**4. Results and discussions**

This section discusses the results obtained from explicit coupled temperaturedisplacement analysis followed by heat transfer analysis in case of LDR frequency excitation based vibro-thermography. First, a steady state analysis of the GFRP plate is performed with a frequency range around the analytical LDR frequency calculated using Eq. (3). The mode shape confirming the LDR frequency of the delamination is found to be 24.8 kHz from the steady state analysis, as shown in **Figure 3**. The LDR frequency excitation in form of single periodic continuous excitation is applied on the transmitter nodes of the numerical model from the top surface.

On performing the explicit coupled temperature-displacement analysis, the amplitude-frequency spectra obtained from a node selected on the top surface of the plate above the delamination location is presented in **Figure 4**. The highest peak in the frequency spectra is obtained at 24.86 kHz which is close to the result obtained from steady state analysis. The highest amplitude of 6.488 <sup>10</sup><sup>6</sup> m was observed at the delamination area.

Subsequently, the average nodal temperature profile at the delamination location during the span of explicit dynamic coupled temperature-displacement analysis is plotted in **Figure 5**. The plot shows variation of temperature at the delamination interface with respect to time of excitation. It is observed that the average nodal temperature at delamination location starts rising after 4 ms of excitation. The nodal temperature at delamination region rises gradually to around *Defect Detection in Delaminated Glass-Fibre/Epoxy Composite Plates Using Local Defect… DOI: http://dx.doi.org/10.5772/intechopen.101178*

**Figure 3.** *Contour plot of the GFRP plate depicting the mode shape of the delamination at LDR frequency of 24.8 kHz.*

#### **Figure 4.**

*Frequency spectra obtained at the delamination location on the top surface of the plate for single periodic LDR excitation.*

293.015 K in 10 ms. Since, the temperature rise is not saturated at the end of excitation, the plate can be excited for more time until the temperature rise saturates.

Moreover, all the elements over the delamination area is selected to plot the elemental temperature rise over delamination during 10 ms of heat transfer analysis, as illustrated in **Figure 6**. The plot shows a rise of temperature from the ambient for some of the elements over the delamination area. It is observed that the maximum temperature recorded during heat transfer analysis is 293.15 K. Since the temperature rise over the delamination region is around 150 mK, the vibrothermography scanning can be done at this instance of time with any IR camera that normally has a resolution of 30 mK.

Furthermore, contour plot for nodal temperature on the delamination surface of GFRP plate after explicit temperature-displacement analysis is illustrated in **Figure 7**. It is clear from the contour plot that the temperature rise is observed only

**Figure 5.** *Average nodal temperature rise at delamination layer for single periodic continuous LDR excitation.*

**Figure 6.** *Elemental temperature rise at delamination layer for single periodic continuous LDR excitation.*

at the delamination location while the rest of the plate shows no thermal signatures at all. However, it is clear that the whole delamination area is not covered by the heat flow at this time instance. Hence, the excitation of the plate must be done for more time period such that the whole delamination area is covered by the heat distribution. Similarly, the elemental temperature is shown in contour plot depicted in **Figure 8**, where heat is distributed to a larger area after heat transfer analysis as compared to the explicit temperature-displacement analysis. Although, the whole delamination is not covered at this instance and more time for excitation is required. The defect imaging at later time increment is advantageous because of better judgement and idea of defect shape and size is detected easily. This is one of the merits of performing LDR based vibro-thermography technique that provides high contrast defect images that can be captured using an IR camera.

*Defect Detection in Delaminated Glass-Fibre/Epoxy Composite Plates Using Local Defect… DOI: http://dx.doi.org/10.5772/intechopen.101178*

#### **Figure 7.**

*Contour plot of nodal temperature on the delamination surface of delaminated GFRP plate after heat transfer analysis.*

#### **Figure 8.**

*Contour plot of nodal temperature on the top surface of delaminated GFRP plate at 10 ms during single periodic continuous LDR excitations.*
