Kinetic Monte Carlo simulations of structural evolution during anneal of additively manufactured materials
Graphical abstract
Introduction
Additive manufacturing (AM) [1] enables rapid prototyping, intelligent material design, low waste production, increased energy efficiency, and reduced material cost. However, microstructures of additively manufactured metals are often more complex than those of wrought materials. More importantly, these microstructures often evolve under either the processing or the service conditions [1]. As one example, we recently explored anneal-induced microstructural evolution of a 316L stainless steel sample manufactured using a powder bed fusion (PBF) AM process. In our anneal treatment, the sample was heated from room temperature up to 1000 °C at a rate of 6 °C/min. Electron backscatter diffraction (EBSD) images of the sample before and after the anneal are shown respectively in Fig. 1(a) and (b), where thickness between additive layers (inter-pass layer thickness) and molten-zone width obtained from other images are indicated schematically. It can be seen that prior to the anneal, the microstructure exhibits vertical elongated grains that often penetrate through several inter-pass layer thicknesses. After the anneal, the microstructure is composed of cubic grains that appear to have sizes close to the inter-pass layer thickness in the vertical direction and the molten-zone width in the horizontal direction (∼50 μm).
The change of microstructure during processing and service is important to understand because it impacts performance reliability during lifetime of AM materials. On the other hand, the cubic grains differ from the conventional equiaxed grains. It is reasonable to assume that the as-manufactured AM sample contains non-uniform residual energy that varies periodically with respect to the inter-pass layer boundaries and molten zone trails. Here our concept of residual energy includes not only the elastic energy due to residual stresses [2], but also defect energy due to dislocations [3] and oxides at prior-particle boundaries. It is unclear if periodically varying residual energy can lead to the cubic grains during anneal. For reliable applications of AM materials, this speculation needs to be explored by either experimental or theoretical studies.
The objective of this paper is to develop a kinetic Monte Carlo (kMC) model capable of simulating the recrystallization of AM materials with a non-uniform residual energy distribution, implement the model in parallel kinetic Monte Carlo code SPPARKS [4], [5], and perform SPPARKS simulations to assess the possibility of forming the cubic grains due to a non-uniform distribution of residual energy.
Section snippets
Literature kinetic monte carlo models
Unlike continuum approaches where microstructural evolution are solved from differential equations (e.g., phase field models [6]), the kMC methods track structural evolution by executing events at discrete locations of a sample based on rate theories. This makes kMC readily extendable to include various events provided that the rate of the events can be calculated. For example, material addition, recrystallization, and grain growth can be easily incorporated as three separate types of events.
Our kinetic monte carlo model
For simplicity, we consider a two-dimensional (2D) model. Note that the 2D model is an appropriate approximation here as our objective is to answer if a non-uniform residual energy distribution can lead to the experimental cubic grains seen in Fig. 1, rather than to reveal three-dimensional (3D) microstructural details. In our 2D model, a material is uniformly divided into n × m grid sites with each site representing an area of Δx2 such that the dimensions of the sample in the x- and y-
Simulated microstructural evolution
The kMC model developed above has been implemented in parallel kMC code SPPARKS [4], [5]. In the Appendix, we perform careful tests to validate that the SPPARKS simulations produce the known phenomena of grain growth kinetics. We now perform SPPARKS simulations to assess the possibility of forming the cubic grains shown in Fig. 1 due to a non-uniform residual energy distribution.
Conclusions
A new kinetic Monte Carlo model incorporating real physical properties and time scale has been developed to simulate grain growth and recrystallization under specified residual energy fields. This model has been incorporated into the parallel kinetic Monte Carlo code SPPARKS. Validation simulations reproduce, at least qualitatively, the recrystallization temperature range and rough kinetics seen in experiments. The major finding of our simulations is that the anneal of a sample with a
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA-0003525. Discussions with A. J. Lew, W. Cai, M. Asta, T. M. Devine, and P. Hosemann are greatly appreciated.
This paper describes objective technical results and analysis. Any subjective views or
References (30)
- et al.
Additive manufacturing of metals
Acta Mater.
(2016) - et al.
3D additive manufactured 316L components microstructural features and changes induced by working life cycles
Appl. Surf. Sci.
(2017) - et al.
Simulation of metal additive manufacturing microstructures using kinetic Monte Carlo
Comp. Mater. Sci.
(2017) - et al.
Computer-simulation of grain-growth – I. Kinetics
Acta Mater.
(1984) - et al.
Computer-simulation of grain-growth - II. Gain-size distribution, topology, and local dynamics
Acta Mater.
(1984) - et al.
Computer simulation of grain growth – IV. Anisotropic grain boundary energies
Acta Metall.
(1985) - et al.
Microstructural evolution in two-dimensional two-phase polycrystals
Acta Metall. Mater.
(1993) - et al.
Nonuniform and directional grain growth caused by grain boundary mobility variations
Acta Mater.
(1998) - et al.
Computer-simulation of grain-growth – III. Influence of a particle dispersion
Acta Mater.
(1984) - et al.
Highly parallel computer simulations of particle pinning: Zener vindicated
Scripta Mater.
(2000)
Computer simulation of recrystallization – I. Homogeneous nucleation and growth
Acta Metall.
Computer simulation of recrystallization in non-uniformly deformed metals
Acta Metall.
Hybrid Potts-phase field model for coupled microstructural-compositional evolution
Comp. Mater. Sci.
Scaling Monte Carlo kinetics of the Potts model using rate theory
Acta Mater.
A new algorithm for Monte Carlo simulation of Ising spin systems
J. Comput. Phys.
Cited by (6)
Parallel simulation via SPPARKS of on-lattice kinetic and Metropolis Monte Carlo models for materials processing
2023, Modelling and Simulation in Materials Science and EngineeringEffects of process parameters on the microstructure of Inconel 718 during powder bed fusion based on cellular automata approach
2023, Virtual and Physical PrototypingMonte Carlo simulations of solidification and solid-state phase transformation during directed energy deposition additive manufacturing
2022, Progress in Additive Manufacturing