Interface reorientation during coherent phase transformations

The universal thermodynamic driving force for coherent plane interface reorientation (IR) during first-order phase transformations (PT) in solids is derived. The relation between the rates of IR and interface propagation (IP) and the corresponding driving forces are derived for combined athermal and drag interface friction. The coupled evolution of IR and IP during cubic-tetragonal and tetragonal-orthorhombic PTs under three-dimensional loading is studied. An instability in the interface orientation is shown to have the features of a first-order PT. Copyright c © EPLA, 2007 Introduction. – The microstructure that is formed, e.g., in ceramics, steels, or a shape memory alloy as a result of a solid-solid PT determines the physical and deformation properties of the material, internal stresses, and possible engineering applications. One of the goals of computational material design is the formation of a desired microstructure [1]. The universal (independent of specific constitutive relations) thermodynamic driving force for IP during solid-solid PT, the celebrated Eshelby driving force [2], and its generalization in the form of the tensor of chemical potential [3] have been known for decades. In marked contrast, the universal driving force for IR has not been previously obtained. The orientation of an invariant plane interface has initially been determined on the basis on crystallographic theory [4] which coincides with the results of direct energy minimization [5]. Orientation of an interface for linear elastic solids when it does not coincide with an invariant plane, i.e. when internal stresses are generated, and changes in its orientation under external stresses are studied in [6–10] using energy minimization. However, these methods explore specific expressions for elastic energy of the mixture of two phases when they are relatively simple. They cannot be used for important cases where athermal interface friction is significant. In this letter, an explicit universal (independent of specific constitutive relations) expression for the driving force for IR is derived for small and large strains. We derive an expression for the dissipation rate for simultaneous IP and IR that accounts for both athermal and drag interface friction. Relationships between the rates of IR and IP and the driving forces for IR and IP are obtained. Athermal friction introduces a nontrivial coupling between IR and IP. In particular, during IP, even an infinitesimal driving force for IR causes a finite IR rate. The nontrivial evolution of IR and IP during cubic-tetragonal and tetragonal-orthorhombic PTs under complex threedimensional loading is studied numerically. An IR instability is revealed, i.e., one interface orientation suddenly transforms to a significantly different one under complex loading. This rapid interface reorientation exhibits the features of a first-order PT, and is usually accompanied by a jump in the stresses and volume fractions. On the other hand, the IR is continuous under other types of loading. A change in temperature can induce IR as well. Universal thermodynamic driving force for interface motion. – Consider a cube V containing two phases, 1 and 2, divided by a plane interface Σ with the unit normal n under external stresses. Let εi and σi be the constant strain and stress tensors in each phase, then ε= ciεi, σ= ciσi, ψ= ciψi(εi, θ), s= cisi(εi, θ) (1) are the strain and stress tensors, as well as the Helmholtz free energy and entropy, both per unit volume, averaged over V , ci is the volume fraction of the i-th phase, θ is the temperature homogeneous in V , and summation over the repeated subscript is assumed. As is usual for strain-dominated PTs with coherent interfaces (displacements are continuous across an interface), we neglect the interface energy (and its orientational dependence) in comparison to the elastic energy. It follows from the thermodynamics of each phase that σi = ∂ψi/∂εi and si =−∂ψi/∂θ. The dissipation rate per unit volume is DV =σ : ε̇− ψ̇− sθ̇ 0, where : designates double contraction of tensors. Inserting in DV the expressions