粘弹性胶层中Ⅰ型裂纹的动态扩展

THE DYNAMIC GROWTH OF MODE Ⅰ CRACK IN VISCO-ELASTIC LAYER

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.

The dynamic stress intensity factor and energy release rate were studied about the Griffith crack in visco-elastic layer under mode Ⅰ load. Firstly, using integral transform, the controlling equations expressed by displacement of viscoelastic layer were deduced. Secondly, by applying inverse Fourier integral transform to the displacement,and uniting the constitutive and geometrical equations, the analytical expression of stress in Laplace domain were derived. Thirdly, by defining dislocation density functions, the Cauchy singular integral equations were obtained according to the boundary condition and interface connection conditions,and the problem was reduced to algebraic equations by Chebyshev orthogonal polynomial. Based the these,the unknown coefficient of the algebraic equations can be solved by Schmidt method. Finally, the time response of dynamic stress intensity factor and energy release rate are obtained by inverse Laplace transform. By analyzing of materials parameters,Some conclusions can be reached as the mode Ⅰ dynamic stress intensity factor and energy release rate increases with decreasing shear relaxation parameter, and decreases with decreasing swelling relaxation parameter, however elastic parameter have little influence on it.