黏弹性体界面裂纹的冲击响应

研究两半无限大黏弹性体界面Griffith裂纹在反平面剪切突加载荷下，裂纹尖端动应力强度因子的时间响应。首先，运用积分变换方法将黏弹性混合边值问题化成变换域上的对偶积分方程。通过引入裂纹位错密度函数进一步化成Cauchy型奇异积分方程。运用分片连续函数法数值求解奇异积分方程，得到变换域内的动应力强度因子。再用Laplace积分变换数值反演方法，将变换域的解反演到时间域内，最终求得动应力强度因子的时间响应，并对黏弹性参数的影响进行了分析。

General Solution to Two-Dimensional Nonslipping JKR Model with a Pulling Force in an Arbitrary Direction

In this paper, a generalized JKR model is investigated, in which an elastic cylinder adhesively contacts with an elastic half space and the contact region is assumed to be perfect bonding. An external pulling force is acted on the cylinder in an arbitrary direction. The contact area changes during the pull-off process, which can be predicted using the dynamic Griffith energy balance criterion as the contact edge shifts. Full coupled solution with an oscillatory singularity is obtained and analyzed by numerical calculations. The effect of Dundurs' parameter on the pull-off process is analyzed, which shows that a nonoscillatory solution can approximate the general one under some conditions, i.e., larger pulling angle (pi/2 is the maximum value), smaller a/R or larger nondimensional parameter value of Delta gamma/E*R. Relations among the contact half width, the external pulling force and the pulling angle are used to determine the pull-off force and pull-off contact half width explicitly. All the results in the present paper as basic solutions are helpful and applicable for experimenters and engineers.

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.

Non-Slipping Jkr Model For Transversely Isotropic Materials

A generalized plane strain JKR model is established for non-slipping adhesive contact between an elastic transversely isotropic cylinder and a dissimilar elastic transversely isotropic half plane, in which a pulling force acts on the cylinder with the pulling direction at an angle inclined to the contact interface. Full-coupled solutions are obtained through the Griffith energy balance between elastic and surface energies. The analysis shows that, for a special case, i.e., the direction of pulling normal to the contact interface, the full-coupled solution can be approximated by a non-oscillatory one, in which the critical pull-off force, pull-off contact half-width and adhesion strength can be expressed explicitly. For the other cases, i.e., the direction of pulling inclined to the contact interface, tangential tractions have significant effects on the pull-off process, it should be described by an exact full-coupled solution. The elastic anisotropy leads to an orientation-dependent pull-off force and adhesion strength. This study could not only supply an exact solution to the generalized JKR model of transversely isotropic materials, but also suggest a reversible adhesion sensor designed by transversely isotropic materials, such as PZT or fiber-reinforced materials with parallel fibers. (c) 2007 Elsevier Ltd. All rights reserved.

Singularity of dynamic stress fields around an interface crack between viscoelastic bodies

The singular nature of the dynamic stress fields around an interface crack located between two dissimilar isotropic linearly viscoelastic bodies is studied. A harmonic load is imposed on the surfaces of the interface crack. The dynamic stress fields around the crack are obtained by solving a set of simultaneous singular integral equations in terms of the normal and tangent crack dislocation densities. The singularity of the dynamic stress fields near the crack tips is embodied in the fundamental solutions of the singular integral equations. The investigation of the fundamental solutions indicates that the singularity and oscillation indices of the stress fields are both dependent upon the material constants and the frequency of the harmonic load. This observation is different from the well-known -1/2 oscillating singularity for elastic bi-materials. The explanation for the differences between viscoelastic and elastic bi-materials can be given by the additional viscosity mismatch in the case of viscoelastic bi-materials. As an example, the standard linear solid model of a viscoelastic material is used. The effects of the frequency and the material constants (short-term modulus, long-term modulus and relaxation time) on the singularity and the oscillation indices are studied numerically.

The mixed-type integral equations for transient elastodynamic plane crack problems

In the present paper, by use of the boundary integral equation method and the techniques of Green fundamental solution and singularity analysis, the dynamic infinite plane crack problem is investigated. For the first time, the problem is reduced to solving a system of mixed-typed integral equations in Laplace transform domain. The equations consist of ordinary boundary integral equations along the outer boundary and Cauchy singular integral equations along the crack line. The equations obtained are strictly proved to be equivalent with the dual integral equations obtained by Sih in the special case of dynamic Griffith crack problem. The mixed-type integral equations can be solved by combining the numerical method of singular integral equation with the ordinary boundary element method. Further use the numerical method for Laplace transform, several typical examples are calculated and their dynamic stress intensity factors are obtained. The results show that the method proposed is successful and can be used to solve more complicated problems.

黏弹性材料界面裂纹应力场奇性分析

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。

正交各向异性功能梯度材料Ⅲ型裂纹尖端动态应力场

研究了无限大正交各向异性功能梯度材料Griffith裂纹受平面剪切冲击作用的问题。材料两个方向的剪切模量假定为成比例按特定梯度变化。通过采用积分变换-对偶积分方程方法，获得了裂纹尖端动态应力场。动态应力强度因子计算结果显示：增加剪切模量梯度或增加垂直于裂纹面方向的剪切模量可以抑制动态应力强度因子的幅值。

Molecular dynamics studies of brittle fracture of SiO2

By applying for molecular dynamics (MD) simulation and Griffith fracture criterion, the brittle behavior of crack extension of mode I type is investigated. The critical stress intensity factor (SIF)K-Ic(MD) of crack extension is calculated, and the evolution of atoms near crack tip is observed. It is found that K-Ic(MD) is in good agreement with the Griffith ftacture criterion K-Ic(Griffith).

粘弹性材料界面裂纹的瞬态响应和散射研究

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．

Effect Of Water On Brittle Fracture Of Sio2 By Molecular Dynamics Study

The influence of water on the brittle behavior of beta-cristobalite is studied by means of molecular dynamics (MD) simulation With the TTAM potential. Crack extension of mode 1 type is observed as the crack opening is filled LIP With water. The critical stress intensity factor K-lc(MD) is used to characterize the crack extension of MD simulation. The surface energy of SiO2 covered with layers of water is calculated at temperature of 300 K. Based oil the Griffith fracture criterion, the critical stress intensity factor K-lc(Griffith) is calculated, and it is in good agreement with that of MD simulation. (C) 2008 Elsevier B.V. All rights reserved.