It is difficult to obtain J-integral values (J-values) for materials using various types of constitutive equations without performing numerical analyses. In this study, the reference plastic slope (RPS) method was applied to obtain J-values for engineering materials, for which the deformation property was expressed by a poly-linear stress-strain curve. The RPS method derives the J-value using bi-linear stress-strain curves obtained from the original stress-strain curve. First, the basic concept and characteristics of the RPS method is explained. It is shown that well-approximated J-values were obtained by assuming bi-linear stress-strain curves whose plastic slope were determined using the reference stress for representative materials (three carbon steels and two stainless steels). Second, it is demonstrated that the J-values for bi-linear stress-strain curves could be estimated by relatively simple equations for a center cracked plate subjected to a tensile load. Third, to apply the RPS method for practical problems, the equations are developed to estimate the J-values for bi-linear stress-strain curves for a straight pipe with a circumferential crack subjected to a tensile or bending load. Finally, it is confirmed that the developed equations could predict the failure load of which error was within 10% at the most unconservative case.

在不进行数值分析的情况下，使用各种类型的本构方程很难获得材料的J积分值（J值）。在这项研究中，参考塑性斜率（RPS）方法用于获得工程材料的J值，其变形特性由多线性应力-应变曲线表示。RPS方法使用从原始应力应变曲线获得的双线性应力应变曲线得出J值。首先，说明RPS方法的基本概念和特征。结果表明，假设双线性应力-应变曲线的塑性斜率是使用代表性材料（三种碳钢和两种不锈钢）的参考应力确定的，则获得了近似的J值。第二，结果表明，双线性应力-应变曲线的J值可以通过相对简单的方程式估算中心开裂板在拉力作用下的值。第三，为了将RPS方法应用于实际问题，建立了方程式，以估计具有拉伸或弯曲载荷的圆周裂纹的直管的双线性应力-应变曲线的J值。最后，可以肯定的是，在最不保守的情况下，所开发的方程可以预测其误差在10％以内的失效载荷。建立方程式以估计具有拉伸或弯曲载荷的圆周裂纹的直管的双线性应力-应变曲线的J值。最后，可以肯定的是，在最不保守的情况下，所开发的方程可以预测其误差在10％以内的失效载荷。建立方程式以估计具有拉伸或弯曲载荷的圆周裂纹的直管的双线性应力-应变曲线的J值。最后，可以肯定的是，在最不保守的情况下，所开发的方程可以预测其误差在10％以内的失效载荷。