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Laser Forming of Metal Foam: Mechanisms, Efficiency and Prediction Laser Forming of Metal Foam: Mechanisms, Efficiency and Prediction Tizian Bucher Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Graduate School of Arts and Sciences COLUMBIA UNIVERSITY 2019 © 2018 Tizian Bucher All rights reserved ABSTRACT Laser Forming of Metal Foam: Mechanisms, Efficiency, and Prediction Tizian Bucher This thesis deals with metal foam, a relatively new material whose tremendous potential has been identified early on. The material is an excellent shock absorber and also has a very high strength-to-weight ratio, properties that are highly desirable particularly within the aerospace and automotive industries. Despite the material’s immense potential, hardly any metal foam products have made it past the prototype stage. The reason is that the material is difficult to manufacture in the shapes required in industrial applications. Oftentimes, applications require sheets to be bent into specific shapes, yet bending is not possible with conventional methods. Laser forming is currently the only method that shows promise to bend metal foam panels to a range of shapes. In this thesis, the analysis of laser forming of metal foam was taken far beyond the experimental work that has been delivered thus far. A thorough analysis was performed of the thermo-mechanical bending mechanism that governs the deformation of metal foam during laser forming. This knowledge was then used to explain the effect of the process condition on the bending efficiency and the bending limit. Additionally, the impact of laser forming on the metal foam properties was explored. Experimental results were complemented by numerical results that were validated both thermally (using infrared imaging) as well as mechanically (using digital image correlation). Numerical models with different levels of geometrical complexities were used, and the effect of the model geometry on the predictive accuracy was explored. In the second half of the thesis, the aforementioned effort was extended to metal foam sandwich panels, in which metal foam is sandwiched between two sheets of solid metal. The material again has a high strength-to-weight ratio and excellent shock absorption capacity, while also being stiff and core-protective. Just like metal foam alone, metal foam sandwich panels are typically manufactured in flat sheets, and failure-free bending can only be achieved using lasers. The analysis was again initiated with the bending mechanism. It was revisited whether the foam core still follows the same bending mechanism, and how its deformation is affected by the interaction with the solid facesheets. This insight was then used to elucidate the bending efficiency and limit at different process conditions, as well as the impact of the process on the material performance. Additionally, the effect of the sandwich panel manufacturing method on the process outcome was investigated. This was achieved by contrasting two sandwich panel types with a different foam core structure, foam core composition, facesheet composition and facesheet attachment method. Lastly, three-dimensional deformation of metal foam sandwich panels into typical non-Euclidean shapes such as bowl and saddle shapes was explored. It was shown that a significant amount of 3D deformation can be induced. At the same time, it was discussed that the achievable deformation is limited to moderate curvatures, since only a limited amount of in-plane strains may be induced using laser forming. The aforementioned experimental efforts were again accompanied by numerical efforts. Sandwich panel models with different levels of geometrical complexity were used to study all aspects pertaining to the process, and the properties to the facesheet/foam core interface were discussed. Overall, the work in this thesis demonstrated that laser forming is capable of bending metal foam panels and metal foam sandwich panels up to large bending angles without causing failures, while maintaining the favorable properties of the material. Conceptual, experimental and numerical groundwork was laid towards a successful implementation of the material in industrial applications. Table of Contents List of Figures ............................................................................................................................... vi List of Tables ............................................................................................................................. xxii Chapter 1: Introduction ............................................................................................................... 1 1.1 Metal Foam ........................................................................................................................... 1 1.2 Sandwich Panels with Metal Foam Cores ............................................................................ 2 1.3 Manufacturing Processes ...................................................................................................... 4 1.4 Laser Forming ....................................................................................................................... 7 1.5 Experiments .......................................................................................................................... 9 1.5.1 Materials ........................................................................................................................ 9 1.5.1.1 AlSi7 Metal Foam ................................................................................................... 9 1.5.1.2 Sandwich Panel Foam Core & Facesheets............................................................ 12 1.5.2 Experimental Methods ................................................................................................. 14 1.5.2.1 Non-Dimensional Analysis of Process Conditions ............................................... 15 1.5.2.2 Thermal Imaging ................................................................................................... 17 1.5.2.3 Digital Image Correlation ..................................................................................... 20 1.6 Simulation ........................................................................................................................... 23 1.6.1 Uncoupling ................................................................................................................... 23 1.6.2 Foam Geometries ......................................................................................................... 30 1.6.2.1 Kelvin-cell Model ................................................................................................. 31 1.6.2.2 Voxel Model ......................................................................................................... 32 1.6.2.3 Equivalent Model .................................................................................................. 34 1.6.3 Heat Transfer through Metal Foam.............................................................................. 36 1.6.3.1 Gas Conduction through Cavities ......................................................................... 37 1.6.3.2 Natural Convection in Cavities ............................................................................. 37 i 1.6.3.3 Thermal Radiation through Foam ......................................................................... 38 1.6.4 Sandwich Modeling ..................................................................................................... 41 1.6.4.1 Interface ................................................................................................................ 41 1.6.4.2 2D Sandwich Models ............................................................................................ 47 1.6.4.3 3D Sandwich Models ............................................................................................ 48 1.6.5 Initial Conditions and Boundary Conditions ............................................................... 49 1.6.6 User Subroutines .......................................................................................................... 49 1.6.6.1 2D Dflux ............................................................................................................... 49 1.6.6.2 3D radial Dflux ..................................................................................................... 52 1.6.6.3 3D circular Dflux .................................................................................................. 53 1.6.6.4 Gapcon .................................................................................................................. 54 1.6.6.5 FILM ..................................................................................................................... 55 1.7 Organization and Objectives of Dissertation ...................................................................... 56 Chapter 2: Effect of Geometrical Modeling on the Prediction of Laser-Induced Heat Transfer in Metal Foam ............................................................................................................. 59 2.1 Introduction ......................................................................................................................... 59 2.2 Background ......................................................................................................................... 62 2.2.1 Heat Transfer in Metal Foams ....................................................................................
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