The 8th International Conference on
Structural Health Monitoring of Intelligent Infrastructure
Brisbane, Australia | 5-8 December 2017

Development of Self-Temperature Compensated Strain Visualization Sheet
S. Umemoto 1, T. Takaki 2, M. Omachi 1, K. Matsuo 1,
N. Miyamoto 1,I. Ishii 2, T. Aoyama 2.
1

Keisoku Research Consultant Co., Japan, Email: umemoto@krcnet.co.jp
2
Hiroshima University, Japan

Abstract
Health monitoring of rapidly-aging structures has become an urgent issue. A strain visualization
device and new strain measurement technology were developed to address this problem. The
device, called the “Strain Visualization Sheet,” enables quantitative visualization of strain based on
the principle of Moiré fringes. It is also possible to obtain extremely accurate strain values fromphotographed digital images. A power supply is not required, as no electrical elements are used,and durability is also excellent. Thus, this is a suitable sensor for long-term monitoring. The effectof temperature was one problem for field application of the Strain Visualization Sheet. When astrain measurement sensor is attached to the material being measured, temperature changes, whichare unrelated to strain due to external force, cause apparent strain as a result of the difference
between the linear thermal expansion coefficients of the object material and the strain measurement
sensor. Therefore, a self-temperature compensated Strain Visualization Sheet which minimizes thisapparent strain was developed and verified for steel and concrete materials. As a result, apparent
strain of less than ±1με was obtained in the temperature range of –20°C to +70°C, demonstrating
successful self-temperature compensation of the Strain Visualization Sheet. As this temperaturecompensation range is wider than that of conventional strain gauges, application to structural healthmonitoring under various environmental temperatures is expected.
1. Introduction
The authors developed a strain visualization device called the “Strain Visualization Sheet” forhealth monitoring of aging structures. The most important feature of the Strain Visualization Sheetis that quantitative visualization of strain is possible by utilizing the principle of Moiré fringes,
without using any electrical elements such as a conventional strain gauge or strain meter. It is also
possible to calculate strain values with high accuracy from photographed digital images of theStrain Visualization Sheet. Because no electrical elements are used, a power supply is not required
and device life is not limited by electrical failure. Laboratory tests have confirmed measurement
accuracy of 50 μm/m by visually reading the strain values and 20 μm/m by digital image analysis.
For application of the Strain Visualization Sheet to steel and concrete structures in the field, thefollowing problems must be solved: (1) Self-temperature compensation suitable for the object ofmeasurement, (2) Improvement of durability and (3) Improvement of ease of installation. This
paper discusses the development of a self-temperature compensated type of Strain Visualization
Sheet which does not cause apparent strain due to temperature. The principle of self-temperaturecompensation is discussed, and the developed Self-Temperature Compensated Strain Visualization
Sheet is introduced. The results of verification tests are also reported.

Thermally-induced
Thermally-induced apparent strain
apparent strain output (µm/m)
output (μm/m)

140120100806040200-20 0-40-60-80-100-120-140

Line grating 1102030405060708090100

Front plate

Back plate

Line grating 2

Fig.2 Basic Structure of Strain
Visualization Sheet

Temperature
Temperature (℃)(℃)

Fig.1 Typical characteristic curve of thermally-induced
apparent strain with strain gauges

2. Outline of Self-Temperature Compensated Strain Visualization Sheet
When a strain measurement sensor is installed on a material being measured, temperaturechanges cause apparent strain in addition to the strain caused by external forces, as a result of thedifference in the linear thermal expansion coefficients of the object material and the strain
measurement sensor. A self-temperature compensated strain measurement sensor is a type of sensor
which minimizes the apparent strain caused by temperature changes. Considering the example of astrain gauge, as shown in Fig. 1, a device which achieves accuracy within ±1.8 μm/m/°C in theprescribed temperature range when installed on a suitable material is called a self-temperaturecompensated gauge. There are also gauges that achieve ±1.0 μm/m/°C in the 20-40°C range, where
they are frequently used. With strain measurement sensors that are self-temperature compensated,the device itself can cancel the apparent strain caused by temperature and output only the straincaused by external force.
3. Principle of Self-Temperature Compensation
3.1 Basic Structure and Measurement Principle of Strain Visualization Sheet
The basic structure of the Strain Visualization Sheet is shown in Fig. 2. Line grating 1 and line
grating 2 are drawn on the front plate and back plate, respectively, the two plates are overlaid, andthe relative displacement of the two plates in the longitudinal direction is detected by the principleof Moiré fringes. As shown in Fig. 3(1), a striped pattern with a pitch W larger than line gratings 1and 2 appears due to the superimposition of line grating 1 with pitch p and line grating 2 with pitch
p+Δp, which is Δp (<<p) larger than the pitch of line grating 1. This pattern is called a Moiré fringe.
The relationship between the Moiré fringe with the pitch W and line grating 1 with the pitch p isshown in Eq. (1). The display of pitch p can be enlarged visually by (p+Δp) / Δp times by the Moiréfringe.
𝑊𝑊 =𝑝𝑝 + ⊿𝑝𝑝・𝑝𝑝
⊿𝑝𝑝

(1)

Line grating 1

Moiré fringeΔxm

Moirè fringe□：Pixeli(i)Line grating 2
Line grating 1

jΔxi(ii)
jj

Intensity(iii)θ0Δθ(b) θ=θ0 + 𝛥𝛥𝜃𝜃(a) θ=θ0i

Fig.4 Phase of a moiré fringeΔxm(=M･Δx)
Fig.3 Example of a moiré fringe

As shown in Fig. 3(2), assuming this magnification factor (p+Δp) / Δp is M, the amount of shift
Δx m of the Moiré fringe in direction (A) when line grating 1 is moved Δx in direction (A) can be
expressed by Eq. (2). In other words, the Strain Visualization Sheet makes it possible to enlarged
display of the very small amount of relative displacement of the two plate Δx as the amount of shift
Δx m of the Moiré fringe.
⊿𝑥𝑥𝑚𝑚 = 𝑀𝑀・⊿𝑥𝑥(2)Here, we consider the case of that the strain value is calculated by acquiring digital images andperforming image processing (Takaki, T. et al. 2012). As shown in Fig. 4, the phase difference Δθ
is calculated by a sine curve approximation of the luminance distribution of the Moiré fringe.
Further, the amount of shift Δx m of the Moiré fringe is calculated from the phase difference Δθ. andthe relationship between Δx m and Δθ is shown by Eq. (3).
Δxm =WΔθ2π(3)Therefore, from Eqs. (1), (2) and (3), the relative displacement of the two plates Δx can beexpressed by Eq. (4).
Δx=p
Δθ
2π(4)

For example, when the amount of relative displacement of the two plate Δx occurs with respect
to the reference length L, strain ε can be obtained by Eq. (5).
ε=pΔθ2πL(5)Front plate

Fix to object ofmeasurement

Back plate

Δlm

Temperature compensating plate
Linear thermal expansion coefficient β2Δlsls
Object material Linear thermalexpansion coefficient β1lm

Δlm

Fig. 5 Proposed self-temperature compensated structure
In addition, in visualization of strain, the Moiré fringe is shown as a numerical value by
providing a grating with numerical characters in place of line grating 2, and a numerical value
corresponding to the amount of actually occurring strain is displayed by adjusting the magnification
factor (Takaki, T. et al. 2012).
3.2 Self-Temperature Compensating Structure
As shown in Fig. 5, the authors conceived a structure in which a temperature compensating plateis incorporated in the basic structure of the Strain Visualization Sheet. When a stress σ acts on anobject material which is subjected to a temperature change Δt, the amount of change Δl m of thelength l m of the object material is equal to the sum of the change of length due to stress σ and thechange of length due temperature change Δt. If the elastic modulus of the object material is E andthe linear thermal expansion coefficient is β 1 , this is expressed by Eq. (6).
𝛥𝛥𝛥𝛥𝑚𝑚 = 𝑙𝑙𝑚𝑚

𝜎𝜎+ 𝛽𝛽1 ･ 𝛥𝛥𝑡𝑡･ 𝑙𝑙𝑚𝑚
𝐸𝐸

(6)

If the linear thermal expansion coefficient of the temperature compensation plate is β 2 , the amountof change Δl s in the length l s of the temperature compensation plate at this time is expressed by Eq.
(7).
𝛥𝛥𝑙𝑙𝑠𝑠 = 𝛽𝛽2 ･ 𝛥𝛥𝑡𝑡･ 𝑙𝑙𝑠𝑠

(7)

𝛥𝛥𝛥𝛥 = 𝛥𝛥𝛥𝛥𝑚𝑚 − 𝛥𝛥𝑙𝑙𝑠𝑠(8)

Because the displacement of the front plate is the same as the change Δl m of the length of theobject material, and the displacement of the back plate is the same as the change Δl s of the length of
the temperature compensation plate, the relative displacement Δx of the front plate and back plate
can be expressed by the following equation.

From Eqs. (6), (7) and (8),𝛥𝛥𝛥𝛥 = 𝑙𝑙𝑚𝑚 ･Assuming l m = l s and β 1 = β 2 ,𝜎𝜎+ 𝛽𝛽1 ･ 𝛥𝛥𝑡𝑡･ 𝑙𝑙𝑚𝑚 − 𝛽𝛽2 ･ 𝛥𝛥𝑡𝑡･ 𝑙𝑙𝑠𝑠
𝐸𝐸

(9)

𝛥𝛥𝛥𝛥 = 𝑙𝑙𝑚𝑚 ･𝜎𝜎𝐸𝐸(10)Accordingly, equalizing the lengths and linear thermal expansion coefficients of the object
material and the temperature compensation plate makes it possible to obtain only the relative
displacement Δx of the front plate and back plate caused by acting stress σ, and relative
displacement due to temperature change Δt does not occur.
4. Structure of Self-Temperature Compensated Strain Visualization Sheet
The appearance and structure of the developed Self-Temperature Compensated Strain
Visualization Sheet are shown in Fig. 6 and Fig. 7, respectively. The device consists of the two
glass plates which form the Moiré fringe pattern and a temperature compensating steel plate, and isassembled in a unit form by using a pair of fixing rings. Its external dimensions are 17 mm x 120
mm x 8 mm (thickness), and its gauge length is 105 mm. The Strain Visualization Sheet consists ofthree types of Moiré fringes. The numbers shown in the upper line are used for strain visualization,
the middle line is used for calculation of strain by image processing, and the lower line is areference moiré for improving the accuracy of image processing. Because the numbers in the upper
line are arranged in the form of a scale with an interval of 100 μm/m, strain values can be readdirectly from this line.
120mm
105mm
14mm

17mm

8mm

1.1mm
1.1mm
1.6mm
Fig. 6 Appearance of Strain Visualization Sheet

Front plate
Adhesion
Mounting jig

Back plate
Adhesion

Adhesion
Adhesion

Adhesion
Fixing ring

Adhesion

Temperaturecompensating plate

AdhesionObject of measurement

Fig.7 Structure of Strain Visualization Sheet

5. Verification of Self-Temperature Compensated Strain Visualization Sheet
5.1 Test Piece
A steel plate (SPCC, linear thermal expansion coefficient: 11.7 μm/m/°C) with dimensions of 50mm x 150 mm (t = 1.6 mm) was used as the test piece. The arrangement of sensors on the test pieceis shown in Fig. 8, and a photograph of the test piece with the installed sensors is shown in Fig. 9.
A conventional strain gauge (gauge length L = 90 mm) was installed on the surface of the steel
plate for comparison with the Strain Visualization Sheet. The same type of strain gauge was also
installed on the back side of the plate to check for bending of the plate due to temperature. A
thermocouple thermometer was installed on the back side of the steel plate to measure thetemperature of the plate.
5.2 Verification Method
The test piece was placed in a thermostatic chamber so as to allow free expansion andcontraction accompanying temperature changes, and a USB camera was also placed in the chamberfor photography (Fig. 10). The USB camera was connected to an external real-time image
processing device, and the signal cables of the strain gauges and thermocouple were connected toan external data logger. After measuring the initial strain values, the temperature was changed in
the range from –20°C to 70°C in steps of 10°C, and the values of the Strain Visualization Sheet andthe strain gauges were recorded when the temperature of the test piece reached the set temperature.
Strain Visualization Sheet

Thermocouple

50mm

Strain gauge

Steel plate (t=1.6mm)

150mm
Test piece (surface)

Test piece (back)Fig.8 Sensor arrangement

USB camera

Test piece

Fig.9 Sensor installation condition
Fig.10 Installation of test piece and USB
camera in the thermostatic chamber

Apparent strain (μm/m)

10050

0-50
No.1-1
No.2-1
No.3
No.4-2
No.5-2-100-150-30-20-100102030

40

No.1-2
No.2-2
No.4-1
No.5-1
Strain Gauge
50607080

Temperature of Test piece (℃)

Fig. 11 Relationship between temperature and apparent strain of test piece

5.3 Results of Verification
The relationship between the temperature of a test piece and apparent strain occurred bytemperature change is shown in Fig. 11. The apparent strain of the Strain Visualization Sheet was <±1.0 μm/m/°C, confirming the self-temperature compensation. It is also noteworthy that the Strain
Visualization Sheet has a wider self-temperature compensation range than the conventional straingauge, showing extremely small apparent strain values of approximately 20 μm/m at the hightemperature of 70°C and approximately –20 μm/m at –20°C below freezing. The results of thisverification test verified the fact that the developed Self-Temperature Compensated Strain
Visualization Sheet is a strain measurement sensor with temperature characteristics superior tothose of conventional strain gauges.
6. Conclusion
With conventional strain gauges, the self-temperature compensation function is realized byadjusting the temperature coefficient of resistance (TCR) of the strain gauge resistance element
material so as to conform to the material being measured. In contrast to this, with the Strain
Visualization Sheet discussed in this paper, self-temperature compensation conforming to mildsteel and concrete was realized by the constituent materials and structure of the device itself. The
development of this new Self-Temperature Compensated Strain Visualization Sheet made it
possible to improve applicability in the field. As future work, verification of durability in the field,
simplification of the installation method and efforts to realize a low-cost device are planned.
References
Takaki, T. et al., 2012, ‘Strain Visualization Sticker using Moiré fringe for remote sensing’, Proceeding of the 6thInternational Conference on Bridge Maintenance, Safety and Management (IABMAS2012), Stresa, Lake Maggiore,Italy, 8-12 July, p. 442.