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## Numerical modeling of Ti-6Al-4V microstructure evolution for thermomechanical process control Permalink

Bhatt, S, Baskaran, A, Lewis, D, and Maniatty, A. "Numerical modeling of Ti-6Al-4V microstructure evolution for thermomechanical process control." Proceedings of NUMIFORM 2019: The 13th International Conference on Numerical Methods in Industrial Forming Processes, 2019

## Physical System modeling and simulation using HPC

Computational Sciences has been at the forefront of Continuum Mechanics research for a long time. With the advent of cheaper and faster compute capability, it is not only possible to study aspects of a physical system where an experimental study might prove difficult, but also to numerically analyze problems with very high granularity. This talk showcased some of the work where High Performance Computing (HPC) was used by me to solve some of these problems - a Conjugate Gradient method based solver to solve systems of linear equations, which was used to solve Laplace Equation in a $1000 \times 1000$ grid (996004 unknowns) within $10^{-6}$ units of the analytical solution. A similar solver based on stabilized bi-conjugate gradient method was used to solve pressure Poisson equation in a level-set based immersed boundary method code to investigate how pitching and heaving affect the propulsion of a self-propelled oscillating airfoil. This study was used to shed some light on the hydrodynamics and flow structures during the transient state of fish like locomotion (the first few cycles during start of the motion). This task would have been especially difficult to simulate using an experimental setup.

## Numerical Modeling of Ti-6Al-4V Microstructure Evolution for Thermomechanical Process Control

A collaborative effort combining simulation, experiments and feedback control has been created to allow for enhanced manufacturing of Ti-6Al-4V by examining the relationship between thermomechanical processing and microstructure evolution. A heating and tensile stage that operates in a scanning electron microscope (SEM) has been developed to enable real-time control of microstructure. Microstructure evolution modelling using Monte-Carlo (MC), finite element crystal plasticity (FECP), and microelasticity theory coupled phase field methods help to interpret the SEM experimental results, and inform the processing conditions for design and control of future experiments. This talk highlighted our work in modelling microstructure evolution under thermomechanical loading. The MC grain growth model, calibrated using literature data, is used to simulate BCC $\beta$-phase grain growth above the $\beta$-transus temperature, FECP is used to simulate deformation induced evolution of the microstructure and compute heterogeneous stored energy providing additional source of energy to MC and phase-field models. This FECP/MC suite would be able to simulate evolution of grains in the microstructure, while the phase-field model helps simulate evolution within an individual beta/$\beta$-grain. This talk gave an overview of the overall project, and then focused on the development and implementation of the FECP and MC models. Some preliminary results were presented.

This research is sponsored through a grant from NSF, Award CMMI-1729336, DMREF: Adaptive control of Microstructure from the Microscale to the Macroscale.

## Numerical Modeling of Ti-6Al-4V Microstructure Evolution for Thermomechanical Process Control

This talk focused on preliminary results on microstructure evolution modeling using finite element crystal plasticity (FECP), MonteCarlo (MC), and phase field (PF) methods. FECP is used to simulate deformation induced evolution of the microstructure and compute heterogeneous stored energy providing additional source of energy to MC and PF models. Preliminary results on deformation simulation of a simpler microstructure in Nickel was presented. The MC grain growth model, calibrated using literature and experimental data, is used to simulate grain growth $\beta$-Ti-6Al-4V. A multi-phase field, augmented with crystallographic symmetry and orientation relationship between $\alpha - \beta$ phases of Ti-6Al-4V, is employed to model simultaneous evolution and growth of all twelve $\alpha$-variants in 3D. The influence of transformation and coherency strain energy on $\alpha$-variant selection is studied by coupling the model with the Khachaturyan-Shatalov formalism for elastic strain calculation. This FECP/MC/PF suite will be able to simulate evolution of grains in the microstructure and within individual $\beta$-grains during typical thermomechanical processing conditions.

This research is sponsored through a grant from NSF, Award CMMI1729336, DMREF: Adaptive control of Microstructure from the Microscale to the Macroscale.

## Numerical Modeling of Columnar Grained Nickel Microstructure Deformation Near Triple Junctions

Macroscopic mechanical properties of a polycrystalline metal depend on the microstructure and micromechanical behavior. Studying the evolution and response of polycrystal microstructures under mechanical loading, especially at microstructural interfaces such as grain boundaries and triple junctions, is important to understanding the microstructure property relationship and for process design to generate materials with enhanced properties. This study is a first step in simulating complex microstructural behavior. This talk presented some results of our work in simulating plastic deformation near triple junctions of a polycrystalline metal. This study follows experimental work of M. Li [1] on a columnar grained pure nickel under 2% tensile strain. A finite deformation based finite element crystal elastic-plastic model is used to simulate the deformation of the microstructure. Elastic deformation is modeled assuming a linear, anisotropic relationship. The plastic deformation considers slip on the slip systems and dislocation entanglement hardening through the Voce-Kocks model. The model is calibrated against macroscale experimental stress-strain observations. Simulation predictions of the dominant slip systems and deformation field are compared to experimental observations.

Acknowledgements: This research is sponsored through a grant from the National Science Foundation, Award CMMI-1729336, DMREF: Adaptive control of Microstructure from the Microscale to the Macroscale.

### References

[1] M. Li (2018), Deformation at triple junctions: dislocation plasticity and strain distribution, Ph.D. thesis, Rensselaer Polytechnic Institute

## Modeling and Simulation of Deformation Caused by Phase Transformation from β to α in Ti-6Al-4V during Processing

Understanding the relationship between process conditions and microstructure evolution is important to materials manufacturers so they can control the processing conditions to produce a desired microstructure and the resulting macroscale properties. In this work, we are studying Ti-6Al-4V – a dual-phase alloy that is characterized by a vanadium stabilized body-centered cubic β phase and an aluminum stabilized hexagonal close-packed α phase. Due to the α+β nature of this alloy, a wide variety of microstructures are possible as a result of the thermomechanical processing. During the cooling cycle, the β to α transformation itself causes significant deformation that can influence the resulting α growth. For an unconstrained single β crystal, this transformation leads to ~10% contraction along <010>β direction and ~1.5% and ~10% expansion along the two perpendicular <101>β directions. This level of strain imposed on the surrounding β grain is expected to be well beyond the elastic limit. The vast majority of current models use elastic analysis to compute the effects such deformation may have on the local energy and α growth. For a more accurate model, we expect that plastic deformation must be considered. Understanding the material response and energy state as a result of the transformation is key to understanding the mechanics of transformation and will give us insight into why certain microstructures form under a given thermomechanical processing condition.