# Competition among basal, prism, and pyramidal slip modes in hcp metals

Research paper by G. Y. Chin, W. L. Mammel

Indexed on: 01 Feb '70Published on: 01 Feb '70Published in: Metallurgical and Materials Transactions B

#### Abstract

The competition of slip among$$(0001)\left\langle {2\bar 1\bar 10} \right\rangle , \left\{ {01\bar 10} \right\}\left\langle {2\bar 1\bar 10} \right\rangle$$, and$$\left\{ {01\bar 11} \right\}\left\langle {2\bar 1\bar 10} \right\rangle$$ slip modes of hcp metals has been analyzed geometrically in terms of a critical resolved shear stress, CRSS, criterion. Under the action of an applied stress slip systems of one or more modes may be activated depending on the value of the CRSS and on the orientation of the slip systems with respect to the applied stress. If the CRSS of a given slip mode should exceed a limiting value relative to the CRSS of the other modes, however, the given mode becomes inoperative even under the most favorably stressed conditions. It is found by an examination of the yield loci that basal slip is inoperative if α2 < cos θ; prism slip is inoperative if α2 < α1 sin θ; and pyramidal slip is inoperative if α2 > cos θ + α1 sin θ where$$\alpha _1 = \tau _{01\bar 10} /\tau _{0001}$$ and$$\alpha _2 = \tau _{01\bar 11} /\tau _{0001}$$ are, respectively, the ratios of CRSS for prism and pyramidal slips relative to basal slip, and ϕ is the angle between the (0001) and$$(01\bar 11)$$ normals. Since the value of ϕ is a function ofc/a, the limiting values of α1 and α1 depend on thec/a ratio of the crystal structure.