temperatures. Modulus of Elasticity (kN/m2)
Temperature (1C)
25 60 85 125 175
4032-O
6061-T6
80.447 79.024 77.832 75.618 72.323
68.815 67.597 66.577 64.684 61.865
Fig. 2. Strain vs. time at different temperatures for 4032-O aluminum alloy. Points are the measured values and solid lines are model predictions. Is at 85 1C, is at 60 1C, is at 50 1C, and is at 40 1C. (a) Milled samples, and (b) fly cut samples.
Table 8 Creep parameters for machined 4032-O aluminum alloy. Qc (cal/mol)
20,167
m
2.423
k Milled
Fly cut
2.880 10 6
1.08 10 6
when tA«tB, and the modulus of elasticity of both layers is equal
εr1 -r2 ¼
tB 1 1 ð3t A þ t B Þ r2 r1 6t A
ð7Þ
Tables 8 and 9 list the calculated creep parameters for the two alloys and Figs. 2 and 3 show a comparison between the measured strain and the strain calculated by Eq. (6) with the creep parameters shown in Tables 6 and 7. Figs. 4 and 5 show plots of the final strain (εf) and Tables 10 and 11 show the values of the constants B and n which were used in Eq. (5). Note that the term k depends on the machining operation so that for the same alloy there is a k value for the milled material that is different from that for the fly cut material. This is because the term k includes not only the vibration frequency of the unit of flow, but also the change in entropy and a factor that depends on structure, i.e., the distribution of dislocations, precipitates and grain boundaries in the alloy [18]. The terms B and n describe the dependency of the final strain on temperature as given by Eq. (5), and therefore they too will depend on the material's structure and hence they too vary with the machining operation.
T.W. Spence, M.M. Makhlouf / Materials Science & Engineering A 630 (2015) 125–130
-2.0
129
5.70 5.72 5.74 5.76 5.78 5.80 5.82 5.84 5.86 5.88 5.90
-2.5
-3.0
-3.5
-4.0
-3.0
ln (T) 5.70
5.72
5.74
5.76
5.78
5.80
5.82
5.84
5.86
5.88
5.90
-3.5
-4.0
-4.5
-5.0
ln (T)
Fig. 4. Plot used to calculate the values of the constants B and n in Eq. (5). (a) Milled 4032-O samples, and (b) fly cut 4032-O samples. Fig. 3. Strain vs. time at different temperatures for 6061-T6 aluminum alloy. Points are the measured values and solid lines are model predictions. is at 125 1C, is at 85 1C, and is at 60 1C. (a) Milled samples, and (b) fly cut samples.
and realizing that ð1 xÞ1 m ¼
7. Application of the creep model
1 ð1 xÞm 1
c1
then Eq. (10) can be written as 7.1. Application of the creep model in the design of stress relief schedules
tffi
Once the creep constants for the alloy have been determined, the creep model can be used to develop economical short term, elevated temperature heat treatment schedules for the components. The stress relief heat treatment would be for the purpose of allowing all surface stresses caused by severe machining to “creep out” under controlled conditions, rather than due to time/temperature exposure in service. The following procedure can be used for the design of a stress relief heat treatment. First, Eq. (4) is solved for time, t, t¼
εf T ðm 1Þkσ in
"
σ in 1
ε εf
1 m
# Qc
ðσ in Þ1 m e RT
ð8Þ
Next, a fraction (x) of stress that is to be relieved is defined and
ε ¼xεf is substituted into Eq. (8) to yield Eq. (9) t¼
εf T
ðm 1Þkσ in
h i Qc ½σ in ð1 xÞ1 m ðσ in Þ1 m e RT
ð9Þ
Substituting Eq. (5) into Eq. (9) gives t¼
i BT n þ 1 σ 1in m h Q ð1 xÞ1 m 1 e RTc Eðm 1Þk
ð10Þ
BT n þ 1 σ 1in m
Eðm 1Þkð1 xÞm 1
Qc
e RT
ð11Þ
Eq. (11) may be used to design the stress relief schedule by calculating the time to reach a fraction x of the final strain (εf) at different temperatures (T). In order to illustrate the procedure, Eq. (11) was used with the appropriate values for fly cut 4032-O aluminum alloy to produce Fig. 6. 7.2. Application of the creep model in forecasting part distortion Eq. (9) may also be used to predict the reliability of machined parts after extended storage times at a given temperature: consider a precision part that has been made by milling 6061-T6 alloy and then stored at 85 1C. When used, the part should not have experienced during storage a strain larger than 1 10–4. Substituting the appropriate parameters in Eq. (9) allows predicting the storage time at temperature beyond which the allowable strain will be exceeded.
8. Conclusions The distortion caused by milling and fly cutting 4032-O and 6061T6 aluminum alloys follows the creep model presented herein as summarized by the following findings: the compressive stresses at the surface of the sample coupons result in an initial curvature away
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5.70 -2.0
5.72
5.74
5.76
5.78
5.80
5.82
5.84
5.86
5.88
200
5.90
T = 60C
180 160
Time (hours)
-2.5
-3.0
-3.5
ln (T) 5.72
5.74
5.76
5.78
5.80
5.82
5.84
5.86
5.88
5.90
-4.0
-5.0
ln (T)
Fig. 5. Plot used to calculate the values of the constants B and n in Eq. (5). Milled 6061-T6 samples, and (b) fly cut 6061-T6 samples.
Table 10 Constants used to determine εf for machined 4032-O aluminum alloy.
9.568
ln (B) Fly cut 9.065
Milled 58.64
B Fly cut 56.87
Milled 3.41 10
Fly cut –26
2.00 10–25
Table 11 Constants used to determine εf for machined 6061-T6 aluminum alloy. n
80 60
T = 80C
40
T = 90C
20
T = 100C 0.5
0.6
0.7
x
0.8
0.9
1
Fig. 6. Time at temperature (T) that is required for strain to reach a fraction (x) of its final magnitude in fly cut 4032-O aluminum alloy.
References
-4.5
n
T = 70C
100
behavior and therefore it can be used for forecasting the effects of long term storage, as well as for designing high temperature, short term stress relief treatments for precision components made of these aluminum alloys. Although the model parameters were developed for two alloys and two machining operations, it is anticipated that with the correct parameters, the model can be used with other aluminum alloys.
-3.5
Milled
120
0
-4.0
5.70 -3.0
140
ln (B)
B
Milled
Fly cut
Milled
Fly cut
Milled
Fly cut
4.409
6.460
28.90
41.95
2.81 10 13
6.04 10 19
from the machined layer. The residual compressive stresses that remain on the machined surface cause the material to creep over time in such a way that the creep rate increases with increasing temperature and the amount of total creep strain increases linearly with increasing temperature. The creep model presented herein can accurately predict this
[1] S. Brunet, et al., Influence of residual stresses induced by milling on fatigue life of aluminum workpieces, Residual Stresses III,ICRS, Tokushima, Japan (1991) 1344–1349. [2] M. Field, Surface integrity in machining and grinding, American society of tool and manufacturing engineers, in: Proceedings of the Creative Manufacturing Seminars, Technical Papers, 2, 1968, p. 21. [3] L. Frommer, E.H. Lloyd, J. Inst. Met. 70 (1944) 91–124. [4] C.W. Marschall, R.E. Maringer, Dimensional Instability: An Introduction, Pergamon Press, New York, NY (1967) 156. [5] A.G. Imgram, M.E. Hoskins, J.H. Sovik, R.E. Maringer, F.C. Holden, Study of Microplastic Properties and Dimensional Stability of Materials AFML-TR-67232, Battelle Memorial Institute (1968) 24, Columbus, Ohio, August. [6] R.G. Treuting, J.J. Jynch, H.B. Wishart, D.G. Richards, Residual Stress Measurements, American Society for Metals, Cleveland, OH (1952) 161. [7] A.G. Hebel, Jr. and A.G. Hebel III, “Stress relief of metals”, US Patent No. 4,968,359, November 1990. [8] M.F. Ashbey, Acta Metall. 20 (1972) 887–897. [9] N.E. Dowling, Mechanical Behavior of Materials, 2nd ed., Prentice Hall Publishing Company, Upper Saddle River, NJ (1998) 718. [10] W. Callister, Materials Science and Engineering: An Introduction, 3rd ed., John Wiley and Sons, New York, NY (1993) 221. [11] A. Ahmadieh, A.K. Mukherjee, Mater. Sci. Eng. 21 (1975) 115–124. [12] R.J. Rourke, W.C. Young, Formulas for Stress and Strain, 5th ed., McGraw Hill Book Company, New York, NY (1975) 112–115. [13] W.P. Evans, Residual Stress Measurement by X-Ray Diffraction, Society of Automotive Engineering, Warrendale, PA (2003) 76–79. [14] ASTM Standard E951, Standard test method for verifying the alignment of X-ray diffraction instrumentation for residual stress measurement annual book of ASTM Standards, 103.01, 2008, pp. 788–790. [15] ASTM Standard E21, Elevated temperature tensile test of metallic materials annual book of ASTM standards, Worcester, Massachusetts, 03.01, 2008, pp. 167–174. [16] T.W. Spence, The Effect of Machining Residual Stresses on the Dimensional Stability of Aluminum Alloys used in Optical Systems (Ph.D. thesis), Worcester Polytechnic Institute, Worcester, Massachusetts (2010) 66. [17] T.W. Spence, The Effect of Machining Residual Stresses on the Dimensional Stability of Aluminum Alloys used in Optical Systems (Ph.D. thesis), Worcester Polytechnic Institute (2010) 35–40. [18] R.W.K. Honeycombe, The Plastic Deformation of Metals, Edward Arnold Pty Ltd., Victoria, Australia (1984) 369.
Contents lists available at ScienceDirect
Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
The effect of machining-induced residual stresses on the creep characteristics of aluminum alloys Timothy W. Spence a, Makhlouf M. Makhlouf b,n a b
BAE Systems Electronics and Integrated Solutions, P.O. Box 868, NHQ3-2145, Nashua, NH 03061, USA Department of Mechanical Engineering, Worcester Polytechnic Institute, Worcester, MA 01601, USA
art ic l e i nf o
a b s t r a c t
Article history: Received 15 October 2014 Received in revised form 3 February 2015 Accepted 9 February 2015 Available online 18 February 2015
Precision components, such as those used in optical systems, often experience distortion of their shape during service. This distortion occurs because of residual stresses that are introduced into the surface of the components during machining and lead to creeping of the material when the component is subjected to elevated temperatures for prolonged periods of time. In this paper, a creep model is developed and used to describe how the residual surface stresses created by milling and by fly cutting affect the geometry of an aluminum alloy component as it creeps. The model is verified by applying it to components that are manufactured from two different aluminum alloys; namely 4032-O and 6061-T6; and then it is used to design efficient stress relief schedules for these alloys. Published by Elsevier B.V.
Keywords: Dimensional stability Creep Mathematical modeling Machining-induced residual stress Aluminum alloys
1. Background Dimensional stability of materials is of paramount importance in the fabrication of precision components such as those used in optical systems. Changes in the geometry of these parts over time are unacceptable; particularly if the changes cause the parts to no longer meet the required tolerance. Many sources of dimensional instability have been identified and studied over the years, important among them is residual stresses induced by machining operations; and although stress relief procedures have been developed for many alloys in order to control these stresses, dimensional instability caused by surface stresses due to machining operations has not been thoroughly characterized and a comprehensive understanding of the magnitude of dimensional changes and the kinetics of the strains that develop in the material over time spans and temperature ranges does not exist. Nevertheless, several studies have been performed to characterize the magnitude of residual stress caused by machining operations. Noteworthy among them is an investigation by Brunet [1] in which he characterized the residual stresses induced in an aluminum alloy (7075-T7351) by milling operations. He found that residual stresses always peaked at the surface of the part and that the milling parameters significantly affect the magnitude of the residual stress. For example, he found that up-milling results
in a residual stress that is 100 MPa less in magnitude than down milling, he also found that reducing the cutting speed by 10 times reduces the residual stress by about 200 MPa and reducing the feed speed by 3 times reduces the residual stress by about 150 MPa. Similarly, Field [2] characterized the residual stresses induced in 4340 steel by grinding operations and found that “gentle” grinding produced small compressive stresses at the surface and virtually no internal stresses, while more aggressive grinding produced large tensile stresses at the surface balanced by compressive stresses deeper within the metal's bulk. Also Frommer and Lloyd [3] characterized the residual stresses in heat treated aluminum alloys that have been subjected to different machining operations. They used x-rays to measure the magnitude of surface stresses and acid etching to estimate the depth of the stressed layer. Their findings are summarized in Table 1. Therefore, it is evident that machining operations invariably produce surface stresses in the machined components and that these stresses can range in magnitude from being insignificant to being highly significant. Moreover, the magnitude and sense of these surface stresses depend to a large extent on the machining operation.
2. Development of the model n
Corresponding author. Tel.: þ 1 508 831 5647; fax: þ 1 508 831 5993. E-mail address: [email protected] (M.M. Makhlouf).
http://dx.doi.org/10.1016/j.msea.2015.02.020 0921-5093/Published by Elsevier B.V.
Generally speaking, material that is in a state of sustained stress will creep and there are two unique characteristics to this situation:
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Table 1 Summary of findings by Frommer and Lloyd related to surface stresses produced by various machining operations. Machining operation
Process details
Stress (MPa)
Depth (mm)
Turning
Flat surface finished with a fine finishing cut (0.038 mm/rev., 0.127 mm depth of cut). Cylindrical surface turned with a rough cut (575 rpm, 0.305 mm/rev., 1.27 mm depth of cut). Surface faced off under conditions that produce chatter marks. Recess made with a flat bottom drill (290 rpm, 0.127 mm/rev.). Flat surface side-milled with a 50.8 long 9.525 diameter end-mill (220 rpm, 0.01 mm/rev., 3.175 mm depth of cut). Flat surface milled with a straddling end-mill (220 rpm, 0.254 mm/rev., 3.175 mm depth of cut).
45 98 282 94 Nil
0.051 0.381 0.610 0.102–0.381 Nil
Nil
Nil
Recessing Surface milling (cutter not enclosed by material)
In Eq. (1), the variables that affect the strain rate ε_ are stress, σ, and absolute temperature, T. The coefficient k, the exponent m, and the activation energy Qc have values that depend on the material and the creep mechanism. A unique condition of creep strain due to residual (not applied) stress in an un-restrained material is that stress is not constant but it is a function of strain, i.e.
Creep strain
Δt
Primary
Δε
σ res ¼ f ðεÞ Given Hooke's Law Secondary
Tertiary
1 E
ε1 ¼ ½σ 1 νðσ 2 þ σ 2 Þ and if
Instantaneous deformation
σ2 ¼ σ3 ¼ 0
Time Fig. 1. Hypothetical creep strain vs. time plot showing (as a dashed line) the region of interest when considering creep induced by residual stresses that are caused by machining operations [10].
1. In general, creep models have a stress term that is raised to an exponent; and for metals, this exponent is larger than unity. Consequently, if a metallic specimen has a non-uniform stress, the more stressed regions will creep at exponentially higher rates than the less stressed regions. 2. As the material strains, the stress level becomes proportionally lower. These two characteristics must be accounted for in any mathematical model that is intended for predicting the dimensional stability of metallic components due to machining residual stresses. The temperature range of interest in this work is 55 1C to þ125 1C. This is known as “the full military temperature range” because it is the service range for a wide variety of military components. The typical magnitude of residual stress caused by machining operations is in the range 100–200 MN/m2 [1–7]. The creep mechanism map for aluminum shows that for this temperature and stress ranges, the operative creep modes are Dislocation Glide and Dislocation Creep [8]. The creep model that is applicable for Dislocation Glide and Dislocation Creep, and also accounts for both stress and temperature is the Power Law [9]. However, the Power Law creep model best represents Secondary Creep; while in this case, the constantly changing stress magnitude (due to creep strain) will keep the creep mode in the Primary Creep regime. Nevertheless, the strains associated with machining residual stresses are small enough and the time spans considered are short enough that a straight line approximation over the range of interest should introduce only a small error into calculations made with the Power Law as shown in Fig. 1. The Power Law Creep equation for crystalline materials [9,11] is given by the following equation: k T
Qc
ε_ ¼ σ m e RT
ð1Þ
then
σ 1 ¼ σ ¼ Eε
ð2Þ
A stress function is then defined with a linear relationship to strain and where the value of stress reduces to zero as strain reaches its final magnitude (εf) as shown in the following equation: ε ð3Þ σ ¼ σ in 1
εf
Substituting Eq. (3) into Eq. (1), and integrating from an initial strain of zero at an initial time of zero, yields an expression that defines strain as a function of initial stress (σin), final strain (εf), stress exponent (m), activation energy (Qc), a constant (k), and time (t) as shown in the following equation: Z ε¼ε Z t¼t Qc σ ε m σ in in dε ¼ ke RT dt ε¼0
εf
t¼0
ε ðm 1Þσ in k RTQ c te þ ðσ in Þ1 m ε ¼ εf f T σ in εf
1 1 m
ð4Þ
It was found that, within the temperature range considered in this work, as the temperature increased, εf also increased. The theoretical maximum creep strain that would be recovered during an isothermal temperature exposure (εf,m) would be in accordance with Hooke's Law (assuming that the initial stress is completely converted to strain), i.e.
εf ;m ¼
σ in E
:
In reality, the theoretical maximum strain is not reached, so an expression is developed to allow predicting εf. The expression includes a material constant, B, and a temperature dependence term, Tn, together with the modulus of elasticity for the material, E, as shown in following equation:
εf ¼ B
σ in E
T n:
ð5Þ
T.W. Spence, M.M. Makhlouf / Materials Science & Engineering A 630 (2015) 125–130
4.1. Measurement of residual stress due to machining
Table 2 Nominal chemical composition of the alloys used. Alloy
Chemical composition
4032 6061
Si
Mg
Cu
Cr
Ni
Zn
Ti
12.2 0.6
1.0 1.0
0.90 0.30
0.10 max 0.20
– 0.9
0.25 max 0.25 max
– 0.15 max
Substituting Eq. (5) into Eq. (4) yields the Creep Model Equation shown as follows:
ε¼B
σ in E
Tn
127
1 1 m Qc BT n ðm 1ÞE k 1m RT þ ðσ Þ te in B E Tnþ1
ð6Þ
Depth-corrected residual stress measurement was performed in accordance with SAE HS-784 [13] in order to assess the magnitude of residual stress in the material after machining. This method uses a series of XRD measurements at increasing depths within the parent material in order to characterize the distribution of residual stress as a function of depth. Depth-corrected residual stress measurements were used because at locations very close to the surface of the coupon, the material relaxes to an extent that can influence the measurements if they were performed with a “surface only” measuring method. A semi-systematic error was determined for the measurements by using a powder metal, zerostress sample that was monitored in accordance with ASTM E915 [14]. This error was determined to be 12.25 MN/m2. Two coupons from each alloy were used for each measurement in order to obtain the average stresses reported in Tables 3–6. The corrected value of stress, which is found just below the surface of the coupon, is highlighted in these Tables.
3. Measurements Coupons made from aluminum alloys 4032-O and 6061-T6 were machined on one side to cause them to curve when they are heated. The magnitude of curvature of these coupons was monitored over an extended period of time at different temperatures. The bimetallic strip model [12] was used to convert these measured curvatures to strains in the machined layer. The creep parameters m, Qc, and k in Eq. (4) were then obtained by fitting the measured strain vs. time and temperature data to curves by means of curve fitting software. The final strain, εf was determined experimentally.
4. Materials and procedures 2.5 15.25 0.15 cm3 coupons that were machined from 4032O and 6061-T6 aluminum alloys that have the nominal chemical composition shown in Table 2 were used. Since the machining operations introduce a stressed layer on all the surfaces of these coupons, the surface layer of the coupons (0.0127–0.0.0152 cm deep1) was removed by etching the coupons for 10 min with a 20% sodium hydroxide solution at 40 1C. The baseline curvature of each coupon was then measured by a CNC vision measuring system2. The etched and measured coupons were then machined on one side by either one of the following operations: (i) Controlled milling; wherein a half inch, 3 flute solid carbide end mill with a 411 rake angle, a 13.71 edge relief angle, and a 9.11 end cutting edge angle was used. The spindle speed was 3000 rpm, the feed rate was 50 cm/min, and the depth of cut was 0.05 cm. Isopropyl alcohol was used as lubricant. (ii) Controlled fly cutting; wherein a single cutting point with a 7.71 back rake angle and a 4.51 end relief angle was used. The spindle speed was 3000 rpm, the feed rate was 75 cm/min, and the depth of cut was 0.05 in. Isopropyl alcohol was used as lubricant. The coupons were heat-treated in a thermal chamber3 with a heating rate of 15 1C/min. Because of the relatively long heat treatment times that were employed, the thermal lag of the coupons during heating and cooling may be ignored without introducing significant errors. The heat treating temperatures were 40 1C, 50 1C, 60 1C, and 85 1C. 1
This thickness was selected based on [5]. 2 Quickvision ELF Pro Inspection System, Mitutoyo Corporation, Kanagawa, Japan. 3 Thermotron Model RA-42-CHV-30-30.
4.2. Measurement of temperature-dependant modulus of elasticity Five specimens from each alloy were used to determine the elevated temperature modulus of elasticity of the coupons. The tensile tests were conducted according to ASTM standard E21 [15] on a Universal Testing machine4 with a ramp rate of 0.127 cm/min. Strain was measured using a high temperature axial extensometer5 that was used until the specimen fractured. The specimens were heated to the test temperature, and tested to fracture in an environment chamber6. Three thermocouples were securely attached to the surface of the specimen inside its reduced section. The measurements were performed after the specimens equilibrated at 25 1C, 60 1C, 85 1C, 125 1C and 175 1C. Table 7 shows the measured elastic modulus vs. temperature for the two alloys.
5. Measurement of coupon curvature As described earlier, curvature of the coupons was measured with a Mitutoyo Quickvision ELF Pro Inspection System. This system utilizes a z-axis camera and an x–y table to perform a series of height measurements that are fit to a diameter. Measurement accuracy values are published by Mitutoyo [16] and are functions of the length of the feature that is being measured. For example the error in measuring 76 cm radius is 70.0018 cm. This error is very small compared to the changes in radius of the coupons, which was on the order of 1.25–25.5 cm.
6. Results, analysis, and discussion The creep parameters m, Qc, and k in Eq. (6) were obtained by fitting the strain vs. time data to curves by means of curve fitting software. Determining these parameters required the raw data (radius of curvature vs. time) to be first converted into strain vs. time data. This was accomplished by means of the simplified version of the bimetallic strip equation given in Eq. (7) [17] where tA and tB are thickness of the stressed and the un-stressed regions respectively, and r1 and r2 are radii of curvature. Eq. (7) is valid 4 Instron model 1332 equipped with an 8500 controller and a 5620 pound load cell. 5 MTS high temperature extensometer model 633.11B-15S/N 173. 6 Instron environment chamber model 3116.
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Table 3 Measured stress distribution in 4032-O coupons that have been milled.
Table 9 Creep parameters for machined 6061-T6 aluminum alloy.
Depth (cm)
Measured stress (MN/m2)
Gradient (MN/m2)
Relaxation (MN/m2)
0.0000 0.0013 0.0025
126.5 7 3.4 177.6 7 3.4 206.17 2.4
59.9 186.4 198.0
59.9 178.9 181.0
Qc (cal/mol)
6907
m
3.583
k Milled
Fly cut
2.717 10 21
7.99 10 22
Table 4 Measured stress distribution in 4032-O coupons that have been fly cut. Depth (cm)
Measured stress (MN/m2)
Gradient (MN/m2)
Relaxation (MN/m2)
0.0000 0.0013 0.0025
31.3 7 3.1 163.3 7 3.4 187.17 3.1
95.9 100.0 183.0
10.1 4.4 5.9
Table 5 Measured stress distribution in 6061-T6 coupons that have been milled. Depth (cm)
Measured stress (MN/m2)
Gradient (MN/m2)
Relaxation (MN/m2)
0.0000 0.0013 0.0025
92.86 7 2.72 143.54 7 2.72 89.80 7 2.72
16.67 146.94 165.99
14.6 141.5 152.7
Table 6 Measured stress distribution in 6061-T6 coupons that have been fly cut. Depth (cm)
Measured stress (MN/m2)
Gradient (MN/m2)
Relaxation (MN/m2)
0.0000 0.0013 0.0025
22.8 72.7 135.072.7 138.1 72.7
68.4 120.7 173.1
186.1 68.7 168.0
Table 7 Modulus of elasticity of 4032-O and 6061-T6 alloys at various temperatures. Modulus of Elasticity (kN/m2)
Temperature (1C)
25 60 85 125 175
4032-O
6061-T6
80.447 79.024 77.832 75.618 72.323
68.815 67.597 66.577 64.684 61.865
Fig. 2. Strain vs. time at different temperatures for 4032-O aluminum alloy. Points are the measured values and solid lines are model predictions. Is at 85 1C, is at 60 1C, is at 50 1C, and is at 40 1C. (a) Milled samples, and (b) fly cut samples.
Table 8 Creep parameters for machined 4032-O aluminum alloy. Qc (cal/mol)
20,167
m
2.423
k Milled
Fly cut
2.880 10 6
1.08 10 6
when tA«tB, and the modulus of elasticity of both layers is equal
εr1 -r2 ¼
tB 1 1 ð3t A þ t B Þ r2 r1 6t A
ð7Þ
Tables 8 and 9 list the calculated creep parameters for the two alloys and Figs. 2 and 3 show a comparison between the measured strain and the strain calculated by Eq. (6) with the creep parameters shown in Tables 6 and 7. Figs. 4 and 5 show plots of the final strain (εf) and Tables 10 and 11 show the values of the constants B and n which were used in Eq. (5). Note that the term k depends on the machining operation so that for the same alloy there is a k value for the milled material that is different from that for the fly cut material. This is because the term k includes not only the vibration frequency of the unit of flow, but also the change in entropy and a factor that depends on structure, i.e., the distribution of dislocations, precipitates and grain boundaries in the alloy [18]. The terms B and n describe the dependency of the final strain on temperature as given by Eq. (5), and therefore they too will depend on the material's structure and hence they too vary with the machining operation.
T.W. Spence, M.M. Makhlouf / Materials Science & Engineering A 630 (2015) 125–130
-2.0
129
5.70 5.72 5.74 5.76 5.78 5.80 5.82 5.84 5.86 5.88 5.90
-2.5
-3.0
-3.5
-4.0
-3.0
ln (T) 5.70
5.72
5.74
5.76
5.78
5.80
5.82
5.84
5.86
5.88
5.90
-3.5
-4.0
-4.5
-5.0
ln (T)
Fig. 4. Plot used to calculate the values of the constants B and n in Eq. (5). (a) Milled 4032-O samples, and (b) fly cut 4032-O samples. Fig. 3. Strain vs. time at different temperatures for 6061-T6 aluminum alloy. Points are the measured values and solid lines are model predictions. is at 125 1C, is at 85 1C, and is at 60 1C. (a) Milled samples, and (b) fly cut samples.
and realizing that ð1 xÞ1 m ¼
7. Application of the creep model
1 ð1 xÞm 1
c1
then Eq. (10) can be written as 7.1. Application of the creep model in the design of stress relief schedules
tffi
Once the creep constants for the alloy have been determined, the creep model can be used to develop economical short term, elevated temperature heat treatment schedules for the components. The stress relief heat treatment would be for the purpose of allowing all surface stresses caused by severe machining to “creep out” under controlled conditions, rather than due to time/temperature exposure in service. The following procedure can be used for the design of a stress relief heat treatment. First, Eq. (4) is solved for time, t, t¼
εf T ðm 1Þkσ in
"
σ in 1
ε εf
1 m
# Qc
ðσ in Þ1 m e RT
ð8Þ
Next, a fraction (x) of stress that is to be relieved is defined and
ε ¼xεf is substituted into Eq. (8) to yield Eq. (9) t¼
εf T
ðm 1Þkσ in
h i Qc ½σ in ð1 xÞ1 m ðσ in Þ1 m e RT
ð9Þ
Substituting Eq. (5) into Eq. (9) gives t¼
i BT n þ 1 σ 1in m h Q ð1 xÞ1 m 1 e RTc Eðm 1Þk
ð10Þ
BT n þ 1 σ 1in m
Eðm 1Þkð1 xÞm 1
Qc
e RT
ð11Þ
Eq. (11) may be used to design the stress relief schedule by calculating the time to reach a fraction x of the final strain (εf) at different temperatures (T). In order to illustrate the procedure, Eq. (11) was used with the appropriate values for fly cut 4032-O aluminum alloy to produce Fig. 6. 7.2. Application of the creep model in forecasting part distortion Eq. (9) may also be used to predict the reliability of machined parts after extended storage times at a given temperature: consider a precision part that has been made by milling 6061-T6 alloy and then stored at 85 1C. When used, the part should not have experienced during storage a strain larger than 1 10–4. Substituting the appropriate parameters in Eq. (9) allows predicting the storage time at temperature beyond which the allowable strain will be exceeded.
8. Conclusions The distortion caused by milling and fly cutting 4032-O and 6061T6 aluminum alloys follows the creep model presented herein as summarized by the following findings: the compressive stresses at the surface of the sample coupons result in an initial curvature away
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5.70 -2.0
5.72
5.74
5.76
5.78
5.80
5.82
5.84
5.86
5.88
200
5.90
T = 60C
180 160
Time (hours)
-2.5
-3.0
-3.5
ln (T) 5.72
5.74
5.76
5.78
5.80
5.82
5.84
5.86
5.88
5.90
-4.0
-5.0
ln (T)
Fig. 5. Plot used to calculate the values of the constants B and n in Eq. (5). Milled 6061-T6 samples, and (b) fly cut 6061-T6 samples.
Table 10 Constants used to determine εf for machined 4032-O aluminum alloy.
9.568
ln (B) Fly cut 9.065
Milled 58.64
B Fly cut 56.87
Milled 3.41 10
Fly cut –26
2.00 10–25
Table 11 Constants used to determine εf for machined 6061-T6 aluminum alloy. n
80 60
T = 80C
40
T = 90C
20
T = 100C 0.5
0.6
0.7
x
0.8
0.9
1
Fig. 6. Time at temperature (T) that is required for strain to reach a fraction (x) of its final magnitude in fly cut 4032-O aluminum alloy.
References
-4.5
n
T = 70C
100
behavior and therefore it can be used for forecasting the effects of long term storage, as well as for designing high temperature, short term stress relief treatments for precision components made of these aluminum alloys. Although the model parameters were developed for two alloys and two machining operations, it is anticipated that with the correct parameters, the model can be used with other aluminum alloys.
-3.5
Milled
120
0
-4.0
5.70 -3.0
140
ln (B)
B
Milled
Fly cut
Milled
Fly cut
Milled
Fly cut
4.409
6.460
28.90
41.95
2.81 10 13
6.04 10 19
from the machined layer. The residual compressive stresses that remain on the machined surface cause the material to creep over time in such a way that the creep rate increases with increasing temperature and the amount of total creep strain increases linearly with increasing temperature. The creep model presented herein can accurately predict this
[1] S. Brunet, et al., Influence of residual stresses induced by milling on fatigue life of aluminum workpieces, Residual Stresses III,ICRS, Tokushima, Japan (1991) 1344–1349. [2] M. Field, Surface integrity in machining and grinding, American society of tool and manufacturing engineers, in: Proceedings of the Creative Manufacturing Seminars, Technical Papers, 2, 1968, p. 21. [3] L. Frommer, E.H. Lloyd, J. Inst. Met. 70 (1944) 91–124. [4] C.W. Marschall, R.E. Maringer, Dimensional Instability: An Introduction, Pergamon Press, New York, NY (1967) 156. [5] A.G. Imgram, M.E. Hoskins, J.H. Sovik, R.E. Maringer, F.C. Holden, Study of Microplastic Properties and Dimensional Stability of Materials AFML-TR-67232, Battelle Memorial Institute (1968) 24, Columbus, Ohio, August. [6] R.G. Treuting, J.J. Jynch, H.B. Wishart, D.G. Richards, Residual Stress Measurements, American Society for Metals, Cleveland, OH (1952) 161. [7] A.G. Hebel, Jr. and A.G. Hebel III, “Stress relief of metals”, US Patent No. 4,968,359, November 1990. [8] M.F. Ashbey, Acta Metall. 20 (1972) 887–897. [9] N.E. Dowling, Mechanical Behavior of Materials, 2nd ed., Prentice Hall Publishing Company, Upper Saddle River, NJ (1998) 718. [10] W. Callister, Materials Science and Engineering: An Introduction, 3rd ed., John Wiley and Sons, New York, NY (1993) 221. [11] A. Ahmadieh, A.K. Mukherjee, Mater. Sci. Eng. 21 (1975) 115–124. [12] R.J. Rourke, W.C. Young, Formulas for Stress and Strain, 5th ed., McGraw Hill Book Company, New York, NY (1975) 112–115. [13] W.P. Evans, Residual Stress Measurement by X-Ray Diffraction, Society of Automotive Engineering, Warrendale, PA (2003) 76–79. [14] ASTM Standard E951, Standard test method for verifying the alignment of X-ray diffraction instrumentation for residual stress measurement annual book of ASTM Standards, 103.01, 2008, pp. 788–790. [15] ASTM Standard E21, Elevated temperature tensile test of metallic materials annual book of ASTM standards, Worcester, Massachusetts, 03.01, 2008, pp. 167–174. [16] T.W. Spence, The Effect of Machining Residual Stresses on the Dimensional Stability of Aluminum Alloys used in Optical Systems (Ph.D. thesis), Worcester Polytechnic Institute, Worcester, Massachusetts (2010) 66. [17] T.W. Spence, The Effect of Machining Residual Stresses on the Dimensional Stability of Aluminum Alloys used in Optical Systems (Ph.D. thesis), Worcester Polytechnic Institute (2010) 35–40. [18] R.W.K. Honeycombe, The Plastic Deformation of Metals, Edward Arnold Pty Ltd., Victoria, Australia (1984) 369.