Piezo-Optical Transducers in High Sensitive Strain Measurements

*Andrey G. Paulish, Peter S. Zagubisalo, Sergey M. Churilov, Vladimir N. Barakov, Mikhail A. Pavlov and Alexander V. Poyarkov*

### **Abstract**

New piezo-optical sensors based on the piezo-optical effect for high sensitive mechanical stress measurements have been proposed and developed. The piezooptical method provides the highest sensitivity to strains compared to sensors based on any other physical principles. Piezo-optical sensors use materials whose parameters practically not change under load or over time, therefore piezo-optical sensors are devoid of the disadvantages inherent in strain-resistive and piezoelectric sensors, such as hysteresis, parameters degradation with time, small dynamic range, low sensitivity to strains, and high sensitivity to overloads. Accurate numerical simulation and experimental investigations of the piezo-optical transducer output signal formation made it possible to optimize its design and show that the its gauge factor is two to three orders of magnitude higher than the gauge factors of sensors of other types. The cruciform shape of the transducer photoelastic element made it possible to significantly increase the stresses in its working area at a given external force. Combining compactness, reliability, resistance to overloads, linearity and high sensitivity, in terms of the all set of these parameters, piezo-optical sensors significantly surpass the currently widely used strain-resistive, piezoelectric and fiber-optic sensors and open up new, previously inaccessible, possibilities in the tasks of measuring power loads.

**Keywords:** piezo-optical transducers, strain gauge, sensor gauge factor, photoelasticity, optoelectronic devices

#### **1. Introduction**

Optoelectronic measurement methods are based on optical effects associated with the electromagnetic radiation interaction with matter. The polarization of the electromagnetic wave during such interaction is the most "susceptible" parameter which ensures high sensitivity of polarization-optical methods in comparison with other measurement methods [1–5]. In addition, the optical measurement method is free from electromagnetic interference and can be used in severe environmental conditions and at high temperature [6].

One of the most important directions in the development of measuring methods and sensors based on them is the monitoring of stress states in various structures both in industry and research-and-development activities. Modern and promising

strain sensors should have low weight, small size, low power, resistance to environmental influences and electromagnetic noise immunity, stability of parameters during operation, and low cost. Today, the most widely used method for strain measuring is based on the strain-resistive effect. The strain-resistive devices are used due to its relatively low cost and easy-to-use design [7]. However, such sensors have a number of unavoidable drawbacks: parameters degradation with time, hysteresis, nonlinearity, small dynamic range, low deformation sensitivity, and dramatic sensitivity to the overloads [7]. However, with the development of technologies, especially precision ones, the requirements for strain gauges increase significantly and strain-resistive gauges do not meet modern requirements.

For measuring vibrations, accelerations, acoustic signals, sensors based on the piezoelectric effect are widely used [8–12]. Such sensors performed well when measuring dynamic deformations (vibrations), but they are not suitable for measuring static loads due to the leakage of the charge induced by the load. Moreover, when such sensors are operated, both reversible and irreversible changes in their gauge factor and other characteristics are possible. This naturally limits the application conditions and is one of the most serious drawbacks of piezoelectric accelerometers.

Fiber-optic sensors are among the modern optical methods for measuring strain. A significant advantage of such sensors is the ability to implement several, up to a hundred, sensors on single optical fiber, which is used in distributed monitoring systems [13–19]. The disadvantages of such sensors include, first of all, low sensitivity (lower than that of strain-resistive gages and piezoelectric ones) and a complex system of optical measurements.

**2.1 Strain-resistive effect and strain gauge sensors**

*Piezo-Optical Transducers in High Sensitive Strain Measurements*

*DOI: http://dx.doi.org/10.5772/intechopen.94082*

*dR <sup>R</sup>* <sup>¼</sup> *<sup>d</sup><sup>ρ</sup> ρ* þ *dL <sup>L</sup>* <sup>þ</sup> <sup>2</sup>*<sup>ν</sup>*

ples are briefly presented.

**Figure 1.**

*density.*

given by expression [7]:

**37**

Strain-resistive gauge sensors have been well known for a long time. At first glance, the design of such a sensor looks rather simple (**Figure 1a**). A typical strain sensor design is a thin serpentine conductor film (thickness – around 0.0025 mm and length – 0.2–150 mm) deposited on a thin polymer support film. The conductor film thickness is made to be thinner and the length longer to obtain a sufficiently large resistance. Therefore, the resistance creates sufficiently large voltage for the measurements. The structure is glued to a controlled specimen and incorporated into the Wheatstone bridge [7] as an alternating resistance *R*<sup>x</sup> (**Figure 1a**). The polymer film is the carrier and insulator. Their production technology is well developed and well controlled. Nevertheless, polymer films, glues, and thin metal films have low plastic deformation threshold. This leads to the problems listed above: hysteresis, nonlinearity, degradation of parameters with time, etc.

*Operation principle of strain gauges based on: (a) Strain-resistive, (b) Fiber–optic and (c) Piezoelectric sensors. F – Measured load, Rx – Alternating resistance, n – Effective refractive index,* Δ*q – Stress-induced charge*

The theoretical foundations of such sensors operation, as well as the technical aspects of their use, are described in detail in work [7]. Here, the basic provisions necessary for comparing such sensors with sensors based on other physical princi-

It is well known that the conductor length increases (*L* þ *dL*), and its cross-

(**Figure 1a**). In case of elastic deformation, the change in relative resistance *dR=R* is

*dL*

where *ρ* is the specific resistivity and *ν* is the Poisson ratio, usually equal to 0.3 [7]. The strain sensitivity, gauge factor, connects the relative deformation value (*dL/L*) with the relative change in the measuring parameter (signal). For the

*<sup>L</sup>* � *<sup>ν</sup>*<sup>2</sup> *dL L* <sup>2</sup>

, (1)

section decreases (*S* � *dS*) under the action of force *F* along the conductor

strain-resistive sensor the GF is determined by the expression [7]:

The most sensitive method for strain measuring is based on the piezo-optical effect, which consists in changing the polarization of light propagating in a transparent stressed material [7, 20]. Such sensors have a significantly higher sensitivity than strain-resistive ones due to the fundamentally high light polarization sensitivity to change in the state of the substance in which light propagates [20]. The attempts to develop the industrially usable deformation sensors based on the piezooptical measuring transducers are known in the literature [21–24]. However, for a number of reasons, primarily of a technological nature, these developments did not lead to the appearance of piezo-optical strain gauges capable of competing with strain-resistive sensors in terms of a price/quality ratio. In the scientific literature, there are no data on the comparative analysis of the gauge factors (the main strain gauge parameter) of strain sensors based on different physical principles, which complicates the objective assessment of their advantages and disadvantages.

The purpose of this work is to develop theoretical foundations and basic design and technological solutions for creating a highly sensitive strain sensor based on a piezo-optical optoelectronic transducer. At the same time, the sensor must meet the requirements of industrial operation, significantly surpass the parameters of modern sensors based on other principles, and be devoid of drawbacks inherent in these sensors: parameters degradation with time, hysteresis, nonlinearity, small dynamic range, low sensitivity to the deformation, and high sensitivity to the overloads.

### **2. Comparative analysis of the sensitivity of strain gauges based on various physical principles**

Here we consider the theoretical foundations of the physical effects that underlie modern strain gauges. We will also determine the gauge factor (GF) for each type of sensor so that the sensitivity of these sensors can be compared. The GF dependence on the sensor design will also be determined.

*Piezo-Optical Transducers in High Sensitive Strain Measurements DOI: http://dx.doi.org/10.5772/intechopen.94082*

**Figure 1.**

strain sensors should have low weight, small size, low power, resistance to environmental influences and electromagnetic noise immunity, stability of parameters during operation, and low cost. Today, the most widely used method for strain measuring is based on the strain-resistive effect. The strain-resistive devices are used due to its relatively low cost and easy-to-use design [7]. However, such sensors have a number of unavoidable drawbacks: parameters degradation with time, hysteresis, nonlinearity, small dynamic range, low deformation sensitivity, and dramatic sensitivity to the overloads [7]. However, with the development of technologies, especially precision ones, the requirements for strain gauges increase significantly and strain-resistive gauges do not meet modern requirements.

For measuring vibrations, accelerations, acoustic signals, sensors based on the piezoelectric effect are widely used [8–12]. Such sensors performed well when measuring dynamic deformations (vibrations), but they are not suitable for measuring static loads due to the leakage of the charge induced by the load. Moreover, when such sensors are operated, both reversible and irreversible changes in their gauge factor and other characteristics are possible. This naturally limits the application conditions and is one of the most serious drawbacks of piezoelectric

Fiber-optic sensors are among the modern optical methods for measuring strain. A significant advantage of such sensors is the ability to implement several, up to a hundred, sensors on single optical fiber, which is used in distributed monitoring systems [13–19]. The disadvantages of such sensors include, first of all, low sensitivity (lower than that of strain-resistive gages and piezoelectric ones) and a com-

The most sensitive method for strain measuring is based on the piezo-optical effect, which consists in changing the polarization of light propagating in a transparent stressed material [7, 20]. Such sensors have a significantly higher sensitivity than strain-resistive ones due to the fundamentally high light polarization sensitivity to change in the state of the substance in which light propagates [20]. The attempts to develop the industrially usable deformation sensors based on the piezooptical measuring transducers are known in the literature [21–24]. However, for a number of reasons, primarily of a technological nature, these developments did not lead to the appearance of piezo-optical strain gauges capable of competing with strain-resistive sensors in terms of a price/quality ratio. In the scientific literature, there are no data on the comparative analysis of the gauge factors (the main strain gauge parameter) of strain sensors based on different physical principles, which complicates the objective assessment of their advantages and disadvantages.

The purpose of this work is to develop theoretical foundations and basic design and technological solutions for creating a highly sensitive strain sensor based on a piezo-optical optoelectronic transducer. At the same time, the sensor must meet the requirements of industrial operation, significantly surpass the parameters of modern sensors based on other principles, and be devoid of drawbacks inherent in these sensors: parameters degradation with time, hysteresis, nonlinearity, small dynamic range, low sensitivity to the deformation, and high sensitivity to the overloads.

**2. Comparative analysis of the sensitivity of strain gauges based on**

Here we consider the theoretical foundations of the physical effects that underlie modern strain gauges. We will also determine the gauge factor (GF) for each type of sensor so that the sensitivity of these sensors can be compared. The GF dependence

accelerometers.

*Optoelectronics*

plex system of optical measurements.

**various physical principles**

**36**

on the sensor design will also be determined.

*Operation principle of strain gauges based on: (a) Strain-resistive, (b) Fiber–optic and (c) Piezoelectric sensors. F – Measured load, Rx – Alternating resistance, n – Effective refractive index,* Δ*q – Stress-induced charge density.*

#### **2.1 Strain-resistive effect and strain gauge sensors**

Strain-resistive gauge sensors have been well known for a long time. At first glance, the design of such a sensor looks rather simple (**Figure 1a**). A typical strain sensor design is a thin serpentine conductor film (thickness – around 0.0025 mm and length – 0.2–150 mm) deposited on a thin polymer support film. The conductor film thickness is made to be thinner and the length longer to obtain a sufficiently large resistance. Therefore, the resistance creates sufficiently large voltage for the measurements. The structure is glued to a controlled specimen and incorporated into the Wheatstone bridge [7] as an alternating resistance *R*<sup>x</sup> (**Figure 1a**). The polymer film is the carrier and insulator. Their production technology is well developed and well controlled. Nevertheless, polymer films, glues, and thin metal films have low plastic deformation threshold. This leads to the problems listed above: hysteresis, nonlinearity, degradation of parameters with time, etc.

The theoretical foundations of such sensors operation, as well as the technical aspects of their use, are described in detail in work [7]. Here, the basic provisions necessary for comparing such sensors with sensors based on other physical principles are briefly presented.

It is well known that the conductor length increases (*L* þ *dL*), and its crosssection decreases (*S* � *dS*) under the action of force *F* along the conductor (**Figure 1a**). In case of elastic deformation, the change in relative resistance *dR=R* is given by expression [7]:

$$\frac{d\mathbf{R}}{R} = \frac{d\rho}{\rho} + \frac{d\mathbf{L}}{L} + 2\nu \frac{d\mathbf{L}}{L} - \nu^2 \left(\frac{d\mathbf{L}}{L}\right)^2,\tag{1}$$

where *ρ* is the specific resistivity and *ν* is the Poisson ratio, usually equal to 0.3 [7]. The strain sensitivity, gauge factor, connects the relative deformation value (*dL/L*) with the relative change in the measuring parameter (signal). For the strain-resistive sensor the GF is determined by the expression [7]:

$$\text{GF} = \frac{d\mathbf{R}/\mathbf{R}}{d\mathbf{L}/\mathbf{L}} = \frac{d\rho/\rho}{d\mathbf{L}/\mathbf{L}} + \mathbf{1} + 2\nu - \nu^2 \left(\frac{d\mathbf{L}}{L}\right). \tag{2}$$

It follows from Eq. (5) that the GF does not depend on the sensor design and is determined only by the piezoelectric element material properties. **Table 1** shows the values of the piezoelectric moduli and Young's moduli taken from [26, 27] and the sensitivity factors calculated by Eq. (5) for some materials widely used for the fabrication of piezoelectric sensors. It is the GF (and not the piezoelectric modulus) that is an objective sensitivity parameter of piezoelectric sensors when compared with the sensitivity of another type of sensors. For example, the piezoelectric modulus for electroactive polymers is more than two orders of magnitude greater than for other piezomaterials. However, this advantage almost vanishes due to the small elastic modulus, and, as a result, GF becomes two orders of magnitude lower than that of the other materials. **Table 1** shows that the piezoelectric sensor GFs are

comparable in order of magnitude with the strain-resistive sensor GFs.

The piezo-optical effect (also called "photoelasticity") used for precision stress (deformation) measurements is known since the 1930s [28]. If a light wave with a linear (circular) polarization (**Figure 2**) is incident upon transparent material

**Material** *dij***, 10<sup>12</sup> C/N** *E***,GPa GF**

PZT 19 160–330 70 11,2–23,1 PZT 21 40–100 90 2,8–7,0 PZTNV-1 160–400 64 10,2–26,6 PZT-5A 274–593 60 16,4–35,6 PZT-6A 80–189 94 7,5–17,8 PZT-6B 27–71 111 3,0–7,8 Crystal quartz 2,33 78,7 0,16 Barium titanate (BaTiO3) 78 100 7,8 Solid solutions (K, Na)NbO3 80–160 104–123 8,3–19,7

Polar polymers (polycarbonate, polyvinyl chloride) 20–40 2,3–3,5 0,05–0,14 Electroactive polymers 30,000 (6–1000)<sup>10</sup><sup>6</sup> <sup>&</sup>lt; 0,03

0,1–1,0 <sup>1</sup>–3 0,1–<sup>3</sup><sup>10</sup><sup>3</sup>

**2.4 Piezo-optical effect and piezo-optical transducers**

*Piezo-Optical Transducers in High Sensitive Strain Measurements*

*DOI: http://dx.doi.org/10.5772/intechopen.94082*

Lead zirconate titanate (PZT)

Nonpolar polymers (polyethylene, rubbers, etc.)

*Parameters of some piezoelectric materials.*

**Table 1.**

**Figure 2.**

**39**

*Effect of photoelasticity.*

It can be seen from Eq. (2) that the GF magnitude depends only on the properties of the conductor material (*dρ=ρ*) and is *independent* of the strain gauge design. Typical gauge factor values for the materials used to create the sensors lie in the range of 2–6 [7].

#### **2.2 Fiber-optic strain gauge sensors**

The sensitive element of the fiber-optic sensors is a Bragg fiber grating which is an optical fiber with a periodically changing refractive index (**Figure 1b**). When light passes through such a structure, part of it with a specific Bragg wavelength (*λ*B) is reflected, and the rest is transmitted further. The reflected light wavelength *λ*<sup>B</sup> is given by the relation *λ*<sup>B</sup> = 2*nL*, where *n* is the effective refractive index of the optical fiber and *L* is the distance between the gratings or the grating period. Stretching/compression of the fiber changes the distance *L* and the refractive index *n* resulting in a change in Bragg wavelength (*λ*<sup>B</sup> � *dλ*B), which is recorded by the optical system. The fiber-optic strain sensor GF is found by analogy with strainresistive sensors [25]:

$$\text{GF} = \frac{d\lambda\_{\text{B}}/\lambda\_{\text{B}}}{dL/L},\tag{3}$$

where *dλ* <sup>B</sup> is the change in the reflected-light wavelength during deformation of the fiber grating and *dL/L* is the relative deformation of the grating. According to [25], the fiber-optic strain sensor GF is about 0.78, which is markedly lower than the strain-resistive sensor GFs. As in case of strain-resistive sensors, it does not depend on the sensor design and is determined by the properties of the fiber-optic material.

#### **2.3 Piezoelectric effect and piezoelectric transducers**

A piezoelectric transducer converts a mechanical force into an electric charge. Its operation is based on the piezoelectric effect which entails the occurrence of dielectric polarization under mechanical stresses (**Figure 1c**). The density of the electric charge induced on the piezoelectric element surface under an external load is described by the Equation [26].

$$
\Delta q = d\_{\vec{\eta}} \sigma,\tag{4}
$$

where Δ*q* is the surface charge density; *dij* is the piezoelectric modulus described by a 3 � 6 matrix with typical component values in the range of 10�10–10�<sup>12</sup> C/N; *<sup>σ</sup>* is the stress in the material under the external load. The sensitivity of these sensors is described by the piezoelectric modulus which complicates their comparison with strain-resistive and fiber-optic sensors. Similarly to Eqs. (2) and (3), the piezoelectric sensor GF should be inversely proportional to the relative deformation *dL/L*. Using Hooke's law *σ* = *E*(*dL/L*) and Eq. (4) we get:

$$\text{GF} = \frac{\Delta q}{\text{dL/L}} = \frac{d\_{\vec{\text{ij}}}\sigma}{\text{dL/L}} = \frac{d\_{\vec{\text{ij}}}\text{E}(d\text{L}/\text{L})}{d\text{L}/\text{L}} = d\_{\vec{\text{ij}}}\text{E}.\tag{5}$$

*Piezo-Optical Transducers in High Sensitive Strain Measurements DOI: http://dx.doi.org/10.5772/intechopen.94082*

It follows from Eq. (5) that the GF does not depend on the sensor design and is determined only by the piezoelectric element material properties. **Table 1** shows the values of the piezoelectric moduli and Young's moduli taken from [26, 27] and the sensitivity factors calculated by Eq. (5) for some materials widely used for the fabrication of piezoelectric sensors. It is the GF (and not the piezoelectric modulus) that is an objective sensitivity parameter of piezoelectric sensors when compared with the sensitivity of another type of sensors. For example, the piezoelectric modulus for electroactive polymers is more than two orders of magnitude greater than for other piezomaterials. However, this advantage almost vanishes due to the small elastic modulus, and, as a result, GF becomes two orders of magnitude lower than that of the other materials. **Table 1** shows that the piezoelectric sensor GFs are comparable in order of magnitude with the strain-resistive sensor GFs.
