功能梯度条共线Griffith裂纹反平面剪切冲击

研究正交各向异性功能梯度条中多个共线Griffith裂纹的反平面剪切冲击问题．材料两个方向的剪切模量假定按比例同时以特定的梯度变化．采用Laplace和Fourier变换及引进位错密度函数将问题化为求解Cauchy奇异积方程，进而化为代数方程数值求解．考查材料非均匀性、正交性和功能梯度条高度对裂尖动态断裂特性的影响．动应力强度因子的数值结果显示：增加剪切模量的梯度和(或)增加垂直于裂纹面方向的剪切模量，可以抑制动应力强度因子的幅度；若功能梯度条较薄，增大条形域的高度也可抑制裂纹扩展．

ANTIPLANE SHEAR IMPACT OF COPLANAR GRIFFITH CRACKS IN A FUNCTIONALLY GRADED STRIP

From the viewpoints of applied mechanics, Functionally Graded Materials (FGMs) are nonhomo-geneous solids. The nonhomogeneity of FGMs has a great influence on their mechanical behavior, especially when the components made of FGMs involve cracks. Recent years, great attentions have been paid to the fracture behavior of FGMs. However, the studies are mainly concentrated on the isotropic cases and the static problems. Reports on dynamic fracture mechanics of anisotropic FGMs are very few. On the other hand, up to now, most of the existing solutions to crack problems related to FGMs usually assume that the materials are unbounded in all directions. However, the FGMs used in the engineering structure are usually finite in some directions. In this paper, the antiplane shear impact response of coplanar Griffith cracks in an orthotropic functionally graded strip is studied. The number of cracks is arbitrary. The main objective is to reveal the effects of nonhomogeneity, orthotropy and highness of the strip on the dynamic fracture mechanics. The shear moduli in two directions of the material are respectively assumed to vary proportionately as a definite gradient. Laplace transform, Fourier transform and dislocation density function are introduced to reduce the problem to a Cauchy singular integral equation, which can be numerically solved to calculate the dynamic stress intensity factor. Numerical results show that the peak of dynamic stress intensity factor can be suppressed by increasing the shear modulus' gradient and/or increasing the shear modulus in the direction perpendicular to crack surface and that if the strip is thinner, increasing the strip's highness can also reduce the peak value of the dynamic stress intensity factor.