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Scripta Materialia 63 (2010) 140–143

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Finite element analysis of the rapid manufacturing of Ti–6Al–4Vparts by laser powder deposition

Antonio Crespo* and Rui Vilar

Materials Engineering Department, Instituto Superior Tecnico, Avenida Rovisco Pais 1, 1049-001 Lisbon, Portugal

Received 9 March 2010; accepted 11 March 2010Available online 15 March 2010

The overlapping of layers during part build-up in rapid manufacturing by laser powder deposition (LPD) causes consecutivethermal cycles in the previously deposited material that often lead to complex phase transformations and difficult to predict distri-butions of microstructure and properties. In this paper a model coupling finite element heat transfer calculations, phase transfor-mation kinetics and microstructure–property relations in Ti–6Al–4V is presented and used to obtain processing maps relating thedeposition parameters to the microstructure and properties of the parts.� 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Laser deposition; Titanium alloys; Finite element analysis; Phase transformation kinetics

Laser powder deposition (LPD) is a rapid man-ufacturing technique that uses a focused laser beam tomelt a stream of metallic powder and deposit the moltenmaterial continuously at precise locations [1,2]. By scan-ning the laser beam and the powder jet according to apredefined trajectory fully dense near-net shaped com-ponents can be manufactured. One important featureof this technique is that, as a result of layer overlappingduring part build-up, the deposited material undergoesconsecutive thermal cycles leading to a progressive mod-ification of its microstructure and properties [3,4]. Toobtain parts fulfilling specific requirements, the manu-facturing process must be optimized, but this is difficultto achieve experimentally since the required experimentsare too expensive and time consuming, in particular be-cause the process is frequently used to manufacture oneof a kind parts within a short delivery time. In contrast,the deposition process can be efficiently optimized usinga computational approach, as shown in a previous pub-lication [3]. In this paper, we describe a thermo-kineticmodel that couples finite element heat transfer calcula-tions with phase transformation kinetics and micro-structure–property relations in Ti–6Al–4V to calculatethe distributions of microstructure and properties inparts manufactured by LPD. The application of themodel is illustrated by evaluating the influence of the

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* Corresponding author. Tel./fax: +351 218418120; e-mail:antoniocrespo@ist.utl.pt

deposition parameters on the microstructure and prop-erties of Ti–6Al–4V single walls.

In the model the temperature evolution in the part iscalculated by solving the heat conduction equation (Eq.(1)) by the finite element method using a step-wise ap-proach to simulate the addition of material (Fig. 1).

qcpð@T=@tÞ ¼ rðkDT Þ ð1ÞThe temperature variation at each point is used as in-

put for a phase transformation kinetics subroutine thatsimulates the microstructural evolution in Ti–6Al–4Vduring the deposition process.

Ti–6Al–4V is an a/b alloy that contains in its compo-sition 6% of an a-stabilizer (Al) and 4% of a b-stabilizer(V) [5]. As a result of the combined effect of these twoelements, the equilibrium microstructure of Ti–6Al–4Vconsists of a mixture of a and b phases at temperaturesbetween room temperature and 980 �C (the b-transustemperature). The equilibrium proportion of b phase de-pends on the temperature and was quantified in themodel by [6]:

fbðT Þ ¼0:075þ 0:925:e½�0:0085ð980�T Þ�; T < b-transus

1; b-transus � T 6 T liq;

(

ð2Þwith T in �C.

After solidification the microstructure of laser depos-ited Ti–6Al–4V consists of b phase. During cooling toroom temperature the b phase may undergo two differ-

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Figure 1. Finite element model for LPD.

A. Crespo, R. Vilar / Scripta Materialia 63 (2010) 140–143 141

ent phase transformations [7]. If the cooling rate is lowerthan 410 �C s�1 a diffusion controlled b ? a transfor-mation takes place, starting at the b-transus temperature(980 �C). The final microstructure consists of a and bphases because the transformation does not reach com-pletion at room temperature. Under isothermal condi-tions the kinetics of this transformation are describedby the Johnson–Mehl–Avrami (JMA) equation:

faðtÞ ¼ 1� expð�ktnÞ; ð3Þwhere fa(t), k and n are the fraction of a phase formedafter time t, the reaction rate constant and the Avramiexponent, respectively. Since in LPD the transforma-tions occur under anisothermal conditions, in the pres-ent model the JMA equation was generalized using theadditivity rule [8]. The values for k and n were deter-mined as a function of temperature by Malinov et al.[9]. For cooling rates higher than 410 �C s�1 the diffu-sional transformation is suppressed and the b phasetransforms by a martensitic mechanism [7]. The propor-tion of b phase transformed into martensite (a0) dependsessentially on the undercooling below the martensitestart temperature (Ms) and in the model was estimatedby [10]:

fa0 ðT Þ ¼ 1� exp½�cðM s � T Þ�: ð4ÞIf the material cools below Mf (the martensite finish

temperature) its microstructure is fully martensitic.The values of c, Ms and Mf used in the present work(0.015 �C�1, 650 �C and 400 �C, respectively), were cal-culated on the basis of the results of Elmer et al. [11].

The deposition of new layers generates new thermalcycles and, as a consequence, the previously depositedmaterial undergoes additional phase transformationswhich depend on its microstructure. When the micro-structure resulting from the first thermal cycle consistsof a + b, reheating will cause a diffusional a ? b trans-formation. If the microstructure is martensitic, heatingup within the tempering temperatures range (>400 �C)leads to the decomposition of martensite into a mixtureof a and b phases. The kinetics of these transformationswere described in the model by the generalized JMAequation, using for the tempering reaction the valuesof k and n determined by Mur et al. [12].

During cooling to room temperature in the secondthermal cycle, the b phase transforms into a phase bya diffusional mechanism if the cooling rate is lower than410 �C s�1. For higher cooling rates the b phase may

undergo a martensitic transformation or be retained atroom temperature, depending on its volume fraction inthe alloy. Fan [13] observed that b phase is completelyretained upon quenching if its proportion in the alloyis lower than 0.25, because this phase becomes enrichedin vanadium, a b stabilizer. If its volume fraction ex-ceeds 0.25 a proportion of b phase given by:

fr ¼ 0:25� 0:25:fbðT 0Þ ð5Þis retained at room temperature [13], where fb(T0) is thevolume fraction of b phase prior to quenching. Theremaining b phase undergoes a martensitic transforma-tion. As a result, cooling an alloy consisting entirely ofb phase at rates higher than 410 �C s�1 produces a fullymartensitic structure, while materials with smaller vol-ume fractions of this phase retain a variable proportionof b phase. In the model the martensite volume fractionwas calculated by:

fa0 ðT Þ ¼ fa0 ðT 0Þ þ ðfbðT 0Þ � frÞ½1� expð�cðM s � T ÞÞ�;ð6Þ

where fa0(T0) is the volume fraction of a0 prior toquenching. Structural evolution continues during subse-quent thermal cycles.

The Young’s modulus and hardness distributionswere calculated from the phase constitution of the alloyusing the rule of mixtures [3,13–15]. The values of theYoung’s modulus for the a, b and a0 phases used inthe model were 117, 82 and 113 GPa, respectively, andthe Vickers hardness values were 320, 140 and 350HV, respectively. The required LPD experiments werecarried out to validate the model and a good correlationwas observed between the model predictions and theexperimental results [16].

The model was used to study the influence of scan-ning speed (v), idle time between the deposition of con-secutive layers (Dt) and substrate temperature (Tsub) onthe microstructure, Young’s modulus and hardness dis-tributions in walls with a width of 1 mm, a length of14 mm and a height of 5 mm, produced by overlapping10 layers of Ti–6Al–4V on a substrate of the same mate-rial with dimensions 100 � 25 � 70 mm. The wall wasassumed to be deposited along the longitudinal directionof the substrate and on its mid plane, so that a symmetryplane existed and only half of the geometry needed to beconsidered for calculation purposes (Fig. 1). A 1000 Wlaser beam focused to a spot of 1.5 mm diameter (at e–

2 of the maximum intensity) was used to create a meltpool of approximately 1 mm diameter, matching thetrack width. An average reflectivity of 0.84 was used inthe calculations [17].

Figure 2a and b shows the Young’s modulus andhardness distributions computed for a scanning speedof 20 mm s�1 and an idle time of 10 s. The resultingmaterial presented a fully martensitic microstructureand uniform distributions of Young’s modulus andhardness, 113 GPa and 350 HV, respectively. The highcooling rates experienced by the material (�103 �C s�1)favor the transformation of the b phase formed uponsolidification by a martensitic mechanism. Some temper-ing occurred due to reheating caused by layer overlap,but its extent was small because the residence time of

Figure 2. Distributions of Young’s modulus (GPa) and Vickers hardness (HV) in longitudinal sections of parts produced with: (a and b) v =20 mm s�1, Dt = 10 s and Tsub = 20 �C; (c and d) v = 5 mm s�1, Dt = 10 s and Tsub = 20 �C; (e and f) v = 20 mm s�1, Dt = 10 s and Tsub = 500 �C.

142 A. Crespo, R. Vilar / Scripta Materialia 63 (2010) 140–143

the material within the tempering temperatures rangeduring the complete build-up process was less than10 s. The idle time between the deposition of consecutivelayers was sufficient for the part to cool down to approx-imately 20 �C before the deposition of each new layer,therefore the average substrate temperature increasedonly slightly during part build-up. Lower idle times ledto a progressive increase in the workpiece temperaturebut the cooling rates remained higher than the martens-ite critical cooling rate (410 �C s�1), asymptoticallyapproaching a limit value between 1500 �C s�1 (forDt = 2 s) and 1900 �C s�1 (for Dt > 30 s) as the numberof deposited layers increased.

The scanning speed plays an important role in themicrostructure of the material because low scanningspeeds lead to longer laser/material interaction timesand lower temperature gradients in the wall, as shownin Figure 3. Since heat conduction to the substrate isthe main mechanism of heat extraction from the interac-tion zone, lower temperature gradients will slow down

Figure 3. Temperature (�C) distribution in par

Figure 4. Processing maps plotting the predicted microstructure and co

the heat flow and cause a reduction in the cooling rate,which is approximately given by (see Eq. (1)):

ð@T=@tÞ ¼ ðk=qcpÞð@2T=@x2Þ; ð7Þwhere xx0 is the build-up (vertical) direction. As a result,for low scanning speeds the material in the last layerscooled down from above the b-transus at rates lowerthan 410 �C s�1 and b phase was transformed by a diffu-sional mechanism, leading to a microstructure contain-ing 0.92 a phase and 0.08 b phase. The final partspresented a non-uniform distribution of hardness –350 HV in the lower region and 305 HV in the top layers(Fig. 2d). The Young’s modulus was practically uniform(Fig. 2c) – 113 GPa in the bottom layers (a0) and114 GPa in the upper ones (0.92 a + 0.08 b). The modelallows building processing maps, such as those plottedin Figure 4, that enable prediction of the microstructureof the material given a set of processing conditions.

The temperature of the substrate affects the phasetransformations in two principal ways. First, preheating

ts deposited at (a) 5 and (b) 20 mm s�1.

oling rate for a substrate at (a) room temperature and (b) 500 �C.

A. Crespo, R. Vilar / Scripta Materialia 63 (2010) 140–143 143

the substrate to temperatures above Mf (400 �C) pre-vents the material from completing the martensitictransformation before the deposition of a new layer.For example, preheating the substrate at 500 �C stopsthe b ? a0 transformation at about 75%. At this temper-ature vanadium diffuses into the b phase (less than 20 sare needed to reach a concentration of 10 wt.% [9,18]),stabilizing this phase and leading to a microstructurewith roughly 0.25 b phase at room temperature [13]. Sec-ond, preheating the substrate decreases the temperaturegradient in the part, leading to a decrease in the coolingrate and favoring the transformation of b into a phaseby a diffusional mechanism. Figure 4b shows the depen-dence of cooling rate on scanning speed and on the idletime for a substrate at a temperature of 500 �C and facil-itates finding the processing window leading to a mar-tensitic transformation. For example, for a scanningspeed of 20 mm s�1 the transformation is martensitic ifan idle time of 5 s is used, while for 16 mm s�1, idle timeslonger than 15 s are necessary to achieve the martensitecritical cooling rate. After deposition of the last layer thematerial is at 500 �C and its microstructure consists ofapproximately 0.75 a0 + 0.25 b, with traces of a phasedue to tempering. Upon cooling to room temperaturethe b phase remains stable due to vanadium enrichment[19] and the final part has a uniform microstructure con-taining 0.75 a0 + 0.25 b [13]. This microstructure pre-sents a hardness of 300 HV and an elastic modulus of106 GPa, which is the minimum that can be achievedfor Ti–6Al–4V. The distributions of Young’s modulusand Vickers hardness are shown in Figure 2e and f,respectively.

The model prediction that b phase transforms into aphase by a diffusional mechanism in Ti–6Al–4V partsproduced by LPD at low scanning speeds was confirmedby the results of Kelly et al. (v = 0.625–2.5 mm s�1) [20]and Qian et al. (v = 6.7–10.0 mm s�1) [21], while theoccurrence of a martensitic transformation for higherspeeds was demonstrated by Groh [22]. The influenceof idle time on the microstructure and properties ofthe material is more significant when deposition takesplace on a preheated substrate. Preheating the substrateallows the microstructure and properties of the materialto be controlled, but it reduces the temperature gradientin the part. If short idle times are used the workpieceprogressively heats up, causing a transition from a mar-tensitic to a diffusional b transformation mechanism andleading to non-uniform distributions of microstructureand properties. To achieve a uniform distribution ofproperties the idle time must be sufficiently long to allowthe part to cool down to its initial temperature beforethe deposition of new layers, thereby ensuring that alllayers of material develop similar thermal histories dur-ing the deposition process.

In summary, a finite element thermo-kinetic modelcoupling heat transfer calculations with phase transfor-mation kinetics and microstructure–property relationswas developed to obtain processing maps relating thedeposition parameters to the microstructure and proper-ties of Ti–6Al–4V parts produced by LPD. The results

show that the selection of scanning speed and idle timeallows the cooling rate during the deposition processto be controlled, which is the main factor determiningthe microstructure and properties of the material. Theidle time plays a critical role when deposition takes placeon a preheated substrate, because low values of thisparameter promote heat accumulation in the part andlead to a transition from a martensitic to a diffusionalb transformation and non-uniform distributions ofmicrostructure and properties. The processing maps cal-culated using the model can be used to plan the process-ing method to produce parts with selected mechanicalproperties, thus avoiding the non-uniform distributionsthat are often reported in experimental papers and leadto unreliable mechanical behavior.

Antonio Crespo acknowledges financial sup-port from Fundac�ao para a Ciencia e a Tecnologia(Grant SFRH/BD/17570/2004). The authors also thankIMPALA Project for financial support (contract num-ber FP7-CP-TP-214380-2).

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