1.4815992

Advances in the modeling of laser direct metal depositionAndrew J. Pinkerton

Citation: Journal of Laser Applications 27, S15001 (2015); doi: 10.2351/1.4815992 View online: http://dx.doi.org/10.2351/1.4815992 View Table of Contents: http://scitation.aip.org/content/lia/journal/jla/27/S1?ver=pdfcov Published by the Laser Institute of America

Articles you may be interested in 2D longitudinal modeling of heat transfer and fluid flow during multilayered direct laser metal deposition process J. Laser Appl. 24, 032008 (2012); 10.2351/1.4726445

Comprehensive predictive modeling and parametric analysis of multitrack direct laser deposition processes J. Laser Appl. 23, 022003 (2011); 10.2351/1.3567962

Modeling of transport phenomena during the coaxial laser direct deposition process J. Appl. Phys. 108, 044908 (2010); 10.1063/1.3474655

Thermal and microstructural aspects of the laser direct metal deposition of waspaloy J. Laser Appl. 18, 216 (2006); 10.2351/1.2227018

Microstructure and corrosion behavior of high power diode laser deposited Inconel 625 coatings J. Laser Appl. 15, 55 (2003); 10.2351/1.1536652

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:188.253.33.225 On: Sun, 21 Jun 2015 15:28:44

Advances in the modeling of laser direct metal deposition

Andrew J. Pinkertona)

Department of Engineering, Lancaster University, Bailrigg, Lancaster LA1 4YR, United Kingdom

(Received 7 March 2013; accepted for publication 4 July 2013; published 9 December 2014)

This paper provides a review of the current state of the art in modeling of laser direct metal

deposition and cladding processes and identifies recent advances and trends in this field. The

different stages of the process and the features, strengths and weaknesses of models relating to them

are discussed. Although direct metal deposition is now firmly in the industrial domain, the benefits to

be gained from reliable predictive modeling of the process are still to be fully exploited. The genuine

progress there has been in this field in the last five years, particularly in discretized modeling, means

modeling cannot be overlooked as an enabling method for academia and industry, but there is still

more work to be done.VC 2014 Laser Institute of America.

Key words: laser, deposition, cladding, model, simulation, review

I. INTRODUCTION

Even finding consensus on a name for the laser direct

metal deposition (laser cladding, direct metal deposition,

direct laser deposition, directed light fabrication, laser pow-

der fusion, laser engineered net shaping, etc) process has

to-date proved impossible. It is, thus, of no surprise that there

is such a disparate range of models of the process. But this

must be viewed as a positive thing: they are advancing the

modeling of the different stages of the deposition process

and, excitingly, the complete process in umpteen ways.

Academic attention to process modeling continues to

increase but has still been outpaced by the growth of additive

manufacturing in general, which has seen double digit growth

for 15 of its 24 yrs.1 Figure 1 illustrates the growth of laser

direct metal deposition (LDMD) modeling of all types and

models describing themselves as numerical in the title or

keywords in particular. Empiricalstatistical and analytical

models were almost exclusively used until the advent of nu-

merical and hybrid analyticalnumerical models, which prin-

cipally refers to those employing the discretization method,

over the last 10 years.

II. EMPIRICALSTATISTICAL MODELS

Empiricalstatistical models have been produced since

the advent of LDMD as they avoid the complexity of analyz-

ing the physical phenomena of the process itself. Direct

metal deposition is typically described as having three

primary process inputs of laser power, powder mass flow

rate, and traverse speed. Most models have concentrated on

relating these to final track geometry, typically using regres-

sion methods to relate input and response variables (Table I).

Other models have addressed less common response parame-

ters such as, clad angle,2 deposition efficiency,3 and uniform-

ity index (clad area / (track width height)),4 while othershave used less common experimental designs, for example

Hartleys plan.5 The process and response variables have

also been related in other ways: Toyserkani et al. proposedElman recurrent neural network modeling6 and Hua and

Choi proposed use of fuzzy logic to adaptively predict and

control clad height as a function of laser power.7

However, examination of Table I shows an inherent dis-

advantage of the empiricalstatistical approach. These mod-

els give broadly similar but seldom exactly the same results,

even though in many cases they are based on similar meth-

ods. Qi et al.8 suggested 1214 factors with a strong effecton final part characteristics, so the models are, at least to

some extent, specific to the values of factors that were fixed.

Despite design of experiment methods, models have not

significantly advanced the number of process variables they

are able to account for in the recent past, and limitations of

experimental time mean there are no indications that they

will in the future. There is thus so real sign that this model-

ing method will change significantly in the future.

III. APPROACHES TO THE PHYSICAL MODELING OFDIRECT METAL DEPOSITION

The large number of variables and diverse phenomena

within the LDMD process means the complete process is

commonly considered in stages and different physical

models applied at each stage. This introduces intermediate

variables that need to be carried over from one stage of the

process to the other. Figure 2 illustrates how the complete

process is typically broken down physically and Fig. 3 the

corresponding model-part this creates. Advances in physical

modeling of the different process stages and the process as a

whole are then considered.

A. Models of the powder stream process

The powder stream and powder stream processes are

highly significant for track formation as they directly affect

beam attenuation and powder distribution, velocity, and tem-

perature at substrate height. The spatial distribution of pow-

der particles beneath a coaxial nozzle and their interaction

a)Electronic mail: [email protected]. Telephone: 44 (0)1524593547.

1042-346X/2015/27(S1)/S15001/7/$28.00 VC 2014 Laser Institute of AmericaS15001-1

JOURNAL OF LASER APPLICATIONS LASER ADDITIVE MANUFACTURING FEBRUARY 2015


with the laser beam have traditionally been described by ana-

lytical methods, typically by approximating the stream shape

to an idealized Gaussian distribution and the particle path to

extensions of the nozzle passages (e.g., Refs. 1719).

Attenuation has been taken care of via the BeerLambert

law and powder temperature from total time of a particle

within the beam.17 The most advanced analytical models can

now account for variable particle velocity20 and return the

values of powder distribution at the substrate level, beam

attenuation, and powder temperature.21 The analytical mod-

els are well tested and still widely used as good approxima-

tions but tend to rely on estimated or experimental values for

variables such as powder stream divergence.

The use of computational fluid dynamics (CFD) methods

is not in itself very new: Lin produced realistic model of mass

flow in the powder stream in 2000. The numerical method

allows stream modeling without many of the assumptions

mentioned above and has shown assumptions like straight

powder paths and constant powder speed to be approximations

rather than reality. Models of this type have increased greatly

in sophistication in the last few years. Pan and Liou22,23 pro-

duced a stochastic model for initial trajectory of the particle

when entering the powder stream and several authors have

produced CFD models of powder flow in the nozzle and

powder stream with different degrees of complexity.2426

The most advanced models of this type now include the

nozzle and stream, account for the size and shape of particle

using a shape factor,27 and provide both particle heating

and mass flow results28 (Fig. 4).

Further, the LDMD process must build on a solid wall or

substrate, but the effect of this on the gas and powder flows

has only just been considered. The gasliquid interface geo-

metry input to the powder stream model shown in Fig. 3

has thus been neglected. Kovalov et al.29 used an advancedCFD model of a three passage nozzle, similar to that of Wen

et al.,28 to consider the substrate effect. The flow was verydifferent from that of a free stream with vortex flows form-

ing above the substrate (Fig. 5). Focussing on powder flow,

Zekovic et al.30 modeled powder flow from a LENS nozzleusing the ke turbulent model and showed changes in pow-der concentrations below the nozzle due to ricocheting par-

ticles when a substrate was in place. Ibarra-Medina and

Pinkerton31 showed the same effect with a coaxial nozzle

and also drew attention to the implications for powder heat-

ing and beam attenuation. This type of model was firmly

confirmed as state of the art by a verified CFD model based

on the same assumptions as that of Zekovic et al. byTabernero et al. in 2010.32,33

Modeling of the powder stream process is advancing

rapidly. Models with the substrate in place would probably

benefit from further testing to establish under what circum-

stances the effects they reveal are significant. However, they

FIG. 1. Growth in the publication of laser cladding and metal deposition

models per year since 1985 [based on SCOPUS data, title and keyword

searches, absolute values give an estimate only].

TABLE I. Empiricalstatistical relationships between track geometry and LDMD primary process variables (P laser power, F powder mass flow rate,V traverse speed, RSM response surface method, RA regression analysis).

Primary process response variable

Work Track height Track width Track depth or melt area

Kumar (Ref. 9) P1/4 V1F1/4 Sun (Ref. 10) (ANOVA, RSM) P, V, F, PF, P2 P, V, F, PV, V2 P, V, F, P2, F2

El Cheikh (Ref. 11) P1/4 V1F3/4 P3/4V1/4 Ln(P4/5F1/4)Davim (Ref. 12) (ANOVA, RA) P, V, F P, V, F P, V, F

Ocelik (Ref. 13) V21F PV1/2 P2V1/2

Davim (Ref. 14) P, V, Fa P, FV, Fa P, Fa

De Oliveira (Refs. 10 and 15) (RA) FV21 PV1/2 PV1/3F1/3

Felde (Ref. 16) P1/2 V1F1/2

aTaking confidence values above 5%.

FIG. 2. (Arbitrary) Stages of direct metal deposition or laser cladding in

terms of physical limits.

S15001-2 J. Laser Appl., Vol. 27, No. S1, February 2015 Andrew J. Pinkerton


could mean the ubiquitous free stream powder model has

been superceded.

B. Models of the melt pool process

Models of the melt pool are at the heart of the deposition

process. The typical assumptions of an analytical model are

quasistationary conditions, a mathematically simple sub-

strate shape (typically semi-infinite or thin plate), and geo-

metrically simple melt pool boundaries, either combinations

of half ellipses34,35 (based on moving source heat theory36,37)

or circles11,38,39 (assuming surface tension normal to the sur-

face shapes the molten pool). Despite these necessary simpli-

fications, there have been some recent informative models

and ones covering the effect of powder types and laser focus

points on wall layer formation4042 and on combining laser

and induction heating for hybrid rapid cladding43 stand out.

The ability to use iterative numerical solution methods for

analytically formulated models44,45 has also reduced the con-

straints of using this modeling method.

Numerical discretized methods more naturally account

for inhomogeneity in problems but in practice makes calcu-

lating melt pool geometry an exacting task. Therefore, mod-

els using this method have tended to focus on calculating the

temperature distributions and thermal history of the final

part.4648 Early models applied a heat flux to an unchanging

surface (e.g., Ref. 49), but more recent models have come to

rely on the element activation (birth) methodology,

although Ye et al.48 have also demonstrated use of the alter-native fixed boundary method (after Refs. 50 and 51).

Models of this type differ in the way heat is added to the sub-

strate: using a heat flux,47 activating the new elements at the

liquidus temperature (assuming particles at this temperature

FIG. 3. Subprocesses and process variables corresponding to the physical stages of deposition shown in Fig. 2.

FIG. 4. Modeled coaxial powder flow and heating (Ref. 28).

FIG. 5. Gas jet flows onto a flat substrate with a triple coaxial nozzlevelocity

field and gas streamlines (Courtesy of Professor O. Kovalev, Theoretical and

experimental investigation of gas flows, powder transport and heating in

coaxial laser direct metal deposition (DMD) process, J. Therm. Spray

Technol. 20, 465478 (2011). Copyright 2011, Springer).

J. Laser Appl., Vol. 27, No. S1, February 2015 Andrew J. Pinkerton S15001-3


and 100% attenuation)48,5254 or using a combination of the

two methods.55 Kumar and Roy56 presented a two-

dimensional finite volume model that explicitly returns solid-

ification front information such as thermal gradient suitable

for use by a solidification model.

The model types above have the failing of not explicitly

calculating fluid flows within the melt pool. Some compen-

sate for it by increasing conductivity within the melt pool.

This can be done either isotropically or anisotropically57 but

requires arbitrary or experimentally set enhancement factors.

A more advanced form of model, incorporating fluid flow

effects and a free-surface method to predict the melt pool

and subsequent track shape, has now emerged.5861 The

most recent and advanced models by Morville et al.59 explic-itly track the dynamic shape of the free surface using an arbi-

trary Lagrangian Eulerian (ALE) moving mesh and

realistically predict thin wall growth including the character-

istic shapes near the limits of the wall.

Despite the importance of this work, probably the state

of the art in melt pool modeling has come from models that

encompass both the powder stream and melt pool processes.

Toyserkani et al.62,63 began by proposing a single modelencompassing the two but with the two processes largely

decoupled. More complex analyticalnumerical and numeri-

cal models have followed.8,61,6473

The levels set method was used by Qi et al. to simulateformation of a single track8 and by He et al. to simulate twooverlapping clad tracks64,65 using an hybrid analytical and nu-

merical discretized model. The powder stream was treated ana-

lytically as Gaussian and the beam subject to BeerLambert

attenuation, while the melt pool simulations were fully numeri-

cal and incorporated Marangoni and capillary effects. Peyre

et al.66 used a similar combination of an analytical powderstream model and a numerical finite element (FE) method for

heat flow within the built part but also incorporated an

approach to model the deposition of vertically aligned tracks.

In further recent work aimed at this subject by Gharbi, Peyre

et al.72,73 a rare analytical model covering both powder streamand melt pool correlates thin wall surface finish to melt pool

size for different thermo-capillary behaviors.

Different from these are the continuum models of Wen

and Shin67 and Ibarra-medina et al.,74 which contain no ana-lytical component. Wen and Shin modeled the LENS pro-

cess, incorporating Marangoni and Capillary effects, and

used a level-set method for melt pool surface tracking (akin

to Han et al.75). Gas flow in the powder stream was taken asturbulent, described by the ke model as reported in anotherpaper dedicated to this subject.67 The model was also applied

to two overlapping tracks,68 off-axis deposition69 and clad-

ding with an additional hard particle phase.70 The model of

Ibarra-medina et al. incorporated the same effects but con-sidered an annular nozzle and used the volume of fluid

(VOF) method (Fig. 6).

In summary, models have advanced by ceasing to consider

purely thermodynamic effects and incorporating fluid dynamics

effects in a predictive way. This means modeling of the melt

pool process is advancing as quickly as that of the powder

stream process. Most benefit in the immediate future would

come from better integration of these state-of-the-art melt pool

models with other subprocess models of the powder stream and

final properties.

C. Models of microstructure, stress, and finalgeometry

Obtaining final part properties is the ultimate aim of the

modeling process. The core ones can be considered as final

geometry (including distortion), microstructure, and stress

distributions. Many other properties can be derived from

these. To obtain the distribution of residual stress, many

FIG. 6. Simulated deposition of a thin wall using a multistage model (Ref. 76).



models consist of a discretized melt pool model of the type

described in Sec. III B and exploit the functionality of commer-

cial software such as ANSYS (e.g., Refs. 77 and 78) and ABAQUS

(e.g., Ref. 79). The stress is affected by variables such as layer

height,80 substrate geometry and temperature fed from the pre-

vious model-part81,82 and from those such as phase transforma-

tion calculated within this process stage.83 Models of this type

are difficult to verify but work by Labudovic et al.,84 using ahigh speed camera and off-line metallographical and x-ray dif-

fraction analyses, and by Rangaswamy et al.85 and Moatet al.,86 using neutron diffraction, has facilitated this.

As a whole, LDMD microstructure modeling is a younger

area than stress modeling. Investigations in this area have

tended to be experimental and concentrate on high perform-

ance materials, particularly titanium8790 and superalloys.9195

Phase-microstructure models are again usually based on dis-

cretized melt pool model of the type described in Sec. III B,

with added subroutines to relate the temperature history at

each node to the final material state. Authors such as Wang

et al.96 have used continuous cooling transformation dia-grams; however, Colaco and Vilar suggest that the nonequili-

brium solidification that can occur in LDMD means that

modified expressions are needed.97 Papers in this area have

considered deposition of a range of materials including stain-

less steels,52,96 medium carbon steel,98 and titanium alloys,55

each using thermo-metallurgical phase transformation models

specific to the material. However, work has not been limited

to purely metallic coatings and phase analysis: Lei et al. con-sidered composite coatings on Ti6Al4V alloys99 using the

WilsonFrenkel growth law to relate the modeled temperature

distribution and history in a test part to the size of TiC par-

ticles that formed. In other work, Pirch et al. concentrated oncalculating dendritic growth direction in multitrack depos-

its.100 Models in this area have advanced by expanding both

the parameters they consider and return. The residual stress

models of Bruckner et al.101 and Alimardani et al.102 includedecoupled analytical model of the powder stream which ena-

ble them to also calculate an (idealized) track geometry. The

former also accounts for phase effects.

IV. SUMMARY

There are some genuinely new analytical models being

produced but the proportion of numerical models, particu-

larly those based on the discretization method, in this field is

continuing to increase. Probably, the most interesting devel-

opment in the last few years has been the growth in analyti-

cal discretized and discretized models that span multiple

stages of direct metal deposition. Further development of

this towards a usable, unified model is an exciting prospect.

But models have many uses.103 An overall process

model (red to red in Fig. 3) could be used for process plan-

ning or design, analytical models are the classic way to

increase understanding of an unfamiliar aspect of the pro-

cess, and there are other opportunities for modelling in con-

trol that have not even been touched on here.104110

There is still plenty of opportunity for genuinely better

models and these could benefit the laser community in multi-

ple ways.

ACKNOWLEDGMENTS

The author is grateful to the authors and publishers who

have allowed him to use their figures in this paper to exam-

ple leading models in the field. Thanks also to Milan Brandt

for giving me this opportunity and to colleagues working on

the INLADE project over the last few years.

1T. Wohlers, Wohlers Report 2012 Additive Manufacturing and 3DPrinting State of the Industry Annual Worldwide Progress Report(Wohlers Associates, Inc, 2012).2G. C. Onwubolu, J. P. Davim, C. Oliveira, and A. Cardoso, Prediction of

clad angle in laser cladding by powder using response surface methodol-

ogy and scatter search, Opt. Laser Technol. 39, 11301134 (2007).3H.-K. Lee, Effects of the cladding parameters on the deposition effi-

ciency in pulsed Nd:YAG laser cladding, J. Mater. Process. Technol.

202, 321327 (2008).4P. Balu, P. Leggett, S. Hamid, and R. Kovacevic, Multi-response optimi-

zation of laser-based powder deposition of multi-track single layer

Hastelloy C-276, Mater. Manuf. Processes 28, 173182 (2013).5Q. Zhang, M. Anyakin, R. Zhuk, Y. Pan, V. Kovalenko, and J. Yao,

Application of regression designs for simulation of laser cladding,

Phys. Procedia 39, 921927 (2012).6E. Toyserkani, A. Khajepour, and S. Corbin, Application of

experimental-based modeling to laser cladding, J. Laser Appl. 14,165173 (2002).7Y. Hua and J. Choi, Adaptive direct metal/material deposition process

using a fuzzy logic-based controller, J. Laser Appl. 17, 200210(2005).8H. Qi, J. Mazumder, and H. Ki, Numerical simulation of heat transfer

and fluid flow in coaxial laser cladding process for direct metal deposi-

tion, J. Appl. Phys. 100, 024903 (2006).9S. Kumar, V. Sharma, A. K. S. Choudhary, S. Chattopadhyaya, and S.

Hloch, Determination of layer thickness in direct metal deposition using

dimensional analysis, Int. J. Adv. Manuf. Technol. 67(912), 26812687(2013).

10Y. Sun and M. Hao, Statistical analysis and optimization of process pa-

rameters in Ti6Al4V laser cladding using Nd:YAG laser, Opt. Lasers

Eng. 50, 985995 (2012).11H. El Cheikh, B. Courant, S. Branchu, J. Y. Hascoet, and R. Guillen,Analysis and prediction of single laser tracks geometrical characteristics

in coaxial laser cladding process, Opt. Lasers Eng. 50, 413422 (2012).12J. P. Davim, C. Oliveira, and A. Cardoso, Predicting the geometric form

of clad in laser cladding by powder using multiple regression analysis

(MRA), Mater. Des. 29, 554557 (2008).13V. Ocelik, U. de Oliveira, M. de Boer, and J. T. M. de Hosson, Thick

Co-based coating on cast iron by side laser cladding: Analysis of process-

ing conditions and coating properties, Surf. Coat. Technol. 201,58755883 (2007).

14J. P. Davim, C. Oliveira, and A. Cardoso, Laser cladding: An experi-

mental study of geometric form and hardness of coating using statistical

analysis, Proc. Inst. Mech. Eng., Part B 220, 15491554 (2006).15U. de Oliveira, V. Ocelk, and J. T. M. De Hosson, Analysis of coaxiallaser cladding processing conditions, Surf. Coat. Technol. 197, 127136(2005).

16I. Felde, T. Reti, K. Zoltan, L. Costa, R. Colaco, R. Vilar, and B. Vero,A simple technique to estimate the processing window for laser clad

coatings, in Surface Engineering Coatings and Heat Treatments 2002:Proceedings of the 1st ASM International Surface Engineering and the13th IFHTSE Congress (Pub. ASM International, OH, 2003), pp.237242.

17Y. L. Huang, J. Liu, N. H. Ma, and J. G. Li, Three-dimensional analyti-

cal model on laser-powder interaction during laser cladding, J. Laser

Appl. 18, 4246 (2006).18Y. Fu, A. Loredo, B. Martin, and A. B. Vannes, A theoretical model for

laser and powder particles interaction during laser cladding, J. Mater.

Process. Technol. 128, 106112 (2002).19O. O. Diniz Neto and R. Vilar, Physical-computational model to

describe the interaction between a laser beam and a powder jet in laser

surface processing, J. Laser Appl. 14, 4651 (2002).20N. Yang, Concentration model based on movement model of powder

flow in coaxial laser cladding, Opt. Laser Technol. 41, 9498 (2009).



21O. O. D. Neto, A. M. Alcalde, and R. Vilar, Interaction of a focused

laser beam and a coaxial powder jet in laser surface processing, J. Laser

Appl. 19, 8488 (2007).22H. Pan and F. Liou, Numerical simulation of metallic powder flow in a

coaxial nozzle for the laser aided deposition process, J. Mater. Process.

Technol. 168, 230244 (2005).23H. Pan, R. G. Landers, and F. Liou, Dynamic modeling of powder deliv-

ery systems in gravity-fed powder feeders, ASME J. Manuf. Sci. Eng.

128, 337345 (2006).24J. Ibarra-Medina and A. Pinkerton, Numerical investigation of

powder heating in coaxial laser metal deposition, Surf. Eng. 27,754761 (2011).

25H. S. Li, X. C. Yang, J. B. Lei, and Y. S. Wang, A numerical simulation

of movement powder flow and development of the carrier-gas powder

feeder for laser repairing, in Conference on Material Processing andManufacturing II (SPIE Digital Library, Beijing, China, 2005), pp.557564.

26J. M. Lin, Numerical simulation of the focused powder streams in

coaxial laser cladding, J. Mater. Process. Technol. 105, 1723 (2000).27A. Haider and O. Levenspiel, Drag coefficient and terminal velocity of

spherical and nonspherical particles, Powder Technol. 58, 6370 (1989).28S. Y. Wen, Y. C. Shin, J. Y. Murthy, and P. E. Sojka, Modeling of

coaxial powder flow for the laser direct deposition process, Int. J. Heat

Mass Transfer 52, 58675877 (2009).29O. B. Kovalev, A. V. Zaitsev, D. Novichenko, and I. Smurov,

Theoretical and experimental investigation of gas flows, powder trans-

port and heating in coaxial laser direct metal deposition (DMD) process,

J. Therm. Spray Technol. 20, 465478 (2011).30S. Zekovic, R. Dwivedi, and R. Kovacevic, Numerical simulation and

experimental investigation of gas-powder flow from radially symmetrical

nozzles in laser-based direct metal deposition, Int. J. Mach. Tools

Manuf. 47, 112123 (2007).31J. Ibarra-Medina and A. J. Pinkerton, CFD model of the laser, coaxial

powder stream and substrate interaction in laser cladding, Phys.

Procedia 5, 337346 (2010).32I. Tabernero, A. Lamikiz, S. Martnez, E. Ukar, and L. N. Lopez deLacalle, Modelling of energy attenuation due to powder flow-laser beam

interaction during laser cladding process, J. Mater. Process. Technol.

212, 516522 (2012).33I. Tabernero, A. Lamikiz, E. Ukar, L. N. Lopez de Lacalle, C. Angulo,and G. Urbikain, Numerical simulation and experimental validation of

powder flux distribution in coaxial laser cladding, J. Mater. Process.

Technol. 210, 21252134 (2010).34K. Partes, Analytical model of the catchment efficiency in high speed

laser cladding, Surf. Coat. Technol. 204, 366371 (2009).35A. Fathi, E. Toyserkani, A. Khajepour, and M. Durali, Prediction of melt

pool depth and dilution in laser powder deposition, J. Phys. D 39,26132623 (2006).

36H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, 2nd ed.(Oxford University Press, Oxford, 1959).

37D. Rosenthal, The theory of moving sources of heat and its application

to metal treatments, Trans. ASME 68, 849866 (1946).38C. Lalas, K. Tsirbas, K. Salonitis, and G. Chryssolouris, An analytical model

of the laser clad geometry, Int. J. Adv. Manuf. Technol. 32, 3441 (2007).39H. El Cheikh, B. Courant, J. Y. Hascoet, and R. Guillen, Prediction andanalytical description of the single laser track geometry in direct laser

fabrication from process parameters and energy balance reasoning,

J. Mater. Process. Technol. 212, 18321839 (2012).40G. Zhu, D. Li, A. Zhang, G. Pi, and Y. Tang, The influence of standoff

variations on the forming accuracy in laser direct metal deposition,

Rapid Prototyping J. 17, 98106 (2011).41G. Zhu, D. Li, A. Zhang, G. Pi, and Y. Tang, The influence of laser and

powder defocusing characteristics on the surface quality in laser direct

metal deposition, Opt. Laser Technol. 44, 349356 (2012).42M. N. Ahsan, A. J. Pinkerton, R. J. Moat, and J. Shackleton, A compara-

tive study of laser direct metal deposition characteristics using gas and

plasma-atomized Ti-6Al-4V powders, Mater. Sci. Eng. A 528,76487657 (2011).

43S. Zhou, X. Dai, and H. Zheng, Analytical modeling and experimental

investigation of laser induction hybrid rapid cladding for Ni-based WC

composite coatings, Opt. Laser Technol. 43, 613621 (2011).44M. N. Ahsan and A. J. Pinkerton, An analytical-numerical model of laser

direct metal deposition track and microstructure formation, Modell.

Simul. Mater. Sci. Eng. 19, 055003 (2011).

45C. Chan, J. Mazumder, and M. M. Chen, Fluid flow in laser melted

pool, in Modeling of Casting and Welding Processes II (New EnglandCollege, Henniker, NH, 1983), pp. 297316.

46M. M. Mahapatra and L. Li, Modeling of pulsed-laser superalloy powder

deposition using moving distributed heat source, in Proceedings of theMinerals, Metals & Materials Society Extraction & Processing Division(EPD) Congress 2012 (John Wiley & Sons Inc., Hoboken, New Jersey,2012), pp. 113120.

47V. Neela and A. De, Three-dimensional heat transfer analysis of

LENSTM process using finite element method, Int. J. Adv. Manuf.

Technol. 45, 935943 (2009).48R. Ye, J. E. Smugeresky, B. Zheng, Y. Zhou, and E. J. Lavernia,

Numerical modeling of the thermal behavior during the LENSVRproc-

ess, Mater. Sci. Eng. A 428, 4753 (2006).49L. Wang and S. Felicelli, Analysis of thermal phenomena in LENS

TM

deposition, Mater. Sci. Eng. A 435436, 625631 (2006).50K. Takeshita and A. Matsunawa, Numerical simulation of the molten-

pool formation during the laser surface-melting process, Metall. Mater.

Trans. B 32, 949959 (2001).51L. Costa, R. Vilar, T. Reti, R. Colaco, A. M. Deus, and I. Felde,

Simulation of phase transformations in steel parts produced by laser

powder deposition, in 4th Hungarian Conference on Materials Science,Testing and Informatics, October 1214 2003 (Trans Tech Publications,Switzerland, 2005), pp. 315320.

52L. Costa, R. Vilar, T. Reti, and A. M. Deus, Rapid tooling by laser pow-

der deposition: Process simulation using finite element analysis, Acta

Mater. 53, 39873999 (2005).53A. Vasinonta, M. L. Griffith, and J. L. Beuth, A process map for consist-

ent build conditions in the solid freeform fabrication of thin-walled

structures, J. Manuf. Sci. Eng. 123, 615622 (2000).54T. B. Chen and Y. W. Zhang, Analysis of melting in a subcooled two-

component metal powder layer with constant heat flux, Appl. Therm.

Eng. 26, 751765 (2006).55A. Suarez, M. J. Tobar, A. Ya~nez, I. Perez, J. Sampedro, V. Amigo, andJ. J. Candel, Modeling of phase transformations of Ti6Al4V during laser

metal deposition, Phys. Procedia 12A, 666673 (2011).56S. Kumar and S. Roy, Development of a theoretical process map for

laser cladding using two-dimensional conduction heat transfer model,

Comput. Mater. Sci. 41, 457466 (2008).57S. Safdar, A. J. Pinkerton, L. Li, M. A. Sheikh, and P. J. Withers, An ani-

sotropic enhanced thermal conductivity approach for modelling laser

melt pools for Ni-base super alloys, Appl. Math. Model. 37, 11871195(2013).

58J. Choi, L. Han, and Y. Hua, Modeling and experiments of laser clad-

ding with droplet injection, ASME Trans. J. Heat Transfer 127, 978986(2005).

59S. Morville, M. Carin, P. Peyre, M. Gharbi, D. Carron, P. Le Masson, and

R. Fabbro, 2D longitudinal modeling of heat transfer and fluid flow dur-

ing multilayered direct laser metal deposition process, J. Laser Appl. 24,032008 (2012).

60F. Kong and R. Kovacevic, Modeling of heat transfer and fluid flow in

the laser multilayered cladding process, Metall. Mater. Trans. B 41,13101320 (2010).

61L. Han and F. W. Liou, Numerical investigation of the influence of laser

beam mode on melt pool, Int. J. Heat Mass Transfer 47, 43854402(2004).

62E. Toyserkani, A. Khajepour, and S. Corbin, 3-D finite element model-

ing of laser cladding by powder injection: effects of laser pulse shaping

on the process, Opt. Lasers Eng. 41, 849867 (2004).63E. Toyserkani, A. Khajepour, and S. Corbin, Three-dimensional finite

element modeling of laser cladding by powder injection: Effects of pow-

der feed rate and travel speed on the process, J. Laser Appl. 15, 153160(2003).

64X. He and J. Mazumder, Transport phenomena during direct metal depo-

sition, J. Appl. Phys. 101, 053113 (2007).65X. He, G. Yu, and J. Mazumder, Temperature and composition profile

during double-track laser cladding of H13 tool steel, J. Phys. D 43,015502 (2010).

66P. Peyre, P. Aubry, R. Fabbro, R. Neveu, and A. Longuet, Analytical

and numerical modelling of the direct metal deposition laser process,

J. Phys. D 41, 025403 (2008).67S. Y. Wen and Y. C. Shin, Modeling of transport phenomena during the

coaxial laser direct deposition process, J. Appl. Phys. 108, 044908(2010).



68S. Y. Wen and Y. C. Shin, Comprehensive predictive modeling and

parametric analysis of multitrack direct laser deposition processes,

J. Laser Appl. 23, 022003 (2011).69S. Wen and Y. C. Shin, Modeling of the off-axis high power diode laser

cladding process, J. Heat Transfer 133, 031007-10 (2011).70S. Wen and Y. C. Shin, Modeling of transport phenomena in direct laser

deposition of metal matrix composite, Int. J. Heat Mass Transfer 54,53195326 (2011).

71M. Alimardani, V. Fallah, M. Iravani-Tabrizipour, and A. Khajepour,

Surface finish in laser solid freeform fabrication of an AISI 303L stain-

less steel thin wall, J. Mater. Process. Technol. 212, 113119 (2012).72M. Gharbi, P. Peyre, C. Gorny, M. Carin, S. Morville, P. Le Masson, D.

Carron, and R. Fabbro, Influence of various process conditions on sur-

face finishes induced by the direct metal deposition laser technique on a

Ti-6Al-4V alloy, J. Mater. Process. Technol. 213, 791800 (2013).73P. Peyre, M. Gharbi, C. Gorny, M. Carin, S. Morville, D. Carron, P. Le

Masson, T. Malot, and R. Fabbro, Surface finish issues after direct metal

deposition, Mater. Sci. Forum 706709, 228233 (2012).74J. Ibarra-Medina, M. Vogel, and A. J. Pinkerton, A CFD model of laser

cladding: From deposition head to melt pool dynamics, in 30thInternational Congress on Applications of Lasers and Electro-optics(ICALEO) (LIA, Orlando, FL, 2011), p. 708.

75L. Han, K. M. Phatak, and F. W. Liou, Modeling of laser deposition and

repair process, J. Laser Appl. 17, 8999 (2005).76J. Ibarra-Medina, A. J. Pinkerton, M. Vogel, and N. NDri, Transient

modelling of laser deposited coatings, in 26th International Conferenceon Surface Modification Technologies (Valardocs, India, 2012).

77G. Palumbo, S. Pinto, and L. Tricarico, Numerical finite element investi-

gation on laser cladding treatment of ring geometries, J. Mater. Process.

Technol. 155, 14431450 (2004).78H.-Y. Zhao, H.-T. Zhang, C.-H. Xu, and X.-Q. Yang, Temperature and

stress fields of multi-track laser cladding, Trans. Nonferrous Met. Soc.

China 19, s495s501 (2009).79G. Yang, W. Wang, L. Qin, and X. Wang, Numerical simulation temper-

ature field of laser cladding titanium alloy, in Applied Mechanics andMaterials (Trans Tech Publications Inc., Durnten-Zurich, Switzerland,2012), Vol. 117119, pp. 16331637.

80A. Nickel, D. Barnett, G. Link, and F. Prinz, Residual stresses in layered

manufacturing, in 10th Solid Freeform Fabrication Symposium,(University of Texas, Austin TX, 1999), pp. 239246; available online

at http://utwired.engr.utexas.edu/lff/symposium/proceedingsArchive/pubs/

Table%20of%20Contents/1999_TOC.cfm.81A. H. Nickel, D. M. Barnett, and F. B. Prinz, Thermal stresses and depo-

sition patterns in layered manufacturing, Mater. Sci. Eng. A 317, 5964(2001).

82R. Jendrzejewski, G. Sliwinski, M. Krawczuk, and W. Ostachowicz,

Temperature and stress fields induced during laser cladding, Comput.

Struct. 82, 653658 (2004).83S. Ghosh and J. Choi, Modeling and experimental verification of tran-

sient/residual stresses and microstructure formation of multi-layer laser

aided DMD process, J. Heat Transfer 128, 662679 (2006).84M. Labudovic, D. Hu, and R. Kovacevic, A three dimensional model for

direct laser metal powder deposition and rapid prototyping, J. Mater.

Sci. 38, 3549 (2003).85P. Rangaswamy, M. L. Griffith, M. B. Prime, T. M. Holden, R. B. Rogge,

J. M. Edwards, and R. J. Sebring, Residual stresses in LENS (R) compo-

nents using neutron diffraction and contour method, Mater. Sci. Eng., A

399, 7283 (2005).86R. J. Moat, A. J. Pinkerton, L. Li, P. J. Withers, and M. Preuss, Residual

stresses in laser direct metal deposited Waspaloy, Mater. Sci. Eng. A

528, 22882298 (2011).87S. H. Mok, G. Bi, J. Folkes, I. Pashby, and J. Segal, Deposition of

Ti6Al4V using a high power diode laser and wire, Part II: Investigation

on the mechanical properties, Surf. Coat. Technol. 202, 46134619(2008).

88E. Brandl, F. Palm, V. Michailov, B. Viehweger, and C. Leyens,

Mechanical properties of additive manufactured titanium (Ti6Al4V)

blocks deposited by a solid-state laser and wire, Mater. Des. 32,46654675 (2011).

89B. Baufeld, E. Brandl, and O. van der Biest, Wire based additive layer

manufacturing: Comparison of microstructure and mechanical properties

of Ti6Al4V components fabricated by laser-beam deposition and

shaped metal deposition, J. Mater. Process. Technol. 211, 11461158(2011).

90B. Baufeld, O. V. d. Biest, and R. Gault, Additive manufacturing of

Ti6Al4V components by shaped metal deposition: Microstructure and

mechanical properties, Mater. Des. 31(1), S106S111 (2010).91M. Gaumann, C. Bezencon, P. Canalis, and W. Kurz, Single-crystal laser

deposition of superalloys: Processing-microstructure maps, Acta Mater.

49, 10511062 (2001).92X. Do, D. Li, A. Zhang, B. He, H. Zhang, and T. Doan, Investigation on

multi-track multi-layer epitaxial growth of columnar crystal in direct laser

forming, J. Laser Appl. 25, 012007 (2013).93R. Vilar, E. C. Santos, P. N. Ferreira, N. Franco, and R. C. da Silva,

Structure of NiCrAlY coatings deposited on single-crystal alloy turbine

blade material by laser cladding, Acta Mater. 57, 52925302 (2009).94M. Rombouts, G. Maes, M. Mertens, and W. Hendrix, Laser metal depo-

sition of Inconel 625: Microstructure and mechanical properties, J. Laser

Appl. 24, 052007 (2012).95A. Clare, O. Olusola, J. Folkes, and P. Farayibi, Laser cladding for railway

repair and preventative maintenance, J. Laser Appl. 24, 032004 (2012).96L. Wang and S. Felicelli, Process modeling in laser deposition of multi-

layer SS410 steel, ASME J. Manuf. Sci. Eng. 129, 10281034 (2007).97R. Colaco and R. Vilar, Phase selection during solidification of AISI 420

and AISI 440C tool steels, Surf. Eng. 12, 319325 (1996).98J. Ahlstrom, B. Karlsson, and S. Niederhauser, Modelling of laser clad-ding of medium carbon steelA first approach, J. Physique IV, 120,405412 (2004).

99Y. Lei, R. Sun, Y. Tang, and W. Niu, Numerical simulation of tempera-

ture distribution and TiC growth kinetics for high power laser clad TiC/

NiCrBSiC composite coatings, Opt. Laser Technol. 44, 11411147(2012).

100N. Pirch, S. Keutgen, S. Gasser, K. Wissenbach, and I. Kelbassa,

Modeling of coaxial single and overlap-pass cladding with laser radi-

ation, in Proceedings of the 37th International MATADOR Conference,edited by S. Hinduja and L. Li (Springer, London, 2013), pp. 337391.

101F. Bruckner, D. Lepski, and E. Beyer, Modeling the influence of process

parameters and additional heat sources on residual stresses in laser

cladding, J. Therm. Spray Technol. 16, 355373 (2007).102M. Alimardani, E. Toyserkani, and J. P. Huissoon, A 3D dynamic

numerical approach for temperature and thermal stress distributions in

multilayer laser solid freeform fabrication process, Opt. Lasers Eng. 45,11151130 (2007).

103H. K. D. H. Bhadeshia, Mathematical models in materials science,

Mater. Sci. Technol. 24, 128136 (2008).104E. Toyserkani and A. Khajepour, A mechatronics approach to laser pow-

der deposition process, Mechatronics 16, 631641 (2006).105A. Fathi, A. Khajepour, M. Durali, and E. Toyserkani, Geometry con-

trol of the deposited layer in a nonplanar laser cladding process using a

variable structure controller, ASME J. Manuf. Sci. Eng. 130, 031003(2008).

106D. Salehi and M. Brandt, Melt pool temperature control using LabVIEW

in Nd:YAG laser blown powder cladding process, Int. J. Adv. Manuf.

Technol. 29, 273278 (2006).107L. Song, V. Bagavath-Singh, B. Dutta, and J. Mazumder, Control of

melt pool temperature and deposition height during direct metal deposi-

tion process, Int. J. Adv. Manuf. Technol. 58, 247256 (2012).108L. Tang and R. G. Landers, Layer-to-Layer Height Control for Laser

Metal Deposition Process, J. Manuf. Sci. Eng. 133, 021009 (2011).109D. Hu and R. Kovacevic, Sensing, modeling and control for laser-based

additive manufacturing, Int. J. Mach. Tools Manuf. 43, 5160 (2003).110T. Lie, R. Jianzhong, T. E. Sparks, R. G. Landers, and F. Liou, Layer-to-

layer height control of laser metal deposition processes, in AmericanControl Conference, 2009. ACC 09 (IEEE, 2009), pp. 55825587.



Documents

1.4815992