无限长条板中弹性与粘弹性界面裂纹尖端场

研究无限长条板中粘弹性-弹性界面Griffith裂纹在 Ⅰ 型突加载荷作用下,裂纹尖端动态应力强度因子的时间响应。利用积分变换方法、Fourier和Laplace变换,分别推导出了弹性和粘弹性问题的控制方程组;引入位错密度函数,并结合边界条件,导出了反映裂纹尖端奇异性的Cauchy型奇异积分方程组,运用Chebyshev正交多项式化奇异积分方程组为代数方程组,用配点法进行求解;最后用Laplace积分变换数值反演方法,将拉氏域内的解反演到时间域内,求得动态应力强度因子的时间响应,并对材料参数的影响进行了分析。结果表明,剪切松弛参量对 Ⅰ 型动应力强度因子的影响小于对 Ⅱ 型的影响,而膨胀松弛参量对 Ⅰ 型动应力强度因子的影响大于对 Ⅱ 型的影响。 

INTERFACE CRACK-TIP FIELD BETWEEN ELASTIC AND VISCOELASTIC MATERIALS IN AN INFINITE LENGTH STRIP

The dynamic stress intensity factor was studied about the Griffith crack between elastic and visco-elastic layers in an infinite length strip under impact load. The controlling equations expressed by the displacement of elastic and viscoelastic materials were deduced separately after using Laplace and Fourier integral transforms of the basic equations. The displacements in the Laplace domain were obtained by inverse Fourier integral transform;uniting the constitutive and geometrical equations, the analytical expressions of stress in Laplace domain were derived. By defining a dislocation density function, the Cauchy singular integral equations were given according to the boundary conditions and the problem was reduced to algebraic equations using Chebyshev orthogonal polynomial; then it can be solved with the method of collocation dots in the Laplace domain. The time response of the dynamic stress intensity factor was calculated with the numerical method and the influence of material parameters on it was analyzed. The results show that the influence of the shear relaxation parameter on mode Ⅰ dynamic stress intensity factor is bigger than on mode Ⅱ ,and the influence of the swelling relaxation parameter is opposite.