Selective Laser Melted (SLM) Additively Manufactured (AM) metal parts are of special interest to many industries because their designs can be made arbitrarily complex while still maintaining bulk type mechanical properties. However, the large thermal gradients inherent to the SLM process generate residual stresses (RS) and distortions that are detrimental to the fit, functionality and integrity of parts. Predicting the state of stresses in as-built 3D printed parts is a difficult problem that currently has only been approached with the use of transient thermomechanical Finite Element Models (FEMs). The nonlinearities associated with AM processes are difficult to capture in these FEMs without incurring into extreme mesh refinements methods which ultimately limit the capability of the simulations. Thus, a significant amount of research has been dedicated to the development of simplified analyses techniques for the prediction of RS due to AM processes. This work presents a novel analytical framework that combines lumped capacitance nonlinear heat transfer with time dependent classical lamination theory and an elastoplastic material model to efficiently and accurately predict residual stresses in as-built SLM parts. The numerical implementation of the analytical model was performed without the need of FEMs, using Python scripting language to generate a simulation capable of producing layer-by-layer temperature time histories as well as time histories of the residual stresses and strains. The simulation was validated using Neutron Diffraction (ND) residual strains measurements of IN718 and Haynes 282 samples, as well as Synchrotron X-Ray Diffraction (XRD) strain data published by the National Institute of Standards and Technology (NIST). Comparisons between the simulation predictions and the experimental data showed excellent agreement for the in-plane strain directions, and general agreement for the out of plane strain component, highlighting an area where further development can be implemented. Significantly, every simulation was able to complete the thermal and structural analysis in a combined time range of 10-20 minutes, compared to the combined solving times associated with nonlinear transient thermal and structural FEA problems, usually in the order of hours to days. The findings of this work pave the way for a better understanding of the cause and effect relationship between SLM printing parameters and the resulting residual stress fields by developing an analytical framework that can incorporate statistical methods, which is not possible with current nonlinear thermomechanical FEMs.


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Graduation Date





Raghavan, Seetha


Doctor of Philosophy (Ph.D.)


College of Engineering and Computer Science


Mechanical and Aerospace Engineering

Degree Program

Mechanical Engineering




CFE0009381; DP0027104





Release Date

December 2022

Length of Campus-only Access


Access Status

Doctoral Dissertation (Open Access)

Included in

Manufacturing Commons