Melt Pool Size Control in Thin-Walled and Bulky Parts via Process Maps

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1 Melt Pool Size Control in Tin-Walled and Bulky Parts via Process Maps Aditad Vasinonta, Jack L. Beut and Raymond Ong Department of Mecanical Engineering Carnegie Mellon University Pittsburg, PA Abstract Control of melt pool size is critical for maintaining consistent build conditions in te solid freeform fabrication of complex sapes. In tis researc, melt pool size in laser-based solid freeform fabrication processes is studied for bot tin-walled structures and bulky parts. Numerical simulations are used to construct non-dimensional plots (termed process maps) tat quantify te effects of canges in part eigt, laser power, deposition speed and part preeating on melt pool size. Strategies for te control of melt pool size suggested by te process maps are similar for te two geometries. Insigts are given as to ow transitions between tese two extremes in geometry can be managed to maintain a consistent melt pool size. Tis modeling work is being performed in tandem wit process development and melt pool imaging and control researc underway on te LENS process at Sandia National Laboratories. Nomenclature T = temperature in degrees Kelvin T m = melting temperature T base = base plate and wall preeat temperature = laser power α = fraction of laser power absorbed by te wall V = laser velocity k = termal conductivity ρ = density c = specific eat t = wall tickness L = part lengt = part eigt W = bulky part widt d = melt pool dept l = melt pool lengt w = melt pool widt Introduction A critical issue in developing solid freeform fabrication (SFF) processes as rapid manufacturing tecniques is te control of "build conditions," defined as termal conditions allowing a particular part to be fabricated. Consistency in build conditions is typically defined in terms of a consistent melt pool size during te construction of a part or feature. Previous work by te autors [1-3] as investigated tis issue for 2-D tin-walled structures and as presented strategies for controlling build conditions (by maintaining a consistent melt pool size) wile also limiting residual stresses (by controlling termal gradients). Te control of melt pool size and termal gradients in 2-D tin-walled structures was addressed via tree-dimensional plots of dimensionless process variables (termed process maps) developed from termal models of laserbased material deposition. Current researc extends te process map concept developed for 2-D tin-walled structures to 3-D bulky parts. A process map for melt pool size for bulky parts as been 432

2 developed troug termal simulations of a simple 3-D structure. It addresses te effect of canges in process variables (laser power, laser velocity and part preeat temperature) and geometry (part eigt) on melt pool size. Comparing te process maps for tin-walled and bulky structures provides insigt into ow to control melt pool size for tese two extremes in geometry and ow to andle transitions between tem in a single part. Furtermore, an understanding of tese two basic types of structures can form te basis for understanding process control issues in te building of muc more complex sapes. Te principal application of tis work is to te Laser Engineered Net Saping (LENS) process currently under development at Sandia National Laboratories [4]. Te process maps presented in tis paper ave been developed to aid in bot manual and automated process control efforts currently underway at Sandia Labs [5]. Altoug tis researc is directed toward te LENS process, te approac taken is applicable to any solid freeform fabrication process involving a moving eat source. Similarly, altoug stainless steel (SS304) is treated in te current work, te same approac can be applied to oter materials. In te next section, te 2-D and 3-D structures analyzed in tis study are presented, along wit details of te finite element models and boundary conditions used. Nondimensionalization scemes used to develop te process maps for bot geometries are given. In te succeeding section, te process maps are presented wit rules for ow results can be applied to te prediction and control of melt pool size. A comparison of melt pool sizes between te two geometries is ten presented. Finally, process control-related insigts for transitions between te two geometries are discussed. Geometry Considered, Numerical Model and Analytical Solution V l x 0 Tin Wall V z 0 l x 0 z 0 L L t Base plate W Figure 1a. Tin-Walled Structure Figure 1b. Bulky Part Scematics of bot te tin-walled and bulky part geometries are sown in Fig. 1. In te LENS process, parts are constructed by focusing a ig power laser onto a metal substrate, were streams of metallic powder are simultaneously injected. Te laser locally melts te powder to form a molten melt pool on te top surface of te growing part. By moving te laser beam, te material is added to te part and te part is built up line-by-line and layer-by-layer. 433

3 In te modeling of tis study, it is assumed tat bot te tin-walled and bulky parts are fabricated on large fixed-temperature metallic substrates, wic act as termal eat sinks. Models are also constructed suc tat te distance traveled by te laser and te lengt of te structures in te x-direction are large enoug tat steady state termal conditions exist at te melt pool. Numerical models used in tis study do not include te effect of convective eat transfer from te wall free surfaces to te surrounding air and do not model convective flows in te melt pool itself. Work by Dobranic and Dykuizen [6] suggests strongly tat te role of tese effects in determining melt pool size is not significant. Te models of tis study also represent te laser as a point source of eat, neglecting te distribution of laser power over te melt pool region. Assuming a point source of power is reasonable given te goal of tis study, wic is to capture canges in melt pool size and oter parameters as a function of canges in te process variables outlined above. Accuracy in te absolute predictions is of secondary importance. However, comparisons between experimentally determined melt pool sizes for tin-walled structures and model predictions sow reasonable agreement [3]. Te meses and boundary conditions used for typical 2-D tin-walled and 3-D bulky part termal models are sown in Figs. 2 and 3 respectively. For bot geometries, a concentrated eat source moves across te top surface of te model, wic is initially at a uniform temperature T = T base. Te finite element models ave been created using te ABAUS software package. Because of ig temperature gradients in te region near eat source, te grid of eac model is biased toward te region tat will surround te eat source at te time wen results are to be extracted from te model. In addition to comparisons wit analytical solutions valid for large substrates, te convergence of eac mes was cecked against a model wit rougly alf te resolution wit no noticeable cange in te results. V x T = T base z L Figure 2. 2-D Termal Model and Boundary Conditions For te case of a tin-walled structure, four-noded bilinear termal elements were used to form te mes of te 2-D model. It is assumed tat te tin wall is fabricated by depositing material along a single row; tus, te tickness of te wall is comparable to te melt pool size. As illustrated in Fig. 2, an insulated boundary condition is imposed on te top and bot vertical sides of te substrate. Sensitivity studies ave sown tat termal results are not significantly affected by boundary conditions along tese surfaces being specified as eiter insulation or convection. By using a 2-D model, it is also assumed tat tere is no eat loss troug te front and back surfaces. Te temperature along te substrate bottom is specified as fixed at te value equal to te temperature of te base plate. A typical mes for a 3-D bulky part simulation is sown in Fig. 3, generated using eigtnoded linear brick termal elements. Because of symmetry across te X 0 -Z 0 plane, only alf of 434

4 te 3-D structure is modeled. Analogous to te 2-D model, insulated boundary conditions are imposed on all free surfaces. Te eat flux across te symmetry plane (te X 0 -Z 0 plane) is set to zero and te temperature of te substrate bottom is eld at te temperature of te base plate. V X 0 Z 0 Y 0 w/2 d X 0 T = T base Y 0 W L Z 0 Figure 3. 3-D Termal Model and Boundary Conditions Termal properties of AISI 304 stainless steel (SS304), wic is used in te LENS and oter SFF metal deposition processes, are used as inputs for te temperature-dependent simulations. Termal properties were taken from [7] and are also comparable to tose used by Cin, et al. [8] and Klingbeil, et al. [9] in termomecanical modeling of te Sape Deposition Manufacturing process. Te properties used in te model tat are set to depend on temperature are specific eat and termal conductivity. Te latent eat of te liquid-solid pase transition is also included in te model. Te normalization scemes used to develop process maps in tis paper are based on te analytical solutions of conductive eat transfer by Rosental [10]. Representation of numerical simulation results in terms of te normalized variables defined below is exact only in te case of temperature-independent termal properties. Te goal of developing process maps for laserbased SFF processes is to use dimensionless variables to collapse a large number of numerical simulations into an easily used format, keeping errors caused by temperature dependent properties witin acceptable limits. As suggested by te Rosental solution for a point source of eat moving across a 2-D semi-infinite tin substrate, a process map for melt pool size for a tinwalled structure is represented troug tree dimensionless variables: te normalized melt pool lengt ( l ), te normalized eigt of te substrate ( ) and te normalized melting temperature ( T m ), wic are defined as follows: l l =, Tbase = and =. (1) α πkt Using tis normalization sceme, results for normalized melt pool lengt, l, are presented as a function of normalized wall eigt,, and normalized melting temperature, T m. 435

5 Analogous to te case of a 2-D tin wall, te 3-D conductive eat transfer solution by Rosental suggests tat te process map for melt pool size of a bulky part can be represented by tree dimensionless variables: te normalized melt pool dept ( d ), te normalized eigt of substrate ( ) and te normalized melting temperature ( T m ). Te melt pool dept is cosen to represent te size of melt pool for 3-D bulky parts because it can be related to ow well newly deposited material is fused to te top surface of te part. Te dimensionless variables for te process map for bulky parts are defined as follows: d d =, Tbase = and =. (2) α πk Note tat te normalized melting temperature ( T m ) for te two geometries is defined differently. Process Map for 2-D Tin-Walled Structures l = l = Tbase = α πkt Figure 4. Process Map for Melt Pool Lengt for 2-D Tin-Walled Structures A process map for melt pool lengt for a tin-walled structure wit a concentrated laser eat source moving across it as been developed and reported in [1-3]. Te work described in [1] uses sligtly different normalization rules tan te more accurate rules used in [2], [3] and erein. Te process map, wic is sown in Fig. 4, consists of tree surfaces plotted on tree coordinate axes. Te middle surface was developed from several numerical simulations wit temperature-independent properties performed wit differing wall eigts in order to get te dependence of l on. Te dependence of l on T m was ten determined from te same simulations by assuming different values of T m. Te results from temperature-dependent simulations are also represented in Fig. 3 by upper and lower surfaces tat bound te temperature-independent results. Te space between tese surfaces reflects te range in results seen wen process variables are varied over te range of specific interest in te LENS process. 436

6 Tat range consists of values of α from 43.2 to 165 W, V from 5.93 to 9.31 mm/sec and T base from 30 C to 400 C. Te maximum range in values of l for fixed and T m due to te temperature dependence of properties is less tan 13% of te nominal value of l. Tus if te mean values of l for a fixed value of T m are consistently used, te maximum error is ± 6.5%. Te detailed assumptions and procedures for obtaining and using te process map for melt pool lengt are given in [3]. In brief, te process map of Fig. 4 can be used effectively for SS304 deposition witin te range of process parameters of interest in te LENS process by applying te following four rules: 1. Properties of SS304 at 1000 K are used in te normalization; 2. For cases involving a cange in preeat, a linear cange in termal conductivity wit a preeat temperature is assumed, as given in te following equation, k = ( T base 30) W /( m K) ; (3) 3. For predicting steady-state melt pool lengts due to a cange in process variables, wall tickness is assumed to scale proportionally wit melt pool lengt; and 4. It is assumed tat te melt pool lengt/wall tickness scaling is unaffected by velocity. Melt pool sizes determined by real-time termal imaging experiments [5] ave been compared wit model predictions using te process map of Fig. 4 and te rules outlined above [3]. Reasonable agreement is seen in melt pool lengt values and te predictions of te process map clearly capture te trends in te measured results. Process Map for 3-D Bulky Structures In tis section, results are presented from modeling te LENS process for deposition of SS304 to form 3-D bulky parts. Te normalization sceme for 3-D structures given in eq. (2) is used. Te process map as been developed using concepts similar to tose used for 2-D tinwalled structures; owever, melt pool dept is cosen to be te parameter representing melt pool size instead of melt pool lengt. Melt pool dept is cosen because it determines ow muc of te top of te existing layer is melted by a newly deposited layer. In laser-based SFF processes, controlling melt pool dept as a part is built is important for ensuring fusion at interlayer boundaries. If te melt pool dept is too small, not enoug of te top portion of te existing material will be melted during deposition and poor interlayer bonding will result. Altoug it is important to control melt pool dept to ensure part quality, it is a difficult parameter to monitor by termal imaging or oter metods. However, te 3-D Rosental solution for a point eat source moving across a semi-infinite substrate suggests tat, for a tall bulky part, te dept of te melt pool is identical to one alf of te widt of te melt pool, independent of laser power, laser velocity and preeat temperature. Tus for tall parts, melt pool widts measured via termal imaging tecniques can be compared directly to predicted melt pool depts. Also, it is planned to use termal model results to quantify te ratio of melt pool widt to melt pool dept as a function of part eigt, to facilitate te use of real-time termal images of melt pool widt to precisely control melt pool dept. It sould be noted tat it is also possible to relate melt pool areas, wic are easily extracted from termal images, to melt pool depts. However, if canges in laser velocity are allowed, te ratio of melt pool area to 437

7 melt pool dept will be a function of laser velocity, laser power and preeat temperature in addition to part eigt. Because of tis, melt pool widt is generally a more useful measurable parameter to control as a means for controlling melt pool dept. d d = T m T = α πk base ( ) = Figure 5. Process Map for Melt Pool Dept for 3-D Bulky Structures Te process map developed for 3-D bulky parts (sown in Fig. 5) consists of tree surfaces plotted on tree coordinate axes, generated using several numerical models wit different part eigts. Similar to te process map for 2-D tin-walled structures, te middle surface is generated from simulations assuming temperature-independent properties. Witin te limitation of tis assumption, tis surface is very general and is applicable to any laser-based SFF process involving termal deposition of any single material. Te two bounding surfaces developed from temperature-dependent simulations reflect te range in results seen wen process variables are varied over te range of practical use in te LENS process. As for te process map for tin-walled structures, results from temperature-dependent simulations are normalized using te properties of 304 stainless steel at 1000 K, wit te linear cange in termal conductivity as given in eq. (3) applied for cases involving a uniform preeat. Te maximum range in values of d for fixed and T m is 16% of te nominal value of d. Tus if te mean values of d for a fixed value of T m are used, te maximum error is ± 8%, wic is sligtly iger tan te range of melt pool lengts (l ) for te process map for 2-D tinwalled structures. If properties at 1100 K are used to normalize te 3-D results, maximum errors can be furter reduced to approximately ± 6.5%. However, use of te same normalization sceme for bot tin-walled and bulky parts offers advantages in comparing melt pool sizes between te two geometries and in understanding transitions between tem. It can be seen in bot Figs. 4 and 5 tat for a fixed value of, melt pool size (l for a 2- D tin wall and d for a 3-D bulky part) increases wit increasing T base or (eiter of wic 438

8 decreases T m ). Moreover, a cange in T base can be compensated for by a cange in, to retain a desired melt pool size. Wen te part is relatively tall, te fixed temperature at te base is not seen at te melt pool, as no significant effect on te size of melt pool, and te results approac tose for an infinitely large part. In contrast, as a considerable effect on melt pool size wen te part is relatively sort, wit d and l dropping rapidly as is reduced. Wen comparing melt pool sizes for te two extreme geometries, it is found tat, for te same set of process variables, melt pool sizes extracted from te process map for 3-D bulky parts are muc smaller tan tose extracted from te process map for 2-D tin-walled structures. For example, for a tall, tin wall, using typical process variables of α = 105 W, V = 7.6 mm/s, and T base = 303 K (and a wall tickness of 1.3 mm) te melt pool lengt calculated from te process map is equal to 1.4 mm. For te same process variables, te melt pool dept and melt pool lengt for a tall, 3-D bulky part are found to equal 0.40 mm and 0.85 mm respectively. Te considerable difference in melt pool lengts between te two geometries (1.4 mm and 0.85 mm) is due to te fact tat tere is more material to conduct eat away from te melt pool in te 3-D bulky part. To keep melt pool size constant wile transitioning from tin-walled to bulky features, laser power must be increased. For te case considered above, to obtain a melt pool size of 1.4 mm in a bulky feature, te absorbed laser power must be increased from 105 W to 160 W. Decreasing laser velocity and using part preeating can also increase melt pool size; owever, tese measures cannot be used alone. Witin te practical range of laser velocity and part preeating in te LENS process, melt pool size canges from eac of tese process canges are not large enoug to regain te tin-walled feature melt pool size. Conclusions In tis paper, process maps ave been presented for predicting and controlling melt pool size in te building of tin-walled and bulky stainless steel structures by laser-based SFF processes. For eac of te two geometries, all numerical model predictions ave been collapsed onto a single tree-dimensional plot of dimensionless process variables. Te process map for bulky parts could ave been made more accurate by developing normalization rules specifically for tat geometry; owever, bot process maps presented erein use te same normalization rules, making a direct comparison between te geometries easier. Te process map for bulky parts quantifies values of melt pool dept, wic is te key parameter to control for consistent build conditions. Altoug melt pool area is typically tracked in bulky parts via termal imaging measurement and control systems, melt pool widt is a better parameter to monitor experimentally, due to its more direct link to melt pool dept. A comparison of melt pool sizes between te two geometries sows tat, for te same set of process variables, te size of te melt pool decreases substantially wen transitioning from tin-walled to bulky features (decreasing by 39% in te example cited erein). To maintain consistent build conditions, decreasing te laser velocity or base plate preeating alone is not sufficient and a substantial increase in laser power is needed (a 52% increase in te cited example). A detailed comparison of predictions from te two process maps (not presented in tis paper) reveals tat most process control-related insigts and implications relevant to 2-D tinwalled structures also apply to 3-D bulky parts. For example, practical levels of uniform part 439

9 preeating, wic is pursued as a means to decrease residual stresses, does not increase melt pool sizes significantly for eiter geometry. Furtermore, any increase in melt pool size can be eliminated by a small decrease in laser power or increase in laser velocity. It is also clear from bot process maps tat considerably smaller melt pool sizes are seen for sort structures. Tus control of melt pool size as a part is built up from a base plate is important. Because it does not significantly cange melt pool size, base plate preeating is not sufficient to address tis problem. Acknowledgements Tis researc as been supported by te National Science Foundation under grant DMI and by Sandia National Laboratories under grant BE Te autors would like to tan Micelle Grifft of Sandia National Laboratories, Albuquerque, NM, for er substantial collaboration on tis researc. References 1. Vasinonta, A., Beut, J.L. and Griffit, M., Process Maps for Laser Deposition of Tin-Walled Structures, Solid Freeform Fabrication Proceedings, D.L. Bourell, J.J. Beaman, R.H. Crawford, H.L. Marcus and J.W. Barlow, eds., Te University of Texas at Austin, August 1999, pp Vasinonta, A., Beut, J.L. and Griffit, M., Process Maps for Controlling Residual Stress and Melt Pool Size in Laser-Based SFF Processes, Solid Freeform Fabrication Proceedings, D.L. Bourell, J.J. Beaman, R.H. Crawford, H.L. Marcus and J.W. Barlow, eds., Te University of Texas at Austin, August 2000, pp Vasinonta, A., Beut, J.L. and Griffit, M., A Process Map for Consistent Build Conditions in te Solid Freeform Fabrication of Tin-Walled Structures, Journal of Manufacturing Science and Engineering, in print. 4. Griffit, M.L., Keicer, D.M., Atwood, C.L., Romero, J.A., Smugeresky, J.E., Harwell, L.D. and Greene, D.L., Freeform Fabrication of Metallic Components Using Laser Engineered Net Saping (LENS), Solid Freeform Fabrication Proceedings, D.L. Bourell, J.J. Beaman, H.L. Marcus, R.H. Crawford and J.W. Barlow, eds., Te University of Texas at Austin, August 1996, pp Griffit, M.L., Sclienger, M.E., Harwell, L.D., Oliver, M.S., Baldwin, M.D., Ensz, M.T., Smugeresky, J.E., Essien, M., Brooks, J., Robino, C.V., Hofmeister, W.H., Wert, M.J. and Nelson, D.V., Understanding Termal Beavior in te LENS Process, Journal of Materials Design, Vol. 20, No. 2/3, 1999, pp Dykuizen, R.C. and Dobranic, D., Analytical Termal Models for te LENS Process, Sandia National Laboratories Internal Report, Dobranic, D. and Dykuizen, R.C., Scoping Termal Calculation of te LENS Process, Sandia National Laboratories Internal Report, Cin, R.K., Termomecanical Modeling of Residual Stresses in Layered Manufacturing wit Metals, P.D. Tesis, Carnegie Mellon University, May Klingbeil, N.W., Beut, J.L., Cin, R.K. and Amon, C.H., Measurement and Modeling of Residual Stress-Induced Warping in Direct Metal Deposition Processes, Solid Freeform Fabrication Proceedings, H.L. Marcus, J.J. Beaman, D.L. Bourell, J.W. Barlow and R.H. Crawford, eds., Te University of Texas at Austin, August 1998, pp Rosental, D., Te Teory of Moving Sources of Heat and Its Application to Metal Treatments, Transactions of te ASME, Vol. 68, 1946, pp