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Investigation of Residual Stresses in the Selective Laser Melting usingFinite Element Analysis

L. Parry 1,a , I. Ashcroft 1,b

1 Additive Manufacturing and 3D Printing Research Group, acu!ty of "ngineering, #he $niversity of %ottingha&, %ottingha&, %G' (RD, $nited )ingdo&

a !u*e.parry+nottingha&.ac.u*, b ian.ashcroft+nottingha&.ac.u*

Keywords: e!ective Laser Me!ting - LM , Residua! tress, inite "!e&ent Ana!ysis - "A

Abstract

The use of (SLM) Selective Laser Melting (SLM) in is an Additive Manufacturing method thatenables greater design freedoms than traditional manufacturing methods in the production of highvalue , low volume production of metallic parts. Despite this now being a well established

processing method s, there are a number of issues impeding industrial upta!e, including thegeneration the implications of residual stress and part distortion inhibit its adoptionduringmanufacture . "rediction of such effectsresidual stress is invaluable for tuning process parameters, and powder metallurg# but fundamentall# optimising the part geometr# and support structures toremove current limitationslimit residual stress based distortion during manufacture . This paperestablishes a thermal modelling strateg# to predict temperature distribution within a $D SLM partthat is a precursor towards a residual stress anal#sis. %inall# the discussion aims to outline researchmotivation and the future applications

Introduction:

SLM is capable of producing full# dense metal parts directl# from the machine. The processinvolves e&posing a powder bed to a laser beam with a high flu& densit# , causing the powder tomelt and solidif# upon cooling. The laser point scans along paths computed from slicing a $D 'ADModel and processing these la#ers . This process is repeated for each la#er slice to produce a $D

part. This process bares great resemblance to welding both in design and anal#sis. The advantage of SLM s abilit# to create full# dense part removes the re uirement for time consuming and e&pensive

post processing.

The high temperature gradients and non uniform thermal e&pansions and contractionslocatedaroundin the *A+ *eat Affected +one (*A+) promote can result in the formation of high residualstresses in the finished component which lead to undesirable effects including the promotion ofcrac!ing, fatigue failure and part distortion. *igh thermal gradients introduce thermal e&pansion ofmaterial around the melt pool and introduce localised compressive and tensile stresses that uponcooling become loc!ed in stresses. Another contribution is wor! hardening through #ielding.

The immediate effect of thermal strains during the build process is distortion which prompts there uirement of support structures. These are an generall# undesirable and as the# are detriment al to

build efficienc#- affecting material resources and postproductionpostprocessing . The abilit# to predict residual stress and distortion will allow optimisation of the build parameters , and modelorientation and position, laser scan strateg# and support structure generation .and to greater effecttopolog# optimisation of geometr# /Dave s paper from our group0 1



Modelling such behaviour using %2A remains challenging , contributed b#owing to the non lineareffects of thermal phenomena and thermall# dependent material behaviour. %urthermore, themagnitude of spatio temporal scale between the localised *A+ and the global model domainintroduce a conflict of model resolution. There is a re uirement to capture a laser spot si3e of theorder ($4 $445m) with in a large global domain si3e (64 $44mm) and a build time that can rangefrom minutes to hours. %urther contributions to model comple&it# arise from a multitude of

ph#sical phenomena including but not limited to Marangoni %low, 7olume "owder Shrin!age,Thermo capillar# and Laser "owder "enetration /8 91. Such computational methods becomeinherentl# e&pensive and re uire a balance between scale, performance and accurac# withoutcomprising the anal#st:s intentions.

Methodology:

The SLM process was modelled using MS' Marc in con;unction with user defined %ortransubroutines for the inclusion of independent powder and consolidated material phases. A transientthermal anal#sis was performed on Stainless Steel $6<L. This material was chosen through thedueto the avauilabilit# of the re uired material data /<1 , however, the model could accept othermaterials provided if thermo ph#sical data is available .

=ased on previous>n the modelling strateg #,ies state variables are used to permit and trac! aunidirectional state change from powder to the consolidated phases upon reaching the melt

temperatureT

L see %ig.6. %undamental re uirements of the model are temperature dependent

material properties for the different material states . Thermo ph#sical material used

currentl#properties re uired are specific heatC

P (T

) , densit# ρ(T ) and, thermal conductivit#

k (T ) .

%ig.6- State change model used within %ortran Subroutines.

Model Definition:

=oundar# conditions and e&perimental material data were ta!en from a previous stud# /<1. Thisincludes a fi&ed temperature boundar# condition for the substrate and forced convection term onthe powder bed surface representative of the argon gas flow. *eat input was provided using a?olda! *eat Source /@1 t#picall# used for welding simulations and this is representative of amoving double ellipsoid ?aussian heat flu&. The inclusion of built in adaptive meshing around the



local domain improve ds the accurac# in the localised *A+ that is sub;ected towhere high thermalgradients and the greatest source of nonlinearit# arise .

A rectangular domain 8 mm & <.B mm & 6.9mm consisting of C node *e&ahedr on C ode alelements was used with a semi infinite laser path across the surface of the powder bed , with thelaser parameters listed in Table 6.

Table 6- Laser Scan "arameters used for the simulation

Results anddiscussion:

The results are broadl# in agreement with other previous findings /$1. %igure 8 illustrates thesignificance of accounting for the change of state from powder to consolidated material in the

model. >t can be noted fromseen in %ig. 8 that there is presence of a characteristic as#mmetricalarger melt pool in the state variable model. This is e&plained b# the consolidated material properties thermal diffusivit# valuelow thermal conductivit# of the material in powder form producing a more concentrated thermal field . >n the state variable model, an elongated rectangulartail is present whereas the single phase model is conical. The difference in shape of heat tail

behind the melt pool, demonstrates the insulated behaviour of the powder surrounding the melt pool. At room temperature thermal diffusivit# of solid to powder is appro&imatel# @9& greatereasing the conduction of heat awa# from the melt pool.

%ig. 8- %inite 2lement anal#sis showing top a plan view of the temperature distribution of SLMLaser Scan- SLM Simulation without state variables (Left), with state variables (Eight)

The melt pool dimensions in the state variable model are 4.B mm & 4.6$ mm & 4.4<Fmm %ig. $with an aspect ratio of $ similar to /@1. The width and depth are in good agreement with the laserspot diameter chosen, however, the laser power chosen is not indicative of a t#pical SLM build.

Laser "ower /G1 $4 Laser Spot Diameter /5m1 684Laser Speed /mmHs1 844 Absorption 2fficienc# I 4.<@



As of a conse uence of the high energ# densit#, the pea! temperature of the melt pool is above thevaporisation transition temperature of steel, similar to other models /8,B,9,<1 and in such state is notsufficient for accurate problem modelling. The current model described in this paper omits the

effects of latent heat released at both theT

L li uidus transition and vaporisation temperature.

The latter has been shown to significantl# affect the melt pool dimensions b# limiting the ma&temperature of the melt pool and as a result increasing melt pool penetration depth /C1.

Jne difficult# for the creation of SLM simulations is having comprehensive thermal material propert# data for metallic powders. Models for emissivit#, thermal conductivit# and specific heathave been proposed but have #et to be verified e&perimentall# /F1. Later revisions of this modelwill include the ph#sical phenomena discussed earlier to enable more effective use of a coupledstructural anal#sis. This residual stress distribution will be validated with a recent techni ue using

anoindentation and A%M /641.

%ig. $- Annotated si3e of melt pool showing top and side cross section temperature distribution of model using state variables.

Additionall# multipath laser scanning will allow enable the anal#sis of more comple& non linear

behaviour such as overlap of hatch scan lines. >t w illas also support further optimisation studies.

Summary:

The state variable model used in %2 anal#sis allowed the prediction of melt pool behaviour andtemperature distribution along a semi infinite laser path with a state change from powder to solidtransition. The present results are in good agreement to previous simulation studies carried out.

References:

/81 >. Eoberts, '. K. Gang, E. 2sterlein, M. Stanford, D. K M#nors. >nternational Kournal of Machine Tools and

Manufacture 7ol. BF.68 (844F), p. F6< F8$./$1 A.7. ?usarov, >. Smurov. Modeling the interaction of laser radiation with powder bed at selective laser melting.

"h#sics "rocedia 7ol. 9 (8464). p. $C6 $FB.



/B1 *. Liu, T. 2. Spar!s, %. G. Liou, D. M. Dietrich. umerical Anal#sis of Thermal Stress and Deformation in MultiLa#er Laser Metal Deposition "rocesses (846$), p. 9@@ 9F6.

/91 ". Mercelis, K.". ruth. Eesidual stresses in selective laser sintering and selective laser melting. Eapid "rotot#pingKournal 7ol. 68.9 (844<), p. 89B 8<9. /@1

/<1 L. =ochuan. %urther process understanding and prediction on selective laser melting of stainless steel $6<L (846$)

/@1 K. ?olda!, A. 'ha!ravarti, M. =ibb#A new finite element model for welding heat sources. MetallurgicalTransactions =, 7ol. 69.8 (6FCB), p. 8FF $49

/C1 %. 7erhaeghe, T. 'raeghs, K. *eulens, L. "andelaers. A pragmatic model for selective laser melting withevaporation. Acta Materialia 7ol. [email protected] (844F)

/F1 A.7. ?usarov, 2. ovalev. Model of thermal conductivit# in powder beds. "h#sical Eeview = 7ol. C4.8 (844F)

/641 L. +hu, =. u, *. Gang, '. Gang. Measurement of residual stress in uenched 64B9 steel b# the nanoindentationmethod. Materials 'haracteri3ation 7ol. <6.68 (8464), pg. 6$9F 6$<8.

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