There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

In an effort to unify the various phase-field models that have been used to study solidification, we have developed a class of phase-field models for crystallization of a pure substance from its melt. These models are based on an entropy functional, as in the treatment of Penrose and Fife, and are therefore thermodynamically consistent inasmuch as they guarantee spatially local positive entropy production. General conditions are developed to ensure that the phase field takes on constant values in the bulk phases. Specific forms of a phase-field function are chosen to produce two models that bear strong resemblances to the models proposed by Langer and Kobayashi. Our models contain additional nonlinear functions of the phase field that are necessary to guarantee thermodynamic consistency.

Thermodynamically-consistent phase-field models for solidification

https://re.public.polimi.it/bitstream/11311/1057188/1/Selective-laser-melting-finite-element-modeling-Validation-with-highspeed-imaging-and-lack-of-fusion-defects-prediction_2018.pdf

Selective laser melting finite element modeling: Validation with high-speed imaging and lack of fusion defects prediction

pdf/rapid-prediction-of-real-time-thermal-characteristics-1wtkpf19o9.pdf

Rapid prediction of real-time thermal characteristics, solidification parameters and microstructure in laser directed energy deposition (powder-fed additive manufacturing)

Additive manufacturing (AM) is a novel fabrication technique capable of producing highly complex parts. Nevertheless, a major challenge is the quality assurance of the AM fabricated parts. While there are several ways of approaching this problem, how to develop informative process signatures to detect part anomalies for quality control is still an open question. The objective of this study is to build a new layer-wise process signature model to characterize the thermal-defect relationship. Based on melt pool images, we propose novel layer-wise key process signatures, which are calculated using multilinear principal component analysis (MPCA) and are directly correlated with the layer-wise quality of the part. The resultant layer-wise quality features can be used to predict the overall defect distribution of a fabricated layer during the build. The proposed model is validated through a case study based on a direct laser deposition experiment, where the layer-wise quality of the part is predicted on the fly. The accuracy of prediction is calculated using three measures (i.e., recall, precision, and F-score), showing reasonable success of the proposed methodology in predicting layer-wise quality. The proposed quality prediction methodology enables online process correction to eliminate anomalies and to ultimately improve the quality of the fabricated parts.

Layer-Wise Modeling and Anomaly Detection for Laser-Based Additive Manufacturing

Selective laser melting (SLM) is an additive manufacturing process that creates 3D parts through layer by layer melting and fusion of a metal powder bed. Although a number of finite element models (FEM) have been developed that describe the coupled and complex physics associated with this process, they are typically not suitable for control algorithm design. In this manuscript, a control oriented reduced order model (ROM) to adequately capture these temperature dynamics is proposed and validated against high fidelity FEM simulations. Further, since the laser paths are often repetitive (or consist of repeating sub-trajectories), iterative learning control (ILC) algorithms can be used to obtain suitable laser power profiles to deliver desired temperature field profiles. However, the process is inherently multiple input single output (MISO), therefore, a suitable output is constructed in such a way so as to the make the system passive. A passivity-based ILC law is then designed to drive this synthesized output to a desired profile and a convergence criterion for this law derived. The proposed ILC update law is implemented on both models and the results are compared for a set of candidate laser paths. Finally, the ILC update law is implemented on the high-fidelity FEM to melt a ring geometry to demonstrate the capability of the ILC algorithm to generate optimal laser power profiles for creating complicated geometries on large powder beds.

Passivity-based Iterative Learning Control Design for Selective Laser Melting

A novel approach and finite element formulation for modeling the melting, consolidation, and re-solidification process that occurs in selective laser melting additive manufacturing is presented. Two state variables are introduced to track the phase (melt/solid) and the degree of consolidation (powder/fully dense). The effect of the consolidation on the absorption of the laser energy into the material as it transforms from a porous powder to a dense melt is considered. A Lagrangian finite element formulation, which solves the governing equations on the unconsolidated reference configuration is derived, which naturally considers the effect of the changing geometry as the powder melts without needing to update the simulation domain. The finite element model is implemented into a general-purpose parallel finite element solver. Results are presented comparing to experimental results in the literature for a single laser track with good agreement. Predictions for a spiral laser pattern are also shown.

Heat transfer model and finite element formulation for simulation of selective laser melting

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Passivity-based Iterative Learning Control Design for Selective Laser Melting

Heat transfer model and finite element formulation for simulation of selective laser melting