Multi-Scale modelling of structure-property relationship in additively manufactured metallic materials
Graphical abstract
Introduction
Powder-bed additive manufacturing (AM) techniques for metallic materials, e.g., selective laser melting (SLM) or electron beam melting (EBM), show prominent advantages owing to the almost unlimited design freedom to produce components with complex 3D shapes without the need for tooling. In essence, AM integrates materials synthesis and manufacturing in a single print, making it attractive for a wide range of technological applications. However, the extremely localized melting, strong temperature gradient, and high solidification front velocity through the AM process generate enormously non-equilibrium microstructures that are distinctive compared with those by conventional manufacturing approaches [1], [2], [3]. Therefore, a fundamental understanding of the structure-property relationship of AMed metals is significant to the engineering applications of these promising techniques.
In literature, several experimental researches have been performed to explore the relationship among the fabrication process, mechanical performance, and microstructure for AMed metals. In the field of process parameters, the effect of laser power on the grain size and tensile performance has been widely studied in AMed metals, e.g., iron [4], Inconel 718 [5], and 316L stainless steel [6]. In general, lower tensile yield and failure strengths are observed in fully dense AMed metals fabricated by higher laser powers, due to the grain coarsening resulting from lower temperature gradient in the fabrication process [5,6]. However, owing to the effect of keyhole mode, finer grain size also would form with higher laser energy [7,8]. For some specific materials, e.g., SLMed Ti-6Al-4V, the grain structure can be modulated by the fabrication process, which leads to different mechanical behaviors [9], [10], [11], [12], [13]. In addition, the effect of post-processing has been thoroughly investigated. The tensile yield and failure strengths of as-built and heat-treated AMed metals, including nickel-based alloy EP718 [14], 316L stainless steel [15,16], alloy Mar-M-509 [17], and Zr-modified aluminum alloy 5083 [18], have been compared, respectively. In these works [14], [15], [16], [17], [18], it has been found that the higher strength in as-built AMed metals is mainly determined by the finer grains generated in the AM process.
Some unique features, e.g., the microstructural inhomogeneity, have also been observed in AMed metals. Sun et al. [19,20] and Wei et al. [21] have analyzed the remarkable microstructural inhomogeneity in the AMed Co-Cr-Mo alloy, respectively, which is attributed to isothermal phase transformation of lower consolidated layers under high ambient temperature. Dilip et al. [22] have obtained the inhomogeneous microstructure in AMed HY100 steel along both the horizontal and vertical directions, which is the result of the multiple thermal cycling effect during layer-by-layer fabrication. In SLSed Ti-6Al-4V, Simonelli et al. [23] and Cho et al. [24] have pointed out the variation of constituent phases along the building direction, respectively, and Vilaro et al. [25] have observed the large discrepancies in tensile strengths along different directions. In contrast, Simonelli et al. [9] have fabricated other SLSed Ti-6Al-4V, for which the laser power is higher than that in [23], but similar microstructure and tensile behavior are obtained along different directions. The similarity in SLSed Ti-6Al-4V along different directions has also been observed in Ref. [11,26,27]. The opposite conclusions in microstructural inhomogeneity of SLSed Ti-6Al-4V should be attributed to the different process parameters, especially the different laser powers [23]. Meanwhile, the residual stress caused by the local high heating and cooling rates is remarkable in AMed metals. In order to measure the residual stress, in-situ neutron and synchrotron X-ray diffraction measurements have been employed in AMed 304L stainless steel [28,29] and 316L stainless steel [30,31], respectively. Overall, it can be found that multiple peculiar features are coupled together in AMed metals, and a suite of new numerical models are urgent in the structure-property analysis.
The stochastic microstructure reconstruction of AMed metals is the essential module in the multi-scale modelling of structure-property relationship. The grain growth algorithms, e.g., cellular automata (CA) [32], [33], [34], [35] and phase-field algorithm [36], are feasible approaches, which can model grain growth by implicitly resolving grains on a discrete grid of cells. The limitation of these approaches is that the parameter calibration is time and resource consuming. By comparison, the image-based reconstruction is concise and efficient. The typical approach is to reconstruct from a series of 2D electron backscatter diffraction (EBSD) images obtained using a dual-beam focused ion beam-scanning electron microscope [37,38]. Moreover, a synthetic microstructure generation approach [38], [39], [40] has been developed based on the captured microstructural information, which has been integrated into the open-source software Dream 3D [41]. With consideration of the particular microstructure features fabricated by AM process, some modification work is necessary for the synthetic microstructure generation approach of AMed metals. Prediction of material properties from process-induced microstructure is enabled by different types of multi-scale material modeling techniques. Specifically, to characterize the deformation and failure mechanism, the crystal plasticity finite element method (CPFEM) is one of the most promising choices [42], [43], [44], [45], [46]. Unlike phenomenological models that capture observed trends in material behaviors based on the macro-scale experimental data [47], CPFEM simulates the anisotropic plastic deformation based on the slip mechanisms in crystal systems. Then, a combination of the synthetic microstructure generation approach of AMed metals and CPFEM is appreciated for better understanding the structure-property relationship of AMed metals.
The present work aims to provide a rapid computational evaluation of the structure-property relationship of AMed metals. Firstly, a new synthetic microstructure generation approach based on the fabrication process is proposed to reconstruct the micro-scale models of AMed metals. On this basis, a single-crystal-scale plasticity model is employed to describe the deformation behavior of individual grains in the micro-scale reconstructed models. In order to reduce the computational cost, a polycrystal-scale plasticity model is further established. Finally, the proposed multi-scale modelling framework is validated with the experimental data of SLMed Ti-6Al-4V.
Section snippets
Multi-scale modelling framework of AMed metals
This section introduces the multi-scale modelling framework of AMed metals. The structure-property relationship of AMed metals is investigated with the micro-scale and homogenized finite element models, respectively. The deformation behavior of AMed metals is first evaluated by combining a new synthetic microstructure generation approach and a single-crystal-scale plasticity model. Further, a polycrystal-scale plasticity model is established to simplify the constitutive relation of the
Application of the multi-scale modelling framework to as-built SLMed Ti-6Al-4V
In this section, a typical SLMed Ti-6Al-4V is adopted to validate the proposed computational framework. The grain orientation distribution of SLMed Ti-6Al-4V is gathered by EBSD characterization. The microstructural information of single track is obtained alternatively with the combination of a high-fidelity powder-scale model [63] and a cellular automata method [35]. Furthermore, uniaxial tensile, compressive, and cyclic tests are performed to validate the predicted mechanical behavior of
Discussion
The proposed multi-scale modelling framework has a broad applicability to a wide range of AMed metals under complex loadings, not just limited to SLMed Ti-6Al-4V. If the twinning is one of the main plastic deformation mechanisms, both tensile and compressive yield stresses of the polycrystal structure used in the polycrystal-scale plasticity model, i.e. Eq. (16), need to be calculated, respectively, and the equivalent relation under tensile and compressive loadings should be different.
CRediT authorship contribution statement
Haibin Tang: Conceptualization, Methodology, Software, Data curation, Writing - original draft, Writing - review & editing. Haijun Huang: Data curation. Changyong Liu: Resources, Funding acquisition. Zhao Liu: Investigation. Wentao Yan: Supervision, Resources, Project administration, Funding acquisition.
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.
Acknowledgement
The authors gratefully acknowledge the contribution of Dr. Guowei Zhou from Ohio State University, Dr. Yang Li from Ford Motor Company, and Mr. Muhammad Tzulkifli from National University of Singapore for the detailed discussion of this work. Changyong Liu acknowledges the support of Shenzhen Bureau of Industry and Information Technology (Grant No. ZDYBH201900000008). Wentao Yan acknowledges the support of the National Natural Science Foundation of China (Grant No. 51975393).
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2023, International Journal of Mechanical SciencesCitation Excerpt :Tang et al. [22] offered a multi-scale framework for AM Ti-6Al-4V alloy modelling where a synthetic microstructural model reproduced grain morphology after solid-state phase transformation in a rather realistic manner. The authors [22–25,30,32,33] demonstrated that considering microstructural features is vitally important for simulations of AM materials. While substantial progress in the simulations of microstructure evolution and deformation behaviour has been attained on a standalone basis, reproducing the whole metal AM process-microstructure-property chain remains a challenging task.
Microstructural modeling and measurements of anisotropic plasticity in large scale additively manufactured 316L stainless steel
2022, European Journal of Mechanics, A/SolidsCitation Excerpt :In literature, several works focus on experimentally observed relations between process, structure and properties (Vahedi Nemani et al., 2021; Köhler et al., 2021; Wang et al., 2020). A few studies tried to quantify these relations using numerical modeling (Laghi et al., 2021; Liu et al., 2017; Tang et al., 2021), but not yet for WAAM produced 316L stainless steel. The present work aims to quantitatively model the effect of WAAM induced microstructural characteristics on the resulting three-dimensional anisotropic plastic mechanical behavior of 316L stainless steel.