基于修正最小应变能密度因子准则下的Ⅰ型裂纹研究

Study on mode I crack based on modified minimum strain energy density factor criterion

扩展应变能密度因子准则首次引入体积改变比能密度因子权重系数β,分析体积与形状改变比能权重对于裂纹扩展形式的影响。基于扩展应变能密度因子准则,考虑Williams应力函数中常忽略的非奇异项部分影响,对最小应变能密度因子准则进行修正完善。探究泊松比μ与权重系数β影响下,纯I型裂纹起裂角随T应力变化规律,并采用形状改变比能准则求得T应力下纯I型裂纹实际临界应力强度因子KIf较传统断裂韧度KIc的比值。研究结果表明:针对纯I型裂纹,修正后的最小应变能密度因子准则对于裂纹起裂角的预测较传统理论的预测精度显著提升。当β值趋于1时,裂纹起裂角随T应力增加过程存在明显的激增现象,起裂角度激增时刻对应的T应力随泊松比μ的增加而增加。当β值趋于0时,起裂角激增现象减弱,与最大周向应力准则(MTS)下曲线变化规律吻合。

Considering the non-singular part of Williams stress function which is often neglected, the traditional strain energy density factor theory is modified by introducing the volume change specific energy weight coefficient β. Under the influence of Poisson’s ratio μ and weight coefficient β, the crack initiation angle of pure mode I crack varies with T-stress, and the actual critical stress intensity factor KIf of pure mode I crack under T-stress is obtained by using the shape change specific energy criterion compared with the traditional fracture toughness KIc. Results show that the modified minimum strain energy density factor theory can significantly improve the prediction accuracy of crack initiation angle for pure mode I crack. As β approaches 1, the crack initiation angle increases sharply with the increase of T-stress, and the critical sensitivity of T-stress increases with the increase of Poisson’s ratio. As the value of β tends to zero, the phenomenon of sharp increase of initiation angle decreases, which coincides with the curve change rule under MTS criterion.