Multi-Scale modelling of structure-property relationship in additively manufactured metallic materials

https://doi.org/10.1016/j.ijmecsci.2020.106185Get rights and content

Highlights

  • A new synthetic microstructure generation approach is proposed for AMed metals according to the characteristics of grain growth in the fabrication process. The constitutive relation of individual grains is provided by the single-crystal-scale plasticity model.

  • To reduce the computational cost, a polycrystal-scale plasticity model is also established. The homogeneous elastic moduli tensor is computed based on Mori-Tanaka's theory, while the plastic deformation is described by the equivalent grain set.

Abstract

This paper presents a multi-scale modelling framework to evaluate the structure-property relationship of metallic materials fabricated by powder-bed additive manufacturing (AM) technique based on crystal plasticity finite element methods. In this framework, a new synthetic microstructure generation approach is proposed to reconstruct micro-scale models of AMed metals according to the characteristics of grain growth in the fabrication process. The constitutive relation of individual grains in the micro-scale reconstructed models is described with the single-crystal-scale plasticity model. Meanwhile, to reduce the computational cost, a polycrystal-scale plasticity model is also established. The homogeneous elastic moduli tensor is computed according to Mori-Tanaka's theory, while the plastic deformation is described by the equivalent grain set. The proposed multi-scale modelling framework is validated against experiments, where the as-built Ti-6Al-4V samples fabricated by selective laser melting (SLM) are tested under uniaxial tensile, compressive, and cyclic loadings. The presented experimental and computational study demonstrates the capability of the proposed multi-scale modelling framework in the structure-property analysis of AMed metals.

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).

References (68)

  • W. Xu et al.

    In situ tailoring microstructure in additively manufactured Ti-6Al-4V for superior mechanical performance

    Acta Materialia

    (2017)
  • D. Ivanov et al.

    Evolution of structure and properties of the nickel-based alloy EP718 after the SLM growth and after different types of heat and mechanical treatment

    Additive Manufacturing

    (2017)
  • F. Bartolomeu et al.

    316L stainless steel mechanical and tribological behavior-A comparison between selective laser melting, hot pressing and conventional casting

    Additive Manufacturing

    (2017)
  • C.A. Bronkhorst et al.

    Structural representation of additively manufactured 316L austenitic stainless steel

    International Journal of Plasticity

    (2019)
  • N.C. Ferreri et al.

    Effects of build orientation and heat treatment on the evolution of microstructure and mechanical properties of alloy Mar-M-509 fabricated via laser powder bed fusion

    International Journal of Plasticity

    (2019)
  • L. Zhou et al.

    Microstructure and mechanical properties of Zr-modified aluminum alloy 5083 manufactured by laser powder bed fusion

    Additive Manufacturing

    (2019)
  • S. Sun et al.

    Phase and grain size inhomogeneity and their influences on creep behavior of Co–Cr–Mo alloy additive manufactured by electron beam melting

    Acta Materialia

    (2015)
  • S.H. Sun et al.

    Build direction dependence of microstructure and high-temperature tensile property of Co–Cr–Mo alloy fabricated by electron beam melting

    Acta Materialia

    (2014)
  • D. Wei et al.

    On microstructural homogenization and mechanical properties optimization of biomedical Co-Cr-Mo alloy additively manufactured by using electron beam melting

    Additive Manufacturing

    (2019)
  • J.J.S. Dilip et al.

    Selective laser melting of HY100 steel: Process parameters,microstructure and mechanical properties

    Additive Manufacturing

    (2017)
  • J.Y. Cho et al.

    Selective laser melting-fabricated Ti-6Al-4V alloy: Microstructural inhomogeneity, consequent variations in elastic modulus and implications

    Optics & Laser Technology

    (2019)
  • W. Sun et al.

    Effects of build direction on tensile and fatigue performance of selective laser melting Ti6Al4V titanium alloy

    International Journal of Fatigue

    (2020)
  • R. Pokharel et al.

    An analysis of phase stresses in additively manufactured 304L stainless steel using neutron diffraction measurements and crystal plasticity finite element simulations

    International Journal of Plasticity

    (2019)
  • X. Wang et al.

    3D printing of polymer matrix composites: A review and prospective

    Composites Part B: Engineering

    (2017)
  • C. Gandin et al.

    A 3D cellular automaton algorithm for the prediction of dendritic grain growth

    Acta Materialia

    (1997)
  • W. Yan et al.

    An integrated process-structure-property modeling framework for additive manufacturing

    Computer Methods in Applied Mechanics and Engineering

    (2018)
  • P.W. Liu et al.

    Integration of phase-field model and crystal plasticity for the prediction of process-structure-property relation of additively manufactured metallic materials

    International Journal of Plasticity

    (2020)
  • M.A. Groeber et al.

    3D reconstruction and characterization of polycrystalline microstructures using a FIB-SEM system

    Materials Characterization

    (2006)
  • M. Groeber et al.

    A framework for automated analysis and simulation of 3D polycrystalline microstructures. Part 2: Synthetic structure generation

    Acta Materialia

    (2008)
  • M. Groeber et al.

    A framework for automated analysis and simulation of 3D polycrystalline microstructures. Part 1: Statistical characterization

    Acta Materialia

    (2008)
  • J. Thomas et al.

    Image-based crystal plasticity FE framework for microstructure dependent properties of Ti-6Al-4V alloys

    Materials Science and Engineering A

    (2012)
  • J.A. Moore et al.

    A crystal plasticity-based study of the relationship between microstructure and ultra-high-cycle fatigue life in nickel titanium alloys

    International Journal of Fatigue

    (2016)
  • Z. Zeng et al.

    Gradient plasticity in gradient nano-grained metals

    Extreme Mechanics Letters

    (2016)
  • S.A.H. Motaman et al.

    Anisotropic polycrystal plasticity due to microstructural heterogeneity: A multi-scale experimental and numerical study on additively manufactured metallic materials

    Acta Materialia

    (2020)
  • Cited by (33)

    • Phase field fracture model for additively manufactured metallic materials

      2023, International Journal of Mechanical Sciences
    • Elastic properties of additively manufactured steel produced with different scan strategies

      2023, International Journal of Mechanical Sciences
      Citation 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/Solids
      Citation 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.

    View all citing articles on Scopus
    View full text