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从Ｊ积分定义出发，应用数学分析方法给出裂纹体受任意一空间载荷作用时的复合型Ｊ积分ＪＭ与各类载荷分量单独作用时的Ｊ积分之间的关系式。各载荷下的Ｊ积分均具有守恒性。用有限元方法对一种材料、两种结构的试样在复合型载荷作用下Ｊ积分的守恒性进行了分析和验证，对Ｊ积分概念在复合型弹塑性断裂分析中的应用及复合型Ｊ判据的建立进行了讨论。
Based on the definition of J integral, the relationship between J integral JM and the J integral when all kinds of load components act alone are given by mathematical analysis method when any crack is subjected to any space load. The J integral under each load is conserved. The finite element method is used to analyze and verify the J-integral conservation of a material and two kinds of structures under the composite load. The application of the J-integral concept in compound elasto-plastic fracture analysis and the composite J The establishment of the criteria was discussed.