Elastic Green’s Function in Anisotropic Bimaterials Considering Interfacial Elasticity

Chen

Berbenni

2020

Philosophical Magazine

In this work, numerical computations of image forces and stored energy during the growth of a strain free grain within a recovered matrix containing an array of identical dislocations are performed. A decrease of the stored energy is observed when image forces are attractive and an increase when image forces are repulsive. The variation of elastic energy depends closely on the material elastic anisotropy, the number of dislocations in the array and its initial distance to grain boundary. For an array of 20 edge dislocations and the motion of a planar grain boundary over approximately 180 atomic spacing, the magnitude of the energy variation is on the order of one dislocation line energy for Al and six for Cu, which is significant in both cases. Furthermore, by sweeping the whole orientation space for FCC crystals, it is shown that grain boundaries near a 111 40˚misorientation are among those that can display the highest attractive forces on edge dislocations. Since grain boundary migration is driven by the reduction of stored energy, the results are analyzed in light of experimental recrystallization data in FCC metals which show that the fastest moving boundaries are often characterized by misorientation axis around 111 and misorientation angle close to 40˚.

Section: Discussionmentioning

confidence: 99%

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

Chen

Berbenni

2020

Philosophical Magazine

“…Besides, it can be underlined that the case of imperfect interfaces was already addressed by Tucker (1969) who obtained elastic field solutions for both perfectly bonded and freely slipping interfaces. Most recently, elastic Green's functions were derived in anisotropic bi-materials by Pan (2003) in three dimensions while considering different kinds of imperfect interface models and by Juan and Dingreville, (2017b) while accounting for interfacial elasticity. Furthermore, it must be noticed also that elastic field solutions due to three-dimensional dislocation loops in anisotropic bi-materials exist (e.g., Han and Ghoniem (2005), Chu et al (2012)).…”

Section: Introductionmentioning

confidence: 99%

Elastic fields due to dislocations in anisotropic bi- and tri-materials: Applications to discrete dislocation pile-ups at grain boundaries

Chen

International Journal of Solids and Structures

Berbenni

2019

Elastic fields due to single dislocations and dislocation pile-ups are computed in heterogeneous media like bi-materials, half-spaces and tri-materials thanks to the Leknitskii-Eshelby-Stroh formalism for two-dimensional anisotropic elasticity. The tri-material configuration allows to consider grain boundary regions with finite thickness and specific stiffness. The effects of these parameters are first studied in the case of a single dislocation in a Ni bicrystal. Image forces may arise because of both dissimilar grain orientations and the presence of a finite grain boundary region. In particular, it is shown that the Peach-Koehler force projected along the dislocation glide direction can exhibit a change of sign with the dislocation position. Therefore, an equilibrium position in the absence of applied stress can be found by coupling an attractive compliant grain boundary region with a repulsive orientation of the adjacent crystal, or a repulsive stiff grain boundary region with an attractive orientation. Regarding dislocation pile-ups, it is shown that the resolved shear stress scales approximately with the inverse of the square root distance from the leading dislocation in the pile-up. This scaling law remains valid in anisotropic elasticity for the chosen heterogeneous media. Both the grain boundary stiffness and grains misorientation influence pile-up length and resolved shear stress, but the effect of misorientation is clearly seen to be predominant. In the case where the leading dislocation is unlocked, the resolved shear stress at a given position in the neighboring grain is reduced when the grain boundary stiffness is increased due to the pushing back of dislocations from the grain boundary.

“…[LBG + 18]), full-field crystal plasticity simulations (e.g. [REH + 10]) or investigations at the dislocation scale like evaluation of image forces on dislocations due to elastic mismatch between phases [PK94,JD18,CRCS19]. Furthermore, anisotropic elastic constants are also needed if one wants to estimate accurately local stresses from elastic strain measurements by diffraction (e.g.…”

mentioning

confidence: 99%

Mechanical derivation of elastic constants of ε-martensite

2019

Scripta Materialia

This work presents direct formulas to compute the HCP elastic constants of ε-martensite from the FCC ones of austenite. The derivation is performed thanks to mechanical compatibility arguments while considering ε-martensite as a laminate structure of twinned and untwinned FCC phases. The formulas are applied to predict the elastic constants of several alloys and very good agreement with measurements is found. According to these relations, directional Young moduli of ε-martensite are most of the time stiffer than the austenite ones and the (0001) shear modulus is always greater than the (111) one, which hardens dislocation glide parallel to the interfaces.