黏弹性材料界面裂纹应力场奇性分析

SINGULARITY OF STRESS FIELD AROUND INTERFACE CRACK BETWEEN VISCOELASTIC BODIES

研究两半无限大黏弹性体间Griffith界面裂纹在简谐载荷作用下裂纹尖端动应力场的奇异特性.通过引入裂纹张开位移和裂纹位错密度函数,相应的混合边值问题归结为一组耦合的奇异积分方程.渐近分析表明裂尖动应力场的奇异特征完全包含在奇异积分方程的基本解中.通过对基本解的深入分析发现黏弹性材料界面裂纹裂尖动应力场具有与材料参数和外载荷频率相关的振荡奇异特性.以标准线性固体黏弹材料为例讨论了材料参数和载荷频率对奇性指数和振荡指数的影响.

The singular characteristics of dynamic stress field around interface Griffith crack be-tween two dissimilar isotropic viscoelastic bodies loaded by harmonic load are studied. The mixed boundary problem is reduced to a set of coupled singular integral equation of crack dislocation density function along normal and tangent of crack. By asymptotic analysis, it is found that the singular characteristics of dynamic stress field are embodied in the fundamental solution of singu-lar integral equation. In light of theory of singular integular equation, the fundamental solution is investigated in detail. It is revealed that the singular index and oscillatory index of stress field are both dependent upon material parameters and frequency of loading for viscoelastic materials, which is different from the well-known conclusion of -1/2 oscillatory singularity for elastic mate-rials. There is the problem of viscosity misfit apart from the elasticity misfit for present interface crack between two dissimilar viscoelstic bodies. It is the viscosity misfit that makes the singularity of stress around interface crack related to frequency of loading and show some new and interesting features different from elastic interface crack. As an example, the standard linear solid model for viscoelastic materials is studied numerically. The singular index and oscillatory index at various frequencies are evaluated. The effects of material parameters, i.e. the short-term modul, the long-term modul and the relaxation time, on the singular index and oscillatory index are discussed in detail.