Most metals and alloys have a negative temperaturecoefficient of modulus of elasticity; that is to say theylose stiffness when heated. They also have a positivecoefficient of thermal expansion, increasing in lengthwhen heated. These two effects are due to increase inenergy of the atoms with increase in temperature. Someferromagnetic materials, however, exhibit markedlydifferent behavior, which can be utilized to designconstant modulus alloys.
The modulus of elasticity (E) of ferromagneticmaterials is a complex function of a number of physicalproperties, related by the adjacent equation.
Each of the factors λ, µ and k is affected bycomposition, strain and temperature. In order that themodulus of elasticity will remain constant withvariation in temperature it is necessary to select a
NI-SPAN-C is a trademark of the Special MetalsCorporation group of companies.
The data contained in this publication is for informational purposes only andmay be revised at any time without prior notice. The data is believed to beaccurate and reliable, but Special Metals makes no representation or warrantyof any kind (express or implied) and assumes no liability with respect to theaccuracy or completeness of the information contained herein. Although thedata is believed to be representative of the product, the actual characteristicsor performance of the product may vary from what is shown in thispublication. Nothing contained in this publication should be construed asguaranteeing the product for a particular use or application.
composition for which λ2µ changes at the same rate andin the same direction as k2.
The same constants are also sensitive to appliedmagnetic fields so that the modulus of elasticitychanges with a change in magnetic field strength.
As these considerations apply only toferromagnetic materials they do not hold when an alloyhas been heated beyond its Curie temperature, the pointat which it changes from ferromagnetic to paramagneticbehavior.
λ = magnetostrictive constantE = where µ = reversible permability
k = electromechanical couplingcoefficient
4πλ2µk2
CCoommppoossiittiioonnThe first alloys developed for constant moduluspurposes were binary iron-nickel compositions. Figure1 shows that a zero temperature coefficient is obtainedwith alloys containing about 27% or 44% nickel,balance iron. These two alloys were found to be toosensitive to small changes in composition to be suitablefor commercial production, a variation of 1% in nickelcontent shifting the coefficient of the 44% alloy about50 x 106/°F.
Addition of chromium to these iron-nickel alloysreduces sensitivity to composition but the resultingternary alloys are still difficult to produce with thedesired characteristics and require heavy coldreductions, seriously limiting sizes.
Addition of titanium to the iron-nickel-chromium
composition produces an alloy with a controllablethermoelastic coefficient, NI-SPAN-C alloy 902. Thisalloy is melted to the close compositional rangesshown in Table 1. The desired thermoelasticcoefficient is then obtained by using cold work and theproper thermal treatment. Cold work produces internalstrains, making the coefficient more negative. Thermaltreatments, in the lower temperature ranges, relievestrain. They also cause complex ordering phenomenawhich make the coefficient more positive. Heating attemperatures above about 900°F causes theprecipitation of an intermetallic compound of titaniumand nickel, withdrawing nickel from the matrix andmoving the coefficient further in the positive direction.
Iron ...............................................................................Balance*
*Reference to the ‘balance’ of a composition does not guarantee this isexclusively of the element mentioned but that it predominates andothers are present only in minimal quantities.
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The thermoelastic coefficient (TEC) of an alloy is the rate ofchange of its modulus of elasticity with change intemperature. It is usually expressed as parts per million perdegree F (e.g. 5 x 10-6/°F).
The first measurements of the TEC of NI-SPAN-C alloy902 were made using a torsion pendulum operating at aboutone cycle per second. These tests are the basis for much ofthe published data on the alloy. However, when these datawere used to design high frequency devices they were foundto produce incorrect results, and a confused situation arose.
Recent work has solved the problem of the conflictingresults. It has been found that operating frequency has amarked effect on TEC. Tests run at Special Metals showedthat the TEC of a given sample increased with increase intest frequency up to about 800 cps. Above 800 cps there wasno frequency effect. Samples from the same heat of material
TThheerrmmooeellaassttiicc CCooeeffffiicciieenntt
6050403020100
300
200
100
0
-100
-200
-300
Nickel Content, %
Tem
pera
ture
Coe
ffici
ent
of M
odul
usof
Ela
stic
ity x
10-6
/°F
FFiigguurree 11. Effect of composition on the temperature coefficient of modulus of elasticity of iron-nickel alloys.
tested at about 1500 cps, and in another laboratory at455,000 cps, gave identical results. Burnette at the NationalBureau of Standards found that a heat treatment whichproduced zero TEC on a sample tested in a torsion pendulumat 1 cps developed a TEC of +40 on a sample tested in free-free vibration at 1000 cps. Figure 2 shows these data and aschematic indication of the frequency effect.
Because of the frequency effect, it is necessary todelineate two areas of application of NI-SPAN-C alloy 902,each requiring different processing to achieve best results.These are:
1. Low frequency devices. These include springs,Bourdon tubes, aneroid capsules, etc.
2. High frequency devices. Tuning forks, vibratingreeds, mechanical filters and similar instrumentation fall inthis category.
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FFiigguurree 22.. Effect of operating frequency on TEC. Free-free specimens heat treated 1200°F/5 hours, pendulum specimen1285°F/3 hours. All specimens cold worked 50% before heat treatment.
Frequency, cycles/second
Ther
moe
last
ic C
oeffi
cien
t, 1
0-6/°
F
Bending, Free-free
Torsion, Free-free
Torsion Pendulum, NBS
See Text
30
20
10
0
-100.1 1 10 100 1,000 10,000 100,000 1,000,000
FFiigguurree 33.. Effect of 5-hour heat treatment at temperature shown on torsional mechanical hysteresis.
Temperature, °F
Mec
hani
cal H
yste
resi
s, %
120010008006004002000
0.20
0.15
0.10
0.05
0
13% Cold Work
71%
35%
The unavoidable differences in chemical compositionbetween heats of the alloy lead to slight variations in elasticproperties. These variations are considerably less than theoverall accuracy of most devices in which the alloy is used,being on the order of ±20 parts per million per degree F. Forvery precise applications, the effect of variation incomposition may be adjusted by processing to obtain thedesired TEC.
PPrroocceessssiinngg LLooww FFrreeqquueennccyy DDeevviicceessLow frequency devices usually require a low TEC, lowmechanical hysteresis and low drift. This can be obtained bycold working about 35% and heat treating at 1100°-1200°Ffor 5 hours. All heats of the alloy, when given this treatment,will have a TEC suitable for most low frequencyapplications. Figure 3 shows that the lowest mechanicalhysteresis is also obtained by this processing. Highestmechanical strength is another desirable result. (See Table5.)
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Very high precision equipment requires that each lot ofmaterial be pilot tested to determine the specific heattreatment necessary to produce the exact TEC required. Aformula relating heat treatment temperature, compositionand amount of cold work has been developed to assist incarrying out pilot tests. The formula, which applies only tohigh frequency applications, appears in the Appendix.
The effect of processing variables on the high frequencyTEC of a typical heat is illustrated in Figures 4, 5 and 6. Itwill be noted that, for this heat, 50% cold work plus 5 hoursat 860°F produced a zero TEC. Increasing the heat treatingtemperature to 1100°F produced a TEC 12 parts permillion/°F higher.
Unless extreme precision is required, processing shouldbe directed toward producing high strength, with itsattendant fatigue resistance, and low mechanical hysteresis(30 to 50% cold work + 1100° to 1200°F/5 hours). Theresultant TEC will be fairly close to zero.
Heat treatment temperature must exceed 600°F to insurestability of properties.
Figure 3 also shows that the heat treating temperature mustbe lowered to 700° to 750°F for material with a high amountof cold work, if lowest mechanical hysteresis is desired. Thisheat treatment will result in a lower TEC.
HHiigghh FFrreeqquueennccyy DDeevviicceess
FFiigguurree 44.. Effect of cold work and 5-hour heat treatment attemperature shown on thermoelastic coefficient.
Temperature, °F
Ther
moe
last
ic C
oeffi
cien
t, 1
0-6/°
F
0% Cold Work (Annealed)
10%
20%
30%
50%
50
40
30
20
10
0
-10
-20
0 200 400 600 800 1000 1200
FFiigguurree 55.. Cold work and 5-hour heat treatment required to producevarious thermoelastic coefficient levels.
FFiigguurree 66.. Effect of cold work and 5-hour heat treatment attemperature shown on TEC.
+10x10-6 TEC+5x10-6 TEC
0 TEC
-5x10-6 TEC
-10x10-6 TEC
60504030201000
400
200
600
1200
1400
800
1000
Cold Work, %
Hea
t Tr
eatin
g Te
mp
erat
ure,
°F
Cold Work, %
Ther
moe
last
ic C
oeffi
cien
t, 1
0-6/°
F
6050403020100
50
40
30
20
10
0
-10
-20
60
70
1200°F
1100°F
1000°F
900°F
800°F
600°F
400°F
As rolled
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TTaabbllee 22 - Physical Constants of NI-SPAN-C alloy 902
The average coefficients of expansion of one melt of thealloy with various heat treatments are shown in Table 4. Itwill be noted that there is no significant change in expansioncharacteristics due to heat treatment. Other tests have shownthat the amount of cold work prior to heat treatment has onlyminor effect on expansion characteristics.
Figure 7 is a graphical representation of the effect oftemperature on thermal expansion. A constant low rate ofexpansion is maintained over the useful working range.Then the curve breaks sharply upward until a comparativelyhigh value is reached. The temperature at which theexpansion rate begins to increase rapidly is known as the“inflection point” or “inflection temperature”. It can bedetermined graphically from the total expansion curve asshown in the figure. This behavior is typical of iron-nickelalloys of the low expansion type.
CCoonnddiittiioonn
As hot rolled 4.5 4.5 4.6 5.3 6.0
1850°F/1 hr, WQ 4.2 4.3 4.4 4.8 5.5
1850°F/1 hr, WQ +
900°F/5 hrs, AC 4.3 4.2 4.3 4.9 5.6
1850°F/1 hr, WQ +
1000°F/5 hrs, AC 4.4 4.2 4.4 5.2 5.9
1850°F/1 hr, WQ +
1100°F/5 hrs, AC 3.9 4.2 4.6 5.5 6.0
AAvveerraaggee CCooeeffffiicciieenntt ooff TThheerrmmaallEExxppaannssiioonn,, iinn..//iinn..//°°FF xx 110066
The tensile modulus of elasticity ranges between about 24 to29 x 103 ksi, depending on the processing. Torsional
modulus range is about 9 to 10 x 103 ksi.Figure 8 shows the effect of cold work and thermal
treatments on the room temperature tensile modulus. Coldwork causes an increase in the modulus. Raising thetemperature of heat treatment also causes an increase.
Figure 9 shows the effect of three heat treatments on thetensile modulus of cold rolled strip at different temperatures.The slope of these curves is the TEC. The figure shows howpositive, zero and negative TEC values may be obtainedfrom the same material by varying the thermal treatment.The sharp rise and fall of the curves above 250°F is due tothe rapid change in magnetic properties above thistemperature. The maximum points on the curves areapproximate measures of the Curie temperatures of thematerials tested.
Figure 8. Effect of cold work and heating for 5 hours attemperature shown on the room temperature modulus of elasticity.
Temperature, °F
Tens
ile M
odul
us o
f E
last
icity
, ks
i x 1
03
29
28
27
26
25100 300 500 700 900 1100 1300
35% Cold Work
71%
13%
0%
900°F/5 hrNegative TEC
1000°F/5 hrZero TEC
1300°F/5 hrPositive TEC
Temperature, °F
Tens
ile M
odul
us o
f E
last
icity
, ks
i x 1
03
4003002001000
27.65
27.55
27.45
27.95
27.85
27.75
28.3
28.2
28.1
28.0
27.9
Figure 9. Effect of various heat treatments on the tensile modulusof elasticity at different temperatures. Material cold worked 50%prior to heat treatment.
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MMeecchhaanniiccaall PPrrooppeerrttiieess
Room temperature tensile and hardness values are shownin Table 5 and Figure 10. The data show why it isdesirable to heat treat at 1100° to 1300°F wheneverpossible. Room temperature fatigue strength appears inTable 6.
Although the alloy was designed for use above-50°F, it has been used successfully at lowertemperatures and some cryogenic data have beenpublished. An abstract of this work is given in Table 7.
The alloy exhibits low damping capacity (high Q).The Q of cold worked material has been reported to beabout 8000, about 4 times greater than the values forannealed forms.
FFiigguurree 1100.. Effect of cold work and 5 hour heat treatment attemperature shown on room temperature hardness.
Cold Work, %
Vic
kers
Har
dne
ss,
VH
N
6050403020100
460
420
380
340
300
260
220
180
140
1300°F
1200°F
1400°F
1100°F
1000°F
800°F600°F
As rolled
TTaabbllee 55 -- Tensile Strength and Hardness of Cold Rolled Stripa
When a spring is loaded and then unloaded, the load-deflection curves do not coincide, even though the elasticlimit of the material is not exceeded. This departure fromlinear elastic behavior, termed mechanical hysteresis, isillustrated in Figure 11. It is expressed quantitatively by theexpression:
100 x maximum width% hysteresis = of hysteresis loop (AB)
maximum deflection (0C)
Mechanical hysteresis values as low as 0.02% have beenobtained for NI-SPAN-C alloy 902 springs by controlledcold work and heat treatment. The effect of these variablesis shown in Figure 3. It will be noted that increase in amountof cold work decreases hysteresis and that increase in heattreatment temperature has a generally similar effect.Minimum hysteresis and maximum strength for the alloy areobtained by cold working 30 to 50% and heat treating atabout 1100° to 1200°F.
The value of mechanical hysteresis depends onmaximum loading stress, increasing with increase in loadingstress. The data shown in Figure 3 were obtained for amaximum torsional loading stress of 25 ksi, which is typicalof normal practice, when fatigue is not a factor.
The alloy has low magnetostrictive properties. However,they are quite adequate for some applications, such as delaylines.
MMaaggnneettiicc PPrrooppeerrttiieess
The saturation magnetization at room temperature isapproximately 5000 gauss. Permeability is affected by coldwork and heat treatment but no extensive investigation hasbeen made to establish values. Figure 12 shows a normalmagnetization curve for cold rolled and aged material. Theeffect of magnetic field intensity on the TEC is illustrated inFigure 13.
FFiigguurree 1122.. Normal magnetization curve. Material cold rolled 40%and heat treated 1000°F/5 hours prior to testing.
FFiigguurree 1133.. Effect of magnetic filed intensity on thermoelasticcoefficient. Material cold rolled 40% and heat treated 1000°F/5hours prior to testing.
Mag
entic
Flu
x D
ensi
ty,
Gau
ssTh
erm
oela
stic
Coe
ffici
ent,
10-6
/°F
Magnetic Field Intensity, Oersteds
Magnetic Field Intensity, Oersteds
24020016012080400
24020016012080400
6000
4000
2000
0
20
-20
-40
0
As in all ferromagnetic alloys, the modulus of elasticity isaffected by magnetization. As magnetic intensity isincreased, modulus decreases until the knee of themagnetization curve is reached. Above this point the trendreverses and modulus increases until magnetic saturation isreached. At higher temperatures these effects occur at lowerfield strengths. See Figure 14.
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FFiigguurree 1144.. Effect of magnetic field intensity on modulus ofelasticity at two temperatures. Material cold rolled 40% andheat treated 1000°F/5 hours prior to testing.
Magnetic Field Intensity, Oersteds
Mod
ulus
of
Ela
stic
ity,
ksi x
103
27.14
27.12
27.10
27.08
27.06
27.04
27.02
27.0024020016012080400
80°F
200°F
HHeeaatt TTrreeaattiinngg
In order to maintain bright surfaces during final heattreatment the process must be carried out in a high vacuumor in a very pure hydrogen atmosphere. Experience hasshown that an absolute pressure of 0.1 micron or less isrequired for bright work in vacuum furnaces. Pressuresaround 1.0 micron may produce a faint straw color.Ultrapure hydrogen, such as that produced by palladiumdiffusion cells, will also maintain brightness.
AAnnnneeaalliinngg
The alloy, as usually supplied by the manufacturer to theuser, is carefully processed and ready for heat treatment afterfabrication. If, for any reason, it is desired to soften thematerial by annealing, the following instructions should becarefully observed:
Heat at 1850°F in a reducing atmosphere free fromsulfur and quench rapidly. Delay in quenching will result inpartial hardening of the alloy and subsequent adjustment ofthe TEC by cold work and heat treatment will be impaired.Annealing time is governed by the dimensions of the work.
WWoorrkkiinngg IInnssttrruuccttiioonnss
PPiicckklliinngg
Thin oxide films formed by heating the alloy in atmospheresless pure than ultrapure hydrogen or in vacuums lower thanthose cited can be removed by mechanical abrasion or bypickling. Pickling the final product will result in a decreasein fatigue strength; therefore abrasive blasting or mechanicalpolishing should be considered for components whichrequire best fatigue resistance.
Pickling can be accomplished by dipping the material inFormula 4 for about 15 minutes, rinsing, dipping intoFormula 9, rinsing and drying. The electrolytic pickle,Formula 15, may also be used. It is particularly convenientfor continuous processing.
FFoorrmmuullaa 44
FFoorrmmuullaa 99
FFoorrmmuullaa 1155
Water 1 gal 1000 ml
Sulfuric acid (66° Be) ¾ pt 95 ml
Sodium nitrate (crude) ½ lb 55 gm
Common salt 1 lb 110 gm
Temperature 180°-190°F 82°-88°C
Water 1 gal 1000 ml
Nitric acid 1 qt 250 ml
Temperature 140°-160°F 60°-71°C
Water 1 gal 1000 ml
Sulfuric acid (66° Be) ¾ pt 95 ml
Sodium fluoride 3 oz 25 gm
Temperature Room
Current density 50 to 100
amps.sq.ft.
JJooiinniinngg
The alloy can be joined by welding, brazing, or soldering ifthe surfaces to be joined have been thoroughly cleaned. Thematerial should be brazed in the heat treated condition inorder to prevent cracking. Autogeneous inert gas fusionwelding has been employed successfully.
In any joining operation the effect of joiningtemperature and time must be considered in relation to itseffect on the thermoelastic characteristics of the device.
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NI-SPAN-C alloy 902 is not “stainless”, as it will acquire anadherent red-brown oxide film when exposed to outdoorenvironments. Tests in industrial and marine atmosphereshave shown corrosion rates of less than 0.001 inch per year.
CCoorrrroossiioonn RReessiissttaanncceeThe alloy is used in many types of precision apparatus whereelastic members are subject to temperature fluctuations.Resonant vibrating systems such as electro-mechanicalfilters, tuning forks and vibrating reeds are typical examplesof devices where a constant frequency is desired. A zeroTEC material may be used for the vibrating member or aslightly positive or negative TEC may be chosen tocompensate for thermal drift due to other components in thedevice.
Another major application is springs. Here the constantTEC property makes deflection independent of temperature.Examples are Bourdon tubes, aneroid capsules, geophysicalinstruments, hairsprings for timing devices, diaphragms, andsprings for weighing instruments.
AApppplliiccaattiioonnss
NI-SPAN-C nickel-iron-chromium alloy 902 is designatedUNS N09902. The alloy is produced in the form of roundbar and strip. Wire, thin gauge strip, round tube, and specialBourdon tubular shapes are available from convertors.
There are three AMS specifications covering the alloy:SAE AMS 5221 - Strip, solution annealedSAE AMS 5223 - Strip, 10% cold rolledSAE AMS 5225 - Strip, 50% cold rolled
A formula has been developed for predicting the heattreatment required to produce the desired TEC for a specificlot of material. The formula was derived by multiplegraphical correlation analysis of experimental data obtainedat a frequency of about 1500 cycles/second, and will give afairly close approximation within the limits shown. Pilottests will still be required for high precision applications butuse of the following equation will simplify testing.
TEC = -12.05 Ni - 16.45 Cr + 10.00 Ti + A + B + 628.68where: LimitsNi = Nickel, % by weight 41.0 to 43.5Cr = Chromium, % by weight 4.90 to 5.75Ti = Titanium, % by weight 2.20 to 2.75A = Effect of heat treating temperature 600° to 1300°FB = Effect of cold work 0 to 100%
Table A lists the values of factor A for varioustemperatures and Table B gives values of factor B for variousamounts of cold work.
Normally all variables except heat treating temperatureare known. Solve the equation for factor A, then determinethe predicted temperature by inspection of Table A. Analternate procedure is to calculate the various values of TECwhich would result from different temperatures, plot theresults, and choose the desired temperature from theresulting graph. This temperature is used for the first pilottest. Final adjustment of temperature is based on test results.
The apparatus used in the laboratory of Special MetalsCorporation to determine TEC is based on that described byRoberts and Northcliffe. A carefully measured specimen issuspended by two strings. Each string terminates in a highoutput crystal phonograph pickup. One pickup is driven by avariable frequency audio oscillator while the other acceptsvibrations from the specimen through its string and feeds itsoutput into a sensitive AC vacuum tube voltmeter. Inoperation the sample is hung in a small chamber providedwith accurate temperature measuring and controllingequipment. After the system has reached thermalequilibrium at the chosen temperature, the operator sends analternating current through the crystal driver and observesthe output signal magnitude on the voltmeter. The signalfrequency is varied to obtain maximum output voltage,which indicates resonance. The resonant frequency is thenaccurately determined with an electronic counter. Resonantfrequency for a rectangular sample is related to itsdimensions and the tensile modulus of elasticity by theequation:
Kt E ½
L2 d
where f = resonant frequencyK = a constant which depends on mode of vibrationt = thickness of strip, in.L = length of strip, in.d = density of material, lb/cu. in.E = modulus of elasticity in tension (Young’s
slope of the plotted frequency vs. temperature curve=
The thermoelastic coefficient can be derived directly fromthe plotted data using the expression:
2 dff dt
where f = resonant frequencydfdt
All tests conducted in the Special Metals laboratory employa specimen 0.125 x 0.250 x 4.00 inches in dimension,vibrated in its fundamental mode of bending. This requires atest frequency of about 1500 cycles/second.
Note: The method of testing described actuallymeasures the change in stiffness of a given specimen withchange in temperature. Change in stiffness has twocomponents, change in elastic modulus and thermalexpansion effects. It is necessary to correct for thermalexpansion if absolute values of TEC are required. Inpractice, change in stiffness is the property which governsactual performance of a device. For this reason, thermalexpansion effects are usually ignored. In this publicationthermoelastic coefficient (TEC) is defined to be the changein elastic modulus uncorrected for thermal expansioneffects.
VVeelloocciittyy ooff SSoouunndd
The theoretical velocity of an extension wave in a wire, suchas in a delay line, is given by:
E ½p
where V = velocity of sound, inches/secondE = modulus of elasticity in tension, psip = density, pounds/cu. in.C = 19.66
V = C
For the range of E obtained in NI-SPAN-C alloy 902 (24 to29 x 103 ksi) the formula predicts a velocity range of178,000 to 196,000 inches/second. Two actual test resultsshowed values of 187,500 to 188,000 inches/secondconfirming the validity of the equation.
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