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1968年赖斯应用全量理论,避开求解裂纹尖端塑性应力场时数学上的困难,提出了解决平面裂纹问题的J积分。其中:是裂纹体中单值应变能密度数函。同时,供出了小范围屈服时的能量解释。 J积分是围绕裂纹尖端任意回路的能量线积分,它与能量的变化极为密切。本文试图从能量的观点出发,由缺口试件能量(势能)变化,扩充到裂纹体,导出能量(势能)变化和J积分的一般关系式,以加位对积分物理意义的认识。
In 1968, Rice applied the full theory to avoid the mathematical difficulties in solving the plastic stress field at crack tip, and proposed J-integral to solve the plane crack problem. Where: is a single value of strain energy density function in a cracked body. At the same time, a small-scale yield energy explanation is given. J Integral is the integral of the energy line around any crack tip, which is very close to the energy change. This paper attempts to extend the energy (potential energy) of the notched specimen to the crack body from the energy point of view and derive the general relation between the energy (potential energy) change and the J integral, so as to add the understanding of the physical meaning of the integral.