Theoretical models of the electric field dependent mode I fracture toughness and fracture strength for ferroelectric ceramics

Theoretical quantitative characterization of electric field dependent mode I fracture toughness and fracture strength is a fundamental issue for evaluating the service performance of ferroelectric ceramic materials, with significant theoretical and engineering value. Based on the Li's Principle of Energy Equivalence, considering the equivalent relationship between electrostatic energy and strain energy, the electric field dependent mode I fracture toughness model and the electric field dependent fracture strength model for ferroelectric ceramics have been developed, respectively. These models reveal a quantitative relationship between electric field strength and mode I fracture toughness/fracture strength to predict the electric field dependent mode I fracture toughness/fracture strength of both polarized and unpolarized ferroelectric ceramic materials over a wide range of electric fields, under electric fields either perpendicular or parallel to the crack plane. The predictions of the electric field dependent mode I fracture toughness model align well with the seven sets of experimental data, while the predictions of the electric field dependent fracture strength model align well with the three sets of experimental data. These models provide an efficient and practical method for service performance evaluation and structural component design of ferroelectric ceramic materials in electric field environments, and also reduce the reliance on difficult-to-conduct experiments.