基于应力梯度的Ⅰ型中心裂纹应力强度因子修正方法分析

Analysis of Stress Intensity Factor Correction Method for Mode I Central Crack Based on Stress Gradient

基于无限大板Ⅰ型中心裂纹尖端附近非均匀应力分布规律,提出一种考虑应力梯度影响的应力强度因子计算方法。首先,利用校正的Westergaard应力函数求解单向拉伸Ⅰ型裂纹尖端附近应力场,分析其对裂纹扩展的作用,采用应力与距离分离形式,更加凸显因距离r值的大小而引起应力发生变化的本质原因;其次,提出应力系数函数用以表征应力场的变化,考虑当相对应力系数梯度函数值变化1%时,应力梯度变化对裂纹的扩展无影响,并定义为特征距离r eff,以此范围内平均应力去修正应力强度因子K;最后,以20Cr钢为研究对象验证本文方法的正确性和可行性,结果表明:本文计算方法得到的应力强度因子为经典断裂学方法的1.22倍,主要原因是考虑了应力梯度的影响,裂纹尖端附近实际承受的应力增大,应力强度因子增大。

Based on the non-uniform stress distribution near the tip of modeⅠcentral crack in infinite plate,a method for calculating stress intensity factor considering the influence of stress gradient is proposed.Firstly,the stress field near the tip of modeⅠcrack under uniaxial tension is solved by using the corrected Westergaard stress function,and its effect on crack propagation is analyzed.The stress and distance separation form are adopted,which highlights the essential reason of stress change caused by the value of distance r.Secondly,a stress coefficient function is proposed to characterize the change of stress field.Considering that the change of stress gradient has no effect on crack propagation when the value of relative stress coefficient gradient function changes by 1%,it is defined as the characteristic distance r eff,and the stress intensity factor K is corrected by the average stress within this range.Finally,the correctness and feasibility of the proposed method are verified by taking 20Cr steel as the research object and the results show that the stress intensity factor obtained by this method is 1.22 times that of the classical fracture method.The main reason is that the influence of stress gradient is considered,and the actual stress near the crack tip increases and the stress intensity factor increases.