一种模拟准脆性断裂问题的相场法能量退化法则

A Novel Degradation Function of the Phase Field Method for Quasi-brittle Fracture

介绍了相场法模拟准脆性断裂问题的基本原理,描述了幂函数能量退化法则与Borden能量退化法则,提出了一种模拟准脆性断裂问题的相场法耦合能量退化法则,该法则通过权重系数将幂函数能量退化法则与Borden能量退化法则进行耦合,可较为全面地反映材料的断裂行为。编制了二维相场法计算程序,以单边缺口正方形板为例,验证了程序的准确性。研究了耦合能量退化法则对单边缺口方形板拉伸断裂行为的影响,耦合能量退化法则参数s与m越大,拉伸荷载峰值越低;增加参数w,拉伸荷载峰值会提高。模拟了直裂缝半圆弯曲岩石试样断裂过程,分析了不同耦合能量退化法则参数下岩石试样的裂缝扩展过程,耦合能量退化法则参数m对荷载峰值影响较小,荷载峰值与参数s负相关,与参数w正相关。耦合能量退化法则可以较好地反映材料的准脆性断裂与脆性断裂行为。

The basic principles and degradation function of phase field method for quasi-brittle fracture are introduced in details.A novel degradation function is proposed,in which the power degradation function and Borden degradation function are coupled by a weight coefficient.The novel degradation function can reflect the fracture behavior of materials comprehensively.A 2D program for the phase field method is implemented.It is confirmed that the program is accurate by using a single-edge-notched square plate subjected to tension.The impact of the novel degradation function on the fracture behavior of single-edge-notched square plate is studied.If the parameter s and m increase,the load peak will decrease.With the increase of parameter,the load peak will increase.Meanwhile,the fracture of notched semi-circular bend(NSCB)rock specimen is modeled,and the effect of the novel degradation function on the fracture propagation of NSCB is analyzed.The parameter m has a less effect on the load peak.The load peak is negatively correlated with parameter s and positively correlated with parameter w.The novel degradation function can reflect the behavior of quasi-brittle fracture and brittle fracture.