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Open AccessArticle

Analytical Modeling of Residual Stress in Laser Powder Bed Fusion Considering Volume Conservation in Plastic Deformation

1
Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA
2
Advanced Manufacturing LLC, 222 Pitkin St, East Hartford, CT 06108, USA
3
School of Material Science and Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA
*
Author to whom correspondence should be addressed.
Modelling 2020, 1(2), 242-259; https://doi.org/10.3390/modelling1020015
Received: 16 November 2020 / Revised: 10 December 2020 / Accepted: 10 December 2020 / Published: 15 December 2020
(This article belongs to the Section Modelling in Engineering Structures)
Residual stress (RS) is the most challenging problem in metal additive manufacturing (AM) since the build-up of high tensile RS may influence the fatigue life, corrosion resistance, crack initiation, and failure of the additively manufactured components. While tensile RS is inherent in all the AM processes, fast and accurate prediction of the stress state within the part is extremely valuable and results in optimization of the process parameters to achieve a desired RS and control of the build process. This paper proposes a physics-based analytical model to rapidly and accurately predict the RS within the additively manufactured part. In this model, a transient moving point heat source (HS) is utilized to determine the temperature field. Due to the high temperature gradient within the proximity of the melt pool area, the material experiences high thermal stress. Thermal stress is calculated by combining three sources of stresses known as stresses due to the body forces, normal tension, and hydrostatic stress in a homogeneous semi-infinite medium. The thermal stress determines the RS state within the part. Consequently, by taking the thermal stress history as an input, both the in-plane and out of plane RS distributions are found from the incremental plasticity and kinematic hardening behavior of the metal by considering volume conservation in plastic deformation in coupling with the equilibrium and compatibility conditions. In this modeling, material properties are temperature-sensitive since the steep temperature gradient varies the properties significantly. Moreover, the energy needed for the solid-state phase transition is reflected by modifying the specific heat employing the latent heat of fusion. Furthermore, the multi-layer and multi-scan aspects of metal AM are considered by including the temperature history from previous layers and scans. Results from the analytical RS model presented excellent agreement with XRD measurements employed to determine the RS in the Ti-6Al-4V specimens. View Full-Text
Keywords: selective laser melting; residual stress; direct metal deposition; thermomechanical analytical modeling; Ti-6Al-4V selective laser melting; residual stress; direct metal deposition; thermomechanical analytical modeling; Ti-6Al-4V
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MDPI and ACS Style

Mirkoohi, E.; Li, D.; Garmestani, H.; Liang, S.Y. Analytical Modeling of Residual Stress in Laser Powder Bed Fusion Considering Volume Conservation in Plastic Deformation. Modelling 2020, 1, 242-259. https://doi.org/10.3390/modelling1020015

AMA Style

Mirkoohi E, Li D, Garmestani H, Liang SY. Analytical Modeling of Residual Stress in Laser Powder Bed Fusion Considering Volume Conservation in Plastic Deformation. Modelling. 2020; 1(2):242-259. https://doi.org/10.3390/modelling1020015

Chicago/Turabian Style

Mirkoohi, Elham; Li, Dongsheng; Garmestani, Hamid; Liang, Steven Y. 2020. "Analytical Modeling of Residual Stress in Laser Powder Bed Fusion Considering Volume Conservation in Plastic Deformation" Modelling 1, no. 2: 242-259. https://doi.org/10.3390/modelling1020015

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