Accurate prediction of melt pool shapes in laser powder bed fusion by the non-linear temperature equation including phase changes - isotropic versus anisotropic conductivity

In this contribution, we validate a physical model based on a transient temperature equation (including latent heat) w.r.t. the experimental set AMB2018-02 provided within the additive manufacturing benchmark series, established at the National Institute of Standards and Technology, USA. We aim at predicting the following quantities of interest: width, depth, and length of the melt pool by numerical simulation and report also on the obtainable numerical results of the cooling rate. We first assume the laser to posses a double ellipsoidal shape and demonstrate that a well calibrated, purely thermal model based on isotropic thermal conductivity is able to predict all the quantities of interest, up to a deviation of maximum 7.3\% from the experimentally measured values. However, it is interesting to observe that if we directly introduce, whenever available, the measured laser profile in the model (instead of the double ellipsoidal shape) the investigated model returns a deviation of 19.3\% from the experimental values. This motivates a model update by introducing anisotropic conductivity, which is intended to be a simplistic model for heat material convection inside the melt pool. Such an anisotropic model enables the prediction of all quantities of interest mentioned above with a maximum deviation from the experimental values of 6.5\%. We note that, although more predictive, the anisotropic model induces only a marginal increase in computational complexity

Suitably graded THB-spline refinement and coarsening: Towards an adaptive isogeometric analysis of additive manufacturing processes

In the present work we introduce a complete set of algorithms to efficiently perform adaptive refinement and coarsening by exploiting truncated hierarchical B-splines (THB-splines) defined on suitably graded isogeometric meshes, that are called admissible mesh configurations. We apply the proposed algorithms to two-dimensional linear heat transfer problems with localized moving heat source, as simplified models for additive manufacturing applications. We first verify the accuracy of the admissible adaptive scheme with respect to an overkilled solution, for then comparing our results with similar schemes which consider different refinement and coarsening algorithms, with or without taking into account grading parameters. This study shows that the THB-spline admissible solution delivers an optimal discretization for what concerns not only the accuracy of the approximation, but also the (reduced) number of degrees of freedom per time step. In the last example we investigate the capability of the algorithms to approximate the thermal history of the problem for a more complicated source path. The comparison with uniform and non-admissible hierarchical meshes demonstrates that also in this case our adaptive scheme returns the desired accuracy while strongly improving the computational efficiency.Comment: 20 pages, 12 figure

An Ontology for Defect Detection in Metal Additive Manufacturing

A key challenge for Industry 4.0 applications is to develop control systems for automated manufacturing services that are capable of addressing both data integration and semantic interoperability issues, as well as monitoring and decision making tasks. To address such an issue in advanced manufacturing systems, principled knowledge representation approaches based on formal ontologies have been proposed as a foundation to information management and maintenance in presence of heterogeneous data sources. In addition, ontologies provide reasoning and querying capabilities to aid domain experts and end users in the context of constraint validation and decision making. Finally, ontology-based approaches to advanced manufacturing services can support the explainability and interpretability of the behaviour of monitoring, control, and simulation systems that are based on black-box machine learning algorithms. In this work, we provide a novel ontology for the classification of process-induced defects known from the metal additive manufacturing literature. Together with a formal representation of the characterising features and sources of defects, we integrate our knowledge base with state-of-the-art ontologies in the field. Our knowledge base aims at enhancing the modelling capabilities of additive manufacturing ontologies by adding further defect analysis terminology and diagnostic inference features

Impact of interaction forces in first order many-agent systems for swarm manufacturing

We study the large time behavior of a system of interacting agents modeling the relaxation of a large swarm of robots, whose task is to uniformly cover a portion of the domain by communicating with each other in terms of their distance. To this end, we generalize a related result for a Fokker-Planck-type model with a nonlocal discontinuous drift and constant diffusion, recently introduced by three of the authors, of which the steady distribution is explicitly computable. For this new nonlocal Fokker-Planck equation, existence, uniqueness and positivity of a global solution are proven, together with precise equilibration rates of the solution towards its quasi-stationary distribution. Numerical experiments are designed to verify the theoretical findings and explore possible extensions to more complex scenarios

Sparse-grids uncertainty quantification of part-scale additive manufacturing processes

The present paper aims at applying uncertainty quantification methodologies to process simulations of powder bed fusion of metal. In particular, for a part-scale thermomechanical model of an Inconel 625 super-alloy beam, we study the uncertainties of three process parameters, namely the activation temperature, the powder convection coefficient and the gas convection coefficient. First, we perform a variance-based global sensitivity analysis to study how each uncertain parameter contributes to the variability of the beam displacements. The results allow us to conclude that the gas convection coefficient has little impact and can therefore be fixed to a constant value for subsequent studies. Then, we conduct an inverse uncertainty quantification analysis, based on a Bayesian approach on synthetic displacements data, to quantify the uncertainties of the two remaining parameters, namely the activation temperature and the powder convection coefficient. Finally, we use the results of the inverse uncertainty quantification analysis to perform a data-informed forward uncertainty quantification analysis of the residual strains. Crucially, we make use of surrogate models based on sparse grids to keep to a minimum the computational burden of every step of the uncertainty quantification analysis. The proposed uncertainty quantification workflow allows us to substantially ease the typical trial-and-error approach used to calibrate power bed fusion part-scale models, and to greatly reduce uncertainties on the numerical prediction of the residual strains. In particular, we demonstrate the possibility of using displacement measurements to obtain a data-informed probability density function of the residual strains, a quantity much more complex to measure than displacements

Additive manufacturing graded-material design based on phase-field and topology optimization

In the present work we introduce a novel graded-material design for additive manufacturing based on phase-field and topology optimization. The main novelty of this work comes from the introduction of an additional phase-field variable in the classical single-material phase-field topology optimization algorithm. This new variable is used to grade the material properties in a continuous fashion. Two different numerical examples are discussed, in both of them we perform sensitivity studies to asses the effects of different model parameters onto the resulting structure. From the presented results we can observe that the proposed algorithm adds additional freedom in the design, exploiting the higher flexibility coming from additive manufacturing technology

Graded-material Design based on Phase-field and Topology Optimization

In the present work we introduce a novel graded-material design based on phase-field and topology optimization. The main novelty of this work comes from the introduction of an additional phase-field variable in the classical single-material phase-field topology optimization algorithm. This new variable is used to grade the material properties in a continuous fashion. Two different numerical examples are discussed, in both of them we perform sensitivity studies to asses the effects of different model parameters onto the resulting structure. From the presented results we can observe that the proposed algorithm adds additional freedom in the design, exploiting the higher flexibility coming from additive manufacturing technology

Structural multiscale topology optimization with stress constraint for additive manufacturing

In this paper a phase-field approach for structural topology optimization for a 3D-printing process which includes stress constraint and potentially multiple materials or multiscales is analyzed. First order necessary optimality conditions are rigorously derived and a numerical algorithm which implements the method is presented. A sensitivity study with respect to some parameters is conducted for a two-dimensional cantilever beam problem. Finally, a possible workflow to obtain a 3D-printed object from the numerical solutions is described and the final structure is printed using a fused deposition modeling (FDM) 3D printer

Additive manufacturing graded-material design based on phase-field and topology optimization

In the present work we introduce a novel graded-material design for additive manufacturing based on phase-field and topology optimization. The main novelty of this work comes from the introduction of an additional phase-field variable in the classical single-material phase-field topology optimization algorithm. This new variable is used to grade the material properties in a continuous fashion. Two different numerical examples are discussed, in both of them we perform sensitivity studies to asses the effects of different model parameters onto the resulting structure. From the presented results we can observe that the proposed algorithm adds additional freedom in the design, exploiting the higher flexibility coming from additive manufacturing technology