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分析和计算了ｆｃｃ金属｛１１１｝<１１０>滑移和｛１１１｝<１１２>孪生的单晶共生屈服应力状态（屈服顶点），求出了相应的活化系及５个独立活化系的组合数，结果表明，只有当孪生与滑移的临界切应力之比为１／≤ξ≤２／时，滑移和孪生才可能同时发生；证明了在此范围内仅存在两种类型的屈服应力状态，并且求出了相应的解析表达式当／２＜ξ＜２／时，总共有２５９种应力状态，在应力空间按晶体结构对称性加以分类，可分为２１组；当１／＜ξ＜／２时，也有２５９种共生屈服应力状态，但分为１９组在这两种类型的屈服应力状态中，１３９种是相同的，１２０种不同，它们分别活化５；６或８个滑移或孪生系，依赖于结晶学上不等价的滑移及孪生系组。
The single crystal symbiotic yield stress state (yield apex) of {111} <110> slippage and {111} <112> twin of fcc metal was analyzed and calculated. The number of combinations of the corresponding activation system and five independent activation systems The results show that slippage and twins are likely to occur simultaneously only when the critical shear stress ratio between twin and slip is 1 / ≤ξ ≤ 2 /; it is proved that there are only two types of yield stress states in this range , And the corresponding analytic expression is obtained. When / 2 <ξ <2 /, a total of 259 stress states are classified into 21 groups according to the crystal structure symmetry in the stress space. When 1 / <ξ < / 2, there are also 259 symbiotic yielding states but 19 groups out of the 19 groups are the same for both types of yield stress conditions, 120 are different and they respectively activate 5; 6, or 8 slip or Twinning, relying on the crystallographic inequality of slippage and twinning.