摘要
在用理论流变力学模型研究蠕变损伤时,以往许多研究按照Lemaitre应变等效原理,根据理论流变力学模型在模型参数为常数条件下得到的蠕变方程,将其中的应力替换成有效应力,以引进损伤变量,并采用适当的损伤演化方程来描述损伤变化规律,由此得到蠕变损伤方程,这等同于将理论流变模型中的流变参数p替换为p(1-D)(D为损伤变量),这时的流变参数是一个变量,这种做法存在着与参数非线性理论流变力学模型研究中相同的问题,即通过直接将常参数条件下的蠕变方程中的参数替换成其相应的函数而得出错误的变参数条件下的蠕变方程。本文先假定蠕变时间与损伤时间一致,给出将理论流变力学模型微分型本构方程中的应力替换成有效应力,再由此解出蠕变损伤方程的方法。在此基础上,进一步证明用叠加原理求解理论流变力学模型蠕变损伤方程的正确性,并据此给出蠕变时间和损伤时间不一致时的理论流变力学模型蠕变损伤方程求解方法。指出以往研究中的一些问题并给出更严谨的结果,可望为以后的研究提供借鉴。
In order to take into consideration of damage in theoretical rheological models（TRM）, current approach, based on Lemaitre equivalent strain theory, is to obtain creep damage equation through the replacement of the Caucy stress with effective stress in creep equation of the TRM with constant rheological parameters, thus the time-dependent damage can be introduced. Such an approach is equivalent to the substitution of the rheological parameters p with p（1--D） in creep equations of TRM. With the parameters being time-dependent, a problem similar to that in nonlinear TRM, the failure to produce correct creep equation of nonlinear TRM via direct replacement of time-dependent rheological parameters in creep equations of linear TRM with functions, will arise. Based on the hypothesis that damage and creep are simultaneous, this paper proposed an alternative way to obtain creep damage equation： to deduct it from the revised constitutive law in which the Caucy stress is replaced by effective stress. Further, another way to obtain creep damage equation, that is through principle of superposition, is given, and its correctness is proven. On the basis of the second way, the method to obtain creep damage equation when damage is not in concurrence with creep is proposed. In addition, problems in some current studies are discussed and more valid answers are suggested.
出处
《岩石力学与工程学报》
EI
CAS
CSCD
北大核心
2012年第A01期3006-3014,共9页
Chinese Journal of Rock Mechanics and Engineering
基金
国家自然科学基金资助项目(40972178
50579088)
铁道部科技攻关项目(2009G009-B-10)
关键词
岩石力学
蠕变
损伤
应变等效原理
rock mechanics creep damage equivalent strain theory
