Simulating recrystallization in titanium using the phase field method

The following problem is addressed: 'Can one synthesize microstructure evolution over a large area given experimental movies measured over smaller regions?' Our input is a movie of microstructure evolution over a small sample window. A Markov Random Field (MRF) algorithm is developed that uses this data to estimate the evolution of microstructure over a larger region. Unlike the standard microstructure reconstruction problem based on stationary images, the present algorithm is also able to reconstruct time-evolving phenomena such as grain growth. Such an algorithm would decrease the cost of full-scale microstructure measurements by coupling mathematical estimation with targeted small-scale spatiotemporal measurements. The grain size, shape and orientation distribution statistics of synthesized polycrystalline microstructures at different times are compared with the original movie to verify the method.

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“…The movie is obtained from a phase field simulation of grain growth [22]. The image size of the original gray-scale movie is 71×71.…”

Section: Synthesis Of a Gray Scale Moviementioning

confidence: 99%

A Markov random field approach for modeling spatio-temporal evolution of microstructures

Acar

Sundararaghavan

2016

Modelling Simul. Mater. Sci. Eng.

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“…Furthermore, the fully recrystallized state assumes no contribution to the stored energy, so that multi-peak stress-strain behavior is out of the scope in that scheme. Gentry and Thornton (2015) investigated recrystallization in titanium, a metal which possesses hexagonal close-packed (hcp) crystallography at room temperature. Their model, however, does not capture twinning and -similar to Chen et al (2015) -nucleation is introduced in a simplified, numerically convenient way (new grains are introduced as spherical, dislocation-free regions held constant for a period of time to prevent the interface energy from forcing the recrystallized grain to disappear).…”

Section: Introductionmentioning

confidence: 99%

Stochastic modeling of discontinuous dynamic recrystallization at finite strains in hcp metals

Tutcuoglu

Vidyasagar

Bhattacharya

et al. 2019

Journal of the Mechanics and Physics of Solids

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We present a model that aims to describe the effective, macroscale material response as well as the underlying mesoscale processes during discontinuous dynamic recrystallization under severe plastic deformation. Broadly, the model brings together two well-established but distinct approaches -first, a continuum crystal plasticity and twinning approach to describe complex deformation in the various grains, and second, a discrete Monte-Carlo-Potts approach to describe grain boundary migration and nucleation. The model is implemented within a finite-strain Fast Fourier Transform-based framework that allows for efficient simulations of recrystallization at high spatial resolution, while the grid-based Fourier treatment lends itself naturally to the Monte-Carlo approach. The model is applied to pure magnesium as a representative hexagonal closed packed metal, but is sufficiently general to admit extension to other material systems. Results demonstrate the evolution of the grain architecture in representative volume elements and the associated stress-strain history during the severe simple shear deformation typical of equal channel angular extrusion. We confirm that the recrystallization kinetics converge with increasing grid resolution and that the resulting model captures the experimentally observed transition from single-to multi-peak stress-strain behavior as a function of temperature and rate.

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“…In phase field community, there also have been successful attempts to model this phenomenon, for instance, see the work of [12][13][14]. GPU-based accelerated schemes were implemented in [15,16].…”

Section: Introductionmentioning

confidence: 99%

A vertex model of recrystallization with stored energy implemented in GPU

Sazo

Torres

Emelianenko

et al. 2019

Mater. Res. Express

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Recrystallization models and simulations have been the subject of much attention in materials community in the past decades due to this process having a significant effect on many technologically important materials characteristics. Statistical analysis performed close to the steady state requires large-scale simulations, which are often prohibitively expensive from computational point of view. Graphical Processing Unit (GPU)-based realizations provide a viable approach to addressing this challenge, yet they remain relatively under-explored in this context.In the present manuscript, we develop a fully-parallelizable matrix-free GPU-based algorithm for implementing a two-dimensional vertex model of recrystallization based on the stored energy formalism. Nucleation is assumed to take place at triple junctions and obeys a Metropolis-type criterion. We include a complete mathematical analysis of the nucleation model deriving conditions under which nucleation is successful. Stability analysis of the dynamics of a triple junction under the presence of bulk energy is provided. On the computational side, we propose a novel polling system for handling topological transitions to ensure robust GPU implementation. Single grain tests are performed for benchmarking purposes. Finally, a set of numerical experiments for large scale systems is presented to explore the effect of initial distributions of stored energy on several statistical characteristics.

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Simulating recrystallization in titanium using the phase field method

Cited by 21 publications

References 17 publications

A Markov random field approach for modeling spatio-temporal evolution of microstructures

A Markov random field approach for modeling spatio-temporal evolution of microstructures

Stochastic modeling of discontinuous dynamic recrystallization at finite strains in hcp metals

A vertex model of recrystallization with stored energy implemented in GPU

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