考虑随机弱化二阶效应的电缆流变断裂学分析

RHEOLOGICAL FRACTURE ANALYSIS OF CABLE BY CONSIDERING THE SECOND ORDER EFFECTS OF RANDOM SLACK

将电缆视作为ｎ股子束构成的线束，而每股子束由ｍ个平行的受拉元件组成，受拉元件就是浸渍于树脂基体的聚合物股绳．未破坏的元件在任一时刻都按照某种规律承载，表现出电缆断裂对持载时间和载荷特征的相依性．从而，电缆的断裂是一个非平衡态不可逆热力学相容的一个非线性动力学演化过程．将聚合物股绳看成是出弹性固体，从带缺陷物体流变学原理出发，在一定的随机假设下，我们考虑了单个元件受载断裂与线束受载的关系．认识到元件的数目一定大时．线束的破坏时间是渐近正态分布的．在探讨了随机弱化的二阶效应后，得知渐近均值和方差都是载荷参数和单个元件流变性质的函数，从而确定了由元件和子束随机弱化引起的线束渐近强度平均中的损失Ｌｓ和元件随机弱化引起的线束渐近强度方差中的损失Δｓ．最终表明，渐近破坏时间对电缆断裂的重要意义，证明电缆的断裂是一个时间相关的流变断裂过程．

in this peper, we consider the cable as a bundle consisting of n sub-bundles, there are m perallel tension members which are polymeric yarns impregnated with a resin matrix, in each of the sub-bundle. The unimpaired members at any instant must share a part of load according to some laws, which clearly expresses the dependence of fracture on the duration and character of loading. So then, the fracture of cable is a nonlinear dynamic evolution process, which oneself accommodate to the non-equilibrium thermodynamics of irreversible processes. Let us assume that the polymeric yarn is viscoelastic solid, under certain assumptions of probability, according to the principles of rheology of bodies with defects, the relationship between the loading and failure of single member and the loading of bundle is investigated. It is shown that the failure time of bundle is asymptotically normal distribution as the number of members is large enough. Through the study to the effects of second order of random slack, we reconizs that the asymptotic mean and variance are functions of the parameters of loading and fheological behavior of single member. Then the losses L. in means of and Δs in variance of asymptotic strength of bundle arised by the random slack of members and sub-bundles are determined. It is also demonstrated in this paper that the fracture of cable is a time dependent prooes of rheolosical fracture.