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

Abstract

Strong incompatibility stresses may develop at grain or twin boundaries because of elastic and plastic anisotropies. Their knowledge at 3 1 1 1 twin boundaries may be of interest for a better understanding of the mechanical behaviour of fcc materials that can display lamellar twin structures, such as twinning-induced plasticity (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 3 1 1 1 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.

Incompatibility Stresses and Lattice Rotations Due to Grain Boundary Sliding in Heterogeneous Anisotropic Elasticity

“…the system (27) becomes similar to the one obtained for the derivation of incompatibility stresses without GBS and thermal expansion in bicrystals or periodic-layered composites [18][19][20]. Therefore, stress jumps solutions can be directly expressed as:…”

Misorientation dependence of the grain boundary migration rate: role of elastic anisotropy

“…Besides, it is assumed that the dislocations are initially in equilibrium in a zero net force configuration, as a result of the balance between the self and image stress fields of the dislocations and an internal stress field σ int due to defects located outside of the two grains. For the sake of simplicity, only one component of σ int is assumed non-zero, the σ 22 one which must be continuous across the perfect interface [14]. σ 22 can therefore be taken homogeneous within the two grains.…”

“…Owing to elastic anisotropy, polycrystals have indeed heterogeneous elastic moduli [14] and image stresses are appended to the dislocation self-stress field (i.e. the one corresponding to an infinite homogeneous medium) in order to satisfy boundary conditions at interfaces.…”

Additive manufacturing of fatigue resistant austenitic stainless steels by understanding process-structure–property relationships

“…Austenitic stainless steels (SSs) in their wrought form are known to be more susceptible to FCI at annealing twin boundaries ( 3-TB) and high angle grain boundaries (HAGB) than nano/micro-scale defects such as intermetallic inclusions and voids [12][13][14][15]. The deformation behaviour at 3-TB and HAGB has been shown to result in both elastic and plastic incompatibilities across the boundary [13][14][15][16][17][18][19][20]. For low applied stresses, such as those in the high-cycle fatigue (HCF) regime, the small differences in elastic deformation near 3-TBs result in elastic mismatches across the boundaries.…”