Analisi micromeccaniche delle fasi di processo per stampa 3D con tecnologia Binder Jetting

Binder Jetting is an efficient and rapid three-dimensional printing method for digital additive manufacturing. This kind of technique belongs to the so-called “powder bed-based methods” and can form parts by selectively gluing a powder with a polymeric liquid binder. The printing process begins with the deposition of a thin micrometric layer of powder leveled by a counterclockwise rotating roller inside a job-box. A movable print-head then selectively pours small droplets of the binding agent over the layer in a fashion that follows the geometry of the final part cross-section, which is given in input by a CAD model. The job-box is finally lowered by a distance equal to the desired layer thickness. The previous operations are repeated for several bidimensional layers which are cyclically stacked together to achieve the three-dimensionality of the part, named green. The green has no remarkable mechanical properties and is characterized by a porous microstructure: this is why it must be subjected to many thermal post-printing processes, like curing, debinding, and sintering, to achieve its definitive features. Thanks to the fact that it deals with single layers, Binder Jetting allows the fabrication of objects with complex geometries often unobtainable by traditional manufacturing operations (i.e., it can create holed parts). Differently from other additive manufacturing techniques, it can also handle a broad range of powder materials, including polymers, metals, and ceramics. Even though Binder Jetting seems to be a very versatile type of fabrication, the identification of the conditions capable of maximizing the final part performances is still an open issue: the influence of the several input and printing parameters on the quality of the produced objects is not comprehensively understood so far, and more research is needed. Powder characteristics are probably the most crucial factor of powder bed-based additive manufacturing because they directly determine the density and the void fraction of the final components, their surface finish, and their mechanical properties; moreover, they govern the permeation mechanisms of the liquid binder into the bed and affects the sinterability. It is generally possible to increase the green density of a printed part by choosing a correct particle size distribution of the constituent powder: this will generally result in the improving of the fully post-processed components properties and of the related dimensional accuracy. In fact, the amount of sintering required to the strengthening directly depends on the green density: more compact parts require less sintering and hence they undergo less shrinkage and distortion during the heat treatment. It follows that a better understanding of the packing behavior of a powder is highly suggested for powder-based manufacturing because it can provide a guideline aimed at the fabrication of better parts, regardless of which machine is used or which kind of material is processed. The characterization of the binder jetted powder bed is usually carried out experimentally with a trial and error approach: the printing parameters and the powder features are varied to determine their best combination which optimize the overall quality of the printed objects. On the contrary, in the this paper is presented an attempt of numerical modeling of the powder packing dynamics that could provide useful support to the prediction of the bed morphology and density. In the first part of the work, a comprehensive description of the state-of-the-art is presented regarding the Binder Jetting technology, listing the critical developments and foundings made until now. The analysis is then moved to the main packing theories reported in the scientific literature: the concept of the Random Close Packing is described and the influence of the dimensions of the powder pseudo-spherical grains on the properties of the discrete systems they form is explained, with particular attention to the particle size ratio parameter: high values of the packing density (> 80%) can be ideally reached by using bimodal systems obtained by the addition of a 30% in volume of a fine fraction to a coarse powder. The information found in the literature helped to interpret the data collected regarding two different available mixtures for Binder Jetting consisting of a gas-atomized AISI 316L steel powder and a ceramic powder. Granulometric and rheological analyses were conducted on the mixtures to evaluate the geometric characterization of their grains, their particle size distribution, and their bulk properties such as the apparent and tapped density and the Hausner Ratio related to their flowability. In the paper it is also described the technique adopted to measure the powder bed density of the stack of layers of the two mixtures deposed by a Binder Jetting 3D machine during the printing process. The numerical simulation of the packing behavior of the powders was first developed through the so-called Lubachevsky-Stillinger Algorithm, a model that creates jammed configurations of rigid spherical particles starting from a random generation of points that grow in size inside a periodic box. It was also written a MATLAB code that allowed to evaluate the packing density of the cluster and its average coordination number, defined as the ratio between the total number of interparticle contacts and the total number of the spheres in the packing. The results were in good agreement concerning the experimental ones, but not very precise because the model was purely geometrical and was not able to take into account the physics involved in the real packing problem. In order to reproduce more accurate analysis, powder packing dynamics were simulated using a Discrete Element Method (DEM) model able to solve the contact forces and moments between single particles thanks to an explicit time integration algorithm. The implementation of the code was done with the open source Linux software YADE based on the c++ and Python languages. In the paper are described the Mass Scaling operations that were adopted to reduce the overall computational simulation time. The real mechanical and geometrical characteristics of the two available powders were considered to recreate the relative packing behavior. Very good results were found in terms of packing density, even neglecting Van Der Waals interparticle forces since the smallest powder grains were sufficiently large (5 - 10 μm). Finally, the DEM analysis was adapted to reproduce the practical process of the layer deposition made a Binder Jetting printer. In the paper are described in detail the computational steps that simulate the creation of a multilayer particle bed leveled by a cylindrical roller. The influence of the layer thickness against the bed void fraction is also shown. The outputs of the model are again validated with respect to the experimental ones. The studies carried out within this document are part of the research project conducted within the FUNTASMA (FUNcTionAl Sintered MAterials) interdepartmental laboratory of the Politecnico di Milano University. The laboratory hosts the first Binder Jetting machine in Italy for the 3D printing of metallic and ceramic powders, which is specifically the Innovent+ model produced by ExOne company. The Innovent+ printer is a multi-purpose additive platform suited to support training and testing or printing methods on a smaller scale.

Il Binder Jetting è un modalità di stampa 3D efficiente e rapida per la produzione digitale additiva. Tale tecnologia appartiene ai metodi di fabbricazione a letto di polvere ed è in grado di realizzare delle componenti tridimensionali attraverso la selettiva deposizione di un legante polimerico liquido su dei layer granulari. Le parti stampate prendono il nome di green, sono contraddistinte da una microstruttura porosa e non presentano caratteristiche meccaniche di rilievo: per tali ragioni, esse vengono sottoposte a dei trattamenti termici tali da conferire loro le proprietà finali desiderate. Il Binder Jetting si dimostra particolarmente versatile in quanto consente di processare indistintamente materiali di natura differente (metalli, ceramici, polimeri, …) e di generare manufatti con geometrie complesse; nonostante ciò, la scarsa comprensione dell’effettiva influenza esercitata dai singoli fattori di stampa sulla qualità delle parti ostacola ad oggi l’introduzione di tale tecnica nella produzione su larga scala. Le caratteristiche morfologiche delle polveri lavorate rappresentano verosimilmente il fattore più cruciale dei metodi additivi a letto: da esse dipendono infatti la densità relativa, le proprietà meccaniche e l’accuratezza dimensionale dei pezzi fabbricati. L’utilizzo di miscele contraddistinte da opportune distribuzioni granulometriche potrebbe incrementare la qualità di questi ultimi a prescindere da quale sia il rispettivo materiale costituente. Ad oggi la ricerca in materia viene perlopiù effettuata attraverso analisi sperimentali mirate a stimare la correlazione empirica che sussiste tra i parametri di processo e gli output di stampa. Nel presente elaborato vengono invece proposti dei tentativi di modellazione del comportamento delle miscele granulari impiegate nel Binder Jetting con lo scopo di fornire un supporto utile per simulazione della microstruttura dei letti e la predizione della rispettiva frazione volumetrica occupata. La riproduzione numerica degli impacchettamenti delle polveri è stata realizzata in prima battuta per mezzo dell’algoritmo Lubachevsky-Stillinger, un metodo in grado di ricreare agglomerati di elementi sferici a partire dalla generazione pseudo-casuale di nuvole di punti che crescono di dimensione all’interno di un dominio periodico. Nonostante i riscontri soddisfacenti, tale modello manifesta una connotazione puramente geometrica e non è stato in grado di cogliere a pieno la fisica alla base del reale problema di packing. Al fine di sviluppare delle analisi più accurate, l’evoluzione dinamica dei sistemi granulari è stata ulteriormente simulata ricorrendo ad un approccio ad elementi discreti (DEM) in grado di calcolare le forze ed i momenti di contatto tra le particelle grazie alla risoluzione di un algoritmo esplicito di integrazione nel tempo. L’implementazione del codice è stata effettuata in un sistema operativo Linux attraverso il software open source YADE basato sui linguaggi c++ e Python. La modellazione ha permesso di riprodurre inoltre il processo di deposizione dei layer di polvere operato dalle stampanti a Binder Jetting. Tutti i risultati numerici sono stati confrontati con quelli ottenuti sperimentalmente attraverso le analisi granulometriche e reologiche di due polveri adibite alla fabbricazione additiva direttamente a disposizione in questa sede e composte nello specifico in acciaio AISI 316L ed allumina. Per entrambe le miscele sono state ricavare le caratteristiche geometriche delle particelle, le densità relative apparenti e tappate e la frazione piena dei letti. Il lavoro discusso nel presente elaborato rientra all’interno del progetto di ricerca del laboratorio interdisciplinare FUNTASMA (FUNcTionAl Sintered MAterials) del Politecnico di Milano, il quale ospita la prima macchina in Italia per la stampa 3D con tecnologia Binder Jetting a letto di polvere per materiali metallici e ceramici.