剪应力作用下Ⅱ型平行节理扩展模式的分叉研究

Bifurcation condition of crack pattern in two-dimensional parallel cracks under far field shear stress

利用伪力法考虑了剪应力作用下Ⅱ型平行节理之间的相互作用,提出利用节理的长度和间距之比,λ=a/H,来确定平行裂纹发生分叉的条件。从理论上研究了2条,3条和任意多条平行节理在剪应力作用下的分叉。对于2条平行节理,当节理的长度和间距之比λcrp大于0.816 497 5时,节理的扩展模式要发生分叉;对于3条平行节理,当节理的长度和间距之比λcpr大于0.717 572 8时,节理的扩展模式要发生分叉;对于无穷多条平行节理,当节理的长度和间距之比λcrp大于0.636 638 5时,节理的扩展模式要发生分叉。计算了2条到150条平行节理的分叉问题,结果表明节理数越大,节理发生分叉时节理的长度和间距之比越小。

The interaction among cracks is studied by using pseudo-traction method. Bifurcation condition of crack growth pattern can be expressed by the crack length/spacing ratio, λ = H / a. The interution among cracks leads to bifurcation of crack growth patterns if λ is larger than a critical value λ^p cr. Bifurcation condition for arrays of 2 parallel cracks, arrays of 3 parallel cracks and arrays of infinite arrays of cracks subjected to shear stress is analysed theoretically. The value of λ^p cr is 0.816 497 5,0.717 572 8 and 0.636 638 5 for arrays of 2 parallel cracks, arrays of 3 parallel cracks and arrays of infinite arrays of cracks respectively. The numerical results show that the value of λ^P cr decreases with increasing the number of cracks.