Erik R. Denlinger

The Finite Element Method for the Thermo-Mechanical Modeling of Additive Manufacturing Processes

This chapter outlines the methodology to numerically solve the equations which describe the thermal and mechanical equations for AM processes. This discussion follows that used by the Netfabb Simulation tool which was used to complete the FE validation studies in the rest of the book. However, the modeling approach is general, and may be applied to any AM code. First the necessity of using the non-linear finite element method is shown then a brief explanation of the non-linear FE process is given. The weakly or decoupled modeling method is described, along with reasons for its usefulness and caveats regarding its limitations. The thermal and mechanical models are described with the relevant boundary conditions. A treatment of the primary methods to model the addition of material is given, along with the advantages and limitations of each method. A brief discussion how temperature dependent material properties are applied in the modeling tool is presented. Meshing concerns and methods are then described. Methods of verifying a model is numerically correct by comparing model results to problems with known answers are discussed at length. Finally validation methods are outlined along with error metrics and a discussion of validation criteria.

Chapter 9 – Residual Stress and Distortion Modeling of Electron Beam Direct Manufacturing Ti-6Al-4V✶

In this work, a finite element model is developed for predicting the thermo-mechanical response of Ti-6Al-4V during electron beam deposition. A three-dimensional thermo-elasto-plastic analysis is performed to model distortion and residual stress in the workpiece and experimental in situ temperature and distortion measurements are performed during the deposition of a single bead wide, 16 layer high wall build for model validation. Post-process Blind Hole Drilling residual stress measurements are also performed. Both the in situ distortion and post-process residual stress measurements suggest that stress relaxation occurs during the deposition of Ti-6Al-4V. A method of accounting for such stress relaxation in thermo-elasto-plastic simulations is proposed where both stress and plastic strain is reset to zero, when the temperature exceeds a prescribed stress relaxation temperature. Inverse simulation is used to determine the values of the absorption efficiency and the emissivity of electron beam deposited wire-fed Ti-6Al-4V, as well as the appropriate stress relaxation temperature.

Chapter 11 – Mitigation of Distortion in Large Additive Manufacturing Parts✶

Distortion mitigation techniques for large parts constructed by Additive Manufacturing (AM) processes are investigated. Unwanted distortion accumulated during deposition is a common problem encountered in AM processes. The proposed strategies include depositing equal material on each side of a substrate to balance the bending moment about the neutral axis of the workpiece and applying heat to straighten the substrate. Small finite element (FE) models are used to predict the effectiveness of the mitigation strategies in order to reduce computation time and to avoid costly experiments. The strategy of adding sacrificial material is shown to be most effective and is then applied to the manufacture of a large electron beam deposited part consisting of several thousand deposition passes. The deposition strategy is shown to reduce the maximum longitudinal bending distortion in the large AM part by 91%. The small FE models accurately predict the distortion mitigation achieved from the manufacture of the large part. Experimental observations made here, as well as FE model results, suggest that the order in which the balancing material is added significantly affects the success of the proposed distortion mitigation strategy.

Development and Numerical Verification of a Dynamic Adaptive Mesh Coarsening Strategy for Simulating Laser Power Bed Fusion Processes

Abstract A key challenge in the modeling of powder bed fusion processes is the extremely dense mesh required to capture the melt pool as using traditional static conforming meshes, good meshing practice would require 1–4 elements across the width of the melt pool to correctly simulate thermal equilibrium. For powder bed processes this would require 1E6 or more elements to model small components, making it computational infeasible to model such behaviors. Implementing nonconforming meshes is a common technique to reduce mesh density, but the method is still bound to the same convergence criteria. This work presents a dynamically adaptive meshing strategy to reduce the computational time of thermal powder bed modeling. A verification study using a static conforming, static nonconforming meshes, and several moving adaptive models is completed. It is shown that using such a dynamic meshing strategy can decrease run time by 432 times from the baseline static conforming mesh while keeping the error in thermal gradients less than 7%.

Thermo-Mechanical Modeling of Large Electron Beam Builds

Abstract A finite element modeling strategy is developed to allow for the prediction of distortion accumulation in additive manufacturing large parts (on the order of meters). A 3D thermo-elasto-plastic analysis is performed using a hybrid quiet inactive element activation strategy combined with adaptive coarsening. At the beginning for the simulation, before material deposition commences, elements corresponding to deposition material are removed from the analysis, then elements are introduced in the model layer by layer in a quiet state with material properties rendering them irrelevant. As the moving energy source is applied on the part, elements are switched to active by restoring the actual material properties when the energy source is applied on them. A layer by layer coarsening strategy merging elements in lower layers of the build is also implemented such that while elements are added on the top of build, elements are merged below maintaining a low number of degrees of freedom in the model for the entire simulation. The effectiveness of the modeling strategy is demonstrated and experimentally validated on a large electron beam deposited Ti-6Al-4V part consisting of 107 deposition layers. The simulation and experiment show good agreement with a maximum error of 29%.A finite element modeling strategy is developed to allow for the prediction of distortion accumulation in additive manufacturing large parts (on the order of meters). A 3D thermo-elasto-plastic analysis is performed using a hybrid quiet inactive element activation strategy combined with adaptive coarsening. At the beginning for the simulation, before material deposition commences, elements corresponding to deposition material are removed from the analysis, then elements are introduced in the model layer by layer in a quiet state with material properties rendering them irrelevant. As the moving energy source is applied on the part, elements are switched to active by restoring the actual material properties when the energy source is applied on them. A layer by layer coarsening strategy merging elements in lower layers of the build is also implemented such that while elements are added on the top of build, elements are merged below maintaining a low number of degrees of freedom in the model for the entire simulation. The effectiveness of the modeling strategy is demonstrated and experimentally validated on a large electron beam deposited Ti-6Al-4V part consisting of 107 deposition layers. The simulation and experiment show good agreement with a maximum error of 29%.

Chapter 13 – Thermomechanical Model Development and In Situ Experimental Validation of the Laser Powder-Bed Fusion Process✶

A three-dimensional finite element model is developed to allow for the prediction of temperature, residual stress, and distortion in multi-layer Laser Powder-bed Fusion builds. Undesirable residual stress and distortion caused by thermal gradients are a common source of failure in AM builds. A non-linear thermoelastoplastic model is combined with an element coarsening strategy in order to simulate the thermal and mechanical response of a significant volume of deposited material (38 layers and 91 mm3). It is found that newly deposited layers experience the greatest amount of tensile stress, while layers beneath are forced into compressive stress. The residual stress evolution drives the mechanical response of the workpiece. The model is validated by comparing the predicted in-situ and post-process distortion to experimental measurements taken on the same geometry. The model accurately predicts the distortion of the workpiece (5% error).