Thermo-mechanical Simulation of Additive Layer ...

Thermo-mechanical Simulation of Additive Layer Manufacturing of Titanium Aerospace structures N. Keller, F. Neugebauer, H. Xu, V. Ploshikhin Airbus endowed chair for integrative simulation and engineering of materials and processes, University of Bremen, Bremen

1

Introduction

In aerospace engineering light weight constructions are mandatory as they reduce the amount of required propellant and thus costs and CO2 emissions. Therefore a part design minimizing mass while satisfying the functionality is desirable. Modern CAE software enables an efficient topology optimization, which leads to the sufficient weight reduction. On the other hand, the possibilities of manufacturing topology optimized parts are either limited or at great expense. For complex parts in aerospace multiple cost-intensive manufacturing processes are necessary resulting in high effort and severe material waste. Parts need also to be constructed from multiple components, which require additional connecting parts (e.g. for rivets and bolts) and therefore additional weight. Additive Layer Manufacturing (ALM) allows the generation of these parts in one piece in only one manufacturing process with a high complexity and filigree structures with preciseness down to 40µm [1]. However, ALM as a series of micro welding has the same difficulties like usual welding processes because of thermal strains resulting in deformation and residual stress. The present paper presents first results of research towards the development of ALM-process oriented thermo-mechanic simulations based on the method of finite elements (FEM) aiming the prediction of residual stress and deformation.

2

Additive Layer Manufacturing

The term “Additive Layer Manufacturing” names several manufacturing processes for manufacturing parts layer by layer [2]. For the generation of (complex) metallic parts powder based processes like “Selective Laser Melting” (SLM) are often used. In powder deposition processes alternatingly a thin layer of powder is spread by a roller and exposed by a laser beam following a pre-defined trajectory (scanning strategy). By heat diffusion the molten layers consolidate. After exposure of a layer the base plate of the build chamber lowers and the next layer of powder is applied. The repetition of these steps generates the parts (figure 1). Fur-

Figure 1: Principle of ALM processes

thermore so-called support structures are also needed to ensure that the process heat can flow to the base plate to avoid overheating. Since SLM can be considered as a series of micro-welding processes [3], the same problems in the context of residual stresses and deformations as in conventional welding arise. Thereby the local energy input, high cool-down rates in combination with complex macroscopic effects due to part topology lead to an unknown distribution of residual stress [4]. After the process the removal of the support structures results in redistribution of residual stresses and final distortion of the manufactured part.

3

Numerical process simulation

In the recent decades the method of numerical process simulation has become an important and powerful tool to predict residual stress and distortion in thermal manufacturing processes. However, only few macroscopic approaches have been developed for prediction of residual stress and distortion in the ALM process. For example [5], [6], [7] introduced a simulation model for calculation of part distortion in additive manufacturing. The simulation results and characteristics of generated simple parts showed significant agreement and hence where able to show high potential of FEM simulations in the field of additive manufacturing. In [8] a linear thermo-elastic model based on the finite-element method has been developed to simulate the electron beam melting process. Furthermore an adaptive mesh refinement strategy has been implemented. In general most of the research has been done on simulation of (local) thermal effects where models have been developed, which are able to investigate effects on size of one layer or below [9] – [13]. The present paper is focussed on a similar macroscopic model like [5] and is based on the finite element method. In addition it is including microscopic aspects by powder-bulk transformation during the cooling procedure. Therefore a fully automated chain of computation starting from the CAD data has been developed.

4

Simulation model

4.1

Process specific layer based meshing

A FEM Simulation of an ALM process needs to be able to reproduce the layerwise built up of a part and a geometrical accurate representation of the part. For this purpose a mesh generator that creates a layered mesh of hexahedral elements based on two-dimensional cross sections of the part (slices) has been developed. The approach consists of the following steps: 

Overlay of a two-dimensional grid with the sliced layers of the CAD where all segments have the size of the estimated elements. The segments of the grid which contain volume of the part are the basis for the mesh.

 

Detection of four points in those segments to get the nodes for the top face of the element. Thereby the intersecting points of the sliced polygons with the grid define the contour. Connection of these segments with the top faces of the previous layer extrudes the face to a three-dimensional cubic element.

The two-dimensional cross sections are either directly provided by the ALM pre-processing or can be obtained by intersecting the polygon faces in the CAD with severe parallel planes. Figure 2 shows an example of the meshing process on a topology optimized bracket.

Figure 2: Layer based FE mesh of a topology optimized bracket

4.2

ALM process simulation

The process simulation method presented here is based on the assumption that geometric effects have a strong influence onto resulting residual stresses and deformations. Therefore in an alternating process a full layer of elements is activated at once and a constant heat flux density is provided on the whole layer for fractional amount of milliseconds. The heat flux density and exposure time are chosen so that the temperature in the highest element layer exceeds melting temperature, as the mechanical properties do not alter for higher temperatures. Since an ALM part with a height of 10cm can have up to 5000 layers, the simulation with realistic layer sizes is not realizable even with today’s computer technology because of the quantity of needed elements. Hence layers will be summarized in bundles. To include thermal [14] and mechanical behaviour of the loose powder homogenized powder properties are assumed and assigned to the newest activated element layer (table 1). At the end of the exposure (i.e. exceeding liquidus temperature) the material properties of this layer are changed to that of the bulk material. Each exposure is followed by a cooling process of about 10 seconds, representing the application of new powder and movement of the roller which is spreading it, multiplied with the number of layers that were taken together. To realize the heat capacity of the base plate with few elements, the specific heat capacity for the base plate elements is scaled by the ratio of the real volume to the mesh base plate volume. For process simulation of the bracket temperature dependent material properties of Ti64, calculated with JmatPro, where used.

__________________________________________________________________________________ Bulk Powder Base plate __________________________________________________________________________________ Heat conductivity Specific heat capacity Young’s modulus Thermal expansion 0 __________________________________________________________________________________ Table 1: Properties of bulk material, homogenized powder and effective base plate

The Simulations are calculated with MSC.MARC and user subroutines for element activation, heat flux input and material conversion are written in FORTRAN 77. Furthermore a method for choosing time steps in which constant time steps during the exposure and adaptive time steps during the following cooling time is included. Figure 3 is showing the boundary conditions used for the transient/static thermo-mechanical simulation.

Figure 3: Boundary conditions and loads

5

Results

In figure 4 the tendencies of residual stress (von Mises) and in figure 5 the distortion before and after post-processing are shown. After process the part is still fixed to the base plate and the highest residual stress is in connection to the base plate. After post-milling stresses relax and lead to visible deformation in the rear arms of the bracket. The front arms exhibit a lower distortion due to a higher inherent rigidity.

Figure 4: Residual stress distribution

Figure 5: Distortion

5

Summary and further developments

Altogether the simulation model presented here is a further step towards FEM based prediction of residual stresses and distortions in generative processes. However, there are still several challenges in the research field of numerical simulations of the ALM process, including long calculation times, exact thermal and mechanical calibration and the investigation of optimization strategies. By solving these challenges in further steps the derivation of optimal process strategies leading to a computer-based process optimization will be possible.

6

Acknowledgement

The author’s would like to thank Wirtschaftsförderung Bremen for founding project InSiGen and Sikker Rosendal for providing the CAD of the bracket. Furthermore the work of student C. Kober is honoured for technical execution of the mesh generator.

7

References

[1] I. Gibson, D.w. Rosen and B. Stucker, Additive Manufacturing Technologies, Springer, New York Heidelberg Dordrecht London, 2010. [2] Wohlers Associates, Wohlers Report 2012. Additive Manufacturing an 3D Printing State of the Industry Annual Worldwide Progress Report, Wohlers Associates, 2013. [3] B. Baufeld, O. Van der Biest and R. Gault, “Additive manufacturing of Ti–6Al–4V components by shaped metal deposition: Microstructure and mechanical properties”, Materials & Design 31, 2010, pp. 106–111. [4] P. Mercelis and J.-P. Kruth, "Residual stresses in selective laser sintering and selective laser melting", Rapid Prototyping Journal, vol. 12, no. 5, 2006, pp.254 – 265. [5] G. Branner, Modellierung transienter Effekte in der Struktursimulation von Schichtbauverfahren., Herbert Utz, München, 2010.

[6] T. A. Krol, „Modelle zur thermomechanischen Simulation metallverarbeitender Strahlschmelzprozesse“, ANSYS Conference & 26th CADFEM Users' Meeting 2009". Leipzig, 19. November 2009. [7] T.A. Krol, S. Westhaeuser, M.F. Zaeh and J. Schilp, “Development of a SimulationBased Process Chain - Strategy for Different Levels of Detail for the Preprocessing Definitions”, in Boedi, R.; Maurer, W. (ed.): ASIM 2011 - 21. Symposium Simulationstechnik, Winterthur, Switzerland. 7.-9. September 2011. [8] D. Riedlbauer, J. Mergheim, A. McBride and P. Steinmann, “Macroscopic modelling of the selective beam melting process”. Proc. Appl. Math. Mech., vol. 12, no.1, 2012, pp. 381–382. [9] R. B. Patil and V. Yadava, “Finite element analysis of temperature distribution in single metallic powder layer during metal laser sintering”, International Journal of Machine Tools & Manufacture, vol. 47, no. 7-8, 2007, pp. 1069-1080. [10] A.V. Gusarov and I. Smurov, “Modeling the interaction of laser radiation with powder bed at selective laser melting”, Physics Procedia, vol. 5, part B, 2010, pp. 381-394. [11] C. Over, Generative Fertigung von Bauteilen aus Werkzeugstahl X38CrMoV5-1 und Titan TiAl6V4 mit "Selective Laser Melting", Shaker, Aachen, 2003. [12] K. Dai and L. Shaw, “Thermal and mechanical finite element modeling of laser forming from metal and ceramic powders”, Acta Materialia, vol. 52, no. 1, 2004, pp. 69-80. [13] L. Ma, H. Bin, Temperature and stress analysis and simulation in fractal scanning-based laser sintering, International Journal of Advanced Manufacturing Technology, vol. 34, no. 9, 2007, pp. 898-903. [14] S. Sih, J. Barlow, “The Prediction of the Emissivity and Thermal Conductivity of Powder Beds”, Particulate Science and Technology, vol. 22, no. 3, 2004, pp. 291-304.