| 单轴拉伸破坏 | $\left[ \begin{array}{c} \sigma _1^{\rm{p} }\\ \sigma _2^{\rm{p} }\\ \sigma _3^{\rm{p} }\\ \end{array} \right] = \left[ \begin{array}{c} \sigma _1^{\rm{p} }\\ 0\\ 0\\\end{array} \right]$ | $\left[ \begin{gathered} \sigma _1^{\rm{r} } \\ \sigma _2^{\rm{r} } \\ \sigma _3^{\rm{r} } \\\end{gathered} \right] = \left[ \begin{gathered} \dfrac{ {\left( {1+2\beta } \right)\sigma _1^{\rm{p} } } }{3} \\ \dfrac{ {\left( {1 - \beta } \right)\sigma _1^{\rm{p} } } }{3} \\ \dfrac{ {\left( {1 - \beta } \right)\sigma _1^{\rm{p} } } }{3} \\ \end{gathered} \right] $ | $\left. {\begin{array}{*{20}{l} }\;\;\;{f_{\rm{p} }^{ {\rm{M} } - {\rm{C} } }\left( { {\sigma ^{\rm{p} } } } \right) = \sigma _1^{\rm{p} } - \dfrac{ {2{c _{\rm{p} } } \cdot \cos {\varphi _{\rm{p} } } } }{ {1 + \sin {\varphi _{\rm{p} } } } } = 0},\\\begin{array}{l}f _{\rm{r} }^{M - C}\left( { {\sigma ^{\rm{r} } } } \right) = \dfrac{ {\left( {1 + 2\beta } \right)\sigma _1^{\rm{p} } } }{3} - \dfrac{ {1 - \sin {\varphi_{\rm{r} } } } }{ {1 + \sin {\varphi_{\rm{r} } } } }\dfrac{ {\left( {1 - \beta } \right)\sigma _1^{\rm{p} } } }{3} - \dfrac{ {2{c _{\rm{r} } } \cdot \cos {\varphi_{\rm{r} } } } }{ {1 + \sin {\varphi_{\rm{r} } } } } = 0.\end{array}\end{array} } \right\}$ | 错误。除了主拉应力方向，横向应力方向也存在残余应力，与事实不符 |
| 单轴压缩破坏 | $\left[ \begin{array}{c} \sigma _1^{\rm{p} }\\ \sigma _2^{\rm{p} }\\ \sigma _3^{\rm{p} }\\\end{array} \right] = \left[ \begin{array}{c} 0\\ 0\\ \sigma _3^{\rm{p} }\\ \end{array} \right]$ | $\left[ \begin{gathered} \sigma _1^{\rm{r} } \\ \sigma _2^{\rm{r} } \\ \sigma _3^{\rm{r} } \\ \end{gathered} \right] = \left[ \begin{gathered} \dfrac{ {\left( {1 - \beta } \right)\sigma _3^{\rm{p} } } }{3} \\ \dfrac{ {\left( {1 - \beta } \right)\sigma _3^{\rm{p} } } }{3} \\ \dfrac{ {\left( {1+2\beta } \right)\sigma _3^{\rm{p} } } }{3} \\ \end{gathered} \right]$ | $\left. {\begin{array}{*{20}{l} }\;\;\;{f_{\rm{p} }^{ {\rm{M} } - {\rm{C} } }\left( { {\sigma ^{\rm{p} } } } \right) = \left( {\sin {\varphi _{\rm{p} } } - 1} \right)\sigma _3^{\rm{p} } - 2{c _{\rm{p} } } \cdot \cos {\varphi _{\rm{p} } } = 0},\\\begin{array}{l}f _{\rm{r} }^{ {\rm{M} } - {\rm{C} } }\left( { {\sigma ^{\rm{r} } } } \right) = \dfrac{ {\left( {1 - \beta } \right)\sigma _3^{\rm{p} } } }{3} - \dfrac{ {1 - \sin {\varphi_{\rm{r} } } } }{ {1 + \sin {\varphi_{\rm{r} } } } }\dfrac{ {\left( {1 + 2\beta } \right)\sigma _3^{\rm{p} } } }{3} - \dfrac{ {2{c _{\rm{r} } } \cdot \cos {\varphi_{\rm{r} } } } }{ {1 + \sin {\varphi_{\rm{r} } } } } = 0.\end{array}\end{array} } \right\}$ | 错误。除了主压应力方向，横向应力方向也存在残余应力，与事实不符 |
| 二向纯剪破坏 | $\left[ \begin{array}{c} \sigma _1^{\rm{p} }\\ \sigma _2^{\rm{p} }\\ \sigma _3^{\rm{p} }\\\end{array} \right] = \left[ \begin{array}{c} \sigma _1^{\rm{p} }\\ 0\\ - \sigma _1^{\rm{p} }\\ \end{array} \right]$ | $\left[ \begin{array}{c} \sigma _1^{\rm{r} } \\ \sigma _2^{\rm{r} } \\ \sigma _3^{\rm{r} } \\ \end{array} \right] = \left[ \begin{array}{c} \beta \sigma _1^{\rm{p} } \\ 0 \\ - \beta \sigma _1^{\rm{p} } \\\end{array} \right]$ | $\left. {\begin{array}{*{20}{l} } {f_{\rm{p} }^{ {\rm{M} } - {\rm{C} } }\left( { {\sigma ^{\rm{p} } } } \right) = \sigma _1^{\rm{p} } - \dfrac{ {1 - \sin {\varphi_{\rm{r} } } }}{ {1+\sin {\varphi_{\rm{r} } } }}\left( { - \sigma _1^{\rm{p} } } \right) - \dfrac{ {2{c _{\rm{p} } } \cdot \cos {\varphi _{\rm{p} } } }}{ {1+\sin {\varphi _{\rm{p} } } }} = 0}, \\ {f _{\rm{r} }^{ {\rm{M} } - {\rm{C} } }\left( { {\sigma ^{\rm{r} } } } \right) = \beta \sigma _1^{\rm{p} } - \dfrac{ {1 - \sin {\varphi_{\rm{r} } } }}{ {1+\sin {\varphi_{\rm{r} } } }}\left( { - \beta \sigma _1^{\rm{p} } } \right) - \dfrac{ {2{c _{\rm{r} } } \cdot \cos {\varphi_{\rm{r} } } }}{ {1+\sin {\varphi_{\rm{r} } } }} = 0}.\end{array} } \right\}$ | 正确。残余阶段满足二向纯剪的应力状态，与事实相符 |