Theoretical models of the strain rate-dependent mode I fracture toughness and fracture strength for ceramics

Theoretical quantitative prediction of strain rate-dependent fracture toughness and fracture strength is crucial for evaluating the service performance of ceramic protective materials. Based on Li's Principle of Energy Equivalence, considering the equivalence between strain energy and work done by external pressure, theoretical models of strain rate-dependent mode I fracture toughness and fracture strength have been developed, respectively. These models quantitatively characterize the effects of strain rate, Young's modulus, and Poisson's ratio on the mode I fracture toughness/fracture strength. The predictions of these models were validated by three groups of all available strain rate-dependent mode I fracture toughness experimental data and 18 groups of all available strain rate-dependent fracture strength experimental data, demonstrating that these models have good predictive capability. These models require one mode I fracture toughness/fracture strength data at quasistatic and one mode I fracture toughness/fracture strength data at high strain rate to conveniently and efficiently evaluate the mode I fracture toughness/fracture strength at different strain rates, especially at intermediate strain rates. This work provides an effective method for quantitatively evaluating the mode I fracture toughness/fracture strength of ceramic materials under different strain rates and a convenient theoretical tool for investigating and applying ceramic materials across a wide strain-rate range.