承受双向等拉应力的平面应变I型裂纹线弹性断裂的I_(1)准则与K准则一致性分析  

Consistency Analysis of I_(1) and K Criterions for Linear Elastic Fracture of Plane Strain Mode I Crack Subjected to Bidirectional Equal Tensile Stress

作　　者：薛钢 XUE Gang(Luoyang Ship Material Research Institute,Luoyang 471023,China)

机构地区：[1]中国船舶集团有限公司第七二五研究所,河南洛阳471023

出　　处：《材料开发与应用》2023年第1期1-8,共8页Development and Application of Materials

摘　　要：采用线弹性有限元方法计算了承受双向等拉应力的平面应变I型裂纹的应力场,分析了裂纹尖端各应力分量间的关系,拟合了各非零应力分量关于裂纹半长度a和裂纹尖端最小网格尺寸l1的函数,分析了应力第一不变量I_(1)与应力场强度因子KI的相关性。结果表明,裂纹尖端各非零应力分量间存在稳定的比例关系;各非零应力分量值和加载应力的比值与裂纹半长度a的1/2次幂呈正比例关系、与裂纹尖端最小网格尺寸l1的1/2次幂呈反比例关系;相同最小网格尺寸条件下,裂纹尖端的应力第一不变量与应力场强度因子的比值l1/KI为与加载应力和裂纹长度无关的常数,证明了承受双向等拉应力的平面应变I型裂纹线弹性断裂的I_(1)准则与K准则具有一致性。The stress field of plane strain mode I crack with bidirectional tensile stress is calculated by using linear elastic finite element method,the relationship between stress components at crack tip is analyzed,the function of each non-zero component stress about half of crack length a and minimum grid size l1 at crack tip is fitted,and the correlation between first invariant of stress I_(1) and stress field intensity factor KI is analyzed.The results show that there is a stable proportional relationship among the non-zero stress components at the crack tip.The ratio of the non-zero stress component and the loading stress is proportional to the 1/2 power of half length of crack a,and is antiproportional to the 1/2 power of minimum mesh size at crack tip l1.Under the same minimum mesh size condition,the ratio I_(1)/KI of the first invariant of stress at crack tip to the intensity factor of stress field is a constant independent of the loading stress and crack length,confirming the consistency of the I_(1) and K criterions for linear elastic fracture of plane strain mode I crack subjected to bidirectional equal tensile stress.

关 键 词：I型裂纹 线弹性断裂 I_(1)断裂准则 K准则 

分 类 号：TG113.252[金属学及工艺—物理冶金]