# Study on Interfacial Crack of Piezoelectric Bimaterials Under Dynamic Loading

## TL;DR

This study analyzes how cracks in piezoelectric materials behave under dynamic loads, showing how crack length and material properties influence stress and electric displacement.

## Contribution

A novel method combining Laplace and Fourier transformations with the Chebyshev point method is used to analyze dynamic crack propagation in piezoelectric bimaterials.

## Key findings

- Crack length increases the dimensionless function, indicating greater stress intensity.
- Smaller elastic parameters lead to lower dynamic stress intensity under certain conditions.
- The random forest model achieved high predictive accuracy (R2 = 0.9886) for stress intensity.

## Abstract

To meet the requirements of effectiveness and strength in actual engineering, based on the dynamic fracture characteristics, the dynamic propagation of orthogonal anisotropic interface cracks in piezoelectric bimaterials was analyzed. By performing Laplace transformation and Fourier transformation on the governing equations, the problem was transformed into a singular integral equation. Using the Chebyshev point method and Laplace inversion, the stress and electric displacement intensity factors at the crack tip of the orthogonal anisotropic interface were obtained. The results show that the crack length affects the dimensionless function. The longer the crack, the larger the dimensionless function. Under certain conditions, the smaller the elastic parameters, the smaller the dimensionless dynamic stress intensity factor. At the same time, the impact time also affects the dynamic crack propagation. With the passage of time, the dimensionless function first increases, then reaches a peak, and finally oscillates and converges to the static value. On this basis, the response surface method was used for analysis and prediction. The R2 value of the random forest model is 0.9886, which indicates that the model has high predictive accuracy. When the optimal values of A (d1/a), B (cpt/a) and C (c44(2)/c44(1)) are 0.4045, 1.6797 and 1.9035 respectively, the stress intensity reaches its maximum value of 1.3375.