Analysis of mechanical property degradation of fracture in phase field model

Abstract

In the AT2 model, there is a problem of premature damage when describing brittle fracture, as well as the length dependence. In this paper, some new degradation function and a parameter are used to characterize fracture in AT2 model. Firstly, new trigonometric and polynomial degradation function are proposed. The mechanical properties of these two functions in describing brittle fracture are theoretically analyzed, the results indicate that the new degradation function can maintain the linear elastic response of the model before fracture. Secondly, the influence of degradation function on fracture characteristic is discussed. A parameter is introduced to characterize the difference in failure performance for degradation function. In addition, a new rational degradation function is proposed based on the polynomial function, which couples the failure strength into the function and attenuates the length dependence of the AT2 model. Finally, the brittle fracture problem under different conditions is studied and compared with the results of classical quadratic degradation function through some representative examples. The results show that the new trigonometric and polynomial degradation functions can reduce the overall performance degradation of material before brittle fracture by nearly 3 orders of magnitude, verifying that the presented degradation functions can better study the brittle fracture, and the effectiveness of the introduced parameter. At the same time, when the rational degradation function is adopted, the model is length-independent, and the results are consistent with experiment and previous numerical results.