ma e ials
A icle
Op imizing Lase Powde Bed Fusion Pa ame e s o
IN-738LC by Response Su ace Me hod
Mi eia Vilano a 1,*, Rubén Esc ibano-Ga cía1, Te esa Gu aya 2and Ma ia San Sebas ian 1
1
LORTEK Technological Cen e, Basque Resea ch and Technology Alliance (BRTA), A anomendia Kalea 4A,
20240 O dizia, Spain; [email p o ec ed] (R.E.-G.); [email p o ec ed] (M.S.S.)
2Depa men o Mining and Me allu gical Enginee ing and Ma e ials Science, Uni e si y o he Basque
Coun y UPV/EHU, Ra ael Mo eno “Pi xi xi”, 2, 48013 Bilbao, Spain; e [email p o ec ed]
*Co espondence: [email p o ec ed]
Recei ed: 5 Oc obe 2020; Accep ed: 27 Oc obe 2020; Published: 30 Oc obe 2020
Abs ac :
A me hod o ind he op imum p ocess pa ame e s o manu ac u ing nickel-based
supe alloy Inconel 738LC by lase powde bed usion (LPBF) echnology is p esen ed. This ma e ial
is known o o m c acks du ing i s p ocessing by LPBF echnology; hus, p ocess pa ame e s ha e
o be op imized o ge a high quali y p oduc . In his wo k, he objec i e o he op imiza ion was
o ob ain samples wi h ewe po es and c acks. A design o expe imen s (DoE) echnique was
implemen ed o de ine he educed se o samples. Each sample was manu ac u ed by LPBF wi h a
speci ic combina ion o lase powe , lase scan speed, ha ch dis ance and scan s a egy pa ame e s.
Using he po osi y and c ack densi y esul s ob ained om he DoE samples, quad a ic models we e
i ed, which allowed iden i ying he op imal wo king poin by applying he esponse su ace me hod
(RSM). Finally, i e samples wi h he p edic ed op imal p ocessing pa ame e s we e ab ica ed. The
examina ion o hese samples showed ha i was possible o manu ac u e IN738LC samples ee o
c acks and wi h a po osi y pe cen age below 0.1%. The e o e, i was demons a ed ha RSM is sui able
o ob aining op imum p ocess pa ame e s o IN738LC alloy manu ac u ing by LPBF echnology.
Keywo ds:
lase powde bed usion (LPBF); Inconel 738LC; esponse su ace me hod (RSM); p ocess
pa ame e op imiza ion; c acking
1. In oduc ion
Lase powde bed usion (LPBF) is an addi i e manu ac u ing echnology in which a lase mel s
successi e powde laye s in o de o build he inal pa [
1
]. Some o he LPBF p ocess pa ame e s
a e lase powe (P), ha ch dis ance (h), lase scan speed ( ), laye hickness ( ), basepla e p ehea ing
empe a u e and lase scan s a egy (
θ
). The la e e e s o he o a ion o successi e laye s du ing he
manu ac u ing p ocess. Combining some o he p ocess pa ame e s, a key ac o o LPBF echnology
known as ene gy densi y can be calcula ed, as shown in Equa ion (1). This ac o indica es he ene gy
p o ided o he ma e ial du ing manu ac u ing p ocess [2]:
Ed=P
·h· (1)
Compa ed wi h con en ional manu ac u ing p ocesses (cas and w ough ), LPBF echnology
o e s some ad an ages, such as design eedom, educed weigh o pa s, p ocessing o complex
pa s, manu ac u ing o nea -ne -shape componen s and educ ion o was e ma e ial [
3
]. Despi e
hese ad an ages, he p esence o de ec s such as po es and c acks in he manu ac u ed inal pa s is a
d awback o he implemen a ion o his echnology in he indus y [
4
]. In pa icula , he exis ence o
po osi y is a ibu ed o di e en mechanisms: insu icien ene gy densi y, po osi y in aw ma e ial,
Ma e ials 2020,13, 4879; doi:10.3390/ma13214879 www.mdpi.com/jou nal/ma e ials
Ma e ials 2020,13, 4879 2 o 12
excessi e ene gy densi y o la ge spa e pa icles [
5
]. Po es o med by an insu icien ene gy densi y
usually ha e i egula mo phology due o he insu icien mel ing o he powde pa icles; ne e heless,
po osi y o med by he o he mechanisms usually p esen s as sphe ical. Fo ins ance, powde pa icles’
inne po osi y may be en apped in he manu ac u ed inal pa s due o he apid solidi ica ion du ing
LPBF p ocess. Addi ionally, when he applied ene gy densi y is oo high, he mel pool becomes
uns able, inducing he o ma ion o sphe ical po es a he bo om o he mel pool which a e known as
keyhole de ec s [2].
The e is a wide ange o ma e ials p ocessable by LPBF echnology, including aluminum (Al)
alloys [
6
–
8
], i anium (Ti) alloys [
9
], s ainless s eels [
10
,
11
], cobal (Co) alloys [
12
], cuppe (Cu) alloys [
13
]
and nickel (Ni) alloys [
14
,
15
]. Among he nickel (Ni)-based supe alloys, Inconel 738LC (IN738LC) is o
huge in e es o componen s o he ho es sec ion o land-based and ae onau ic gas u bine engines
because o i s co osion esis ance and c eep p ope ies a high empe a u es [
16
]. The mic os uc u e
o he supe alloy consis s o a ace cen e ed cubic (FCC) ma ix s eng hened by he p ecipi a ion o he
o de ed second phase
γ
’ which has a nominal composi ion o Ni
3
(Al, Ti) [
17
]. The co osion esis ance o
he alloy is achie ed by he o ma ion o he C
2
O
3
p o ec i e laye a he su ace, whe eas he ou s anding
mechanical p ope ies a high empe a u es a e ob ained by he p ecipi a ion o he γ’ phase.
Ne e heless, IN738LC alloy is no conside ed p ocessable by LPBF echnology because o i s high
suscep ibili y o c acking du ing manu ac u ing p ocess. In he li e a u e, he c acking suscep ibili y o
IN738LC is explained by h ee main mechanisms: liqua ion c acking, solidi ica ion c acking and s ain
age c acking [
18
,
19
]. Liqua ion c acking occu s when he ma e ial is hea ed jus below he liquidus
empe a u e whe e some low mel ing poin componen s—ca bides,
γ
/
γ
’ eu ec ic, bo ides, e c.—could
su e pa ial o o al mel ing. In he case o solidi ica ion c acking, i occu s a he inal s ages o
solidi ica ion when he liquid ac ion p esen in he ma e ial is a ound 6–10% [
20
]. This liquid is
en iched in some elemen s, such as zi conium (Z ) and bo on (B), which dec ease he solidi ica ion
empe a u e o he alloy known as he solidus. Ac ually, he emaining liquid ac ion accumula es
in he in e g anula zones, causing s ess du ing i s solidi ica ion, which ac s as an ini ial poin o
c acking. While liqua ion and solidi ica ion c acking a e liquid s a e mechanisms, s ain age c acking is
solid s a e mechanism which occu s du ing he p ecipi a ion o he
γ
’ phase. As he misma ch be ween
Ni ma ix and
γ
’ p ecipi a es is below 1%, p ecipi a ion o he second phase occu s ex emely apidly,
in ol ing la ge amoun o s ess which could cause he sepa a ion o g ain bounda ies. This ype o
c acking ends o ake place in Ni alloys wi h Al and Ti amoun s highe han 4.5% (w %) [21].
Some au ho s ha e ocused on elimina ing he c acking phenomenon in Ni supe alloys using
di e en app oaches. Rickenbache e al. [
17
] educed c ack densi y in he IN738LC supe alloy h ough
he op imiza ion o LPBF p ocess pa ame e s. Howe e , in o de o ob ain manu ac u ed pa s wi hou
c acks, hey conduc ed HIP (ho isos a ic p essing) as a pos -p ocessing s ep. Xu e al. [
18
] asse ed ha
using a su icien ly high p ehea ing empe a u e, i is possible o dec ease he alloy’s he mal ange and
o change he mic os uc u e om columna o equiaxial g ains. This mic os uc u al change implies a
mo e homogeneous dis ibu ion o he liquid along g ains, educing o e en elimina ing he o ma ion
o c acks. In ac , hey manu ac u ed c ack- ee IN738LC pa s by applying a p ehea ing empe a u e
o 1050
◦
C. Cloo s e al. [
19
] sugges ed ha he o ma ion o c acks in he IN738LC supe alloy occu s
by solidi ica ion c acking mechanism due o he p esence o a hin liquid ilm along he in es iga ed
c acks. They con i med by a om p obe omog aphy echnique ha he liquid ilm along he c acks
was ich in Z and B elemen s. They concluded ha in o de o elimina e c acking, i would be
necessa y o minimize as much as possible he con en o B and emo e Z om he alloy o ally. Finally,
Ca e e al. [22]
sugges ed ha by con olling scan s a egy o manu ac u ed samples, i was possible
o signi ican ly educe c acking densi y. Ac ually, hey s udied island and simple scan s a egies and
de e mined ha he e we e di e ences in he c ack densi y alues o he samples manu ac u ed wi h
each one o he s a egies.
Due o he o ma ion o de ec s in IN738LC pa s, i is challenging ying o op imize p ocess
pa ame e s. Fu he mo e, aking in o accoun he manu ac u ing p ocess a iables and all hei
Ma e ials 2020,13, 4879 3 o 12
possible combina ions, i would be una o dable o ind he op imum p ocess pa ame e s by means o
ial and e o me hod. Fo his eason, Pe e oshchiko a e al. [
23
] used Doehle ’s design o op imize
lase powe , lase scan speed and ha ch dis ance p ocess pa ame e s o manu ac u e samples wi h
minimum po osi y.
In his wo k, he au ho s p opose he applica ion o he esponse su ace me hod (RSM) o op imize
lase powe , ha ch dis ance, scan speed and scan s a egy p ocess pa ame e s wi h a educed numbe o
ials. RSM consis s o a design o expe imen s (DoE), polynomial model i ing and op imiza ion wi h
a combina ion o desi abili ies and he s eepes ascen me hod. The esponse su ace me hod has been
es ed in se e al ields o e he decades; howe e , he me hod does no ensu e he expec ed esul s, so
expe imen al e i ica ion is needed. The po en ial p oblems o RSM a e ela ed o he modeling e o
ha could be induced by he measu emen challenges. In he case o addi i e manu ac u ing, ano he
p oblem could be caused by he sample’s posi ion on he pla o m. In addi ion, one o he limi a ions
o RSM may be he numbe o inpu s, because when inpu s a e inc eased he numbe o samples o
building he models is also exponen ially inc eased. I may be impo an o poin ou ha wi hou
p e ious in o ma ion abou he ma e ial, i will be necessa y o build mo e han one model o se he
app op ia e p ocess pa ame e ange.
In he ield o addi i e manu ac u ing, se e al esea che s ha e used RSM o p ocess pa ame e
op imiza ion. Wang e al. [
24
] in es iga ed he in luences o some LPBF p ocess pa ame e s on he
mic os uc u e and mechanical p ope ies o manu ac u ed samples by RSM. They concluded ha i
was possible o inc ease he mechanical p ope ies by he op imiza ion o p ocess pa ame e s h ough
applying RSM. In addi ion, Deng e al. [
25
] manu ac u ed 316L s ainless s eel samples wi h high densi y
and low oughness using RSM o he p ocess op imiza ion. Te ne e al. [
26
] op imized he lase powe
and scanning speed p ocessing pa ame e s by using RSM o manu ac u e Co-C Mo samples wi h a
esidual po osi y and an inc ease in he ha dness o he ma e ial. In his s udy, he op imiza ion was
ca ied ou o ob ain samples wi h minimum po osi y and no c acks. The me hod ollowed minimizes
manu ac u ing ime, ma e ial was e, pos p ocessing asks and e alua ion ime.
2. Me hodology
2.1. Response Su ace Me hod
RSM is a me hod ha uses DoE, eg ession models and desi abili y unc ions [
27
]. The objec i e
o RSM is o explo e he ela ions be ween inpu a iables and esponse a iables, and o ind he
op imum wo king poin using he minimum numbe o ials. DoE is a collec ion o echniques
( ull ac o ial, cen al composi e, box-Behnken, e c.) o de ine a educed se o ials whose esul s
depend on inpu ac o s. Cu en ly, hese me hodologies a e widely used o pe o m mul i-objec i e
op imiza ions o manu ac u ing p ocesses [
28
,
29
]. DoE de e mines he numbe o cases, combina ions,
andomiza ion, eplica ion and blocking o he ac o s o s udy cause–e ec ela ionships wi h a ce ain
deg ee o con idence.
The numbe o combina ions wi h ou ac o s is 3
4
=81 conside ing h ee le els pe ac o .
This kind o design is called ull h ee-le el design (also called 3k) because i conside s all possible
combina ions o ac o s wi h h ee le els. In his case, manu ac u ing 81 cases (o cubes) is e y
expensi e and ime consuming in e ms o manu ac u ing and measu ing. The numbe o samples can
be educed o 15 using a cen al composi e design (CCD), which is an adequa e ac ional ac o ial
design o i quad a ic models.
A e sample manu ac u ing, ou pu s a e measu ed o all he cases. Then, a polynomial model is
adjus ed o each ou pu using he inpu s and he esul s o he 15 samples om he CCD:
Y= (x1,x2,. . . ,xn)(2)
whe e Yis a calcula ed ou pu , is a polynomial unc ion and x
i
a e he inpu s o he eg ession model.
The quad a ic eg ession model is a polynomial unc ion ha is widely used because i conside s
Ma e ials 2020,13, 4879 4 o 12
non-linea e ec s and allows inding combined in luences o inpu s aken in pai s. The gene al o m o
he quad a ic models is as ollows:
Y=b0+
n
X
i=1
bi·xi+
n
X
i=1
bii·x2
i+
n−1
X
i=1
n
X
j=i+1
bij·xi·xj+e(3)
whe e b
0
is he independen e m; he i s and second summa ions a e linea and quad a ic e ms;
he hi d summa ion is he c oss p oduc o all inpu ac o s; and eis he e o . Analysis o a iance
(ANOVA) can be used o e alua e he adjus men o he eg ession models o he expe imen al da a.
In mul i-objec i e op imiza ion, esponses can con lic wi h each o he , which means ha a
solu ion can p o ide he op imal esponse o some objec i es and poo esponses o he es . In hese
cases, gene ally no unique esul achie es he bes solu ion o all objec i es a he same ime. Ins ead,
se e al Pa e o-e icien solu ions canno be imp o ed in any objec i e wi hou wo sening o he ones.
Ha ing on p oposed e alua ing he o e all esponse by applying he ollowing exp ession [27,30]:
D=(d1·d2·. . . ·dm)1/m(4)
whe e Dis he o e all desi abili y o a ce ain solu ion (inpu s combina ion), mis he numbe o
ou pu s and d
i
he desi abili y o he ou pu i. The desi abili y o each ou pu is de ined depending
on objec i e ype (maximum, minimum, a ge , e c.). In his s udy, he objec i es a e o minimize he
po osi y (φ) and c ack densi y (CD). These objec i es desi abili y is de ined as ollows:
d=
1 i Y≤Lmin
Lmax−Y
Lmax−Lmin si Lmin <Y≤Lmax
0 i Y≥Lmax
(5)
whe e L
min
and L
max
a e he limi alues and sis an exponen speci ied by he use . The exponen s
de ines he shape o he desi abili y unc ion and is equal o one in his s udy because bo h ou pu s a e
conside ed equally impo an .
2.2. Ma e ials
Conside ing he speci ica ions o LPBF echnology, gas a omized IN738LC powde was supplied
by Aube and Du al as eeds ock ma e ial. Powde chemical composi ion, de ailed in Table 1, was
measu ed by induced coupled plasma (ICP) echnique and by LECO o ca bon and oxygen elemen s.
Table 1. Composi ion o he IN738LC supe alloy used o manu ac u ing.
Elemen C Co W Ti Al Ta Mo Fe Nb
w % 15.8 8.6 2.7 3.3 3.6 1.8 1.8 0.04 0.8
Elemen Si Z Mn B C O N Ni
w % 0.02 0.04
0.002 0.0009
0.1 0.02
0.006
Bal.
Powde pa icle size dis ibu ion (PSD) measu ed by image analysis is shown in Figu e 1a,
whe eas D10 and D90 alues we e 32.57 and 64.06
µ
m espec i ely. Powde pa icles’ mo phology was
e alua ed by scanning elec on mic oscopy (SEM, Zeiss, Jena, Ge many), and as p esen ed in Figu e 1b
he mo phology was gene ally sphe ical, al hough some i egula pa icles and sa elli es may be seen,
which a e indica ed by ed a ows.
Ma e ials 2020,13, 4879 5 o 12
Ma e ials 2020, 13, x FOR PEER REVIEW 5 o 12
(a) (b)
Figu e 1. (a) Pa icle size dis ibu ion o IN738LC; (b) SEM image o he powde pa icles showing
di e ences in size and p esence o sa elli es and i egula pa icles ( ed a ows).
Samples we e manu ac u ed by LPBF in a RenAM 500Q Renishaw machine which employs ou
Yb- ibe lase s in a con inuous way wi h a maximum powe o 500 W and a lase spo size o 85 µm.
Fo he design o expe imen s, 24 samples we e manu ac u ed in he same basepla e (Figu e 2a) wi h
dimensions desc ibed in Figu e 2b. All he samples we e cu in building di ec ion (x–z plane) o
in es iga e he c acking phenomenon.
.
(a) (b)
Figu e 2. (a) Twen y- ou manu ac u ed cubes; (b) dimensions o he samples.
In o de o de ine p ocess pa ame e s’ anges o IN738LC, he pa ame e s used by Renishaw
o IN718 ma e ial (which is a Ni based alloy p ocessable by LPBF) and he ones op imized by o he
au ho s o IN738LC [23] we e aken in o accoun . In his case, ou inpu ac o s we e op imized:
lase powe , lase scan speed, ha ch dis ance and scan s a egy. Table 2 summa izes he ac o s,
symbols, anges and uni s used in his wo k. O he p ocess pa ame e s we e kep cons an , such as
laye hickness (60 µm) and p ehea ing empe a u e (170 °C).
Table 2. Fac o s, anges and uni s o he design o expe imen s.
Fac o Symbol
Range Uni
Min Max
Lase powe P 180 280 W
Lase scan speed 700 1100 mm/s
Ha ch dis ance h 0.08 0.12 mm
Scan s a egy θ 0 90 °
Samples we e p epa ed me allog aphically by g inding up o 2500 µm SiC pape and polishing
wi h 6, 3 and 1 µm diamond pas e. Las ly, he manu ac u ed samples we e cha ac e ized by ligh
mic oscope (GX51 Olympus) and a Zeiss Ul a Plus FEG-SEM (Zeiss, Jena, Ge many).
0
20
40
60
80
100
0
2
4
6
8
10
12
14
16
18
0 102030405060708090
Accumula ed olume %
Volume %
Pa icle size (µm)
Figu e 1.
(
a
) Pa icle size dis ibu ion o IN738LC; (
b
) SEM image o he powde pa icles showing
di e ences in size and p esence o sa elli es and i egula pa icles ( ed a ows).
Samples we e manu ac u ed by LPBF in a RenAM 500Q Renishaw machine which employs ou
Yb- ibe lase s in a con inuous way wi h a maximum powe o 500 W and a lase spo size o 85
µ
m.
Fo he design o expe imen s, 24 samples we e manu ac u ed in he same basepla e (Figu e 2a) wi h
dimensions desc ibed in Figu e 2b. All he samples we e cu in building di ec ion (x–z plane) o
in es iga e he c acking phenomenon.
Ma e ials 2020, 13, x FOR PEER REVIEW 5 o 12
(a) (b)
Figu e 1. (a) Pa icle size dis ibu ion o IN738LC; (b) SEM image o he powde pa icles showing
di e ences in size and p esence o sa elli es and i egula pa icles ( ed a ows).
Samples we e manu ac u ed by LPBF in a RenAM 500Q Renishaw machine which employs ou
Yb- ibe lase s in a con inuous way wi h a maximum powe o 500 W and a lase spo size o 85 µm.
Fo he design o expe imen s, 24 samples we e manu ac u ed in he same basepla e (Figu e 2a) wi h
dimensions desc ibed in Figu e 2b. All he samples we e cu in building di ec ion (x–z plane) o
in es iga e he c acking phenomenon.
.
(a) (b)
Figu e 2. (a) Twen y- ou manu ac u ed cubes; (b) dimensions o he samples.
In o de o de ine p ocess pa ame e s’ anges o IN738LC, he pa ame e s used by Renishaw
o IN718 ma e ial (which is a Ni based alloy p ocessable by LPBF) and he ones op imized by o he
au ho s o IN738LC [23] we e aken in o accoun . In his case, ou inpu ac o s we e op imized:
lase powe , lase scan speed, ha ch dis ance and scan s a egy. Table 2 summa izes he ac o s,
symbols, anges and uni s used in his wo k. O he p ocess pa ame e s we e kep cons an , such as
laye hickness (60 µm) and p ehea ing empe a u e (170 °C).
Table 2. Fac o s, anges and uni s o he design o expe imen s.
Fac o Symbol
Range Uni
Min Max
Lase powe P 180 280 W
Lase scan speed 700 1100 mm/s
Ha ch dis ance h 0.08 0.12 mm
Scan s a egy θ 0 90 °
Samples we e p epa ed me allog aphically by g inding up o 2500 µm SiC pape and polishing
wi h 6, 3 and 1 µm diamond pas e. Las ly, he manu ac u ed samples we e cha ac e ized by ligh
mic oscope (GX51 Olympus) and a Zeiss Ul a Plus FEG-SEM (Zeiss, Jena, Ge many).
0
20
40
60
80
100
0
2
4
6
8
10
12
14
16
18
0 102030405060708090
Accumula ed olume %
Volume %
Pa icle size (µm)
Figu e 2. (a) Twen y- ou manu ac u ed cubes; (b) dimensions o he samples.
In o de o de ine p ocess pa ame e s’ anges o IN738LC, he pa ame e s used by Renishaw
o IN718 ma e ial (which is a Ni based alloy p ocessable by LPBF) and he ones op imized by o he
au ho s o IN738LC [
23
] we e aken in o accoun . In his case, ou inpu ac o s we e op imized: lase
powe , lase scan speed, ha ch dis ance and scan s a egy. Table 2summa izes he ac o s, symbols,
anges and uni s used in his wo k. O he p ocess pa ame e s we e kep cons an , such as laye
hickness (60 µm) and p ehea ing empe a u e (170 ◦C).
Table 2. Fac o s, anges and uni s o he design o expe imen s.
Fac o Symbol Range Uni
Min Max
Lase powe P 180 280 W
Lase scan speed 700 1100 mm/s
Ha ch dis ance h 0.08 0.12 mm
Scan s a egy θ0 90 ◦
Samples we e p epa ed me allog aphically by g inding up o 2500
µ
m SiC pape and polishing
wi h 6, 3 and 1
µ
m diamond pas e. Las ly, he manu ac u ed samples we e cha ac e ized by ligh
mic oscope (GX51 Olympus) and a Zeiss Ul a Plus FEG-SEM (Zeiss, Jena, Ge many).
Ma e ials 2020,13, 4879 6 o 12
2.3. Po osi y and C acking Quan i ica ion
Po osi y and c ack densi y we e measu ed o e alua e he numbe s o de ec s in all manu ac u ed
samples. On he one hand, po osi y quan i ica ion was pe o med by image analysis using i e images
o each sample cap u ed wi h he ligh mic oscope. A h eshold alue was applied in o de o sepa a e
de ec s om consolida ed ma e ial [
26
,
31
]. This was done by ying di e en h eshold alues and
inally selec ing he one wi h which he noise o he image was elimina ed wi hou elimina ing he
smalles po es o 10
µ
m. Wi h espec o c ack quan i ica ion, c ack densi ies we e measu ed ollowing
he me hodology desc ibed by Ca e e al. [
32
]. Finally, c ack densi y alue was calcula ed di iding
he o al c ack leng h by o al a ea.
3. Resul s and Discussion
3.1. DoE and Sample Cha ac e iza ion
Table 3summa izes he inpu pa ame e s applied be ween he speci ied anges acco ding o
cen al composi e design (CCD) and he measu ed ou pu s. As p e iously explained, 15 samples
we e enough o build he model; howe e , any numbe o samples g ea e han 15 allows he en i e
polynomial o be i ed and ha is why 24 samples we e manu ac u ed. All cubes we e manu ac u ed
in one basepla e and we e andomized o a oid bias due o non-con ollable ac o s, such as a gon
low inside LPBF chambe . The andomiza ion also a oids bias du ing measu emen and calcula ion
ou pu s. In addi ion, Table 3p esen s he ou pu esul s and de ec ype ound in each sample:
LOF—lack-o - usion de ec s; P—po es; and C—c acks.
Table 3. Design o expe imen s and esul s.
nInpu s Ou pu s De ec
P h θ φ CD * Type
1180 700
0.08
0
0.15
0.00 P
2280 700
0.08
0 - -
3180 1100
0.08
0
0.23
0.00 P
4280 1100
0.08
0
0.09
0.00 P
5180 700
0.12
0
1.26
0.16 LOF/P/C
6280 700
0.12
0
0.11
0.16 P/C
7180 1100
0.12
0
13.74
0.00 LOF
8280 1100
0.12
0
0.17
0.00 P
9180 700
0.08
90
0.15
0.64 P/C
10 280 700
0.08
90
0.13
0.45 P/C
11 180 1100
0.08
90
0.21
0.04 P/C
12 280 1100
0.08
90
0.10
0.08 P/C
13 180 700
0.12
90
0.24
0.10 P/C
14 280 700
0.12
90
0.10
0.68 P/C
15 180 1100
0.12
90
12.21
0.33 LOF
16 280 1100
0.12
90
0.40
0.11 P/C
17 180 900
0.10
67
0.27
0.03 P/C
18 280 900
0.10
67
0.04
0.00 P
19 230 700
0.10
67
0.09
0.06 P/C
20 230 1100
0.10
67
0.25
0.01 P/C
21 230 900
0.08
67
0.16
0.00 P
22 230 900
0.12
67
0.20
0.26 P/C
23 230 900
0.10
0
0.11
0.00 P
24 230 900
0.10
90
0.07
0.09 P/C
* C ack densi y measu emen speci ied in his wo k doesn’ de ec c acks smalle han 10 µm.
Ma e ials 2020,13, 4879 7 o 12
Figu e 3shows di e en ypes o de ec s obse ed in IN738LC samples manu ac u ed based on
he DoE. The de ec s we e classi ied mainly as: (a) lack o usion due o low ene gy densi y, (b) po es
due o excessi e ene gy densi y and (c) c acks because o he se o pa ame e s selec ed.
Ma e ials 2020, 13, x FOR PEER REVIEW 7 o 12
Figu e 3 shows di e en ypes o de ec s obse ed in IN738LC samples manu ac u ed based on
he DoE. The de ec s we e classi ied mainly as: (a) lack o usion due o low ene gy densi y, (b) po es
due o excessi e ene gy densi y and (c) c acks because o he se o pa ame e s selec ed.
(a) (b) (c)
Figu e 3. IN738LC samples showing di e en ype o de ec s: (a) lack o usion, (b) po es and (c)
c acks (indica ed by an a ow) and po es.
3.2. In luence o P ocess Pa ame e s on De ec ology
A e analyzing he manu ac u ed samples, an op imal ene gy densi y ange be ween 38 and 80
J/mm
3
was desc ibed o a oid lack o usion de ec s. Howe e , he pa ame e s selec ed o sample
numbe wo induced an ene gy densi y highe han 100 J/mm
3
, which p oduced an ou o plane
dis o ion in he sample. As his e ec damaged he wipe du ing he manu ac u ing p ocess, sample
numbe wo was dismissed.
A e sample cha ac e iza ion and de ec quan i ica ion, i was possible o de e mine he
co ela ion o each p ocess pa ame e and each combina ion (c oss p oduc s) wi h he o ma ion o
po es and c acks, as shown in Figu e 4. Co ela ion is de e mined by he deg ee o in luence o one
a iable on ano he , and i is exp essed in absolu e alue, which means ha he co ela ion be ween
p ocess pa ame e s and de ec ology may be posi i e o nega i e. In he case o po osi y o ma ion,
lase powe and ha ch dis ance a e he mos in luen ial p ocess pa ame e s because hey a e ela ed
o he appea ance o a lack o usion de ec s. In ac , when lase powe is oo low, powde pa icles
a e no comple ely mel ed and a lack o usion de ec s is obse ed [33]. In he same way, i ha ch
dis ance is oo high, a p ope o e lap is no ensu ed, which induces a lack o usion de ec s in he
mel ed ma e ial [34]. The e o e, he mos e ec i e way o educe sample po osi y would be by
changing he lase powe o ha ch dis ance alues.
(a) (b)
Figu e 4. In luences o p ocess pa ame e s on de ec o ma ion. (a) Po osi y; (b) c acking.
When he o ma ion o c acks is conside ed, i is shown ha he mos in luen ial pa ame e s a e
lase scan speed and he combina ion be ween lase powe and scan s a egy. Fi s ly, Cloo s e al.
[19] s a ed ha a ia ion o scan speed a ec s mel pool mo phology, which in luences he c i ical
0%
5%
10%
15%
20%
25%
30%
35%
40%
P h P· P·θ θ h·θ ·θ ·h P·h
Co ela ion
P ocess pa ame e s
Po osi y
0%
10%
20%
30%
40%
50%
60%
P·θ θ h·θ ·h P· ·θ P·h P h
Co ela ion
P ocess pa ame e s
C ack densi y
Figu e 3.
IN738LC samples showing di e en ype o de ec s: (
a
) lack o usion, (
b
) po es and (
c
) c acks
(indica ed by an a ow) and po es.
3.2. In luence o P ocess Pa ame e s on De ec ology
A e analyzing he manu ac u ed samples, an op imal ene gy densi y ange be ween 38 and 80
J/mm
3
was desc ibed o a oid lack o usion de ec s. Howe e , he pa ame e s selec ed o sample
numbe wo induced an ene gy densi y highe han 100 J/mm
3
, which p oduced an ou o plane
dis o ion in he sample. As his e ec damaged he wipe du ing he manu ac u ing p ocess, sample
numbe wo was dismissed.
A e sample cha ac e iza ion and de ec quan i ica ion, i was possible o de e mine he co ela ion
o each p ocess pa ame e and each combina ion (c oss p oduc s) wi h he o ma ion o po es and
c acks, as shown in Figu e 4. Co ela ion is de e mined by he deg ee o in luence o one a iable
on ano he , and i is exp essed in absolu e alue, which means ha he co ela ion be ween p ocess
pa ame e s and de ec ology may be posi i e o nega i e. In he case o po osi y o ma ion, lase
powe and ha ch dis ance a e he mos in luen ial p ocess pa ame e s because hey a e ela ed o he
appea ance o a lack o usion de ec s. In ac , when lase powe is oo low, powde pa icles a e no
comple ely mel ed and a lack o usion de ec s is obse ed [
33
]. In he same way, i ha ch dis ance is oo
high, a p ope o e lap is no ensu ed, which induces a lack o usion de ec s in he mel ed ma e ial [
34
].
The e o e, he mos e ec i e way o educe sample po osi y would be by changing he lase powe o
ha ch dis ance alues.
Ma e ials 2020, 13, x FOR PEER REVIEW 7 o 12
Figu e 3 shows di e en ypes o de ec s obse ed in IN738LC samples manu ac u ed based on
he DoE. The de ec s we e classi ied mainly as: (a) lack o usion due o low ene gy densi y, (b) po es
due o excessi e ene gy densi y and (c) c acks because o he se o pa ame e s selec ed.
(a)
(b)
(c)
Figu e 3. IN738LC samples showing di e en ype o de ec s: (a) lack o usion, (b) po es and (c)
c acks (indica ed by an a ow) and po es.
3.2. In luence o P ocess Pa ame e s on De ec ology
A e analyzing he manu ac u ed samples, an op imal ene gy densi y ange be ween 38 and 80
J/mm3 was desc ibed o a oid lack o usion de ec s. Howe e , he pa ame e s selec ed o sample
numbe wo induced an ene gy densi y highe han 100 J/mm3, which p oduced an ou o plane
dis o ion in he sample. As his e ec damaged he wipe du ing he manu ac u ing p ocess, sample
numbe wo was dismissed.
A e sample cha ac e iza ion and de ec quan i ica ion, i was possible o de e mine he
co ela ion o each p ocess pa ame e and each combina ion (c oss p oduc s) wi h he o ma ion o
po es and c acks, as shown in Figu e 4. Co ela ion is de e mined by he deg ee o in luence o one
a iable on ano he , and i is exp essed in absolu e alue, which means ha he co ela ion be ween
p ocess pa ame e s and de ec ology may be posi i e o nega i e. In he case o po osi y o ma ion,
lase powe and ha ch dis ance a e he mos in luen ial p ocess pa ame e s because hey a e ela ed
o he appea ance o a lack o usion de ec s. In ac , when lase powe is oo low, powde pa icles
a e no comple ely mel ed and a lack o usion de ec s is obse ed [33]. In he same way, i ha ch
dis ance is oo high, a p ope o e lap is no ensu ed, which induces a lack o usion de ec s in he
mel ed ma e ial [34]. The e o e, he mos e ec i e way o educe sample po osi y would be by
changing he lase powe o ha ch dis ance alues.
(a)
(b)
Figu e 4. In luences o p ocess pa ame e s on de ec o ma ion. (a) Po osi y; (b) c acking.
When he o ma ion o c acks is conside ed, i is shown ha he mos in luen ial pa ame e s a e
lase scan speed and he combina ion be ween lase powe and scan s a egy. Fi s ly, Cloo s e al.
[19] s a ed ha a ia ion o scan speed a ec s mel pool mo phology, which in luences he c i ical
0%
5%
10%
15%
20%
25%
30%
35%
40%
P h P· P·θ θ h·θ ·θ ·h P·h
Co ela ion
P ocess pa ame e s
Po osi y
0%
10%
20%
30%
40%
50%
60%
P·θθh·θ ·h P· ·θP·h P h
Co ela ion
P ocess pa ame e s
C ack densi y
Figu e 4. In luences o p ocess pa ame e s on de ec o ma ion. (a) Po osi y; (b) c acking.
Ma e ials 2020,13, 4879 8 o 12
When he o ma ion o c acks is conside ed, i is shown ha he mos in luen ial pa ame e s a e lase
scan speed and he combina ion be ween lase powe and scan s a egy. Fi s ly,
Cloo s e al. [19]
s a ed
ha a ia ion o scan speed a ec s mel pool mo phology, which in luences he c i ical empe a u e
ange (CTR) o he ma e ial. In ac , hey assu e ha he olume o ma e ial ha is in he CTR has
a signi ican impo ance on c ack o ma ion. Thus, hese au ho s concluded ha lowe scan speeds
inc eased mel pool dep h and he olume o ma e ial in he CTR, which a o ed c ack de elopmen .
Secondly, Ca e e al. [
22
] e ealed he connec ion be ween scan s a egies and o ma ion o c acks.
These au ho s showed ha depending on he scan s a egy used, i was possible o change samples g ain
s uc u e, which is ela ed o g ain miso ien a ion. Ac ually, hey obse ed by elec on backsca e ed
di ac ion (EBSD) maps ha he majo i y o c acks appea in g ain bounda y egions wi h high
miso ien a ion le el. The e o e, he mos e ec i e way o educe sample c ack densi y would be by
changing he lase scan speed alue o scan s a egy selec ed.
Models o p edic op imum p ocess pa ame e s we e buil using inpu s and ou pu s om Table 3
by means o “R” s a is ical package [
35
]. Two kinds o quad a ic models we e buil : he i s one using
all he manu ac u ed samples and he second one only using samples wi hou lack o usion de ec s,
which means ha samples 5, 7 and 15 p esen ed in Table 3we e dismissed. Finally, he second op ion
was selec ed because he p edic ion e o was lowe han in he i s case. This ac could be due o a
massi e appea ance o po es in he o m o lack-o - usion de ec s. The po osi y ela ed o lack-o - usion
p esen ed a maximum alue o 13.74%, while he maximum alue o po osi y wi hou lack-o - usion
de ec s was 0.40%, which is signi ican ly lowe . This may indica e ha he excessi e a ia ion be ween
po osi y alues o samples wi h and wi hou lack-o - usion de ec s could inc ease he model’s e o ,
and because o ha , i was decided o dismiss he samples wi h lack-o - usion de ec s. Fu he mo e,
he quad a ic models we e i ed (Equa ions (6) and (7)) using no malized da a in o de o s udy he
impo ance o p ocess pa ame e s and hei combina ions. In ha way, e ms wi h highe coe icien s
in absolu e alue ha e mo e in luence on he ou pu han e ms wi h lowe coe icien s.
ϕ=−0.5088 −0.7363·P· +0.492· 2−1.1766·h
+0.9205· ·h+0.9615·h2+1.0268·θ−1.0944·θ2(6)
CD =0.0112 −0.7517·P+0.3391·P· +0.39371· 2−0.63914·h
+0.73062·P·h+0.49322· ·h+0.884·h2+0.46287·P·θ
−1.26285· ·θ−0.64007·h·θ+0.91777·θ2
(7)
Addi ionally, mean absolu e e o (MAE) and oo mean squa e e o (RMSE) we e calcula ed
acco ding o Equa ions (8) and (9).
MAE =1
k·
k
X
i=1
|ei|=1
k·
k
X
i=1
Yi exp −Yi model(8)
RMSE =
1
k·
k
X
i=1
e2
i
0.5
=
1
k·
k
X
i=1
Yi exp −Yi model2
0.5
(9)
Table 4p o ides p- alues and MAE and RMSE e o s; p- alues a e low in bo h cases, which
means he quad a ic models we e s a is ically signi ican . The c ack densi y model p esen s a be e
p- alue and lowe e o s han he po osi y model. This e els po osi y has much mo e a iabili y,
which could be p o oked by he manu ac u ing p ocess.
Ma e ials 2020,13, 4879 9 o 12
Table 4. p- alue and e o s o he quad a ic models.
De ec Type p-Value MAE RMSE
φ0.07 10.1% 13.6%
CD 0.02 3.6% 5.5%
Once he models we e ob ained and e alua ed, i was possible o ind he op imum wo king
poin . Package “desi abili y” [
36
], a ailable in “R,” was used o calcula e he po osi y, c ack densi y
and o e all desi abili ies (see Equa ion (5)). The de e mina ion o he wo king poin wi h maximum
desi abili y was achie ed by applica ion o he s eepes ascen me hod [
37
]. The objec i es o he
op imiza ion we e o minimize c ack densi y and po osi y. The esul s o he op imiza ion a e lis ed in
Table 5.
Table 5. Op imiza ion esul s.
P ocess Pa ame e and De ec Type Ta ge Value Desi abili y
PIn ange 272.60 W 1.00
In ange 799.50 mm/s 1.00
hIn ange 0.11 mm 1.00
θIn ange 1.54◦1.00
φMinimize 0.07% 0.94
CD Minimize 0.00 mm/mm21.00
O e all desi abili y: 0.97
The op imal wo king poin (Table 5) was used o p epa e a new manu ac u ing un. Fi e samples
we e ab ica ed wi h he same op imal pa ame e s o alida e he me hod. Table 6compa es he
calcula ed alues wi h he expe imen al ones. I was necessa y o ound some inpu pa ame e s o se
up he LPBF machine.
Table 6. Op imiza ion esul s compa ison.
P ocess Pa ame e and De ec Type Calcula ed Expe imen al Di e ence
P (W) 272.6 273.0 0.4
(mm/s) 799.5 800.0 0.5
h (mm) 0.11 0.11 0.00
θ(◦)1.54 0.00 −1.54
φ(%) 0.07 0.09 ±0.01 0.02
CD (mm−1)0.00 0.00 0.00
As expec ed, he calcula ed po osi y had a ce ain e o compa ed wi h he expe imen al one,
al hough all he samples p esen ed esidual po osi y below 0.1%. Those esul s we e ob ained
because he selec ed combina ion o p ocess pa ame e s induced su icien ene gy densi y o p e en
lack-o - usion de ec s, bu a oided keyhole po es o med by excessi e ene gy densi y. Addi ionally, no
c acks we e ound in he manu ac u ed samples, which indica es ha he p ocess pa ame e s selec ed
by he model educe he c ack sensi i i y o IN-738LC supe alloy.
As shown in Figu e 5, he sample manu ac u ed wi h op imal p ocess pa ame e s had educed
po osi y and no c acks. Consequen ly, i is demons a ed ha using he pa ame e s ob ained
om Equa ions (6) and (7), i is possible o manu ac u e samples o IN738LC supe alloy wi hou
signi ican de ec s.
