Characterization of plastic formability and failure mechanisms in FDM additively manufactured PETG and PCL sheets

Polyme Tes ing 134 (2024) 108431 A ailable online 26 Ap il 2024 0142-9418/© 2024 The Au ho s. Published by Else ie L d. This is an open access a icle unde he CC BY-NC-ND license (h p://c ea i ecommons.o g/licenses/by- nc-nd/4.0/). Cha ac e iza ion o plas ic o mabili y and ailu e mechanisms in FDM addi i ely manu ac u ed PETG and PCL shee s A. Rosa-Sainz a , I. Fe e b , M.L. Ga cia-Romeu b , * , G. Cen eno a a Depa men o Mechanical and Manu ac u ing Enginee ing, School o Enginee ing, Uni e si y o Se ille, 41092, Se ille, Spain b Uni e si y o Gi ona, Depa men o Mechanical Enginee ing and Indus ial Cons uc ion, Gi ona, Spain ARTICLE INFO Keywo ds: Fo mabili y Failu e Addi i e manu ac u ing Nakajima PETG PCL ABSTRACT This esea ch wo k p esen s an expe imen al in es iga ion on he o mabili y and ailu e o addi i ely manu- ac u ed polyme shee s. To his ega d, Nakajima o mabili y es s ollowing di e en p incipal s ain pa hs ha e been conduc ed on 2 selec ed FDM-p in ed polyme shee ma e ials, polye hylene e eph hala e glycol and polyc ap olac one, his being ca ied ou o he i s ime e e , as a as he plas ic beha io and o mabili y s udy o his kind o 3D p in ed ma e ials has been limi ed so a uniquely o con en ional ension o comp ession es s. The analysis includes he e alua ion o he di e en ypes o ailu e unde plas ic de o ma ion o each ma e ial conside ed, allowing he assessmen o he o e all o mabili y limi s wi hin he ma e ials o ming limi diag ams combined wi h he ailu e e alua ion pe o med ia op ical mic oscopy. Thus, he esul s p o ided he o e all cha ac e iza ion in e ms o shee o mabili y and he comp ehensi e assessmen o he di e en ailu e modes and he o ming condi ions upon which each ype o ailu e is a ained o each o he wo p in ed ma- e ials. Fu he mo e, hese esul s allow he au ho s o c ea e an essen ial e alua ion amewo k o he ongoing esea ch on p ocess hyb idiza ion including he combina ion o 3D p in ing echnologies wi h inno a i e o ming p ocesses such as inc emen al shee o ming. 1. In oduc ion Manu ac u e s cons an ly sea ch o new echnologies o sa is y all aspec s o he g owing demand o he ma ke . Fo his pu pose, addi i e manu ac u ing (AM), which s a ed ou as a apid p o o yping ech- nique, is nowadays e olu ionizing and decen alizing indus ial p o- duc ion. The e a e se e al AM echnologies a ailable o me al, polyme and, mo e ecen ly, o composi e ma e ials [1], sha ing se e al bene i s, being one o he mos no able is he educ ion in ime equi ed o b ing a p oduc o ma ke , achie ed h ough he accele a ion o he p o o yping p ocess and a dec ease in he cos s associa ed wi h p oduc de elopmen [2]. Fu he mo e, he ange o AM applica ions co e s con en ional o ad ance indus ies as ae ospace o he au omo i e [3], a ac ed by he ligh weigh ing o s uc u es in he sea ch o g een mobili y, supe io uel e iciency, and handling. Beyond ha , he biomedical sec o is also in he lis o applica ions o AM due o i s in e es in he manu ac u ing o cus omized p os heses [4,5] o in issue enginee ing appealing o he possibili y o he manu ac u ing o pe sonalized sca olds ha allow he in eg a ion o medicaliza ion [6–8]. Among all he a ailable AM echnologies, Fused Deposi ion Modeling (FDM) (see Fig. 1a), also known as 3D p in ing, Fused Fila- men Fab ica ion (FFF) o in a new and b oad conside a ion as Ma e ial Ex usion (MEx), is being a widely used op ion and a p o i able oppo - uni y. Fu he mo e, due o he ease o p in ing and he use o ad anced he moplas ics such as Polye he e he ke one (PEEK) [9], polyme s a e ecei ing inc easing in e es o he p oduc ion o ligh weigh and s uc u al pa s. The main esea ch ac i i ies in he ield o AM, and pa icula ly in FDM, a e ocused oday on in es iga ing a numbe o he p in ed com- ponen s such as he mal conduc i i y, elec ical conduc i i y o chem- ical esis ance [10–14]. Howe e , a signi ican numbe o esea ch wo ks in he ield o AM/FDM aim o e alua ing hei mechanical p ope ies, including ensile s eng h, lexu al s eng h o impac esis- ance bo h o i gin o combined ma e ials. Rela ed o his, some e- iews ha e ecen ly come o ligh ha include ecommended guidelines in a s anda dized app oach ha can allow he compa ison o published esul s and help in he de elopmen o FDM echnology o ad anced applica ions [15]. O he wo k documen s he la es ad ances in in e - ace p in ed pa s o p o ide a comple e unde s anding o he p ocess, s uc u e, and in e laye bond o his echnology [16]. * Co esponding au ho . E-mail add ess: [email p o ec ed] (M.L. Ga cia-Romeu). Con en s lis s a ailable a ScienceDi ec Polyme Tes ing jou nal homepage: www.else ie .com/loca e/poly es h ps://doi.o g/10.1016/j.polyme es ing.2024.108431 Recei ed 9 Janua y 2024; Recei ed in e ised o m 21 Ma ch 2024; Accep ed 18 Ap il 2024 Polyme Tes ing 134 (2024) 108431 2 As has jus been poin ed ou , he mechanical cha ac e iza ion o p in ed pa s is cap u ing enough esea ch a en ion as FDM con inues o ad ance, since he e is s ill he p oblem o con e ing p in ed pa s in o unc ional componen s o ac ual use. To his ega d, esea che s ha e been mainly ocused on unde s anding and e alua ing he mechanical p ope ies due o he weak and aniso opic mechanical beha io o he 3D p in ed componen s compa ed o hose ob ained by con en ional p ocessing. In he speci ic case o FDM, he lack o app op ia e s an- da ds, speci ically designed o consis en ly es he ensile p ope ies o polyme ic pa s and compa e hem wi h common p oduc s, is a majo obs acle o he wide applica ion o addi i ely manu ac u ed polyme pa s in indus y [17]. Rela ed o ha , e y ew pape s ha e deal so a wi h he e alua ion o he plas ic beha io o 3D p in ed ma e ials, nei he in FDM no in any o he AM echnology. As exposed abo e, he wo k analysing 3D p in ed pa s o mabili y is limi ed o he ma e ial plas ic cha ac e iza ion ia uniaxial ension (o comp ession) es s. Howe e , he e is a lack o knowledge abou o he plas ic beha io p ope ies including hei e alua ion unde di e en s ain pa hs. This ac o is o key impo ance in p ocess hyb idiza ion, including he combina ion o AM echnologies wi h con en ional shee - o ming p ocesses o e en inno a i e p ocesses such as inc emen al shee o ming. One o he main limi a ions o using inc emen al shee o ming o a ce ain pu pose, such as he manu ac- u e o biocompa ible shee p os heses, is ha he de ini ion o he shee blank is limi ed by he indus ial supplie s. In his espec , no e e y hickness migh be po en ially a ailable and some imes he blank ge- ome ies need p e ious machining ope a ions ha may no be sui able in he biomedical sec o . Thus, he use o AM echnologies could allow manu ac u es o ob ain and design hei own shee blank including con olled ma e ials, shapes, and hicknesses, in his la e case allowing blank wi h a iable shee hickness ha could be sui able, a e o ming and he expec ed local hickness a ia ions, o ce ain analy ical con- ou s. Beyond ha , shee o ming allows o , in many cases, he imp o emen o ce ain ma e ials p ope ies such as he ma e ial s eng h ia yielding. In his con ex , shee o mabili y is he e m used o de e mine he deg ee o de o ma ion o which a shee ma e ial can be subjec ed du ing a o ming p ocess ollowing a speci ic s ain pa h. This de o ma ion can be e alua ed using he in-plane p incipal majo s ain ( ε 1) and mino s ain ( ε 2) in he so-called o ming limi diag am (FLD) (schema ically depic ed in Fig. 1b). Indeed, FLD is an expe imen al analysis ool in which he majo s ain is ep esen ed on he o dina e axis and he mino s ain on he abscises axis in he Ca esian plane, and i p esen s he de o ma ion s a e o he ma e ial, he ela ion be ween he mino s ain ε 2 and he majo s ain ε 1 he s ain a io (β), and is gi en by β= ε 2/ ε 1. The unde s anding o he limi s o o mabili y wi hin he p incipal s ain space enables he de elopmen o a comp ehensi e amewo k o analyzing ac u e limi s, which is c ucial in shee o ming p ocesses. Al hough he e a e widely used and alida ed echniques o de e mine necking and ac u e in shee me al o ming, he e is an absence o dedica ed me hodologies and p ocedu es o polyme s, since he o m- abili y o hese ypes o ma e ials is in luenced by se e al ac o s, including he molecula s uc u e, molecula weigh , o ien a ion o he polyme chain, empe a u e, s ain a e, and p esence o any ille s o addi i es [18]. In his con ex , Rosa-Sainz e al. [19] adap ed me hod- ologies commonly used in shee me al o ming o polyme ic shee s, wi h he goal o de e mining he o mabili y limi s by necking and ac u e. These me hodologies we e alida ed o a ious polyme ic shee s, including polyca bona e (PC) [19,20], polye he e he ke one (PEEK) [9], and ul a-high molecula weigh polye hylene (UHMWPE) [21]. In his global con ex , he objec i e o his expe imen al in es iga ion is o apply o he i s ime e e he p e iously desc ibed me hodologies o his new kind o polyme ic shee ma e ials, i.e. FDM addi i ely manu ac u ed polye hylene e eph hala e glycol (PETG) and poly- c ap olac one (PCL) shee s, in o de o cha ac e ize he o mabili y limi s by necking and ac u e and ob ain he esul ing ma e ials o ming limi diag am o FLD. The expe imen al wo k is conduc ed by pe - o ming Nakajima es s a oom empe a u e using ou di e en ge- ome ies co esponding o he same numbe o s ain pa hs om ensile s ain owa ds equibiaxial s ain o bo h PETG and PCL shee s. The esul s a e p o ided no only in e ms o he limi ing s ain assessed wi hin he FLD ma e ial bu also analyzing he di e en modes o ailu e a ained and he es ing condi ions upon which each ype o ailu e is a ained. In his sense, di e en kinds o ailu e occu ed depending on hose es ing condi ions and s ain pa hs conside ed, including localized necking, duc ile ac u e, and a a e ailu e phe- nomenon iden i ied by he au ho s as in e laye gliding. In summa y, a signi ican con ibu ion o his esea ch wo k lies in being he i s ime, as a as he au ho s a e awa e, ha Nakajima es s a e used o cha ac e ize addi i ely manu ac u ed shee s. Addi ionally, his allowed he assessmen o he di e en modes o ailu e, including he new limi wi hin he FLD o he PCL shee de ined by ailu e ia in e laye gliding. Finally, i mus be poin ed ou ha his expe imen al Fig. 1. Schema ic ep esen a ion o (a) used deposi ion modeling and (b) o ming limi diag am (FLD) depic ing he FLC o Fo ming Limi Cu e and he FFL o F ac u e Fo ming Limi . A. Rosa-Sainz e al. Polyme Tes ing 134 (2024) 108431 3 analysis allows he au ho s o c ea e an essen ial e alua ion amewo k o subsequen e alua ion in incoming esea ch pape s dealing wi h p ocess hyb idiza ion, including he combina ion o addi i e manu ac u ing wi h inno a i e o ming p ocesses such as ISF o o he , enabling he u iliza ion o his hyb idiza ion o a ious applica ions. 2. Me hodology This sec ion includes he me hodology employed, which is di ided in o he 3D p in ing o PETG and PCL shee s, and he subsequen cha - ac e iza ion o hese p in ed shee s u ilizing Nakajima es s wi hin he amewo k o addi i e manu ac u ing. 2.1. 3D p in ing The in es iga ion was ca ied ou on shee s o polye hylene e e- ph hala e glycol (PETG) and polycap olac one (PCL) bo h wi h 2 mm hickness, ob ained by used deposi ion modeling (FDM). PETG ma e ial wi h a diame e o 2.85 mm was p o ided by Sma Ma e ials 3D, while Facilian™ PCL 100 ilamen , wi h a diame e o 2.85 mm, was acqui ed om he 3D4MAKERS™ ma e ial supplie . Table 1 indica es he mechanical p ope ies o he 3D4MAKERS™ PETG ilamen ma e ial and he Facilian™ PCL 100 ilamen . Acco ding o he ma e ial supplie , he mechanical p ope ies o PETG we e es ed using ensile es s acco ding o he ASTM D638 s anda d and impac es s acco ding o he ASTM D256 s anda d. Fo PCL ma e ial, ensile es s we e pe o med acco ding o he ISO 527-1 s anda d and impac es s ollowing he ISO 180-1 s anda d. The Ul imake S3 3D p in e was used o p in he ma e ial shee s, and Table 2 con ains he p in ing pa ame e s used, whose alues we e de e mined on he p e ious wo ks [22] and some p e ious es s ca ied ou in he labo a o y. Rega ding he PCL, he p in ing empe a u e was es ablished a he highes alues o he supplie ”s ecommended ange o a oid clogging o he p in co es, maximize he ma e ial lowabili y, and minimize he in e nal po ous. Wi h espec o he ecommended PETG empe a u e, a da a shee was used. As will be seen and expec ed, empe a u e will be an impo an pa ame e ha a ec s laye composi ion o he shee and i s o mabili y. The o he impo an p ocess pa ame e is he heigh o he laye , which also signi ican ly a ec s he p in ing quali y o shee s, so wi h g ea e laye heigh s exhibi ed ea lie c acking and b eakage and c acking [22]. As a gene al guideline, laye heigh s be ween 0.08 and 0.3 mm we e conside ed sui able o 0.4 mm nozzles, al hough he bes esul s we e ob ained wi h shee s p in ed a 0.08 and 0.1 mm wi hou much a ia ion be ween hem. Thus, he 0.1 mm se ing was selec ed due o a subs an ial educ ion in he p in ing ime. 100 % in ill densi y was es ablished o all manu ac u ed specimens o imi a e he condi ions o a homogeneous and iso opic solid s uc u e [23,24]. The p in ing pa e n also played a c ucial ole in o ming beha io , jus as i a ec s he esul s o mechanical p ope ies [22]. 2.2. Ma e ial cha ac e iza ion This sec ion con ains he me hodology ollowed o de e mine he o mabili y limi s by necking and ac u e o shee s manu ac u ed by 3D p in ing wi h PETG and PCL. The me hodologies we e adap ed om hose commonly applied om me als o polyme ic shee s and we e used o he i s ime in Re . [19]. The Nakajima geome ies we e p in ed using FDM, and subsequen ly, pe iphe ical inishing machining was ca ied ou on hei no ch zones o imp o e he su ace quali y and p e en s ess concen a ions, ensu ing a de ec - ee su ace and p e- en ing p ema u e ailu e. These specimens we e iden i ied as ensile s ain (TS), plane s ain (PS), biaxial s ain (BS), and equibiaxial s ain (EBS). The dimensions o he specimens and ope a ing condi ions o he geome ies conside ed a e p esen ed in Table 3. The punch speed was se a 1 mm/s, ollowing he ecommended condi ions desc ibed in s anda d ISO 12004–2:2008 [25]. Rega ding he clamping o ce, he necessa y o ce was applied o p ope ly secu e he shee . Fo PCL, 30 kN was used, while o PETG, 10 kN was used. This di e ence was due o PETG expe iencing ea ing i a o ce g ea e han 10 kN was applied as he punch ascended. One limi a ion o 3D p in ing is ha each shee may ha e a sligh ly di e en hickness om one p in o ano he . To minimize hese di - e ences, ba ches o shee s we e p in ed and only hose wi h a hickness o 2 ±0.05 mm we e selec ed o ensu e ha all es pieces had he co ec hickness. To ensu e he epea abili y o he esul s, h ee ep- lica ions o each geome y es we e pe o med. The o mabili y limi s by necking and ac u e o bo h polyme ic ma e ials we e de e mined using Nakajima es s ollowing he ISO 12004-2 s anda d [25] on a uni e sal es ing machine (model 142–20 E ichsen) a oom empe a u e (25 ◦C). The expe imen al se up employed o pe o m he Nakajima es s comp ises h ee p ima y com- ponen s: (i) a uni e sal shee es ing machine, (ii) a digi al image co - ela ion (DIC) sys em, and (iii) a o ce and displacemen acquisi ion sys em. A schema ic ep esen a ion o his se up is p o ided in Fig. 2a. In he Nakajima es , he specimen is placed be ween he blank holde and he backing pla e, and he punch is sc olled un il he specimen ac u es, o he ace end is eached. S ain measu emen s in he de o ma ion a ea we e ob ained using he DIC sys em (ARAMIS® 6.2.0 6, GOM, Ge - many), which is equipped wi h 2 CCD came as wi h an angle o 23.6◦ be ween hem and a lens wi h a ocal leng h o 50 mm (see he schema ic ep esen a ion in Fig. 2a). Image acquisi ion was se a 12 ames pe second wi h a ace size o 13 ×11 pixels. The DIC sys em equi es a black and whi e s ochas ic pa e n on he su ace o he specimen, which was ob ained by sp aying ma e black on a whi e backg ound, esul ing in he s ochas ic pa e n. To minimize ic ion be ween he punch and he polyme ic specimens, we sandwiched a laye o poly e a luo o- e hylene (PTFE) be ween wo laye s o Vaseline. The o mabili y limi s by necking and ac u e o bo h polyme ic ma e ials we e cha ac e ized by Nakajima es s. In his sense, necking is a mode o ailu e ha occu s unde ension when la ge amoun s o s ain a e disp opo iona ely loca ed in a small egion o he ma e ial. The ime-dependen me hodology p e iously desc ibed by Re . [7] was used o de ec he onse o necking in 3D p in ed polyme ic shee s in his expe imen al esea ch. This app oach is based on expe imen al e idence o ini ia ion and de elopmen , and uses he empo al analysis o majo s ain ε 1 and i s i s - ime de i a i e ˙ ε 1, o majo s ain a e, o a se ies o poin s along a sec ion pe pendicula o he necking a ea. P e ious esea ch by he au ho s [7] showed ha he o iginal app oach needed o be adap ed o accoun o he con as be ween he localized hinning Table 1 Mechanical and he mal p ope ies o PETG and PCL ma e ials a 25 ◦C ex ac ed om supplie s. PETG PCL Densi y (g/cm 3 ) 1.27 1.1 Tensile s eng h (MPa) 50 45 Tensile modulus (MPa) 2100 350 IZOD Impac S eng h (kJ/m 2 ) 8.1 8 Mel ing empe a u e (◦C) 260 60 Table 2 P in ing pa ame e s o PETG and PCL polyme ic ma e ials. P in e pa ame e s PETG PCL Laye heigh (mm) 0.1 0.1 Wall line coun 3 3 In ill densi y (%) 100 100 P in ing empe a u e (◦C) 250 160 Build pla e empe a u e (◦C) 60 60 P in speed (mm/s) 75 50 P in ing di ec ion −45/+45 −45/+45 A. Rosa-Sainz e al. Polyme Tes ing 134 (2024) 108431 4 cha ac e is ic o me als and he necking beha io o polyme s. In his con ex , Fig. 2b schema ically shows he Nakajima es o he TS specimen, indica ing a se ies o poin s on he su ace o he specimen o es ablish he ins abili y egion o he necking zone. The p ocess o applying he ime-dependen me hodology is de ailed as ollows: (i) Iden i y he wo e e ence poin s a he necking zone: poin A and poin B (PA and PB). Poin A co esponds o whe e necking s a s, and poin B is he i s poin whe e s ain s a s o dec ease. The ep esen a ion o he majo s ain wi h ime was ca ied ou o se e al poin s along a sec ion pe pendicula o he necking si e (e.g., poin s PA, P1, …, PN, PB) was ca ied ou o iden i y hese wo poin s (see Fig. 2b). (ii) Iden i y he bounda y o he ins abili y egion be ween poin A and poin B. This egion allows one o obse e how he poin s ha e a mono onic inc ease in s ains, which ceases a poin B (see Fig. 2b). (iii) Fig. 2c ep esen s he e olu ion o he s ain a e o poin B wi h ime. The me hodology assumes ha he onse o necking occu s a he ins an when he s ain a e o poin B eaches a local maximum (poin B s ain a e max in Fig. 2c). (i ) Finally, he limi s ains a he onse o he necking will co espond o he s ains a poin A (depic ed in Fig. 2c) a he ins an o ime “ necking”. Rega ding ac u e o mabili y limi s, he au ho s in p e ious expe imen al wo k [9,19,20] discussed ha he ini ial me hodology o de e mining he ac u e o ming limi in me al shee s [26] mus be adjus ed o polyme s due o he p opaga ion o necking in polyme s along he en i e leng h o he specimen. In his ega d, due o he ela- i ely low alue o he Young modulus o elas ici y o polyme ic ma e- ials compa ed o me allic ma e ials, signi ican ma e ial elas ic eco e y occu s a e ac u e. Fo his, he me hodology included in Re . [19], shown ha i was mo e accu a e o conside ha he mino ac u e s ain a ac u e (designa ed as ε * 2 ) is ob ained conside ing ha he slope o he local s ain loading pa h slope (i.e. β*= ε 2/ ε 1) emains cons an . The slope (β*)was ob ained a he las measu ed s ains by DIC sys em ( ε DIC 1, ε DIC 2) as: β*=d ε DIC 2/d ε DIC 1 o de e mining he ac u e o ming limi (FFL). Mo e de ails on his me hodology can be ound in Re . [19]. In addi ion o he ime-dependen me hod, he e olu ions o o ces and displacemen will be analyzed o each ma e ial and each specimen, wi h he aim o quali a i ely assessing he p esence o plas ic ins abili y leading o necking [27]. 3. Expe imen al esul s This sec ion p esen s he esul s o applying he p e ious Table 3 Summa y o he expe imen al wo k plan o PCL and PETG specimens. Tes geome y Specimen Ope a ing condi ions Geome y Dimensions (mm) Blank holde o ce (kN) Veloci y (mm/min) PCL PETG Tensile s ain (TS) l=200 w=30 l 0=5 w0=15 =25 30 10 60 Plane s ain (PS) l=200 w=114 l 0=4 w0=45 =25 30 10 Biaxial s ain (BS) l 0=5 w0=150 =25 d=182 30 10 Equibiaxial s ain (EBS) d=182 30 10 Table 4 Shows he pai o neck s ains ob ained o he TS specimen by applying he ime-dependen app oach. The esul s indica ed ha he s ain le els we e nea ly iden ical o he h ee specimens conside ed. The p incipal s ain a necking and ac u e e alua ed using he DIC sys em a e p esen ed in Table 4 along wi h he s anda d de ia ion o hese esul s. As explained in Sec ion 2.2, hese ac u e s ains allow he de e mina ion o he FFL.Table 4. Summa y o he necking and ac u e esul s o PETG ma e ial. Tes geome y Repe i ion Onse o necking ε 1,lim ε 2,lim TS_PETG I 0.083 −0.017 II 0.084 −0.015 III 0.087 −0.013 Mean 0.084 −0.015 S anda d de ia ion 0.0021 0.002 Onse o ac u e using DIC TS_PETG I/II/III 0.2079/0.1993/ 0.2199 −0.0656/-0.0565/- 0.0634 Mean 0.2088 −0.0618 S anda d de ia ion 0.0103 0.0047 PS_PETG I/II/III 0.1824/0.1756/ 0.1791 −0.0021/-0.0056/ −0.0043 Mean 0.1790 −0.004 S anda d de ia ion 0.0034 0.0017 BS_PETG I/II/III 0.1496/0.1562/ 0.1587 0.0367/0.0402/0.0391 Mean 0.1547 0.0386 S anda d de ia ion 0.0047 0.0018 EBS_PETG I/II/III 0.1568/0.1672/ 0.1593 0.0432/0.0501/0.0456 Mean 0.1610 0.0462 S anda d de ia ion 0.0054 0.0035 A. Rosa-Sainz e al. Polyme Tes ing 134 (2024) 108431 5 me hodologies desc ibed in sec ion 2 o he e alua ion o he o mabili y limi s by necking and ac u e o PETG and PCL wi h 2 mm hickness ma e ials. 3.1. PETG This sec ion shows he esul s ob ained o PETG ma e ial, including he esul s o de e mining he o mabili y limi s by necking and ac u e o es ablish he PETG o ming limi diag am in p incipal s ain space. As s a ed in Sec ion 2, PETG Nakajima specimens we e 3D p in ed wi h di e en geome ies, including TS, PS, BS, and EBS. 3.1.1. Necking and ac u e analysis Fig. 3 p esen s he ime-dependen app oach o he PETG TS Naka- jima specimen. Fig. 3a shows he e olu ion o poin s loca ed on a pe pendicula sec ion o he necking a ea o es ablish he ins abili y zone (i.e., be ween Poin A and Poin B). Addi ionally, he majo s ain dis ibu ion ob ained by he ARAMIS® sys em is indica ed in Fig. 3a. Fig. 3b shows he e olu ion o he majo s ain wi h ime o Poin A and Poin B, as well as he majo s ain a e o Poin B. In his sense, he e olu ion o he majo s ain a e o Poin B enabled iden i ica ion o i s local maximum and hus he ins an aneous ime o he onse o necking. The me hodology used allowed o he de e mina ion o he limi s ains Fig. 2. (a) Schema ic ep esen a ion o he Nakajima es . (b) E olu ion o he majo s ains o e ime o he necking egion and (c) he ime-dependen app oach adap ed om Re . [19]. Fig. 3. Applica ion o he me hodology o ob ain he onse o neck s ains o a TS Nakajima specimen. (a) Expe imen al ime e olu ion o he majo s ain along he poin s o he selec ed sec ion. (b) Applica ion o he ime-dependen app oach. A. Rosa-Sainz e al. Polyme Tes ing 134 (2024) 108431 6 a he poin o he onse o necking, which co esponded o he s ains a Poin A du ing he TS PETG Nakajima specimen a a speci ic momen in ime. Fig. 4a, b, and 4c show he a emp o apply he ime-dependen app oach o PS, BS, and EBS Nakajima specimens, espec i ely. The app oach e ealed ha he s ain o a se ies o poin s along a sec ion pe pendicula o he necking a ea did no show cessa ion, as p e iously obse ed o he TS PETG Nakajima specimens. The analysis o he majo s ain e olu ion o PS, BS and EBS o e ime e ealed ha he poin A, whe e necking begins, unde goes he mos signi ican de o ma ion and e en ually leads o he ac u e o he specimen. On he o he hand, he o he poin s unde go a g adual de o ma ion and do no achie e highe s ains, as he specimen ac u es be o e hey can con inue o de o m u he . The conclusion d awn was ha he neck was no disce nible h ough he ime-dependen app oach, as e idenced by examining he poin s in a pe pendicula sec ion, and no decele a ion was obse ed. As a esul , i was no easible o iden i y poin B, and hus, he ins abili y egion could no be de e mined using he ime-dependen app oach o PS, BS and EBS specimens. The analysis u ilizing a ime-dependen me hodology e ealed he PETG Nakajima onse o necking in he TS specimen, in addi ion, i was indica ed ha necking was no a mode o ailu e o he PS, BS, and EBS Nakajima specimens. This conclusion was suppo ed by he analysis o he o ce-displacemen beha io , as depic ed in Fig. 5a, which displays a sligh educ ion in o ce a he momen o necking o he Nakajima TS es , and by he uni o m dis ibu ion o he majo s ain o Nakajima PS, BS and EBS es s up o ailu e by ac u e. As can be obse ed o he ou specimens, he o ce-displacemen cu e shows noise h oughou he es . This phenomenon may be due o he low adhesion be ween he laye s o p in ed ma e ial, in he case o PCL, as will be seen la e , his obse a ion in he o ce-displacemen is no qui e as no iceable. Fu he mo e, Fig. 5b depic s he Nakajima specimens a e es ing, as can be obse ed, he ma e ial exhibi s a lack o duc ili y, b eaking a a low deg ee o de o ma ion. Fig. 6 shows he ac og aphies o he examined specimens, which we e analyzed using a NIKON® SMZ800 N a a magni ica ion o ×10. The specimens we e sec ioned along he indica ed do ed ed line in each image, polished, and subsequen ly obse ed on he su ace using an op ical mic oscope. In gene al, o polyme s, h ee dis inc egions a e clea ly disce nible: he necking zone (indica ed as “I”), he ansi ion zone (ma ked as “II”) and he ac u e zone ( ep esen ed as “III”) [28]. The neck zone ep esen s he a ea whe e signi ican localized de o - ma ion occu ed, while he ansi ion zone deno es he bounda y be- ween he neck egion and he elonga ed a ea. The ac u e zone deno es he loca ion whe e he specimen expe ienced a ac u e. In Fig. 6a, he c oss sec ional ac og aphy o he TS specimen can be obse ed, along wi h he TS specimen o he igh o he image. In his ac og aphy, a local necking (ma ked I) can be obse ed in he spec- imen, wi h a smoo h ansi ion zone (II) be ween his necking and he unde o med a ea, ollowed by an open ac u e (ma ked III). Addi ion- ally, a second necking is obse ed in his specimen, indica ed by a whi e ec angle, whe e a ansi ion zone in he local necking can be obse ed. Fig. 4. Expe imen al ime e olu ion o he majo s ain along he poin s o he selec ed sec ion o (a) PS, (b) BS and (c) EBS PETG Nakajima specimens. A. Rosa-Sainz e al. Polyme Tes ing 134 (2024) 108431 7 In Fig. 6b, he ac og aphic analysis o he cu sec ion o he PS specimen is depic ed, accompanied by he PS specimen posi ioned o he igh wi hin he image. In con as o he p e ious TS Nakajima spec- imen, he p esence o a isually dis inguishable neck zone was no obse ed in his pa icula specimen, as de e mined by ime-dependen analysis. The ac og aphy only e ealed he p esence o he ac u e zone. Fu he mo e, ac og aphies o bo h BS and EBS specimens we e pe o med in o de o alida e he absence o localized neck ailu e mode. 3.1.2. Failu e modes Fig. 7 p esen s he ac og aphies o he TS and EBS specimens o he pu pose o analyzing hei mode o ailu e. Acco ding o he li e a u e [29], he ac u e p ocess o p in ed pa s is p ima ily a ibu ed o he addi i e manu ac u ing p ocess ha leads o delamina ion be ween adjacen laye s o welded ma e ial. Po ous egions o inadequa e in e laye bonding (ligh delamina ion) can se e as a poin o c ack ini ia ion and esul in p ema u e ailu e o componen s. The esul s o he Nakajima es s indica e ha PETG exhibi s a duc iless ac u e. The ac og aphy o he TS specimen in Fig. 7a depic s ano he ins ance o he TS specimens conduc ed o ensu e epea abili y. In his con ex , i p esen s a ac u e e mina ion sligh ly di e en om ha o he TS specimen depic ed in Fig. 6a, speci ically wi h a mo e igh ly closed ac u e obse ed in his case. In bo h ac og aphs (TS and EBS speci- mens), he p in ed laye s in he ma e ial can be obse ed. As desc ibed in sec ion 2.2, he Nakajima es s we e conduc ed a 60 mm/min as indica ed in he ISO s anda d o he de e mina ion o he FLC in shee me al [25]. The esul s o he PETG ma e ial subjec ed o hese es s showed a lack o duc ili y in he ma e ial when es ed a he men ioned speed. In his sense, his esul is consis en wi h he indings o he s udy conduc ed by E gene and Bola [30], whe e uniaxial ensile es s we e pe o med on PETG AM manu ac u ed specimens a h ee di e en es speeds: 5 mm/min, 25 mm/min, and 50 mm/min. Failu e was e alua ed h ough inspec ions o de o ma ion on bo h mac o and mic o-scales. The esul s showed ha PETG specimens unde wen duc ile de o ma ion a a low es speed o 5 mm/min, and as he es speed inc eased, mixed-mode mechanisms became inc easingly domi- nan , leading o comple ely b i le damage obse ed in he PETG spec- imens a es speeds o 25 mm/min and 50 mm/min. Me cado-Colmene o e al. [31] ound he same esul o AM-made PETG ma e ial, e ealed ha he ac u e p ocess o s uc u al ele- men s manu ac u ed in he Z di ec ion was he esul o he delamina- ion and b eakage o he plas ic ilamen s in he adjacen laye s loca ed on he suppo s. Fu he mo e, he s udy [31] demons a ed ha his o m o ac u e is no comple ely b i le, as he plas ic ma e ial un- de goes a ha dening p ocess h ough plas iciza ion in he egions whe e he ac u es a e p opaga ing. 3.1.3. FLD Fig. 8 shows he PETG 3D p in ed shee s in he o ming limi diag am (FLD) in p incipal s ain space. In he FLD, he p incipal s ain pa h o one ep esen a i e es o each Nakajima geome y is p esen ed. Howe e , i mus be poin ed ou ha a leas 3 success ul es s we e conduc ed o each geome y in o de o p o ide s a is ical meaning o he esul s. Fo bo h necking ( o de e mine he o ming limi cu e, FLC) and ac u e s ains ( o de e mine he ac u e o ming limi line, FFL), he mean alue o he co esponding p incipal s ain esul s is depic ed Fig. 5. (a) Fo ce displacemen o PETG Nakajima es s and (b) specimens a e ac u e. Fig. 6. F ac og aphy o PETG Nakajima specimens: (a) TS and (b) PS. A. Rosa-Sainz e al. Polyme Tes ing 134 (2024) 108431 8 in he FLD. Only he TS specimen demons a ed necking as a ailu e mode. Consequen ly, he FLC cu e was no included. Ins ead, a g ay squa e ep esen s he s ain pai s a he onse o he neck, co esponding o he condi ions o he TS specimen. The FFL was cons uc ed using black solid ma ke s, which co espond o he s ain pai s a he inal DIC measu emen acco ding o he me hodology explained in sec ion 2. Upon examina ion o he s ain pa hs, i was obse ed ha he TS specimen app oached β= − 0.3, which was a esul o i s ini ial ge- ome y. The PS specimen adhe ed o he plane s ain pa h imposed by i s ini ial geome y. Rega ding he BS and EBS specimens, a he beginning o he es he s ain pa hs ollow a condi ion o biaxiali y and equi- biaxiali y, bu hen hey change owa ds a plane s ain condi ion (a app oxima ely a majo s ain o 0.04 o bo h specimens, as can be seen in Fig. 8). When he punch s a s o con ac he su ace o he shee , he side in con ac wi h he punch migh be unde comp ession, whe eas he o he side is unde ension. As he punch p og esses, he ension on he ou e su ace o he shee induces hese laye s o ac u e. The obse ed change o BS and EBS may be due o he in insic cha ac e is ics o he p in ed ma e ial and he p in ing p ocess. Ne e heless, a mo e in-dep h s udy would be needed o unde s and he easons ha may cause his cli age o he s ains unde hese condi ions. 3.2. PCL This sec ion ou lines he indings conce ning he PCL ma e ial, explained in necking and ac u e analysis, discussion o ailu e modes, and he ob ained o ming limi diag am. 3.2.1. Necking and ac u e analysis PCL shee s we e p in ed o ob ain Nakajima specimens wi h di e en geome ies, including ensile s ain (TS), plane s ain (PS), biaxial s ain (BS), and equibiaxial s ain (EBS). Fig. 9 shows he applica ion o he ime-dependen app oach o Nakajima specimens TS (Fig. 9a and b) and PS (Fig. 9c and d), along wi h a specimen image o he majo s ain p o ided by he DIC sys em. Fo he PCL TS Nakajima specimen, he ime-dependen app oach allowed he iden i ica ion o Poin A and B, which de ined he ins abili y egion (Fig. 9a), whe e poin B is he i s poin whe e he s ain s a s o dec ease (Fig. 9b). By means o he e olu ion o he s ain a e o Poin B, he local maximum was clea ly iden i ied ˙ ε B 1,max and hus, he ime ins an a he onse o necking necking. Finally, his app oach allowed o ob ain he limi s ains a he onse o necking ha co espond o he s ains a poin A s ains, ε 1,lim, ε 2,lim a he ime ins an necking. Fig. 9c and d shows he applica ion o he ime-dependen app oach o a PS Nakajima specimen, which was simila o he p e ious case (TS specimen). The ins abili y egion was de ined be ween poin A and Poin B, wi h Poin B being he i s poin whe e he s ain begins o dec ease (see Fig. 9c). Fig. 9d allowed he de e mina ion o he local maximum ˙ ε B 1,max o Poin B o es ablish he onse o necking. Table 5 con ains he pai o neck s ains ob ained o he TS and PS specimens by applying he ime-dependen app oach. The esul s showed ha he s ain le els we e nea ly iden ical o he h ee speci- mens conside ed and o each o he geome ies. Addi ionally, Table 5 p esen s he s ain measu emen s ob ained by he DIC sys em, alongside hei co esponding s anda d de ia ions. As explained in Sec ion 2.2, hese s ain alues a e used o de e mine he FFL. Fig. 10 shows he applica ion o he ime-dependen me hodology o BS and EBS Nakajima specimens. S a ing wi h he BS specimen (as depic ed in Fig. 10a), he analysis showed ha he s ain o a se ies o poin s along a sec ion pe pendicula o he c ack did no show any Fig. 7. Laye obse a ion in (a) TS and (b) EBS Nakajima PETG specimens. Fig. 8. Fo mabili y limi s o 3D p in ed PETG shee s wi h 2 mm hickness ob ained by means o Nakajima specimens. A. Rosa-Sainz e al. Polyme Tes ing 134 (2024) 108431 9 dec ease. The same esul was obse ed o he EBS Nakajima specimen (see Fig. 10b), whe e he s ain o a se ies o poin s con inuously inc eased un il he end o he es . The e o e, he de i a i e o he majo s ain o all he poin s s udied canno exhibi a maximum alue. This obse a ion p o ided he ini ial indica ion ha necking may no be a mode o ailu e o PCL-made BS and EBS specimens. Howe e , he DIC images showed a concen a ion o s ain in he cen al egion o he specimen. To es ablish whe he necking ook place in he BS and EBS specimens, an analysis o he o ce displacemen esul s was conduc ed. Fig. 11 illus a es he e olu ion o o ce wi h displacemen o he geome ies s udied. Addi ionally, Fig. 11b p o ides a isual ep esen- a ion o Nakajima specimens o TS, PS, BS, and EBS. As obse ed, he PCL p in ed ma e ial demons a ed high duc ili y, wi h none o he specimens unde going ac u e du ing he es and eaching he maximum displacemen allowed by he E ichsen es ing machine. In e ms o o ce-displacemen esul s, a dec ease in o ce is obse ed in he TS and PS specimens due o he plas ic ins abili y o he necking. In he case o he BS and EBS specimen, a smoo he dec ease is obse ed as a esul o a educ ion in hickness. Fo a ho ough examina ion o hese ailu e modes, a de ailed analysis o he specimen ac og aphies was unde aken. Fig. 12 p esen s he image analysis o he TS, PS, BS and EBS speci- mens using he op ical mic oscope. The specimens we e cu along he do ed ed line indica ed in each image, polished, and hen obse ed on he su ace h ough an op ical mic oscope. The images we e cap u ed om he on al plane o he specimens o de ec a eas o necking o i s absence. TS and PS specimens exhibi ed necking du ing he es , in his sense, di e en zones can be obse ed: designa ed as “I” o necking and (“II”) ansi ion zone ( ansi ion be ween he necked a ea and he elonga ed zone). In his case, “zone III” does no apply since none o he specimens ac u ed. As o he BS and EBS specimens, hey displayed a new ailu e mode, as he specimen was capable o de o ming due o he sepa a ion o i s laye s un il i eached a s a e whe e i was p ac ically a ilm. In his expe imen al s udy, he speci ic ailu e mode has been called “in e laye gliding”. This ailu e consis s in a sepa a ion o he di e en ma e ial laye s (i.e. “in e laye ”) and he co esponding h ough hickness Fig. 9. Expe imen al ime e olu ion o he majo s ain along he poin s o he selec ed sec ion and applica ion o he ime-dependen app oach: (a) (b) TS Nakajima specimen, and (c) (d) PS Nakajima specimen. Table 5 Summa y o he necking and ac u e esul s o PCL ma e ial. Tes geome y Repe i ion Onse o necking ε 1,lim ε 2,lim TS_PCL I 0.119 −0.030 II 0.116 −0.028 III 0.112 −0.022 Mean 0.116 −0,027 S anda d de ia ion 0.0035 0.0042 PS_PCL I 0.110 0.003 II 0.116 0.002 III 0.113 0.003 Mean 0.1128 0.0028 S anda d de ia ion 0.0027 0.0004 Onse o ac u e using DIC TS_PCL I/II/III 0.8945/0.8912/ 0.8901 −0.0656/-0.0565/- 0.0634 Mean 0.8919 −0.1760 S anda d de ia ion 0.0022 0.0056 TS_PCL I/II/III 0.9050/0.9123/ 0.9165 −0.04/-0.041/-0.038 Mean 0.9112 −0.0396 S anda d de ia ion 0.0058 0.0015 BS_PCL I/II/III 0.8475/0.8498/ 0.8325 0.3305/0.3300/0.324 Mean 0.8432 0.3283 S anda d de ia ion 0.0093 0.0037 EBS_PCL I/II/III 0.7558/0.754/ 0.7405 0.5825/0.5973/0.603 Mean 0.7501 0.5942 S anda d de ia ion 0.0083 0.0106 A. Rosa-Sainz e al.