7.2.1 Electromechanical response

Three tensile tests of piezo-resistive sensor wire were performed. The Young modulus and yield strength of the tested samples were about 1348.5 and 20.13 MPa, respectively. The stress-strain behavior of untwisted coated yarn is shown in Figure 7a. Stress and electrical response of the untwisted yarn are plotted simultaneously in Figure 7b. The resistance was changed at the same time as the failure started to initiate, and, as the test progressed, the resistance increased gradually when the number of fractured filaments was increased. Ultimately, when the untwisted yarn was fractured completely, the resistance went to maximum value. The results were very encouraging, and piezo-resistive flexible sensor was responding very well to any change in load.

### 7.2.2 Damage modes

After tensile test, fractured samples were studied using SEM technique, and it appeared that there were two distinct morphologies. Some filaments exhibited a clean ductile failure in which both the coating and the fiber showed a clean cut; however, other filaments showed a pull-out of the coating or flaking off, Figure 8.

This established that some parts of the coating might not have developed strong adherence with the nylon fiber during the fabrication process. However, it did not affect the overall response of the sensor because of two reasons: first, the pull-out of coating happened during damage initiation and damage propagation just before the failure and did not affect the performance of the sensor before that; the second reason is that there were approximately 100 fibers in the single yarn and fiber pullout happened in less than 5–10% of fibers, which is almost negligible. Nevertheless, the surface adhesion can be improved during the fabrication process by further improving the surface roughness by etching process before application of coating

The untwisted coated yarn was modeled as a ductile material using the built-in elastic, plastic, and ductile damage criteria of Abaqus because both silver and nylon are ductile in nature. Electrical conductance of both materials nylon and Ag thin film was defined in Abaqus to model the electrical response during the mechanical analysis, Table 1. For the numerical analysis, experimental tensile behavior of pure silver thin film was applied [45] in addition to the mechanical response of untwisted

Furthermore, the rate-dependent power law was defined using the experimental curves in the plasticity model because it plays a vital role in damage initiation and neck formation during ductile failure. Therefore, strain hardening stress coefficient

> <sup>n</sup> <sup>¼</sup> log <sup>σ</sup><sup>2</sup> � log <sup>σ</sup><sup>1</sup> log ε<sup>2</sup> � log ε<sup>1</sup>

where σ1,2 are stress points in the plastic region, ε1,2 are the corresponding strain

Ductile damage criteria built in Abaqus was used to define model failure. Damage initiation depended on fracture strain, strain rate, and stress triaxiality whereas damage evolution required displacement at failure, Table 1. The evolution of the damage defined the material's behavior by illustrating the degradation of material stiffness after damage initiation. Scalar damage approach was used for formulating the rate of damage as given in (3). D is the overall damage variable showing the combined effect of all active damage mechanisms, and when it reached 1, fracture

> Poisson ratio

Nylon 1 � <sup>10</sup>�<sup>15</sup> 1348.5 0.39 20.13 0.12 5 Silver 63 � <sup>10</sup><sup>3</sup> 47,230 0.37 431.1 0.08 60 � <sup>10</sup>�<sup>5</sup>

points in the plastic region, K is the strain hardening stress, and n is the strain

Young's modulus, MPa

Experimental elastic, plastic, and failure data of nylon and pure Ag-thin film.

logK � log σ<sup>1</sup> ¼ nð Þ log x � log ε<sup>1</sup> (2)

σ ¼ ð Þ 1 � D σ́ (3)

Fracture strain

Strain rate, mm/min

Yield strength, MPa

(1)

K and strain hardening index n were calculated using Eqs. (1) and (2).

because rough surfaces have better adhesion properties.

Nanotechnology and Development of Strain Sensor for Damage Detection

DOI: http://dx.doi.org/10.5772/intechopen.82871

7.3 FE analysis

nylon yarn, Table 1.

hardening exponent.

Material Electrical

conductance, S/mm

occurred.

Table 1.

105

Figure 7.

Electromechanical behavior of untwisted nylon yarn: (a) mechanical behavior of untwisted nylon yarn and (b) electromechanical response.

#### Figure 8.

SEM characterization of fractured samples confirms that the coating thickness was approximately 1–2 μm: (a) shows a clear ductile failure of both core and coating material and (b) depicts the second phenomenon, that is, flaking off of coating.

Nanotechnology and Development of Strain Sensor for Damage Detection DOI: http://dx.doi.org/10.5772/intechopen.82871

This established that some parts of the coating might not have developed strong adherence with the nylon fiber during the fabrication process. However, it did not affect the overall response of the sensor because of two reasons: first, the pull-out of coating happened during damage initiation and damage propagation just before the failure and did not affect the performance of the sensor before that; the second reason is that there were approximately 100 fibers in the single yarn and fiber pullout happened in less than 5–10% of fibers, which is almost negligible. Nevertheless, the surface adhesion can be improved during the fabrication process by further improving the surface roughness by etching process before application of coating because rough surfaces have better adhesion properties.

#### 7.3 FE analysis

The untwisted coated yarn was modeled as a ductile material using the built-in elastic, plastic, and ductile damage criteria of Abaqus because both silver and nylon are ductile in nature. Electrical conductance of both materials nylon and Ag thin film was defined in Abaqus to model the electrical response during the mechanical analysis, Table 1. For the numerical analysis, experimental tensile behavior of pure silver thin film was applied [45] in addition to the mechanical response of untwisted nylon yarn, Table 1.

Furthermore, the rate-dependent power law was defined using the experimental curves in the plasticity model because it plays a vital role in damage initiation and neck formation during ductile failure. Therefore, strain hardening stress coefficient K and strain hardening index n were calculated using Eqs. (1) and (2).

$$n = \frac{\log \sigma\_2 - \log \sigma\_1}{\log \varepsilon\_2 - \log \varepsilon\_1} \tag{1}$$

$$
\log K - \log \sigma\_1 = n(\log \pi - \log \varepsilon\_1) \tag{2}
$$

where σ1,2 are stress points in the plastic region, ε1,2 are the corresponding strain points in the plastic region, K is the strain hardening stress, and n is the strain hardening exponent.

Ductile damage criteria built in Abaqus was used to define model failure. Damage initiation depended on fracture strain, strain rate, and stress triaxiality whereas damage evolution required displacement at failure, Table 1. The evolution of the damage defined the material's behavior by illustrating the degradation of material stiffness after damage initiation. Scalar damage approach was used for formulating the rate of damage as given in (3). D is the overall damage variable showing the combined effect of all active damage mechanisms, and when it reached 1, fracture occurred.

$$\boldsymbol{\sigma} = (\mathbf{1} - \mathbf{D}) \,\mathsf{/}\mathsf{/}\mathsf{T} \tag{3}$$


Table 1.

Experimental elastic, plastic, and failure data of nylon and pure Ag-thin film.

Figure 7.

Figure 8.

104

is, flaking off of coating.

(b) electromechanical response.

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Electromechanical behavior of untwisted nylon yarn: (a) mechanical behavior of untwisted nylon yarn and

SEM characterization of fractured samples confirms that the coating thickness was approximately 1–2 μm: (a) shows a clear ductile failure of both core and coating material and (b) depicts the second phenomenon, that

where σ is the stress due to damage response, D is the damage variable, and σ ́is the stress due to undamaged response.

#### 7.4 Verification of sensor response

The nylon monofilament coated with silver thin film was subjected to tensile elongation until failure. Results showed that it was viable to use one filament to validate the piezo-resistive behavior of untwisted coated yarn. The true stress-strain behavior showed a good correlation with the experimental results in the elasticplastic region, Figure 9. It can be seen in the results that it was fine to use coated monofilament model to verify the result because the plane of stress is same. However, there is a slight difference in the failure initiation and breakage, which is understandable because: in experimental results, the failure shows gradual breakage of all the monofilaments, whereas in the numerical model, the set of monofilaments is modeled by a single thread. Electrical response was recorded as electrical current density (ECD) in Abaqus which was then converted to resistance response using Eqs. (4)‑(6) to validate the experimental piezo-resistive behavior of sensor wire. Electromechanical behavior of the monofilament is shown in Figure 10.

$$J = aE \text{ with } a = \frac{1}{\rho} \tag{4}$$

$$J = \frac{E}{\rho} \Rightarrow J\infty \frac{1}{\rho} \tag{5}$$

$$R = \frac{\rho L}{A} \tag{6}$$

7.5 Experimental results of instrumented composite specimen with nylon/silver

FE analysis of electromechanical response of Ag-coated monofilament.

Nanotechnology and Development of Strain Sensor for Damage Detection

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Three tensile tests were performed with the composite specimen incorporated with sensor wire. The mechanical response including Young's modulus and yield strength of the tested samples showed that it was not affected by insertion of sensor in the sample and the sensor did not act as intrusive element. The mechanical response of composite specimen and electrical response of the sensor were correlated simultaneously. The resistance was changed at the same time as the failure started to initiate, and, as the test progressed, at the point of failure, the resistance of the sensor started to increase and eventually went to infinity, Figure 12. The sensor was reporting what was going on as the fracture formed. The results were

sensor

Figure 10.

Figure 11.

107

3D discrete model (a) before failure and (b) after failure.

where J is the current density, E is the electric field, α is the electrical conductivity, ρ is the resistivity, L is the length, A is the cross-sectional area, and R is the resistance.

It was observed that till the plastic region, the electrical resistivity of the yarn changed, but this change in resistance was very small as compared to change in resistance on damage when there was complete breakage in current flow. No gradual increase in the resistance was seen like in experimental results because of the monofilament model. The 3D discrete model of coated monofilament before and after failure is shown in Figure 11.

Figure 9. Numerical verification of experimental mechanical behavior of Ag-coated untwisted nylon yarn.

Nanotechnology and Development of Strain Sensor for Damage Detection DOI: http://dx.doi.org/10.5772/intechopen.82871

Figure 10. FE analysis of electromechanical response of Ag-coated monofilament.
