NON-SCHMID EFFECTS AND TWIN-SHEAR-STRESS CRITERION OF PLASTIC DEFORMATION IN CRYSTALS AND POLYCRYSTALLINE METALS
YU Maohong; HE Li'nan (Xi'an Jiaotong University)
Cite this article:
YU Maohong; HE Li'nan (Xi'an Jiaotong University). NON-SCHMID EFFECTS AND TWIN-SHEAR-STRESS CRITERION OF PLASTIC DEFORMATION IN CRYSTALS AND POLYCRYSTALLINE METALS. Acta Metall Sin, 1983, 19(5): 114-120.
Abstract The maximum shear stress yield criterion in macromechanics was given by Tresca (1864), and the critical shear stress law of the crystal was established by Schmid in 1924. Their criteria agree with experimental data of some materials and crystals. But owing to complexity and variety of slip in materials and crystals, there exist some deviations from Tresca criterion of yield and Schmid shear stress rule of slip for many materials and crystals. The researches made by a number of investigators show that some shear stress may affect the plastic deformation both in yield of isotropic material and in slip of crystal.A macroscopic twin-shear-stress yield criterion was proposed by the author (Yu Maohong) in 1961. Twin-shear-stress yield criterion assumes that yielding begins when the sum of the two larger principal shear stresses reaches a magnitude C. Thus the yield function isf=τ_(13)+τ_(12)=σ_1-1/2(σ_2+σ_3)=C, when τ_(12)≥τ_(23);f=τ_(13)+τ_(23)=1/2(σ_1+σ_2)-σ_3=C, when τ_(12)<τ_(23)The multiple slip systems and non-Schmid effect of slip in crystals were observed for many years. Taira and Hayashi show that the crystal in polycrystalline metal do not deform in simple slip systems but on multiple slip systems. Since slips on simple systems would create gaps at the grain boundaries and this is not the case, A crystal in a polycrystalline aggregate must slip on more than four slip systems in order to satisfy mechanical condition. So a unit octahedron, a unit dodecahedron, a 24-hedron were used to represent the multiple slip systems. In this paper, the twin-shear-stress yield criterion is generalized to slip of crystal and polycrystal. A critical twin-shear-stress criterion of slip in crystal is proposed here. The rhombic dodecahedral model and orthogonal octahcdral model are proposed to represent the multiple slip systems of crystal under complex stress state. The critical twin-shear-stress criterion of slip in crystal assumes that the slip of crystal begins when the sum of two shear stresses in dodecahedral multiple slip systems reaches a critical value. It seems that the critical twin-shear-stress criterion may be used to expound multiple slip systems and the non-Schmid effect of some crystals and polycrystals.
