Fracture criteria and rheological fracture mechanism of brittle materials based on Eshelby stress
摘要
In the course of damage and fracture, the material undergoes energy evolution. The crack driving force, known as configurational force or material force, is generated due to the change of potential energy. We employed the configurational force approach in conjunction with the viscoelastic–elastic correspondence principle to investigate the mechanisms of crack initiation, propagation, and rheological fracture. The configurational force balance equation is obtained by evaluating the first-order variation of potential energy functionals within the undeformed configuration and deformed configuration. The boundary of the crack-tip plastic zone is assessed by both Mises Cauchy stress and Mises configurational stress under the conditions of small scale yielding. Furthermore, the critical crack-tip plastic zone area is used to predict the fracture load. The fracture mechanisms of viscoelastic bodies are elucidated based on the viscoelastic correspondence principle. The crack-tip plastic zone and fracture loads at different times are computed using the standard linear body. The critical size and load for delayed instability of cracks are derived, and then the crack state factor is proposed. Additionally, the Kachanov creep law is employed to characterize the viscoelastic fracture behavior. The results show that the size, shape, and other characteristics of the crack-tip plastic zone, evaluated by Mises Cauchy stress and Mises configurational stress, exhibit consistency. The critical plastic zone area is performed using functions of dimensionless factors, and the predicted results are consistent with experimental observations and those obtained by the maximum tangential stress fracture criterion. Over time, the crack-tip plastic zone exhibits a progressive enlargement, while the critical load envelope undergoes a gradual reduction. The crack state factor relates to the crack inclination angle and