周期裂纹和刚性线尖端场干涉效应研究

STUDY ON THE INTERACTION OF TIP FIELDS BETWEEN PERIODIC CRACKS AND PERIODIC RIGID LINE INCLUSIONS

研究双周期裂纹和刚性线夹杂非均匀材料的反平面剪切问题.基于保角变换技术和椭圆函数理论,获得了问题应力场的全场精确解,给出了裂纹和刚性线尖端应力强度因子的封闭形式解答,讨论了裂纹和刚性线尖端场的干涉效应.数值结果表明:改变水平和垂直分布周期对裂纹和刚性线尖端场影响明显不同;裂纹长度2a逐渐增大时(0≤a/ω1≤0.5),裂纹尖端应力强度因子从1逐渐增大到无限大,而刚性线的尖端场变化不大;刚性线长度2d逐渐增大时(0≤d/ω2≤1),刚性线尖端应力强度因子逐渐减小,而裂纹的尖端场仅略微增大.

The problem about a doubly periodic array of cracks and rigid line inclusions in an infinite medium under far-field antiplane shear is solved.By employing the conformal mapping technique and the elliptical function theory,an exact solution of the full field stress is obtained.A closed form expression for the stress intensity factor at the tips of cracks and rigid line inclusions are presented.Based on these,the interaction of the tip fields between cracks and rigid line inclusions is carefully discussed.Our results show that:(a)the tip fields of cracks and rigid line inclusions show different laws when their horizontal and vertical distribution periods change;(b)with the increase of the length of cracks 2a(0≤a/ω1≤0.5),the stress intensity factor of cracks increases monotonously,whereas the stress intensity factor of rigid line inclusions is almost not changed;(c)when the length of rigid line inclusions 2d(0≤d/ω2≤1)increases,the stress intensity factor of rigid line inclusions gradually decreases from 1to 0,whereas the stress intensity factor of cracks is only slightly increased.