Knowledge Management System of Institue of Mechanics, CAS
| 粘弹性材料界面裂纹的瞬态响应和散射研究 | |
| 魏培君 | |
| Thesis Advisor | 张双寅 ; 吴永礼 |
| 1999 | |
| Degree Grantor | 中国科学院研究生院 |
| Place of Conferral | 北京 |
| Subtype | 博士 |
| Degree Discipline | 固体力学 |
| Keyword | 粘弹性 界面裂纹 冲击响应 散射 奇异积分方程 Viscoelastic Interface Crack Shock Response Scattering Singular Integral Equation |
| Other Abstract | 本文研究粘弹性材料界面裂纹对冲击载荷的瞬态响应和对广义平面波的稳态散射。相对于已有广泛研究的弹性材料裂纹瞬态响应和稳态散射问题，本文的研究有三个突出特点：1）粘弹性材料；2）界面裂纹；3）广义平面波入射。粘弹性材料界面裂纹对冲击载荷的瞬态响应和对广义平面波的散射尚无开展研究，本文在弹性材料相应问题的研究基础上，首先开展了这一问题的研究。对于冲击载荷下粘弹性界面裂纹的瞬态响应问题，利用Laplace积分变换方法，将粘弹性材料卷积型本构方程转化为Laplace变换域内的代数型本构方程，从而可以在Laplace变换域内象处理弹性材料的冲击响应一样，将相应的混合边值问题归结为关于裂纹张开位移COD的对偶积分方程，并进一步引入裂纹位错密度函数CDD （Crack Dislocation Density），将对偶积分方程化成关于CDD的奇异积分方程（SIE）。用数值方法求解奇异积分方程得到变换域内的动应力强度因子数值解，最后利用Laplace积分逆变换数值方法得到时间域内的动应力强度因子的时间响应。理论分析考虑了两种裂纹模型，即Griffith界面裂纹和柱面圆弧型界面裂纹。考虑的载荷包括反平面冲击载荷和平面冲击载荷。对于平面冲击载荷，通过对裂尖应力场的奇性分析，首次发现粘弹性界面裂纹裂尖动应力场奇性指数不是常数0.5，而是与震荡指数一样依赖材料参数。针对反平面冲击载荷给出了一个算例，计算了裂尖动应力强度因子的时间响应，并与弹性材料的结果作了比较，发现粘弹性效应的影响不仅使过冲击峰值降低，而且使峰值点后移。粘性效应较大时，过冲击现象甚至不出现。关于粘弹性界面裂纹对广东省义平面波的散射问题，首先研究广义平面波在无裂纹存在的理想界面的反射和透射，再研究由于界面裂纹的存在而产生的附加散射场。利用粘弹性材料的复模量理论，可将粘弹性材料的卷积型相构方程化成频率域内的代数型本构方程。类似弹性平面波的处理，在频率域内将问题最终归结为关于裂纹位错密度CDD的奇异积分方程。数值方法求解奇异积分方程即可得到频率域内的散射场，并进而得到裂尖动应力强度因子和远场位移型函数和散射截面。理论分析考虑了两种裂纹模型：Griffith界面裂纹和柱面圆弧型界面裂纹。研究的入射波有广义的SH波和P波。对于广义平面P波入射的情况，通过对裂尖应力场的奇性分析，同样发现粘弹性界面裂纹裂尖动应力场奇性指数不地常数0.5，而是与震荡指数一样依赖于材料参数。对柱面裂纹散射远场的渐近分析，发现远场位移和应力除含有几何衰减因子外，都含有一个材料衰减速因子。散射截面由于材料衰减因子的存在也成为依赖散射半径的量。为了使散射截面仍有意义，文中提出一种修正办法。对Griffith界面裂纹，给出了一个广义平面SH波入射的算例；对柱面界面裂纹，给出了一个广义平面P波入射的算例。计算了不同入射角和入射频率下裂纹的张开位移和动就应力强度因子，并分析了其依赖关系。求解奇异积分方程的数值方法和Laplace积分逆变换数值方法是本文的基本数值方法。本文对这两种方法作了大量的调研和系统的研究。在对比分析的基础上，对现有的各种方法从原理，适用范围，计数效率，优势及特点进行了归纳总结。并尝试了奇异积分方程的最新数值方法--分片连续函数法，证实了其适用性和方便性．; The instantaneous response of interface crack between two dissimilar viscoelastic materials to shock load and the scattering of harmonic general plane wave around it are investigated. As compared with corresponding problem of crack in elastic material, there are three remarkable characteristics, that is: 1) viscoelastic material; 2) interfacial crack; 3) general plane wave. The problems of instantaneous response to shock load and scattering of harmonic general plane wave for interface crack in viscoelastic materials have not been studied yet by now. In the present dissertation, the problems are initiated on the basis of the research on corresponding elastic problems. In the research of instantaneous response of interface crack, the Laplace integral transformation method is used to transform the viscoelastic convolution constitutive equations into an algebraic version in transformation domain. Then the mixed boundary value problem in transformation domain is reduced to dual integral equations for crack open displacement (COD) which is furthermore changed into singular integral equations by introducing crack dislocation density function (CDD) just like the process dealing with shock response of elastic material. Then numerical method is used to solve the singular integral equations and thus dynamic stress intensity factor (DSIF) is evaluation in Laplace transformation domain. Finally, the numerical method of Laplace inverse transformation is used to reconvert the dynamic stress intensity factor to that in time domain from transformation domain. Two interface crack models, namely plane Griffith crack and curve cylinder crack, are considered. The shock load considered includes anti-plane and in-plane loads of Heaviside pattern. In the case of in-plane shock load, it is found that singular index of dynamic stress fields is not a constant of - 0.5, but dependent on material parameters such as oscillation index etc. The numerical example is also given for the case of anti-plane shock load. The dynamic stress intensity factor is evaluated and compared with that of corresponding elastic crack. It is found that viscosity effects alleviate the overshoot and delay its occurrence. When viscosity is strong enough, the overshoot even does not appear. |
| Call Number | 29876 |
| Language | 中文 |
| Document Type | 学位论文 |
| Identifier | http://dspace.imech.ac.cn/handle/311007/23920 |
| Collection | 力学所知识产出(1956-2008) |
| Recommended Citation GB/T 7714 | 魏培君. 粘弹性材料界面裂纹的瞬态响应和散射研究[D]. 北京. 中国科学院研究生院,1999. |
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