Thermal stresses and deposition patterns in layered manufacturing

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1 Materials Science and Engineering A317 (2001) Thermal stresses and deposition patterns in layered manufacturing A.H. Nickel *, D.M. Barnett, F.B. Prinz Department of Materials Science and Engineering, Stanford Uni ersity, Stanford, CA 94305, USA Abstract In layered manufacturing, objects are constructed by sequential deposition of material layers. When the deposition process involves temperature gradients, thermal stresses develop. This paper examines the effect of deposition patterns on the resulting stresses and deflections in laser deposited metal parts. Finite element modeling of the deposition processes showed that the deposition pattern has a significant effect on the part stresses and deflections. Experiments performed using these same deposition patterns yielded sample deflections, which were in agreement with the finite element modeling predictions Elsevier Science B.V. All rights reserved. Keywords: Layered manufacturing; Thermal stresses; Finite element modeling; Deposition patterns 1. Introduction * Corresponding author. Layered manufacturing is a process by which objects are produced by sequential deposition of material layers. The manufacturing of an object begins with a computer model of the part decomposed into thin layers. For each layer, the computer generates the necessary deposition paths and sends this information to the deposition equipment. The part is then built up layer by layer to completion. Some commercial examples of this process include stereolythography (SLA) [1], selective laser sintering (SLS) [2], fused deposition modeling (FDM) [3], and fused deposition of ceramics (FDC) [4]. This paper focuses on layered manufacturing process developed jointly at Carnegie Mellon University and Stanford University called shape deposition manufacturing (SDM) [5]. SDM s key features include material removal after each layer is deposited and the use of a sacrificial support material to facilitate the deposition of overhanging structures. Layered manufacturing, and specifically SDM, has several advantages over conventional manufacturing. First, since SDM reduces part building to the deposition of thin two-dimensional layers, it is possible to automate the manufacturing process. This reduces both the production time and the amount of human intervention needed for each new part. In addition, the use of support material in SDM allows for fully assembled mechanisms to be built such as a freely spinning axle in a hub. SDM can also produce parts with multiple materials and functionally gradient materials where the material properties can be tailored throughout the part to meet design goals. Many layered manufacturing processes including SDM are accompanied by the development of residual stresses. These stresses arise from the contraction associated with the deposition of a layer. These stresses cause distortions and possibly failure by layer delamination or cracking. Many authors have investigated these stresses. Karapatis et al. [6] and Dalgarno et al. [7] investigated residual stresses in SLS. Also, Jacobs [1] discusses residual stresses in SLA parts. In addition, Chin and coworkers [8,9] and Klingbeil and coworkers [10,11] investigated residual stresses in metal parts produced using SDM. Through finite element modeling and experimentation they determined that substrate preheating and rigid bolting of the substrate reduces the resulting part distortion. The pattern used to deposit a layer of material has a significant effect on the resulting residual stresses and deformation. Other authors have considered the effect of deposition patterns on the deflection of parts produced using layered manufacturing. Jacobs [1] discusses the development of new deposition strategies that reduced the curling of cantilever structures in SLA /01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S (01)

2 60 A.H. Nickel et al. / Materials Science and Engineering A317 (2001) McIntosh et al. [4] noted that the deformation of the green ceramic parts produced using FDC depended on the deposition pattern. Also, Klingbeil et al. [11] experimentally observed different deflected shapes for microcast metal parts produced using SDM. This paper investigates the effect of deposition pattern on laser deposited metal parts produced using SDM. Metal parts are produced using a 2.4 KW Nd:YAG laser which is focused onto the surface of the substrate forming a molten pool. Metal powders are fed into both the molten pool and the laser beam, melting the powder. The laser and powder feed are then scanned across the surface of the substrate to produce a 0.75 mm thick layer of deposited metal. After several laser passes, the desired layer thickness is achieved and the excess material is then removed with a CNC milling machine. The effect of deposition pattern was investigated using a combination of experiments and finite element modeling employing the ABAQUS code. The resulting finite element (FEM) calculations were compared to the experimental observations. Fig. 1. Beam and substrates. Fig. 2. Deposition patterns for beam substrates. Fig. 3. Stresses resulting from long raster deposition pattern.

3 A.H. Nickel et al. / Materials Science and Engineering A317 (2001) Fig. 4. Stresses resulting from short raster deposition pattern. 2. Finite element model A three dimensional FEM was developed to examine the deposition pattern effect on distortions induced during the SDM process. This model is similar to models developed to investigate thermal stresses in welding and a general treatment of the subject is found in the book, Analysis of Welded Structures, by Masubuchi [12]. In addition, a survey of advances in modeling thermal stresses in welding was done by Chandra [13] in An uncoupled thermal and mechanical analysis was performed. As shown in Fig. 1a cm steel beam substrate and a cm steel plate substrate were considered. To reduce the computation time for both geometries the deposition pattern was approximated with a pattern that has two symmetry planes. With this approximation only 1/4 of the beam or the plate needed to be analyzed. A uniform and relatively coarse mesh of cm 3 elements for the beam and cm 3 elements for the plate model was used. This mesh density was chosen to keep the computation time under 100 h using an Ultra 5 Sun Sparc Station. In addition, to simplify the model, material deposition was not considered. The laser was scanned over the surface of the substrate causing the substrate to melt locally but without adding any metal powder to the molten pool. With this assumption, there are no material discontinuities or geometry changes during the process. The heat transfer analysis was performed first. The energy the substrate absorbed from the laser was modeled as a constant heat flux applied to the top surface of the beam. It was assumed that 1000 W of laser energy was absorbed by the substrate. In the experiment the laser was continuously scanned. However, in the FEM an entire deposition line was heated at the same instant. The deposition line was then allowed to cool before heating the next line so that the total time to scan each deposition line was the same in the experiment and the model. All boundaries were assumed to be insulating except for the bottom surface of the substrate which was assumed to be isothermal at room temperature. The isothermal assumption was chosen since the substrate is bolted to a cm 3 aluminum block which acts as a heat sink. In this model, temperature independent material properties were assumed using 1117 steel room temperature values. The values used were 52 W mk 1 [14] for the thermal conductivity, 480 J kgk 1 [14] for the specific heat, and 7800 kg m 3 [15] for the density. Also no latent heat, radiation, or convection effects were considered. The resulting temperature profiles were then applied to a mechanical model. Since the aluminum block was four times thicker than the substrate, the distortions of the aluminum were small compared to the distortions of the steel substrates. The aluminum block was therefore modeled as a rigid surface. The bolts were modeled by constraining the material near the bolts from moving off of the rigid surface. After the substrate cooled to room temperature, the boundary conditions were re- Fig. 5. Beam deflections.

4 62 A.H. Nickel et al. / Materials Science and Engineering A317 (2001) Fig. 6. Deposition patterns for plate substrates. defined to remove the restraint due to the bolts and the deflection was measured as shown in Fig. 1. Room temperature material properties for annealed 1117 steel were used. The value for the modulus of elasticity was 200 GPa, Poisson s ratio was 0.3, the yield strength was 230 MPa, the ultimate tensile strength was 430 MPa, the elongation was 23 percent, and the expansion coefficient was 12 m mk 1 [14]. All material properties were assumed to be temperature independent except for the yield strength, which varies linearly from its room temperature value to 10 percent of its room temperature value at the melting temperature. Strain hardening was included into the model. It was assumed that the stress was linear in-between the yield strength at the elastic strain limit and the ultimate tensile strength at the strain at failure. The effect of creep was not included in the model since the material was at a high temperature for a relatively short time [16,17]. These assumptions were made to simplify the model and reduce the computation time. While these simplifications may introduce errors, all calculated results were compared to experimental values to confirm the finite element results. stress shown in Fig. 3b. The second observation is that the highest stresses were found where the last line was remelted. This is demonstrated in Fig. 4b and Fig. 4d. These figures show the highest stresses moving from the first deposition line in Fig. 4b to the last deposition line in Fig. 4d. Fig. 7. Plate deflection for raster pattern. 3. Beam substrate This FEM was used to investigate two different deposition patterns on a beam substrate, a long raster pattern and a short raster pattern (Fig. 2). Figs. 3 and 4 show the FEM calculated principal stresses in the x and y directions on the top surface of the beam after the first line has been remelted and cooled and after the last line has been remelted and cooled. Only 1/4 ofthe beam is shown due to the two symmetry planes used in the analysis. Two observations may be made from these stress plots. First, the highest principal stresses were found in the direction of the long axis of the deposition line. This is demonstrated in Fig. 3a and Fig. 3b where the deposition line is oriented along the X-axis. The xx stress in Fig. 3a is larger then the corresponding yy Fig. 8. Plate deflection for spiral pattern scanned from the inside to the outside.

5 A.H. Nickel et al. / Materials Science and Engineering A317 (2001) Fig. 9. Plate deflection for spiral pattern scanned from the outside to the inside. The deposition pattern resulting in the lowest deflection for a beam substrate was determined using the previous observations. For a beam, the majority of the deflection is along the X-axis. This deflection is largely determined by the xx stress and is therefore minimized by minimizing xx. The short raster pattern with scan lines perpendicular to the X-axis produces a lower xx than the long raster pattern, and thus the short raster pattern produces smaller deflections. This result is shown for both calculated and experimentally determined deflections in Fig. 5. The error bars in Fig. 5 are the 95 percent confidence ranges calculated from eight experimental measurements. Due to the assumed symmetry, each substrate tested produced two sets of data. The experimentally determined deflections are in reasonable agreement with the calculated deflections. 4. Plate substrate The finite element model was next applied to patterns on plates. Three different patterns were considered, a raster pattern, a spiral pattern scanned from the inside to the outside, and a spiral pattern scanned from the outside to the inside (Fig. 6). The resulting deflections for the raster pattern are shown in Fig. 7. The results, both FEM and experimental, show a higher deflection along the X-axis than along the Y-axis. This follows from the observations made from the FEM calculated stresses in beam patterns. Since the deposition lines are oriented along the X-axis, xx will be larger than yy and therefore the deflection will be larger along the X-axis. A symmetric deposition pattern such as a spiral pattern results in more uniform deflections as seen in Figs. 8 and 9. There is, however, a dependence on the direction in which the spiral is scanned. From the observations of stresses on beam substrates, the highest stresses are found along the last line remelted. For the case of a spiral that starts on the outside and ends on the inside the last line scanned is shorter than for the spiral scanned in the opposite direction. The spiral pattern beginning from the outside therefore produces a smaller region of high stresses and smaller deflections. For all three patterns the corresponding experimental deflection values are also reported. They are in reasonable agreement with the calculated values and verify the observed trends. From these results the best pattern for the case of a plate substrate was a spiral pattern started from the outside due to the low and uniform deflections. Klingbeil et al. [11] experimentally observed very similar deflections for microcast patterns on plate substrates. 5. Conclusions The pattern used to deposit a layer of material in SDM has a significant effect on the deflection of the manufactured part. For a beam substrate, a raster pattern with lines oriented 90 from the beam s long axis produces the lowest deflections. For a plate geometry, the spiral pattern scanned from the outside to the inside produces low and uniform deflections. While these results were found by investigating SDM, similar results would be anticipated from other related layered manufacturing processes. Acknowledgements The authors gratefully acknowledge the Department of the Army administrating contract cdaah for the Defense Advance Research Projects Agency and the Office of Naval Research ( cn ) for their support of this research. References [1] P. Jacobs, Rapid Prototyping and Manufacturing: Fundamentals of StereoLithography, Dearborn, MI, SME, [2] J. Beaman, J. Barlow, D. Bourell, R. Crawford, H. Marcus, K. McAlea, Solid Freeform Fabrication: A New Direction in Manufacturing, Kluwer, Dordrecht, [3] C. Deckard, Selective Laser Sintering, Ph.D. Thesis, University of Texas at Austin, [4] J. McIntosh, S. Danforth, V. Jamalabad, in: Proc. Solid Freeform Fabrication Sym., University of Texas Austin, 1997, pp [5] R. Merz, F.B. Prinz, K. Ramaswami, M. Terk, L. Weiss, in: Proc. Solid Freeform Fabrication Sym., University of Texas Austin, 1994, pp [6] N. Karapatis, Y. Guidoux, P. Gygax, R. Glardon, in: Proc. Solid Freeform Fabrication Sym., University of Texas Austin, 1998, pp

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