Kinetic Monte Carlo simulations of structural evolution during anneal of additively manufactured materials

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Abstract

POur experiments indicated that upon a post-processing anneal, an additively manufactured 316L stainless steel exhibits cubic grains rather than the conventional equiaxed grains. Here, we have used kinetic Monte Carlo simulations to explore the origin of these cubic grains. First, we implemented a new kinetic Monte Carlo model in parallel code SPPARKS to simulate grain growth and recrystallization under a residual energy distribution. Our model incorporates physical properties and real-time, as opposed to generic properties and relative time. We further validated that our SPPARKS simulations reproduced the expected kinetic behavior of single-grain evolution. We then used the validated approach to simulate the anneal of an additively manufactured material under the same conditions used in our experiments. We found that the cubic grains can origin from a periodically varying residual energy that may be present in additively manufactured materials.

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

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