Estimation of Back Stress Produced by Dislocation Interaction in Icosahedral Al-Pd-Mn
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Estimation of Back Stress Produced by Dislocation Interaction in Icosahedral Al-Pd-Mn Hisatoshi Hirai1, Akira Kitahara1, Fuyuki Yoshida2 and Hideharu Nakashima2 1 Kyushu National Industrial Research Institute, Tosu, Saga 841-0052, Japan 2 Kyushu University, Graduate School of Engineering Science, Kasuga, Fukuoka 816-0811, Japan ABSTRACT We attempted to calculate the breakaway stress σ b of dislocation from attractive junction made by reaction of dislocations. Assuming that the force f acting on the unit length of dislocation with the Burgers vector B under a shear stress τ a is f = τ a b // where b // is the phonon component of B, and that the elastic energy per unit length of dislocation W is approximated by W = G ( b //
2
2
+ c 2 b ⊥ ) where G is the shear modulus, b ⊥ the phason
component of B and c2 a coefficient of about 3.1 x 10-3. Using the values G = 48.4 GPa at 1070 K, the Taylor factor M = 3 and the measured dislocation density of 1.8 x 1013 m-2, we calculated σ b for 21 possible dislocation reactions. Picking up the most possible dislocation reactions, σ b distributed between 50 and 80 MPa, and the average of them was 64 MPa. This result strongly suggested the possibility that the main part of the internal stress of the high-temperature deformation of icosahedral Al-Pd-Mn is explained by σ b. INTRODUCTION Icosahedral Al-Pd-Mn is known as one of the most stable quasicrystals, so that the mechanical properties of it are extensively investigated and revealed that it is deformed by viscous motion of dislocations at high temperatures [1, 2]. As for the internal stress of hightemperature deformation, stress-transient dip test yields a low value of about 20 to 30 % of the applied stress [2, 3], whereas the method of Kikuchi et al. [4] produces a relatively high value ranging from 50 to 90 % of the applied stress [5]. Recently, the reactions of dislocations in icosahedral Al-Pd-Mn was investigated in detail [6], and revealed that a number of reactions can produce the attractive junction of dislocations. In this study, we attempt to calculate the breakaway stress of the attractive junctions made by the dislocation reactions in icosahedral AlPd-Mn. We also compare the results with the measured internal stress and discuss the mechanisms that produce the internal stress of deformation of icosahedral Al-Pd-Mn. CALCULATION Characteristics of Dislocation in Icosahedral Al-Pd-Mn The six-dimensional (6D) Burgers vector B of the dislocation in icosahedral Al-Pd-Mn is decomposed into B = b // + b ⊥ , where b // and b ⊥ is the phonon and phason component of B, respectively. The prevailing slip plane and slip direction is fivefold plane and twofold direction, respectively [3]. However, there are several dislocations that have the same direction of B in the
K9.14.1
physical space but different strain accommodation parameter ζ (defined as ζ = b ⊥ / b // ) [2,3,7]. Table I summarizes the 6D indices of B of possible dislocations with their directions in the physical space, b // and ζ. We use the same notation and the direc
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