Analytical expressions of incompatibility stresses at Σ3⟨111⟩ twin boundaries and consequences on single-slip promotion parallel to twin plane

Thiebaud Richeton (1, 2) , I. Tiba (1, 3) , Stéphane Berbenni (1, 2) , O. Bouaziz (1, 2)

1 LEM3 - Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux
2 Labex DAMAS
3 Universität des Saarlandes [Saarbrücken]

Strong incompatibility stresses may develop at grain or twin boundaries because of elastic and plastic anisotropies. Their knowledge at Σ3 < 111 > twin boundaries may be of interest for a better understanding of the mechanical behaviour of f.c.c. materials that can display lamellar twin structures such as TWIP steels or general nanotwinned materials. In this paper, incompatibility stresses arising at general twin boundaries are explicitly derived for a given twin volume fraction. They are deduced from the solutions of the general infinite bicrystal, which is equivalent to a periodic layered structure. In the case of pure elasticity and Σ3 < 111 > twin boundaries, the result is of remarkable simplicity. The incompatibility stress field reduces to a shear stress acting upon a plane orthogonal to twin plane. Simple analytical expressions of the resolved shear stresses are also determined according to the twin boundary orientation, the twin volume fraction and the elastic anisotropy factor. Such expressions allow performing a comprehensive study of slip initiation. In particular, there exists a large physical domain, depending on the three above parameters, where simultaneous slip parallel to twin plane in the parent and in the twin is greatly promoted. There is also a restricted domain where simultaneous single slip parallel to twin plane is promoted. The conditions for these promotions are realistic considering the literature data on TWIP steels. The present results hence support the high ductility and strong contribution of kinematic hardening observed in TWIP steels and agree with composite hardening models with single and multislip deforming grains.

Keywords: TWIP; grain boundary engineering; plasticity; anisotropic elasticity; incompatibility stress; twinning

Domains: Mechanics [physics.med-ph]; Materials; Mechanics [physics]; Mechanics of materials [physics.class-ph]; Material chemistry

Thiebaud Richeton, I. Tiba, Stéphane Berbenni, O. Bouaziz. Analytical expressions of incompatibility stresses at Σ3⟨111⟩ twin boundaries and consequences on single-slip promotion parallel to twin plane. Philosophical Magazine, 2015, 95 (1), pp.12-31. ⟨10.1080/14786435.2014.984787⟩. ⟨hal-01676352⟩