复合材料Ⅰ+Ⅱ混合型周期平行裂纹尖端场  

Crack-Tip Field for ModeⅠ + Ⅱ Periodic Parallel Crack of Composite Materials

作　　者：余路娟 张雪霞[1] 赵文彬[1] 李婵[1] 

机构地区：[1]太原科技大学应用科学学院,太原030024

出　　处：《太原科技大学学报》2014年第3期221-225,共5页Journal of Taiyuan University of Science and Technology

基　　金：太原科技大学博士启动基金(20122005);太原科技大学研究生科技创新项目(20125027;20111028)

摘　　要：研究了裂纹面内均匀载荷作用下的正交各向异性复合材料板周期平行裂纹尖端场问题。利用复变函数方法,将力学问题化为偏微分方程边值问题。根据叠加原理,将偏微分方程边值问题化为Ⅰ型和Ⅱ型两个边值问题求解。在复数域内,利用双曲函数的周期性,通过构造适当的Westergaard应力函数,将周期平行裂纹尖端场问题化为单一裂纹尖端场问题。得到混合型周期平行裂纹尖端附近的应力强度因子和应力场的解析表达式。由于平行裂纹的周期性分布,应力强度因子的大小取决于形状因子。所得结果表明,当裂纹间距趋于无穷大时,应力强度因子退化为含单个中心裂纹时的结果,并且所得到的解析解更好的体现了平行裂纹分布的周期性。研究结果为结构和材料的强度设计提供了有意义的参考。The problem for periodic parallel cracks in an orthotropic composite plate subjected to the uniformly distributed load within the cracks surface is studied. The complex function method is used to turn the mechanical problem into the boundary value problem of partial differential equation. The superposition principle is used to convert the boundary value problem of partial differential equation into those of mode Ⅰ and mode Ⅱ. In the complex domain, by using the periodicity of the hyperbolic function and constructing proper Westergaard stress function, the tip field problem of periodic parallel cracks is turned into a tip field problem of a single crack. The analytic expressions for stress intensity factor and stress field of the mixed mode periodical parallel cracks-tip are achieved. Due to the periodicity of parallel crack distribution, the stress intensity factor depends on the shape factor. The result showed that when the distance between the cracks tends to infinity, the stress intensity factor is degenerated into a single central crack situation, and the analytic solutions obtained can well reflect the periodicity of parallel crack distribution. In addition, the present solution can be used to study the structural integrity assessment.

关 键 词：正交各向异性板 均匀载荷 混合型裂纹 应力强度因子 复变函数方法 

分 类 号：TB332[一般工业技术—材料科学与工程]