A Review of Computational Approaches to the Microstructure-Informed Mechanical Modelling of Metals Produced by Powder Bed Fusion Additive Manufacturing
Abstract
1. Introduction
2. Microstructural Features of Materials Fabricated by PBF
2.1. Melt Pool Pattern
2.2. Grains
2.3. Cellular–Dendritic Substructure
3. Process-Structure-Properties-Performance Concept
4. Microstructure Modelling in AM
4.1. Physically Based Microstructure Modelling
4.2. Geometrically Based Microstructure Modelling and Image Reconstruction
5. BVP Formulation for Microstructure-Based Mechanical Simulations of Additively Manufactured Metallic Materials
5.1. FE Implementation of a Boundary-Value Problem
5.2. Kinematics and Constitutive Laws
5.3. Constitutive Models of the Plastic Behaviour of Grains
5.4. Description of Hardening Mechanisms in PBF-Produced Materials
6. Microstructure-Informative Mechanical Simulations of Additively Manufactured Metallic Materials
6.1. Two-Dimensional Microstructure-Based Mechanical Simulations
6.2. Three-Dimensional Mechanical Simulations for Synthetic Microstructures
6.3. Process–Structure–Property–Performance Computational Analysis
7. Summary and Future Directions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Topic, Reference | Highlights | Hardening Law |
---|---|---|
Damage modelling of alloys produced by LPBF [146] | Two-dimensional FE structure–property model developed for uniaxial tensile loading of as-built LPBF 316L steel. Incorporates a simplistic synthetic grain structure that fits a melt pool (Figure 7a). Implemented in the FE commercial software Abaqus using a user material (UMAT) subroutine. Compared with an experimental stress–strain curve of the as-built LPBF 316L steel. | . (20) Here, areare the hardening moduli, including (no sum on ) and () which denote self and latent hardening moduli, respectively, as introduced by Peirce et al. [178], , . Here, is the initial hardening modulus; stands for accumulated shear strain; is the saturation stress; is the initial stress and denotes the ratio of latent to self-hardening. Latent hardening represents the increment of flow stress on the slip system due to a shear increment on the slip system . As pointed out by Peirce et al. [178], the components of the hardening matrix represent ‘the most elusive parameters’ in the constitutive equations. In a later study [179], Taheri Andani and coworkers adapted the model proposed in [180] where they considered the slip system hardening model as (no sum on ), where a single slip hardening rate ; is the Kronecker delta; and ; , are the slip system hardening parameters which were set to be identical for all slip systems. |
Micromechanical modelling of single track deformation, phase transformation and residual stress evolution during laser surface remelting [175] | Two-dimensional FE structure–property model developed to estimate residual stresses that are formed due to the laser surface remelting of H13 tool steel. Incorporates a simplistic synthetic equiaxed grain structure and takes into account martensitic and austenitic phases. Implemented in the FE software Zset [181]. When determining single crystal model parameters, the authors compared a calculated macroscopic stress–strain curve with an experimental one for H13 samples that were cast and heat-treated [182]. | Martensite: . (21) Here, the self-hardening resistance which is usually defined as a constant, are considered. Here, is the hardening coefficient characterising the dislocation network interactions [183]; stands for the minimum length of the screw segment. is the effective stress, i.e., mean stress driving dislocation motion; the line tension model goes to the classical formulation proposed by Taylor. The average obstacle strength is a function of the densities of different defects, are the planar densities of carbides and solute clusters, respectively. A similar hardening model was adapted for austenite: . (22) Here, is the Hall–Petch term. Dislocation density evolution is estimated using a classical equation which describes the evolving mean free path during the accumulation of dislocations. The model is largely adopted from [184]. |
Microstructural effects on the elasto-viscoplastic deformation of dual-phase Ti-6Al-4V produced by PBF [185] | laths. Equation (23) is calibrated with the experimental stress–strain curve of the as-built EPBF Ti-6Al-4V [186]. | A modified version of the Voce hardening model , (23) stands for the back-extrapolated CRSS. |
CP modelling of the anisotropic tensile behaviour of LPBF Ti-6Al-4V [36] | laths. Implemented in the FFT software DAMASK [157]. Equation (24) is calibrated with experimental the stress–strain curves of the heat-treated LPBF Ti-6Al-4V ELI. | The slip resistance , (24) denotes the saturation value of the slip resistance. |
CP modelling of the structure–property relationship in LPBF Ti-6A-4V [152] | ’ laths. Implemented in Abaqus using a UMAT subroutine. The results are compared with the experimental stress–strain curves obtained under tension, compression, and cyclic loading along the BD of LPBF Ti-6Al-4V. | , where (25) stands for CRSS. |
Macroscale and microscale stress–strain relations of LPBF AlSi10Mg alloy [187] | Three-dimensional FFT structure–property model developed for the uniaxial tensile loading of as-built LPBF AlSi10Mg. Incorporates a synthetic grain structure (columnar or equiaxed), Si particles, and the porosity with a prescribed volume fraction. Implemented in DAMASK [157]. Compared the computationally obtained stress–strain curves with the experimental one from the in situ synchrotron X-ray diffraction experiment [188]. | (26) stands for the initial slip resistance. |
Phase stress partition and its correlation with the mechanical anisotropy of LPBF AlSi10Mg [189] | Three-dimensional FE structure–property models developed for uniaxial tensile loading of the as-built LPBF AlSi10Mg in two different directions. Incorporate a synthetic Al-Si cellular substructure. Implemented in Abaqus using a UMAT subroutine. The results are compared with the experimental stress–strain curves obtained under tension along the BD and TD of LPBF AlSi10Mg [190]. | The traditional CP model 191 and the mechanism-based strain gradient crystal plasticity model (MSG-CP) [192] were employed. The former considered the hardening law suggested by Peirce et al. [178], as described in Equation (20). The MSG-CP defined the effective slip resistance following the Taylor hardening relation: , (27) ), in Equation (13). |
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Zinovieva, O.; Romanova, V.; Dymnich, E.; Zinoviev, A.; Balokhonov, R. A Review of Computational Approaches to the Microstructure-Informed Mechanical Modelling of Metals Produced by Powder Bed Fusion Additive Manufacturing. Materials 2023, 16, 6459. https://doi.org/10.3390/ma16196459
Zinovieva O, Romanova V, Dymnich E, Zinoviev A, Balokhonov R. A Review of Computational Approaches to the Microstructure-Informed Mechanical Modelling of Metals Produced by Powder Bed Fusion Additive Manufacturing. Materials. 2023; 16(19):6459. https://doi.org/10.3390/ma16196459
Chicago/Turabian StyleZinovieva, Olga, Varvara Romanova, Ekaterina Dymnich, Aleksandr Zinoviev, and Ruslan Balokhonov. 2023. "A Review of Computational Approaches to the Microstructure-Informed Mechanical Modelling of Metals Produced by Powder Bed Fusion Additive Manufacturing" Materials 16, no. 19: 6459. https://doi.org/10.3390/ma16196459
APA StyleZinovieva, O., Romanova, V., Dymnich, E., Zinoviev, A., & Balokhonov, R. (2023). A Review of Computational Approaches to the Microstructure-Informed Mechanical Modelling of Metals Produced by Powder Bed Fusion Additive Manufacturing. Materials, 16(19), 6459. https://doi.org/10.3390/ma16196459