岩石亚临界裂纹扩展应力强度因子Williams级数计算及数值模拟

Williams series calculation and numerical simulation for stress intensity factor of rock subcritical crack growth

引入Williams级数,提出一种计算双扭试验中应力强度因子的新方法,并运用ANSYS数值模拟软件,对双扭试验进行数值模拟。通过理论分析和数值模拟2种方法,分别计算大理岩和花岗岩在亚临界裂纹扩展中的应力强度因子IK?和IK?。同时,将理论分析和数值模拟所得的应力强度因子IK?和IK?与试验所得的应力强度因子IK进行比较。研究结果表明:理论分析、数值模拟与试验这3种方法所得的应力强度因子均随裂纹的扩展而减小,与断裂力学理论相符;对于同一种岩石试样,理论分析所得的IK?与试验所得的IK的拟合曲线相比斜率偏小,但偏差较小;模拟所得的IK?与试验所得的IK的拟合曲线斜率基本一致,说明理论分析、数值模拟与试验过程中应力强度因子减小规律相同,能反映试验的基本过程,可见理论分析与数值模拟结果可靠,能为岩土工程稳定与时间的相关性研究提供依据。

A new method to calculate the stress intensity factor was proposed by using Williams series and some numerical simulations were made with ANSYS software. Though theory analysis and simulation calculation, the stress intensity factors were obtained during the subcritical crack growth for marble and granite. And the stress intensity factor KI ＇ obtained by theory analysis, KI ＇＇obtained by numerical simulation were compared with the stress intensity factor KI obtained by double-torsion test. The results show that the stress intensity factors obtained from three methods decrease while the crack propagates. And to the same rock, the slope of fitting curves for KI ＇ is lower than that of the fitting curves for KI, but the deviation is small. KI and KI ＇＇ have almost the same decline rate, and the slope of fitting curves is basically identical, which shows that the reduce rule of stress intensity factor is identical to those of the theory analysis, simulation calculation and test, and so the results of theory analysis and simulation calculation are reliable, which can provide the basis for studying time-dependency of rock stability.