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用数学分析方法论证了焊缝区有垂直裂纹时J积分的守恒性，又用弹塑性有限元方法进行了数值验证．首次提出了J积分与路径有关的理论证明，为J积分在压力容器缺陷安全评定的应用提供了必要的依据．
Mathematical analysis method is used to demonstrate the conservation of J-integral when there is vertical crack in the weld zone, and the numerical simulation is done by the elastoplastic finite element method. It is the first time to put forward the theoretical proof of J integral and path, which provides the necessary basis for the application of J integral in the safety assessment of pressure vessel defects.