T应力作用下的J积分理论研究  

Theoretical Study on J-integral Subjected to T-stress

作　　者：谌赫 魏豪杰[1] 王文胜[1] CHEN He;WEI Haojie;WANG Wensheng(School of Civil Engineering and Architecture,Henan University of Scince and Technology,Luoyang 471023,China)

机构地区：[1]河南科技大学土木建筑学院,河南洛阳471023

出　　处：《河南科技大学学报（自然科学版）》2024年第2期44-55,M0005,共13页Journal of Henan University of Science And Technology:Natural Science

基　　金：国家自然科学基金项目(51875197)。

摘　　要：T应力是表征裂尖应力场所必需的物理量之一,在其作用下J积分的性质有待研究。推导了J积分在考虑T应力情况下的表达式,采用数值模拟方法在Ⅰ型、Ⅱ型和Ⅰ+Ⅱ复合型加载工况下对该表达式进行验证,给出一种基于J积分的裂尖应力场参数计算方法。理论推导证明,J1积分的路径守恒性不受T应力影响,但J2积分的数值与积分路径起止点到裂尖距离r的平方根之间满足线性关系,J2-r曲线的系数与T应力相关。有限元仿真结果表明,试样裂纹长度对J积分的影响较为显著,网格尺寸对J积分计算结果的影响很小;相同载荷工况下,不同尺寸试样的J积分数值不同,但J2-r曲线的变化趋势与理论推导的表达式相符;在Ⅱ型和Ⅰ+Ⅱ复合型载荷工况下,T应力的求解精度较高,而在Ⅰ型载荷工况下,J2≈0,受舍入误差等因素影响,求解精度降低。T-stress is one of the necessary physical quantities to characterize the stress field at the crack tip,and the properties of J-integral under its action remain to be investigated.The expression of J-integral considering T-stress was derived in this paper.The numerical simulation method was used to verify the expression under mode I,mode II and mixed mode I+II loading conditions,and a calculation method of crack tip stress field parameters based on J-integral was given.The theoretical derivation proves that the path conservation of the J 1-integral is not affected by T-stress,but the value of the J 2-integral meets the linear relationship with the square root of the distance from the start and end point of the integral path to the crack tip,and the coefficient of J 2-r curve is related to T-stress.The finite element simulation results show that the crack length of the specimen has a significant effect on the J-integral,while the mesh size has a small effect on the J-integral calculation results.Under the same loading condition,J-integral values of different sizes specimens are different,but the trend of J 2-r curve change is consistent with the expression derived from theory.Under modeⅡand mixed modeⅠ+Ⅱloading conditions,the solving accuracy of T-stress is high,while under modeⅠloading conditions,J 2≈0,the solving accuracy is reduced due to factors such as rounding error.

关 键 词：J积分 T应力 复合型断裂 数值模拟 

分 类 号：O34[理学—固体力学]