## 4 Conclusions  
The effects of mechanical vibrations and thermal variations on the electrical properties of thin copper films of 18 \(\upmu\)m thickness bonded to FR4 epoxy laminate of 1.5 mm thickness were determined experimentally for the first time. It was evident from the results obtained at zone C that the stress induced by mechanical vibrations plays an important role in the electrical properties of PCBs. Resistance values increased up to 1657% of the initial value after 800 k vibration cycles. These changes were associated with a 95% decrease in conductivity (from 4.1 \(\times\) 10\({}^{7}\) to 2.3 \(\times\) 10\({}^{6}\) S/m). This was due to the surface damage caused by mechanical vibrations near this zone. Interestingly, no such behavior was observed at zones A and B. At these zones, the electrical properties of the samples before and after mechanical vibration cycles were almost the same. No cracks were found near these zones, whereas the apparent density of cracks at zone C, as seen by ESEM, increased from \(\sim\)3 cracks per mm at 200 k cycles to \(\sim\)8 cracks per mm at 800 k cycles. This indicated the dependence of the overall damage on the number of cycles. Interestingly, very little change in the electrical properties was observed due to temperature rise.  
The surface composition analysis indicated that vibration stress only produced physical damage and not chemical processes such as oxidation. The samples were also analyzed using water droplet contact angle measurements. The observed contact angles for untreated samples (78 to 95 degrees) were found to be lower than those after mechanical vibrations (117-119 degrees). This marked change in contact angle could be attributed to increased surface roughness and the accumulation of very small air bubbles on the cracks, which made water contact with the surface difficult. Further studies will also address the influence of film thickness, material, and vibration frequency on the electrical performance of these composites under mechanical vibrations.  
The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app13137941/s1](https://www.mdpi.com/article/10.3390/app13137941/s1)]([https://www.mdpi.com/article/10.3390/app13137941/s1](https://www.mdpi.com/article/10.3390/app13137941/s1)). Figure S1: Photograph of the dual axes four point probe (DA4 PP) device. Figure S2: Photograph of the wiring between probe head and keithley2400 source measure unit. Figure S3: Screenshot of the GUI: (a) For probe head movement; (b) For sheet resistance measurement. Figure S4: Plot of the force sensor: (a) In the time domain; (b) In the frequency domain. Figure S5: Frequency response of the accelerometer: (a) At position (1); (b) At position (2). Figure S6: Comparison of the sheet resistance values measured by two devices.  
S.A. conceptualization, methodology, investigation, data curation, writing--original draft preparation; M.K.H. conceptualization, validation; S.M. methodology, project administration, funding acquisition; A.F. conceptualization, writing--review and editing, supervision. All authors have read and agreed to the published version of the manuscript.  
This work has been funded by the Deanship of Scientific Research at Umm Al-Qura University. Grant code: 23 UQU4330020 DSR01.  
Not applicable.  
All data are included I the text.  
The authors would like to thank the Deanship of Scientific Research at Umm Al-Qura University for supporting this work under grant 23 UQU4330020 DSR01.  
The authors declare no conflict of interest.