An investigation of non-planar austenite–martensite interfaces

Abstract

Abstract. Motivated by experimental observations on CuAlNi single crystals, we present a theoretical investigation of non-planar austenite-martensite interfaces. Our analysis is based on the nonlinear elasticity model for martensitic transformations and we show that, under suitable assumptions on the lattice parameters, non-planar interfaces are possible, in particular for transitions with cubic austenite.

On the interplay of anisotropy and geometry for polycrystals in single-slip crystal plasticity

“…The next theorem can be seen in turn as a special case of the work by Ball & Carstensen [4], often cited in the literature, e.g., in [5,7,9,10]. However, to the best of our knowledge, the reference [4] has not yet been published, which is why we include here a detailed proof for the reader's convenience.…”

“…To be precise, let Ω be a C 1 -domain and suppose that for F ∈ F M (Ω, R * ) there is a solution u ∈ C 1 (Ω; R 2 ) to (P M ). It then follows from [9,Theorem 3.2] that F lies in…”

“…For instance, in the case of Lipschitz maps, rank-one compatibility conditions between the polyconvex hulls of the sets of essential gradients (i.e., the smallest closed set containing all gradients up to a set of measure zero) on different sides of an interface are established in [4,30]. The authors of [9,10] show under additional regularity assumptions, namely continuous differentiability up to the interfacial boundary or locally bounded variation of the gradients, that the (approximate) gradients along the interface are rank-one connected pointwise (almost everywhere). Recently, the Hadamard jump condition was investigated in the context of moving interfaces in [26]; we also refer to this paper for a more detailed overview of the history of the problem.…”

Geometry of polycrystals and microstructure

“…The generalizations of the Hadamard jump conditions considered in [4] (see also [23]) are also insufficiently general and tractable. As well as for polycrystals, such generalized jump conditions are potentially relevant for the analysis of nonclassical austenite-martensite interfaces as proposed in [24,25], which have been observed in CuAlNi [26,27], ultra-low hysteresis alloys [28], and which have been suggested to be involved in steel [29].…”

Variational analysis of multiscale problems with differential constraints

“…For instance, in the case of Lipschitz maps, rank-one compatibility conditions between the polyconvex hulls of the sets of essential gradients (i.e., the smallest closed set containing all gradients up to a set of measure zero) on different sides of an interface are established in [17,117]. The authors of [22,25] show under additional regularity assumptions, namely continuous differentiability up to the interfacial boundary or locally bounded variation of the gradients, that the (approximate) gradients along the interface are rank-one connected pointwise (almost everywhere). Recently, the Hadamard jump condition was investigated in the context of moving interfaces in [81]; we also refer to this paper for a more detailed overview of the history of the problem.…”