The effect of short range order on the thermal output and gage factor


    The operating characteristics of resistive metal foil strain gages are influenced by many parameters,  probably the most fundamental of which are the backing material (plastic insulator) and the resistive sensing material (metal conductor).  While there are many other parameters including size, electrical resistance, orientation of sensing grid, etc., it is the backing material and the resistive sensing material which respond directly to the strain developed on the substrate (Perry et al., 1962; Watson, 2008).  Furthermore, it is the resistive sensing material which controls such factors as strain sensitivity (gage factor), cyclic endurance, elongation, temperature range, temperature sensitivity (thermal output), and long-term stability, so many would say it is the most important consideration for making a strain gage selection decision (Sciammarella et al., 2012).

    The two most popular materials used for the resistive sensing element in metal foil strain gages are alloys of Cu-Ni (constantan) and Ni-Cr (karma).  These materials have sufficient strain sensitivity for most applications with gage factors of approximately 2.0.  Furthermore the temperature sensitivity can be minimized by thermal-mechanical treatment of the rolled foil to achieve thermal outputs of approximately 1 ppm/ºF (1.8 ppm/ºC) near room temperature for a wide variety of substrate materials (steel, aluminum, ceramic, etc).  This latter characteristic is referred to as self-temperature-compensation and is a desirable characteristic when trying to determine mechanical strain when ambient temperature is not constant during strain measurement (Murray et al., 1992).  Less widely used to manufacture metal foil strain gages are alloys of Ni-Fe-Cr (isoelastic) and Pt-W (alloy 479).  These materials have higher gage factors of approximately 3.5 and 4, respectively.  There are additional benefits including the high fatigue strength of Ni-Fe-Cr which can be used at alternating strain levels exceeding + 1500 με.  Also, the stability and oxidation resistance of Pt-W enables strain measurements at temperatures in excess of 1200 ºF (Murray et al., 1992).   However, neither Ni-Fe-Cr nor Pt-W is capable of self-temperature-compensation with thermal output magnitudes about two orders of magnitude higher than Cu-Ni and Ni-Cr.  A comparison of gage factor and thermal output magnitudes for these four materials is provided in Table 1.1.

    In addition to metal foil strain gages there are also semiconductor strain gages which are typically made of single crystal silicon, doped with impurities of boron or arsenic.  The gage factor and thermal output of semiconductor strain gages depend upon the impurity level.  For an impurity concentration of 1019 atoms/cm3 the gage factor of P-type semiconductor strain gages is about 109, a magnitude as much as 50 times higher than metal foil strain gages.   Unfortunately, the thermal output is about 1000 ppm/ºF (Shukla et al., 2010).  Additional disadvantages are brittle construction requiring careful handling, nonlinear gage factor, significant resistance change during installation, and nonuniform properties from strain gage to strain gage (Murray et al., 1992).     

    Ni-Fe-Cr alloys have been used to manufacture metal foil strain gages for both stress analysis applications like design validation and failure studies; and for precision transducers sensing weight, pressure, displacement, etc.  Historical use of these alloys for resistive sensing material has involved compromise.  The high strain sensitivity is an attractive characteristic to achieve higher signal levels but the high sensitivity to temperature must be carefully managed.  Typical stress analysis applications involve dynamic loading where the high gage factor and fatigue strength can be used to advantage and the effect of thermal output can be minimized or ignored.  Typical applications in precision transducers often involve dynamic loading also and/or careful exercise of Wheatstone bridge circuit cancelation of like-thermal output in adjacent arms. 

    Metal foil strain gages are typically manufactured in batch form with hundreds of strain gage images produced side-by-side on a single piece of foil as shown in Figure 1.1.  Strain gages made of Cu-Ni and Ni-Cr materials possess excellent uniformity from strain gage to strain gage with typical gage factor uniformity of + 0.5 percent and thermal output uniformity of 0.2 ppm/ºF (Watson, 2008).  A review of the literature for materials used for the resistive sensing element in metal foil strain gages did not produce any data about the uniformity of thermal output in Ni-Fe-Cr alloys.  Perhaps the conventional wisdom was the alloy had so much output due to temperature there was no incentive to try to use it for any applications other than those involving dynamic loading or specialized transducers.  If the Ni-Fe-Cr alloys used historically for strain gage manufacture were also to possess good thermal output uniformity then it might be possible to broaden their use beyond the traditional dynamic loading applications. 

    Finally, there are other Ni-Fe-Cr alloys which have not been used to manufacture metal foil strain gages but which do respond to thermal-mechanical processing: specifically the high nickel Ni-Fe-Cr alloys with about three times as much nickel as iron (75Ni-25Fe).  These so-called permalloys have been studied extensively (Franke et al., 2011), principally for their magnetic properties.  They undergo a change in crystalline structure when subjected to temperatures below approximately 932 ºF (500 ºC).  This varying response to thermal-mechanical processing included change in electrical resistivity and may have implications for self-temperature-compensation.  Additionally, the gage factor of Ni-Fe-Cr alloys is known to be high so there could be additional incentive if high gage factor and reduced thermal output were both possible.  


    Two Ni-Fe-Cr alloys were selected for study – one rich in iron (36Ni-57Fe-7Cr) and one rich in nickel (70Ni-27.5Fe-2.5Cr) for application in metal foil strain gages.  The motivation was to examine the high, resistance – strain sensitivity (gage factor) characteristic of these alloys which would be attractive for improving signal-to-noise level; while being mindful of their high, resistance – temperature sensitivity (thermal output) characteristic which could limit their range of practical application.  Some examples of applications for strain gages with high gage factor include surface strain measurement on manufacturing machinery designed with large safety factor; measurements of residual stress; fatigue-rated load cells; impact-rated load cells (automobile crash tests); and accelerometers. 

    The iron-rich alloy (36Ni-57Fe-7Cr) was already known to possess high gage factor and high thermal output, but nothing was published about the thermal output uniformity.  Consequently, the historical application of the material for strain gages was limited primarily to cases involving dynamic loading due to a belief that static loading measurements would be impaired by inability to correct (remove) the high thermal output component.  The performance of the nickel-rich alloy (70Ni-27.5Fe-2.5Cr) was completely unknown for application in metal foil strain gages.  However, considerable foundational research was available on the capability of this alloy to form an ordered crystalline structure through thermal-mechanical processing and this provided an opportunity to extend the research into the area of strain measurement.


    The primary goal of this research is to evaluate two specific Ni-Fe-Cr alloys for the application of metal foil strain gages with regard to temperature sensitivity (thermal output) and strain sensitivity (gage factor).  These two properties are fundamental to experimental strain measurement as the former usually represents an extraneous input and must be corrected or minimized to insure accuracy.  Many other properties of metal foil strain gages would need to be evaluated for a full characterization including gage factor variation with temperature, transverse sensitivity, fatigue strength, maximum strain range (elongation), linearity, and hysteresis.  Furthermore an evaluation of manufacturing process variables would also be required such as metal working (hot and cold rolling), annealing, etching, soldering, and cleaning.  These additional properties and process variables are beyond the scope of this initial research but may be noted (such as linearity and annealing parameters) when they apply to the evaluation of the principal scope characteristics: temperature sensitivity and strain sensitivity.

    The two Ni-Fe-Cr alloys (36Ni-57Fe-7Cr and 70Ni-27.5Fe-2.5Cr) reside in different positions in the Ni-Fe phase diagram and respond quite differently to thermal-mechanical processing as described in greater detail in Chapter 2 Materials and Processing.  In addition to reporting on the performance of these materials individually, their responses to identical process parameters are compared to each other so that inferences and conclusions can be made.  Specifically, the nickel-rich alloy (70Ni-27.5Fe-2.5Cr) is known to develop an ordered crystalline structure following application of post-rolling annealing temperature up to 900 ºF (482 ºC) and duration up to 16 hours.  Whereas the iron-rich alloy (36Ni-57Fe-7Cr) is known to not develop an ordered condition.  Therefore when both alloys are subjected to an identical annealing process, for example 850 ºF (454 ºC) for 12 hours, it may be possible to conclude an effect of crystalline ordering on the property.  For additional comparison, measurements of thermal output and gage factor are included for strain gages made with 55Cu-45Ni (constantan) and 92Pt-8W (alloy 479) materials.  These materials are commercially available as metal foil strain gages with the former being the most widely used alloy for both general purpose strain measurement such as design validation and failure analysis as well as in precision transducers measuring weight, force, pressure, etc.  The latter material possesses high gage factor and high thermal output like the subject Ni-Fe-Cr alloys.

    Crystalline order in Ni3Fe binary and several Ni3Fe ternary alloys has been reported extensively in the literature, primarily on two types of topics: the effect of crystalline order on material property; and the method by which crystalline order is detected.  Material properties have included hardness and work hardening (Vidoz et al., 1963), elastic constants and strength (Stoloff et al., 1968), thermal conductivity, electrical resistivity and Seebeck coefficient (Moore et al., 1971), specific heat (Binnatov et al., 1975), and magnetic permeability (Pfeifer et al., 1983).  The material property may actually be quite sensitive to crystalline order as reported by Binnatov et al. (1975) where specific heat appeared to be more sensitive than Mossbauer spectroscopy in detecting crystalline order.  Regarding the specific strain gage properties of thermal output and gage factor in Ni3Fe ternary alloys no prior research relating these to crystalline order was found.

    Detection of crystalline order has typically been by indirect measurement, most notably electrical resistivity, Mossbauer spectroscopy, and x-ray diffraction (XRD), but also by direct observation with transmission electron microscopy (TEM).  Electrical resistivity is perhaps the most widely used indirect measure of crystalline order because of its simplicity and its particular sensitivity to the microstructure of materials (Chen et al., 2007).  In this research TEM, energy dispersive spectroscopy (EDS), electrical resistivity, and XRD were used to attempt to detect crystalline order in 70Ni-27.5Fe-2.5Cr as described in greater detail in Chapter 2 Materials and Processes, but electrical resistivity measurement proved to be the only effective method.     

    In fact, the bonded electrical resistance strain gage may be ideally suited for detection of crystalline order as seen in subsequent Chapter 3 Thermal Output and Chapter 4 Gage Factor.  These properties both involve change in electrical resistivity with the former being from change in temperature and the latter being from change in applied strain.  There is a clear response in thermal output and gage factor in strain gages made of 70Ni-27.5Fe-2.5Cr foil which was pre-processed according to annealing temperatures and durations used by others to establish crystalline order.  Further confirmation is made by the much lower response in thermal output and gage factor in strain gages made of 36Ni-57Fe-7Cr foil which was pre-processed identically and known to not develop crystalline order.

    In Chapter 3 Thermal Output strain gages made of 36Ni-57Fe-7Cr and 70Ni-27.5Fe-2.5Cr foil are subjected to temperatures from -40 to 248 ºF (-40 to 120 ºC) and the change in relative resistance (ΔR/R) is recorded for a variety of substrates and post-rolling annealing processes.  Particular emphasis is placed on thermal output uniformity.  The thermal output of both Ni-Fe-Cr alloys is known to be high, being at least two orders of magnitude higher than 55Cu-45Ni (constantan).  The potential for a uniform response of electrical resistivity to temperature (thermal output) exists because of the uniform microstructure and single phase composition.  If thermal output uniformity is verified, then there is a better chance for correction techniques to be effective (like mathematical subtraction and Wheatstone bridge circuit cancellation).  There may be potential for self-temperature-compensation for strain gages made of 70Ni-27.5Fe-2.5Cr foil.  Thermal output is expected to change depending upon the annealing process because of changes in crystalline order.

    In Chapter 4 Gage Factor strain gages made of 36Ni-57Fe-7Cr and 70Ni-27.5Fe-2.5Cr foil are subjected to applied strains up to 3300 με and the change in relative resistance (ΔR/R) is recorded for a variety post-rolling annealing processes.  The effect of crystalline order on the gage factor of strain gages made of 70Ni-27.5Fe-2.5Cr is observed.  Expressions for gage factor are derived which include geometric effects and piezoresistive effects.  The latter includes the effect of electron mobility (mean free path), so some response of the gage factor of 70Ni-27.5Fe-2.5Cr is expected because of the migration of nickel and iron atoms to preferred locations on the face and corners of the face-centered-cubic lattice, respectively.  The ordered condition may also be responsive to applied strain as a result of crystal lattice deformation which could result in nonlinear response of gage factor to applied strain.

    In Chapter 5 Demonstrations the purpose is to show the feasibility of meaningful strain gage measurements with foil made of 36Ni-57Fe-7Cr and 70Ni-27.5Fe-2.5Cr under static loading conditions at room temperature and at 0 and 150 ºF (-18 and 66 ºC).  The demonstrations are chosen to feature two thermal output correction techniques: mathematical subtraction of the thermal output portion from the total signal; and Wheatstone bridge circuit cancellation of like-changes in fractional resistance (ΔR/R) occurring in adjacent arms of the bridge.  An additional demonstration is provided featuring favorable combination of high gage factor with high thermal output uniformity to achieve a zero-load temperature specification; rather than achievement of higher signal level alone.

    In the final Chapter 6 Conclusions and Recommendations for Future Work additional characterization of 36Ni-57Fe-7Cr strain gages is suggested based upon encouraging results of thermal output uniformity presented herein.  Further alloy development of the Ni3Fe ternary alloys for strain gage application is also suggested using transition elements of higher atomic number based upon work performed by others.


Table 1.1 Characteristics of some strain gage materials

(Holman, 1989; Shukla et al., 2010)



Trade name



Resistivity at 20 ºC


Temperature coefficient of resistance (ppm/ºC)



























How to cite this article: Kieffer TP, Peters KJ. The effect of short range order on the thermal output and gage factor of Ni3FeCr strain gages. Strain. 2017;e12253.

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