Almost compatible microstructures in shape memory alloys

Almost compatible X-microstructures in CuAlNi shape memory alloy

“…In case of the β 1 → γ 1 transformation in CuAlNi, the stretch parameters are α = 1.0619, β = 0.9178 and γ = 1.0230 [5]. Note that the numbering of variants used in this work is consistent with that used, for instance, in [1,5], but different than that used in [11,20,22]. Here and below, the components of vectors and tensors are provided in the cubic basis of austenite.…”

“…Microstructures of the first type, see Fig. 6a and b, have been obtained for the variant triples (1,3,5) and (1,3,6). Note that, in view of the assumption ω i = 1 4 , the two microstructures shown in Fig.…”

“…Clearly, the necessary conditions (11) are satisfied if φ = ψ = 0. Note that the incompatibility indicator ψ defined above is not equivalent to the incompatibility indicator ψ introduced by Balandraud et al [1] in the context of wedge microstructures, though formally it bears some similarity.…”

“…In case of the (1, 2) pair and the crystallographically equivalent pairs, namely the (3, 4) and (5, 6) pairs, the two solutions are the compound twins with rational twinning plane normals. In case of the (1, 3) pair and all the remaining pairs, which are crystallographically equivalent to (1,3), the first solution is a Type I twin and the second solution is a Type II twin with, respectively, rational and irrational twinning plane normals.…”

“…Balandraud et al [1,2] have examined almost compatible wedge microstructures by virtually releasing the mid-rib interface. They have introduced an incompatibility indicator that measures the "mode-I" opening angle in this relaxed microstructure and have assumed that almost compatible wedges characterized by a small incompatibility indicator are most likely to form.…”