A mathematical model for predicting the electro-mechanical behavior of biomimetic crack sensors: Effect of crack depth and gap

Various biomimetic microstructures, such as porous, cracks, wrinkles, micro-pyramids, and micro-domes, are applied to improve the sensing performance of mechanical sensors. Among them, the crack-based strain sensors are widely investigated due to high sensitivity and fast response time. To clearly describe the relationship between crack morphology and sensor sensitivity, a mathematical model is developed for investigating the performance of a poly(3,4-ethylenedioxythiophene)-silicon oxide/polydimethylsiloxane (SiOx/PDMS) based crack strain sensor. First, the displacement field of a crack tip is calculated based on the theory of fracture mechanics, and the mathematical relationship between the crack depth, crack gap, and strain is obtained. The predicted crack depth of the SiOx thin film's thicknesses in 7.91 μm (SiOx/PDMS-7.91) is 2.82 μm, with the error of 3.75% compared to the experimental result. Correspondingly, the deviation of SiOx/PDMS-7.91 is 5.74% between the predicted crack gap and the experimental data. Second, above the aforementioned crack tip characteristics, the mathematical model based on crack edges contacts probability (CECP) is used to construct the relationship between the crack tip characteristics, applied stress, and device sensitivity. The maximum predicted sensitivity can reach 3562.68 compared with the experimental data of 3800.44, and the deviation is about 6.26%. Moreover, the CECP model has good universality with the other reported crack-based strain sensors. It can be concluded that crack morphology affects the distribution and quantity of conductive paths. When the strain sensor is subjected to external forces, brittle thin films generate a certain number of bumped-like elements for microcracks. The wider and deeper crack will increase the relative resistance change and the decrease of conductive paths, resulting in a rapid increase in the sensitivity of the strain sensor.