The mixed yield surfaces of fcc single crystals for slip on ｛111｝〈110〉 and mechanical twinning on ｛111｝〈112〉 systems have been derived when their critical resolved shear stresses are equal. It has been found that there are 259 stress states that can be classified into 21 groups according to the crystal symmetry. Each group activates 5, 6 or 8 slip or/and twinning systems depending on crystallographically non equivalent slip or/and twinning systems groups. Among all those stress states, 3 groups activate 8 systems, including 21 stress states; 9 groups activate 5 systems, including 70 ones; the remaining 9 groups activate 5 systems, including 168 ones.
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