Co-yield surfaces for {111}〈110〉 slip and {111}〈112〉 twinning in fcc metals

Abstract

The co-yield surfaces in fcc single crystals for slip on 〈1111〈1〈110〉 and twinning on {111}〈112〉 systems have been analyzed and derived systematically for the first time. The results demonstrated that only if the ratio ξ of the critical resolved shear stress (CRSS) for twinning to that for slip is within the range of $1/\sqrt 3 \leqslant \xi \leqslant 2/\sqrt 3$, slip and twinning can occur together. There are only two types of co-yield surfaces when ξ is within this range. The corresponding analytical expressions of all possible types of yield vertices are also derived and tabulated. One type consists of 259 co-yield stress states when $\sqrt 3 /2 < \xi < 2/\sqrt 3$, which can be classified into 21 groups in stress space according to the crystal symmetry. The other type contains 259 co-yield stress states also when $1/\sqrt 3 < \xi < \sqrt 3 /2$, which can be subdivided into 19 groups. Of the two types of the co-yield stress states, 139 ones are common and 120 ones are different.