连续损伤力学基临界奇异指数与破坏时间预测

响应量在临近破坏时呈现出临界幂律奇异性加速特征,是一种被广泛证实的灾变破坏前兆,并被火山、滑坡和岩石破坏实验等后验预测结果证实为一种对破坏时间进行短临期预测的可行方法.但是,奇异性指数测量值的较大分散性导致了对其具体取值的争议和预测效果的不确定性.因此,理解奇异性指数取值特征及其内在物理控制因素,成为了一个核心问题.本文基于连续介质损伤力学和材料时间相关失效特征,构建了刻画损伤加速发展通向破坏过程的力学模型.导出了恒名义应力蠕变加载和控制名义应力随时间线性增大两种典型加载方式下,损伤和应变率加速发展通向破坏的临界幂律奇异性前兆特征.阐明了临界幂律奇异性指数取值依赖于材料损伤与承受真应力之间的非线性关系这一内在物理根源,表明了实际测量中奇异性指数的分散性不完全归结于测量数据误差,而是有着内在物理控制因素.针对破坏前奇异性指数的不确定性,建议了在未知奇异性指数条件下预测破坏时间的方法,并基于花岗岩脆性蠕变破坏实验进行了验证和说明. 

CONTINUUM DAMAGE MECHANICS-BASED CRITICAL SINGULARITY EXPONENT AND FAILURE TIME PREDICTION1)

The accelerating increase of response quantities, such as strain and acoustic emission signals in the vicinity of failure time, has been revealed as a precursor of catastrophic failure. This critical precursor has been widely validated as a valid way to predict failure time by the retrospective prediction of volcanic eruptions, landslides and laboratory experiments of rock failures. But the scatter of exponents in the critical power law singularity relationship that describes acceleration in precursory signals leads to a debate on the actual value of critical exponent and the uncertainty of failure time prediction. Consequently, the uncertainty resulting from the scatter of exponents is a key difficulty in using such methods for prediction of the failure time through the use of acceleration precursors. Thus understanding the underlying mechanisms for the magnitude and variation of critical power-law exponents becomes a central problem for understanding the process of failure and failure time prediction. This paper presents a multi-scale damage mechanic model describing the accelerating process of time dependent failure. Theoretic derivations and demonstrations of critical power law relationship are presented for two typical load process, i.e. brittle creep failure under constant nominal stress and the load process of linearly increasing the nominal stress with time. It is found that values of the singularity exponents have a relationship with the parameter that defines the nonlinear level of damage evolution rate depending on to the local true stress. The physical expressions of critical parameters are deduced and the physical meanings of these critical parameters are explained. It is declared that the observed variation of the critical power law exponents not only due to the fluctuation in the measurement data, but has its intrinsic physical controls. Then a method is suggested to predict the failure time when the critical singularity exponent is unknown. This proposed methodology is validated through granite creep failure experiments in laboratory and the challenges for practical applications are demonstrated.