Evolution and Interaction of Dislocations in Intermetallics: Fully Anisotropic Discrete Dislocation Dynamics Simulations
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0980-II05-16
Evolution and Interaction of Dislocations in Intermetallics: Fully Anisotropic Discrete Dislocation Dynamics Simulations Qian Chen and Bulent Biner Ames Laboratory(USDOE), Iowa State University, Ames, IA, 50011
ABSTRACT In this study, the origin of large ductility that is seen in recently discovered rare-earth intermetallic compounds: YCu, YAg and YZn is explored by using fully anisotropic 3D dislocation dynamics simulations. The stability of the glide dislocations, the behavior of the Frank-Read sources and the strength of junctions are evaluated and compared to those seen for the common intermetallics, NiAl and Fe-25Al.
INTRODUCTION Most intermetallic alloys exhibit very limited ductility at room temperatures and their brittle behavior, in both single and polycrystalline forms, has been extensively investigated [1-2]. A new class of highly ordered, ductile intermetallic systems has been discovered recently [3]. These alloys have the B2 structure and are based on a rare-earth element and a late transition metal or an early p-element. Apparently, there are 120 such alloys, most of these have not been studied, but at least 12 such compounds have been found to possess significantly high ductility and fracture toughness when tested at room temperature and in air [3].
COMPUTATIONAL METHODS The elastic energy, E, per unit length of a straight dislocation in a linearly anisotropic elastic crystal is given by: K b2 ⎛ R ⎞ E= ln ⎜⎜ ⎟⎟ 4π ⎝ r0 ⎠
(1)
where K is the energy factor for the dislocation and is a function of both the elastic constants of the anisotropic crystal and the orientation of the dislocation line with its Burgers vector; R is the outer radius of integration; and r0 is the dislocation core radius, which is of the order of b, the magnitude of the Burgers vector. The line tension TL per unit length of a straight dislocation depends on the energy factor K and its second derivative as
TL =
b 2 ⎛ R ⎞⎛ ∂ 2 K (θ ) ⎞ ⎟ ln⎜⎜ ⎟⎟⎜⎜ K (θ ) + 4π ⎝ r0 ⎠⎝ ∂θ 2 ⎟⎠
(2)
If the logarithmic term in Eqn.1 is assumed to be constant for all dislocation orientations, the 1/K plots are equivalent to the inverse Wulff plots (1/E). There are two criteria for dislocation line instability, the concavity of the inverse Wulff plot and the negative line tension. The latter is a sufficient but not necessary condition for instability. All straight dislocations satisfying these conditions will relax their energy by transforming into V-shaped bends or zigzagged bends. In discrete dislocation dynamics simulations, the forces per unit length causing the mobility of the dislocations is obtained from Peach-Koehler formula: r v r r F = ((σ D + σ A ) • b ) ×ν + Fself
(3)
where σ D is the sum of the stress tensor from other remote dislocation segments, σ A is the applied stress tensor, b is the Burgers vector and ν is the unit tangent vector of the dislocation line and Fself is force arising from the line tension of the dislocation segment. In the evaluation of σ D , the elastic distortion tensor associated with dislocation l
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