反平面扩展裂纹的J积分与COD

给出一个以任意速率扩展的反平面裂纹与路径无关的Ｊ积分，证明Ｊ积分扩展裂纹尖端的张开位移（动态ＣＯＤ）之间有的简单的关系，Ｊ积分与能量释放率，动应力强度因子之间也有简单关系，利用这些关系，给出了动态ＣＯＤ与动应力强度因子之间的关系式。     

多个纵向环形界面裂纹对P波散射的动应力强度因子

研究多个纵向环形界面裂纹的Ｐ波散射问题。以裂纹面的位错密度函数为未知量,利用Ｆｏｕｒｉｅｒ积分变换,将问题归结为第二类奇异积分方程,然后通过数值求解,获得裂纹尖端的动应力强度因子。最后给出了双裂纹动应力强度因子随入射波频率变化的关系曲线。     

粘弹性胶层中Ⅰ型裂纹的动态扩展

研究粘弹性胶层中Griffith裂纹在Ⅰ型载荷作用下,裂纹尖端动态应力强度因子和能量释放率的时间响应.首先,利用积分变换方法,推导出粘弹性层的控制方程组;其次,引入位错密度函数,并结合边界条件和界面连接条件,导出反映裂纹尖端奇异性的Cauchy型奇异积分方程组,然后,应用Chebyshev正交多项式化奇异积分方程组为代数方程组,并采用Schmidt方法对其数值求解,最后,经过Laplace逆变换,求得动态应力强度因子和能量释放率的时间响应.通过对材料参数的讨论,得到动应力强度因子和能量释放率随剪切松驰参量的减小而增大,随膨胀松弛参量的减小而减小,弹性参数对其影响较小.     

两种正交异性材料界面上裂纹冲击后的动态响应

本文研究了两种不同正交异性材料界面半无限长裂纹，在冲击荷载下的动态弹塑性响应。通过积分变换，Ｗｉｅｎｅｒ－Ｈｏｐｆ方法和Ｃａｇｎｉａｒｄ－ｄｅＨｏｏｐ反演围通技术，求得一般解析解，获得了该裂纹的动应力强度因子；通过采用Ｄｕｇｄａｌｅ模型，建立了裂纹尖端塑性区延伸速度与裂纹扩展速度的关系，以及动态ＣＯＤ与裂纹扩展速度的关系。     

功能梯度压电带中裂纹对SH波的散射

研究功能梯度压电带中裂纹对SH波的散射问题,为了便于分析,材料性质假定为指数模型,并假设裂纹面上的边界条件为电渗透型的.根据压电理论得到压电体的状态方程,利用Fourier积分变换,问题转化为对偶积分方程的求解.用Copson方法求解积分方程.求得了裂纹尖端动应力强度因子、电位移强度因子的解析表达式,最后数值结果显示了标准动应力强度因子与入射波数、材料参数、带宽、波数以及入射角之间的关系.     

界面超高速自相似动态分层分析：反平面情况

对材料界面超高速自相似动态分层的反平面问题进行了解析分析。分层模拟为界面裂纹由零长度自相似扩展，扩展速度为蹭音速或超音速。首先考虑运动集中载荷作用下界面动态分层的情况，利用界面裂纹自相似扩展的运动位错模型将问题归结为奇异积分方程，并求得解析解，分析了裂纹尖端的应力奇性，获得了动应力强度因子。最后，利用叠加原理给出了ｘ＾ｎ型载荷作用下界面动态分层的解。     

SH波与功能梯度材料静止裂纹的相互作用

利用功能梯度材料剪切模量和密度的指数模型，利用积分变换－积分方程方法，对无限大体SH波作用下的功能梯度材料理解纹进行了求解。通过理论分析给出了裂纹尖端的动应力强度因子，通过数值计算给出了材料的剪切模量梯度，频率对动应力强度因子的影响。     

压电材料反平面运动裂纹的能量释放率与分叉角

用复变函数方法,研究了压电材料中反平面运动裂纹的动态断裂问题,研究表明：介质内的耦合场与裂纹运动速度有关,在裂纹尖端有奇异。应力强度因子与裂纹运动速度无关,与纯弹性结构一致,沿裂纹延长线扩展的动态能量释放率可用应力强度因子表示,而与电载荷无关,裂纹运动的高速度具有止裂作用,在一定条件下,裂纹有扩展成曲线裂纹或分叉的趋势。     

拱形试件动态断裂的动光弹分析

本文采用动光弹方法,分析了对带边裂纹的拱形三点弯曲试件在抢击加载条件下的瞬态反应。从多火花动光弹仪记录下来的16幅断裂过程的照片和微机输出的电火花光信号图上,得到了各时刻的等差线图形和裂纹长度。使用运动裂纹尖端附近的应力场解,去计算动应力强度因子。对环氧树脂材料,测定了动态应力强度因子与裂纹扩展速度之间的关系,并给出了当裂纹扩展速度达到410m/s时,为裂纹产生分叉的条件。     

SH波对内含裂纹衬砌结构的散射及动应力集中

当衬砌结构内含裂纹时 ,采用Green函数的方法 ,研究了SH波对裂纹的散射及其动应力集中 ,构造了在含有半圆形衬砌的弹性半空间上 ,在水平面上任一点承受时间谐和出平面线源载荷作用时的位移函数作为Green函数 ;推导了SH波对衬砌内有裂纹的散射定解积分方程组 ,进而求得裂纹尖端的动应力因子 ,重点讨论了衬砌及周围介质对裂纹尖端动应力因子的影响 ,给出了介质参数变化对裂纹尖端动应力因子的影响曲线 ,为工程设计提供了依据。     

The scattering of general SH plane wave by interface crack between two dissimilar viscoelastic bodies

The scattering of general SH plane wave by an interface crack between two dissimilar viscoelastic bodies is studied and the dynamic stress intensity factor at the crack-tip is computed. The scattering problem can be decomposed into two problems: one is the reflection and refraction problem of general SH plane waves at perfect interface (with no crack); another is the scattering problem due to the existence of crack. For the first problem, the viscoelastic wave equation, displacement and stress continuity conditions across the interface are used to obtain the shear stress distribution at the interface. For the second problem, the integral transformation method is used to reduce the scattering problem into dual integral equations. Then, the dual integral equations are transformed into the Cauchy singular integral equation of first kind by introduction of the crack dislocation density function. Finally, the singular integral equation is solved by Kurtz's piecewise continuous function method. As a consequence, the crack opening displacement and dynamic stress intensity factor are obtained. At the end of the paper, a numerical example is given. The effects of incident angle, incident frequency and viscoelastic material parameters are analyzed. It is found that there is a frequency region for viscoelastic material within which the viscoelastic effects cannot be ignored. This work was supported by the National Natural Science Foundation of China (No.19772064) and by the project of CAS KJ 951-1-20     

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出载荷下,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黑社会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分析。     

三点弯曲试样动态应力强度因子计算研究

利用Hopkinson压杆对三点弯曲试样进行冲击加载,采集了垂直裂纹面距裂尖2mm和与裂纹面成60°距裂尖5mm处的应变信号。根据裂尖附近测试的应变信号计算试样的动态应力强度因子,并与有限元计算结果进行比较,结果表明由于裂尖有一段疲劳裂纹区,通过裂尖附近应变信号来计算动态应力强度因子时,如果裂尖位置确定不准及粘贴应变片位置不够准确对计算结果将带来很大影响。因此利用应变片法计算动态应力强度因子时,为了获得更准确的计算结果,在实验后应对试件裂纹面进行分析测量,重新确定裂尖位置,必要时需对应变片至裂尖距离进行修正后再计算动态应力强度因子值。     

Interaction of general plane P wave and cylindrical inclusion partially debonded from its viscoelastic matrix

The interaction of a general plane P wave and an elastic cylindrical inclusion of infinite length partially debonded from its surrounding viscoelastic matrix of infinite extension is investigated. The debonded region is modeled as an arc-shaped interface crack between inclusion and matrix with non-contacting faces. With wave functions expansion and singular integral equation technique, the interaction problem is reduced to a set of simultaneous singular integral equations of crack dislocation density function. By analysis of the fundamental solution of the singular integral equation, it is found that dynamic stress field at the crack tip is oscillatory singular, which is related to the frequency of incident wave. The singular integral equations are solved numerically, and the crack open displacement and dynamic stress intensity factor are evaluated for various incident angles and frequencies. The project supported by the National Natural Science Foundation of China (19872002) and Climbing Foundation of Northern Jiaotong University     

Dynamic crack propagation in a viscoelastic strip

The dynamic propagation of a semi-infinite crack in a finite linear viscoelastic strip subjected to Mode I loading is investigated. Through the use of integral transforms the problem is reduced to solving a Wiener-Hopf equation. The asymptotic properties of the transforms are exploited to establish the stress intensity factor. Plane-stress and plane-strain stress intensity factors as a function of crack speed for both fully-clamped and shear-free lateral boundaries are presented for the standard linear viscoelastic solid. Comparisons are made with previously obtained asymptotic stress intensity factors and with stress intensity factors for the equivalent elastic strips.     

Viscoelastic composite with a cracked layer under anti-plane shear

A viscoelastic cracked sandwich composite under anti-plane load is presented via the application of the Laplace transform and the complex variable formulation. Using a special technique of analytical continuation associated with the method of image, the triple-layered problem is reduced to a singular function by simple algebraic manipulations. The superposition method and the singular integral equation is applied to deal with the concentrated load and crack problem. Finally, some typical viscoelastic models and its corresponding stresses and stress intensity factors are also discussed. The results show that the time dependent stress intensity factor is affected by the relative strength of creep compliances of each layer.     

The dynamic behavior of two collinear interface cracks in magneto-electro-elastic materials

In this paper, the dynamic behavior of two collinear symmetric interface cracks between two dissimilar magneto-electro-elastic material half planes under the harmonic anti-plane shear waves loading is investigated by Schmidt method. By using the Fourier transform, the problem can be solved with a set of triple integral equations in which the unknown variable is the jump of the displacements across the crack surfaces. To solve the triple integral equations, the jump of the displacements across the crack surface is expanded in a series of Jacobi polynomials. Numerical solutions of the stress intensity factor, the electric displacement intensity factor and the magnetic flux intensity factor are given. The relations among the electric filed, the magnetic flux field and the stress field are obtained.     

A contour integral method for dynamic stress intensity factors

The contour integral method previously used to determine static stress intensity factors is applied to dynamic crack problems. The required derivatives of the traction in the reference problem are obtained numerically by the displacement discontinuity method. Stress intensity factors are determined by an integral around a contour which contains a crack tip. If the contour is chosen as the outer boundary of the body, the stress intensity factor is obtained from the boundary values of traction and displacement. The advantage of this path-independent integral is that it yields directly both the opening-mode and sliding-mode stress intensity factors for a straight crack. For dynamic problems, Laplace transforms are used and the dynamic stress intensity factors in the time domain are determined by Durbin's inversion method. An indirect boundary element method, incorporating both displacement discontinuity and fictitious load techniques, is used to determine the boundary or contour values of traction and displacement numerically.