This is the preprint of an article that will appear in International Journal of Fracture (IJF)

Title: Numerical simulation of intergranular and transgranular crack propagation in ferroelectric polycrystals

Authors: Amir Abdollahi and Irene Arias, Universitat Politecnica de Catalunya (UPC), Barcelona

Abstract:

This is the preprint of an article that will appear in Modelling and Simulation in Materials Science and Engineering (MSMSE)

Title: Phase-field simulation of anisotropic crack propagation in ferroelectric single crystals: effect of microstructure on the fracture process

Authors: Amir Abdollahi and Irene Arias, Universitat Politecnica de Catalunya (UPC), Barcelona

Abstract:

A typical two phase microstructure consists of a topologically continuous `matrix' phase in which islands of `precipitate' phase are embedded. Usually, the matrix phase is also the majority phase in terms of volume fraction. However, sometimes this relationship between the volume fraction and topology is reversed, and this reversal is known as phase inversion. Such a phase inversion can be driven by an elastic moduli mismatch in two-phase solid systems. In this paper (submitted to Philosophical magazine), we show phase inversion, and the effect of the elastic moduli mismatch and elastic anisotropy on such inversion.

During solid-solid phase transformations elastic stresses arise due to a difference in lattice parameters between the constituent phases. These stresses have a strong influence on the resultant microstructure and its evolution; more specifically, if there be externally applied stresses, the interaction between the applied and the transformation stresses can lead to rafting.

Rafting is the preferential coarsening of (dilatationally) misfitting precipitates in a direction parallel (P-type) or perpendicular (N-type) to an applied stress. In the materials literature, it is sometimes argued that rafting is an elasto-plastic phenomenon, and that plastic pre-strains are essential for rafting. In this paper (which we have submitted to Acta Materialia) we show that purely elastic stress driven rafting is a distinct possibility.

I am very happy to be part of iMechanica, and what best way to start than post some stuff that I have been doing recently. I received my PhD for a thesis I submitted to the Department of Materials Engineering (formerly Department of Metallurgy), Indian Institute of Science, Bangalore 560012 INDIA titled Elastic Inhomgeneity Effects on microstructures: a phase field study.

A mismatch in elastic moduli is the primary driving force for certain microstructural changes; for example, such a mismatch can result in rafting, phase inversion, and thin film instability.

My thesis is based on a phase field model, which is developed for the study of microstructural evolution in elastically inhomogeneous systems which evolve under prescribed traction boundary conditions; however, we show that it is also capable of simulating systems which are evolving under prescribed displacements.

The (iterative) Fourier based methodology that we adopt for the solution of the equation of mechanical equilibrium is characterised by comparing our numerical elastic solutions with corresponding analytical sharp interface results; in addition to being accurate, this solution methodology is also very efficient. We integrate this solution methodology into our phase field model, to study microstructural evolution in systems with dilatational misfit.