1. Flexible, Highly Sensitive Strain Gauges for Large Scale Applications
Thomas Porkka, Nicolas Salazar, Mateus Horvath, Ganesh Bade, Zhibin Yu PhD.
Industrial Engineering, FAMU-FSU College of Engineering
2525 Pottsdamer St., Tallahassee, Florida 32310
Abstract
Strain gauges are of interest to many applications including structural health monitoring
and active input control devices. Optimizing the mechanical and electrical properties of strain
gauges allows for new applications and improvement upon existing ones. This paper explores the
use of flexible and robust substrates along with carbon nanotube doped silver nano-ink to create
highly sensitive and flexible strain gauges. The piezoresistive effect is the working mechanism of
these strain gauges created by laying a conductive ink on a highly elastic substrate which translates
strain into a change in resistance by compacting or separating the silver nanoparticles. The
manufacturing methods and materials laid out in this research are scalable with existing printing
technology making these strain gauges exciting prospects for large-scale applications.
Introduction
Strain sensing is important to processes involving movement and stress allowing them
active monitoring and control of a system. When a strain gauge is mechanically deformed its
corresponding resistance change can be used to prevent or detect failure in a structure, improve
operation efficiency of input controlled devices, and provide a tactile sensation to robotic limbs
and artificial limbs. Current strain gauges for large-scale use are dominated by two technologies:
semiconducting silicon crystal gauges (piezoelectric) and metallic foil gauges (piezoresistive).
Piezoelectric gauges offer high sensitivity (gauge factor of -125-250) but are more rigid and too
fragile for dynamic applications. Metallic foil gauges are more robust but lack sensitivity (gauge
factor of 2-5). Nanoparticle strain sensors offer improvements upon existing strain gauge
technology in strength, flexibility, and sensitivity for use in areas such as structural health
monitoring, machine movement control, and large interactive displays due to their large active
area and scalable printing methods.
Flexible strain gauges require bendable substrates and circuitry. Many micro fabrication
techniques have been demonstrated for strain sensors in wearable electronics including
photolithography and metallization but are limited to centimeter scale samples4. Large-scale arrays
of strain sensors manufactured with these techniques are costly and impractical for most
applications whereas direct printing of strain gauges increases their scalability and affordability.
Conductive nano-inks are promising materials for scalable manufacturing processes as
they can easily be printed with existing and reliable printing methods; inkjet, aerosol, screen,

2. gravure. Printing techniques explored in recent literature about creating scalable, bendable strain
gauges include; inkjet printing1, stamping with a micro-structured stamp2, 5, and drop casting3.
Existing literature reports using either pure silver nanoparticle2, 5 or nanowire3 ink, pure carbon
based inks1, or other pure conductive or semi-conductive materials1. Pure silver nano-inks are
highly conductive but without embedding them entirely in a robust substrate such as
polydimethylsiloxane (PDMS) they are very brittle and unreliable for long-term strain sensing
required for structural health monitoring2. In addition to the scalability, most structural health
monitoring applications require maximum robustness and sensitivity to detect small strains in
various environments. To achieve these requirements this paper explores using carbon nanotube
doped silver nano-ink for the active region of the gauge, using a thermally, mechanically, and
chemically robust polyimide film as a base substrate and an elastomer region partially
surrounding the gauge’s active region. This elastic region drives the piezoresistive effect of the
gauge for high sensitivity.
Experimental Methodology
Gauge Manufacturing
Polyimide (Kapton from DuPont, USA, .04mm) film was used as the base substrate which
layers of polydimethylsiloxane (PDMS; Sylgard 184 from Dow Corning, USA; 10:1 elastomer
base to curing agent concentration) were laid on top surrounding the silver nano-ink. The
polyimide film was cleaned with soap and water, acetone, isopropanol, and DI water before being
treated with oxygen plasma to improve adhesion to the base PDMS layer. The samples were
cleaned after each layer was applied to remove any residue left from application of each previous
layer and the samples were treated with oxygen plasma before each subsequent layer was applied
(oxygen plasma treatment with Cute Plasma System; Femto Science for 4 minutes at 100W,
100sccm). Hexane was added to the PDMS to lower the viscosity and allow thinner layers of
PDMS (~10-40µm) to be drop casted on the polyimide film. The samples were partially cured at
100Cfor 2 minutes before the masks were removed and allowed to sit at room temperature (23C)
for 10 minutes to taper edges before being fully cured in the oven (100C for 10 minutes). This
tapered edge prevents a pronounced step from forming where the PDMS meets the polyimide film
which compromises the integrity of the circuit. The silver nano-ink (PG-007AA from Paru
Corporation, Korea) doped with carbon nanotubes (VC101 from SWeNT Inc, USA) was applied
by drop casting over a polyimide tape mask with a simple straight line design. Previous designs
that attempted to maximize surface area for improved spatial resolution were constructed (Figure
2) but due to the high variance in uniformity among samples this was simplified to more directly
compare the varying responses to the type of ink and substrate construction. A top layer of PDMS
(~10-40um) was applied over the circuit leaving the leads exposed for testing and was cured for
10 minutes in the oven at 100C. The fully constructed samples were then annealed on a hot plate
at 175C for 20 minutes and allowed to cool slowly by remaining on the turned off hot plate.

3. Figure 1: Flow chart of manufacturing process to sandwich Ag/CNT nano-ink between PDMS
elastomer before testing.
Figure 2: Fully manufactured strain gauges
featuring different designs. The active area of the
gauge is sandwiched between layers of PDMS. The
simplified design on the left was used for testing to
minimize the effects of gauge geometry variation
and to allow the different ink concentrations to be
tested with similar PDMS thicknesses.

4. Gauge Testing
The strain gauge sensitivity was tested by bending around glass tubes of varying radii. A
multimeter was used to test the resistance under tension and compression. The testable strain was
limited by the ability to touch the gauge’s leads with the multimeter’s probes (minimum radius
tested was 12.44mm).
Results and Data Analysis
Strain and Gauge Calculation
When a material experiences stress there is an associated strain with it. There are different
types of stresses/pressures that can be applied to materials. For the sake of simplicity, our
description of the stress state will be limited to bending stress. Bending stress is exhibited when
materials are bent about some curvature. Depending on the curvature and direction of the bending
action the material will either experience tensile stress or compressive stress. Equation 1 describes
the strain as a function of the radius of curvature (r) and the distance from the neutral axis (y).
𝜺 = −
𝑦
𝑟
(1)
Electrical resistance is defined as the hindrance of charge flow. It depends on the properties and
geometry of a given material. Below is the equation for electrical resistance. The resistivity of a
material is denoted by ρ, which is an intrinsic property of the material. L and A are the length
and cross-sectional area of a given specimen, respectfully.
𝑅 = 𝜌
𝐿
𝐴
(2)
A measure of the success of a particular sensor would be the measure of its sensitivity. Equation
3 is the gauge factor, which measures the sensitivity of strain gauges. ∆𝑅 is the change in
resistance with the applied bending stress. RG is the resistance of specimen before deformation or
before bending occurs. And ε is the bending strain that was discussed earlier.
𝐺𝐹 =
∆𝑅
𝑅 𝐺
𝜀
(3)

5. PDMS Effect of Sensitivity
The elastomer (PDMS) contacting the middle portion of the circuit increased strain
sensitivity dramatically (Figure 2). Samples tested with only a bottom layer of PDMS show that
the bottom layer is most important to the gauge’s functionality. The top layer of PDMS acts more
for protection against buckling and circuit breaks. However, with this protection we still
experienced a high failure rate (~85%) in manufacturing and during testing. Most often these
failures were due to breaks in the circuit where the Kapton film meets the PDMS. Our working
samples show high sensitivity with average gauge factors of 406.2 under tensile strain and -232.6
under compressive strain (Table 1).
Figure 3: Strain sensitivity comparison of an Ag/CNT 76:1 strain gauge with and without PDMS
under layer. This sample of Ag:CNT 76:1 & PDMS was used because the base resistance was
closest to that of Ag:CNT 76:1 sample without PDMS.
GF = 313.8
GF = -182.0
GF = 20.1
GF = -13.4
-1.5
-1
-0.5
0
0.5
1
1.5
2
0.00% 0.10% 0.20% 0.30% 0.40% 0.50% 0.60%
ΔR/RG
Strain (%)
PDMS & Ag:CNT tension PDMS & Ag:CNT compression
Ag:CNT tension Ag:CNT compression

6. Silver Ink Solution Effect on Sensitivity
Our results suggest that a higher concentration of carbon nanotubes improves the
sensitivity of the strain gauge (Table 1). This needs to be further explored by obtaining more data
and better quality control of manufacturing processes to create many samples with uniform gauge
geometry. Our samples base (undeformed) resistance ranged from 2-42 ohms. This base range
makes conductance comparisons between the two inks inconclusive though it is predicted the
higher concentration of silver would increase conductance.
Sample
Description
Tension
Gauge
Factor
Compression
Gauge Factor
Ag:CNT 76:1 +406.2 -232.6
Ag:CNT 100:1 +212.7 -66.8
Ag:CNT 76:1
(No PDMS)
+24.0 +13.6
Ag:CNT 100:1
(No PDMS)
27.1 +31.6
Gauge Material Gauge Factor
Metal foil strain gauge 2-5
Thin-film metal 2
Single crystal silicon (Piezoelectric) -125 to + 200
Polysilicon ±30
Thick-film resistors 100
Table 2: Gauge factors of existing
strain gauge technology popular for
large-scale commercial applications.
Table 1: Average gauge factors of our
tested strain gauges. Shows high
sensitivity to both tensile and
compressive strain. 76:1 Ag:CNT
concentration gauges show highest
sensitivity. Gauges manufactured
without PDMS elastomer have poor
sensitivity and directionality.

7. Discussion
Assumed Gauge Behavior and Alternative Mechanisms
Our gauges show improved sensitivity upon current metal foil and silicon crystal gauges under
compression and tension (Table 2). Previous literature of gauges using silver nano-ink report the
mechanisms of the silver nanoparticles when strained and conductive ink binding properties to
PDMS2. We hypothesized that our gauges work in a similar fashion though we have not graphically
confirmed that the silver nanoparticles are separating during tension and compacting during
compression. This behavior is intuitive to the observed results but in order to confirm this
mechanism we need to view the gauges under various strains via scanning electron microscopy.
Alternative explanations for the obtained results include micro-cracks2 forming in the circuit after
bending and geometry changes of the carbon nanotubes.
Figure 4: Assumed Gauge Behavior showing silver nanoparticle separation (resistance increase)
during tensile strain and compaction (resistance decrease) during compressive strain. The carbon
nanotubes

8. Further Testing
Along with manufacturing optimization, testing the gauges needs to be more controlled in
future tests. Very few of the circuits created lasted through testing due to the multimeter’s tendency
to damage the exposed leads of the gauge. Using a source meter with more delicate leads will
improve testing and yield more conclusive data. Once manufacturing processes allow more
accurate comparisons between samples, pressure sensitivity could be tested with varying PDMS
and circuit thicknesses. Understanding the pressure sensitivity including maximum and minimum
detectable loads is important for applications providing tactile sensations to machines and
monitoring loads on structures.
Future Implementations
Besides obtaining further strain and stress data on the existing gauges, new components
could be integrated onto the polyimide substrate to further the gauge’s functionality. By adding an
inductor and capacitor, Radio Frequency Identification (RFID) technology would allow wireless
monitoring by measuring the change in the strain gauge’s resonant frequency5.
Conclusions
This research shows a new way of producing highly flexible strain gauges with carbon
nanotube doped silver nano-ink. Extensive testing and methods were exhausted throughout this
research to develop strain gauges with optimum mechanical and electrical properties. The biggest
challenge faced during research and to be improved upon is maintaining conductivity through the
gauge’s active region after repeated bending by further improving the robustness of the conductive
ink. The mechanical properties of pure silver nano-ink used in our early research were unsuccessful
and posed a great threat to the success of this concept. This problem led us to implement a carbon
nanotube solution into the previously used silver ink. Although this did not solve the problem
entirely, it did allow for the necessary testing required to demonstrate the promising future of this
technology.
.

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interactive electronic skin for instantaneous pressure visualization”, Nature Mater., 12,
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