A Thermodynamic Framework for Additive Manufacturing, using Amorphous Polymers, Capable of Predicting Residual Stress, Warpage and Shrinkage

TL;DR

This paper introduces a thermodynamic framework for amorphous polymers in additive manufacturing that predicts residual stresses, warpage, and shrinkage by modeling thermal and mechanical interactions during cooling and solidification.

Contribution

It develops a novel thermodynamic model incorporating shrinkage and viscosity changes to predict residual stresses and distortions in FDM 3D printed parts.

Findings

Nearly equibiaxial tensile stress in the core region predicts crack propagation.

Layer interactions cause complex residual stress distributions.

The model suggests potential failure modes like delamination during cooling.

Abstract

A thermodynamic framework has been developed for a class of amorphous polymers used in fused deposition modeling (FDM), in order to predict the residual stresses and the accompanying distortion of the geometry of the printed part (warping). When a polymeric melt is cooled, the inhomogeneous distribution of temperature causes spatially varying volumetric shrinkage resulting in the generation of residual stresses. Shrinkage is incorporated into the framework by introducing an isotropic volumetric expansion/contraction in the kinematics of the body. We show that the parameter for shrinkage also appears in the systematically derived rate-type constitutive relation for the stress. The solidification of the melt around the glass transition temperature is emulated by drastically increasing the viscosity of the melt. In order to illustrate the usefulness and efficacy of the derived constitutive relation, we consider four ribbons of polymeric melt stacked on each other such as those extruded using a flat nozzle: each layer laid instantaneously and allowed to cool for one second before another layer is laid on it. Each layer cools, shrinks and warps until a new layer is laid, at which time the heat from the newly laid layer flows and heats up the bottom layers. The residual stresses of the existing and newly laid layers readjust to satisfy equilibrium. Such mechanical and thermal interactions amongst layers result in a complex distribution of residual stresses. The plane strain approximation predicts nearly equibiaxial tensile stress conditions in the core region of the solidified part, implying that a pre-existing crack in that region is likely to propagate and cause failure of the part during service. The free-end of the interface between the first and the second layer is subjected to the largest magnitude of combined shear and tension in the plane with a propensity for delamination.