Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Analytical Modeling of Residual Stress in Laser Powder Bed Fusion

Version 1 : Received: 23 January 2020 / Approved: 23 January 2020 / Online: 23 January 2020 (16:12:51 CET)

How to cite: Mirkoohi, E.; Ning, J.; Liang, S. Analytical Modeling of Residual Stress in Laser Powder Bed Fusion. Preprints 2020, 2020010268. Mirkoohi, E.; Ning, J.; Liang, S. Analytical Modeling of Residual Stress in Laser Powder Bed Fusion. Preprints 2020, 2020010268.


Rapid and accurate prediction of residual stress in metal additive manufacturing processes is of great importance to guarantee the quality of the fabricated part to be used in a mission-critical application in the aerospace and automotive industries. Experimentation and numerical modeling are valuable tools for measuring and predicting the residual stress; however, to-date conducting experimentation and numerical modeling is expensive and time-consuming. Thus, herein, a physics-based thermomechanical analytical model is proposed to predict the residual stress of the additively manufactured part rapidly and accurately. A moving point heat source approach is used to predict the temperature field by considering the effects of scan strategies, heat loss, and energy needed for solid-state phase transformation. Due to the high temperature gradient in this process, part experiences a high amount of thermal stress following solidification which may exceed the yield strength of the material. The thermal stress is obtained using Green’s function of stresses due to the point body load. The Johnson-Cook flow stress model is used to predict the yield surface of the part under repeated heating and cooling. As a result of the cyclic heating and cooling and the fact that the material is yielded, the residual stress build-up is predicted based on incremental plasticity and kinematic hardening behavior of the metal according to the property of volume invariance in plastic deformation in coupling with the equilibrium and compatibility conditions. The computational methodology is realized with the laser powder fusion of maraging steel 350 as a material of example. The validation of the predictive models has been presented in terms of the comparison of predicted and measured scan-direction and build-direction residual stress distributions along depth of build under various process parameter combinations. Moreover, for the first time, the Jonson-Cook parameters of maraging steel 350 are predicted using analytical modeling of machining forces and non-linear optimization techniques.


residual stress prediction; maraging steel 350; experimental measurement of residual stress


Engineering, Mechanical Engineering

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