Rheological characteristics of Fe–C–Cr(Ni) alloys

Ci a ion: Rosypalo á, S.; ˇ Reháˇcko á, L.; No ák, V.; Kawuloko á, M.; Váˇno á, P.; Koneˇcná, K.; ˇ Du ico á, B. Rheological Cha ac e is ics o Fe–C–C (Ni) Alloys. Ma e ials 2023, 16, 2656. h ps://doi.o g/10.3390/ ma16072656 Academic Edi o s: And es So elo, Vlassios Likodimos, F ank Cze winski and Xiangyang Ma Recei ed: 30 Janua y 2023 Re ised: 10 Ma ch 2023 Accep ed: 21 Ma ch 2023 Published: 27 Ma ch 2023 Copy igh : © 2023 by he au ho s. Licensee MDPI, Basel, Swi ze land. This a icle is an open access a icle dis ibu ed unde he e ms and condi ions o he C ea i e Commons A ibu ion (CC BY) license (h ps:// c ea i ecommons.o g/licenses/by/ 4.0/). ma e ials A icle Rheological Cha ac e is ics o Fe–C–C (Ni) Alloys Sil ie Rosypalo á*, Lenka ˇ Reháˇcko á, Vlas imil No ák , Monika Kawuloko á, Pe a Váˇno á, Ka eˇ ina Koneˇcnáand Ba bo a ˇ Du ico á Facul y o Ma e ials Science and Technology, VŠB-Technical Uni e si y o Os a a, 17. lis opadu 15, Po uba, 708 00 Os a a, Czech Republic *Co espondence: sil ie. [email p o ec ed] Abs ac : The p incipal objec i e o his p ojec was o in es iga e he heological p ope ies o Fe–C– C and Fe–C–Ni-based low-alloy s eels using an An on Paa high- empe a u e o a ional iscome e up o 1550 ◦ C. The emphasis was placed on de e mining he liquidus empe a u es and e alua ing he low and iscosi y cu es and he empe a u e dependence o dynamic iscosi y. All we e s udied depending on he change in he con en o ch omium (0.010–4.863 w %), nickel (0.001–4.495 w %), and ca bon (0.043–1.563 w %). I was shown ha he dynamic iscosi y dec eases wi h inc easing nickel con en and inc eases wi h inc easing ca bon and ch omium con en . The expe imen al da a o he low cu es we e i ed using he He schel–Bulkley model wi h a good ag eemen be ween he measu ed and calcula ed alues. Cha ac e iza ion o he in e nal s uc u e was pe o med by SEM and EDX analyses, con i ming non-signi ican changes in he mic os uc u e o he o iginal and emel ed samples. The phase composi ion o he selec ed samples was also de e mined using JMa P o 12.0 simula ion so wa e (Sen e So wa e L d., Guild o d, UK). Keywo ds: ch omium; nickel; iscosi y; low cu e; iscosi y cu e; low-alloy s eel 1. In oduc ion Since hei in oduc ion, s eels ha e made signi ican p og ess and ha e ceased o be “me e” i on-ca bon alloys, wi h imp o ed p ope ies such as ac u e esis ance and s eng h. Today, s eels a e modi ied wi h a ious alloying elemen s added, o en in minu e quan i ies, o sui speci ic applica ions. Ad ances in compu e echnology and an e e - expanding ange o ma e ial- es ing ins umen s ha e acili a ed he p oduc ion o s eels wi h a na ow composi ional scope and a wide a ie y o p ope ies [ 1 ]. Low-alloy s eels wi h composi ions anging om 2 w % o 10 w % o alloying elemen s belong o a b oad g oup o e ous ma e ials wi h a wide ange o po en ial uses. Signi ican a e he ones mainly con aining nickel, ch omium, and o he alloying elemen s such as anadium, niobium, and i anium [ 2 ]. I is well-es ablished ha nickel and ch omium enhance he mechanical p ope ies o low-alloy s eels, especially s eng h, oughness, and ha denabili y, which is e lec ed in he mic os uc u al changes a e quenching [ 3 – 5 ]. Low-alloy s eels a e used o nuclea p essu e essels, s eam gene a o s, and o he applica ions in nuclea powe plan s whe e con en ional s eels do no mee he equi ed endu ance s eng h. F om his pe spec i e, hey a e essen ial ma e ials o ensu ing highe sa e y and du abili y o nuclea powe plan s and con ibu e o inc easing powe gene a ion e iciency [ 6 – 8 ]. Howe e , low-alloy s eels a e also used as special s uc u al pa s in he ae ospace and au omo i e indus ies and in he p oduc ion o gea s and c anksha s, whe e high equi e- men s a e imposed o high ensile s eng h, empe a u e esis ance, co osion esis ance, a igue esis ance, and ac u e oughness [ 9 – 13 ]. Despi e hei widesp ead use, mainly due o he ad an ageous combina ion o hei cos and unique p ope ies, he e is s ill a pauci y o he mophysical and especially expe imen al da a in he li e a u e ega ding hei heological p ope ies. Ma e ials 2023,16, 2656. h ps://doi.o g/10.3390/ma16072656 h ps://www.mdpi.com/jou nal/ma e ials Ma e ials 2023,16, 2656 2 o 13 The de e mina ion o iscosi y and o he heological pa ame e s o mol en me als, s eels, and alloys is highly demanded as hey play a c ucial ole in mass ans e p ocesses and enable he design and op imiza ion o he mel ing, cas ing, and welding p ocesses o Fe-based alloys [ 14 , 15 ]. This de e mina ion is also challenging because he sys ems unde in es iga ion ha e high liquidus empe a u es, oxidize easily, and he s abili y o he measu ing sys em mus be ensu ed du ing expe imen s. In addi ion, he measu ed iscosi y alues a e ypically in he o de o mPa·s [16,17]. The main componen o low-alloy s eels is i on, whose iscosi y measu ed a mel ing empe a u e is abou 6 mPa · s. Speci ically, Chapman de e mined i o be app oxima ely 6.5 mPa · s [ 18 ], Ba ezza i 5.5 mPa · s [ 19 ] and B ooks 6.93 mPa · s [ 16 ]. Howe e , e en in he case o bina y and e na y sys ems, he iscosi y o i on-based alloys can a y by uni s o mPa · s, wi h he addi ion o alloying elemen s in he o de o en hs o uni s o pe cen [ 20 , 21 ]. Fu he mo e, i is wo h no ing ha he e ec o he same dissol ing elemen on iscosi y may di e o bina y and mul icomponen mel s, and i can be assumed ha speci ic in e ac ions be ween he componen s change he pa e ns o hei e ec on iscosi y [ 22 ]. O e he pas wo decades, s udies ha e been pe o med add essing he e ec o ch omium and nickel on he iscosi y o bina y and mo e complex sys ems. Sa o examined he iscosi ies o bina y sys ems, including Fe–Ni, o e he whole concen a ion ange using an oscilla ing iscome e up o 1600 ◦ C, showing a good ma ch wi h A henius linea i y [ 23 ]. A simila e ec o nickel on he iscosi y o Fe–Ni bina ies was ound in a icle [ 24 ]. A s udy o he dependence o kinema ic iscosi y on ch omium con en in he Fe–C mel s showed ha he iscosi y iso he m is nonmono onic wi h a minimum a 5 w % and a maximum a 12 w %. The inc ease in c ys alliza ion endency was ela ed o a oms’ geome ic and chemical a angemen o e sho dis ances [ 25 ]. The iscosi ies o he C –Fe–Ni e na y sys em we e s udied a ele a ed empe a u es, and i was ound ha he iscosi ies inc eased mono onically wi h inc easing i on and ch omium con en [ 14 ]. Liu calcula ed iso iscosi y cu es o he e na y Fe–Ni–C sys em using Gibbs ee ene gy o mixing and geome ical models ope a ing wi h excess ac i a ion ene gies o sub-bina y sys ems. Nickel dec eased iscosi y o e he en i e concen a ion ange, bu ch omium only did so a con en s exceeding 20 mol% [ 26 ]. The iscosi y o Fe–C –Mn–Ni alloys wi h nickel con en s up o 20% in he empe a u e ange o 1723–1873 K was measu ed using a ib a ing inge iscome e . Nickel was ound o dec ease iscosi y wi hin his ange, which was ela ed o he change in he p ima y solidi ica ion s uc u e om a body- cen e ed cubic uni cell o a ace-cen e ed cubic uni cell [ 27 ]. The e ec o nickel on he iscosi y o Fe-based mul icomponen mel s was e alua ed in [ 28 ], whe e nickel dec eased he iscosi y and inc eased he ac i a ion ene gy, wi h he change in iscosi y being ela ed o s uc u al changes and decomposi ion o high- empe a u e clus e s o cemen i e and silicon oxides. A la ge amoun o published da a on he iscosi y o me als, alloys, and in e me allic compounds is gi en in [19]. The p esen s udy was designed o de e mine he e ec o alloying elemen s such as nickel, ch omium, and ca bon on he heological p ope ies o selec ed low-alloy s eels. Since in es iga ed sys ems we e poly-componen and, in hese cases, he p ope ies a e di icul o calcula e o simula e h ough ad anced applica ions, his s udy sough o ob ain da a ha would help add ess co esponding esea ch gaps. Fo hese easons, he measu emen s we e pe o med on a highly sensi i e ins umen unde condi ions no signi ican ly a ec ing he composi ion and s uc u e o he specimens. 2. Ma e ials and Me hods 2.1. Sample P epa a ion Alloy samples we e p epa ed om pu e me als (Fe, Ni, C , pu i y 99.99%), ca bon (pu i y 99.99%), and Fe 2 O 3 able s (pu i y 99.999%) by acuum induc ion mel ing using a Leybold He aeus u nace. The mel was cas in o he e ically o ien ed mold, yielding 3 kg ingo s om which ods o diame e 27 mm and, subsequen ly, cylind ical specimens (27 mm diame e × 38 mm heigh ) we e made. The chemical composi ion o all samples, Ma e ials 2023,16, 2656 3 o 13 de e mined by a Spec uma GDA 750 HP op ical emission spec ome e (GDOES), is lis ed in Table 1. The ca bon, oxygen, and sul u con en s we e de e mined by El a 200 CS and El a 2000 ONH combus ion analyze s. Table 1. Chemical composi ion o Fe–alloys (w %). Sample C C Ni O P S Mn Cu N Ti W 1 0.382 0.010 1.084 0.002 0.004 0.006 0.030 0.014 0.003 0.004 <0.001 2 0.338 0.010 4.478 0.001 0.005 0.006 0.031 0.012 0.003 0.003 <0.001 3 0.344 0.924 0.001 0.002 0.005 0.068 0.056 0.007 0.026 - - 4 0.34 4.796 0.001 0.002 0.002 0.006 0.042 0.005 0.001 0.010 0.044 5 0.043 0.013 4.465 0.005 0.004 0.006 0.062 0.007 0.002 0.003 <0.001 6 1.563 0.011 4.495 0.002 0.005 0.006 0.046 0.009 0.003 0.004 <0.001 7 0.043 4.863 0.001 0.022 0.004 0.064 0.053 0.006 0.024 - - 8 1.378 4.591 <0.001 0.011 0.004 0.054 0.047 0.007 0.016 <0.001 0.038 2.2. De e mina ion o Liquidus Tempe a u e Di e en ial he mal analysis (DTA), 3D di e en ial scanning calo ime y (3D DSC), and an op ical me hod we e used o de e mine he liquidus empe a u e [ 29 ]. A Se a am SETSYS 18TM labo a o y sys em and a Se a am Line 96 Mul i High-Tempe a u e Calo ime- e (MHTC) we e used o DTA and DSC analyses, espec i ely. The samples we e analyzed in high-pu i y co undum c ucibles. Be o e analyses, he alloys wi h he app oxima e masses o 190 mg (DTA) and 1200 mg (DCS) we e b ushed and cleaned in ace one. A dynamic a - mosphe e o A (pu i y 99.9999%) was main ained o p o ec he samples agains oxida ion. Liquidus empe a u es o each alloy we e ob ained h oughou he hea ing uns. The DTA and DCS uns we e ca ied ou a a hea ing a e o 10 ◦ C · min −1 and 5 ◦ C · min −1 , espec- i ely. The ob ained liquidus empe a u es we e co ec ed o he mel ing empe a u es o high-pu i y me als, Ni and Pd, and o he expe imen al condi ions. The op ical me hod was ca ied ou by sessile d op in a CLASIC high- empe a u e obse a ion u nace. The alloy sample was placed in an Al 2 O 3 subs a e and inse ed in o he u nace ube, which was he me ically sealed, e acua ed o 0.1 Pa, and pu ged wi h A (pu i y 99.9999%). Liquidus empe a u es we e de e mined op ically based on changes in he sample silhoue es aken wi h a CANON EOS 550D du ing hea ing (hea ing a e o 5◦C·min−1). 2.3. De e mina ion o Rheological P ope ies (Pa ame e s) The heological measu emen s we e ca ied ou wi h an An on Paa FRS 1600 high- empe a u e o a ional iscome e (An on Paa GmbH, G az, Aus ia). This ins umen combines a labo a o y u nace and a DSR 301 measu ing head wi h ai bea ings. The u nace allows measu emen s o up o 1550 ◦ C egis e ed by a P –13% Rh/P he mocouple. The heome e is ai -cooled o p o ec mechanical and elec onic componen s om o e - hea ing. The measu ing sys em consis s o an alumina spindle moun ed on a long ce amic sha connec ed o he heome e head and an alumina c ucible ixed o a lowe ce amic sha . The expe imen s we e conduc ed in o a ion mode by measu ing he o que o a spindle o a ing in a c ucible illed wi h mol en alloy. P io o he expe imen , he alloy samples we e ho oughly cleaned mechanically o emo e su ace oxides. The co undum c ucible con aining he alloy sample was placed in he u nace. To p e en oxida ion o he samples, a gas mix u e o a gon (99.9999% pu i y) and hyd ogen (2.6 ol%, 99.999% pu i y) was used a a low a e o 150 L · h −1 . The u nace was hea ed o 1550 ◦ C a a hea ing a e o 17 ◦ C · min −1 . The sample was kep a his empe a u e o 150 min o empe a u e s abiliza ion and homogeniza ion. Subsequen ly, he alumina spindle was imme sed in he mel , and low cu es we e eco ded a a empe a u e o 1550 ◦ C. Based on measu emen s o iscosi y dependence on he shea a e, an op imum shea a e o 10 s −1 was chosen o he iscosi y measu emen , Ma e ials 2023,16, 2656 4 o 13 pe o med du ing cooling a a a e o 2.5 ◦ C · min −1 in he empe a u e ange om 1550 ◦ C o he empe a u e a which he samples began o solidi y. 2.4. SEM and EDX Me hods Fi s ly, me allog aphic samples we e polished and e ched (ni al e ching p ocess). Consequen ly, he s uc u es we e examined using an Olympus IX70 (LM) ligh mic oscope (Olympus, Mel ille, NY, USA) and a JEOL 6490 LV scanning elec on mic oscope ((JEOL L d., Akishima, Japan)) ope a ing in a seconda y elec on mode, equipped wi h an INCA EDX (Ene gy Dispe si e X– ay Spec oscopy) analyze (Ox o d Ins umen s, Ox o d, UK) enabling X- ay analysis. The SEM se ings we e as ollows: he mionic ca hode LaB6, ol age 20 kV, and he specimen chambe kep a 10−3and 25 Pa. 3. Resul s and Discussion 3.1. Liquidus Tempe a u es The liquidus empe a u es we e ob ained using h ee expe imen al me hods: DTA, DSC, and op ical. The expe imen ally ob ained alues we e hen compa ed wi h hose heo e ically calcula ed by The moCalc 2019a so wa e. All empe a u es a e lis ed in Table 2. Table 2. Measu ed and calcula ed liquidus empe a u es (◦C). Sample DTA DSC Op ical Me hod The moCalc 1 1495 1498 1502 1503 2 1492 1493 1500 1497 3 1501 1504 1512 1506 4 1496 1500 1496 1501 5 1514 1515 1516 1516 6 1405 1406 1404 1403 7 1522 1527 1532 1524 8 1417 1421 1408 1428 Elemen s ha we e no included in he equilib ium calcula ions we e: P, O, Cu, N, Ti, and W. Good ag eemen was obse ed when compa ing he liquid empe a u es ob ained using he DTA and DSC me hods, wi h a maximum di e ence no exceeding 5 ◦ C. Howe e , conce ning he empe a u es ob ained by he op ical me hod, he di e ences we e mo e signi ican , especially o samples 3 (0.344 w % C, 0.924 w % C ), 7 (0.043 w % C, 4.863 w % C ), and 8 (1.378 w % C, 4.591 w % C ), whe e he maximum di e ence was 13 ◦ C o sample 8. A possible explana ion o his migh be ha he op ical me hod conside s he empe a u e o he liquid as ha a which he sample assumes a pe ec d op shape. I is wo h no ing ha de e mining liquid empe a u es a high empe a u es en ails se e al challenges, including hose ela ing o he expe imen al se up, expe imen al condi ions (hea ing a e, sample weigh ), o changes in he chemical composi ion o he samples du ing hea ing (oxida ion, deca bu iza ion) [ 30 – 32 ]. As o he alues calcula ed wi h The - moCalc 2019a so wa e (The mo-Calc So wa e, S ockholm, Sweden), one mus conside ce ain simpli ica ions ha he so wa e ope a es wi h, e.g., he absence o ce ain elemen s, equilib ium condi ions, and o he s. 3.2. Flow and Viscosi y Cu es The low cha ac e is ics o sys ems in he liquid s a e espec he heological equa ions o s a e desc ibing he ela ionship be ween shea s ess and luid de o ma ion. The low beha io can be ep esen ed by he low and iscosi y cu es. Based on hei shape, he New onian o non-New onian beha io o he mel unde in es iga ion can be de e mined. Fo New onian mel s, he shea s ess is di ec ly p opo ional o he shea a e, and he iscosi y depends only on he empe a u e, i.e., i is independen o he shea a e. In he case o non-New onian mel s, he iscosi y is dependen on he shea a e. Figu e 1shows low and iscosi y cu es o all samples a 1550 ◦ C. The low cu es a e p esen ed as Ma e ials 2023,16, 2656 5 o 13 he dependence o shea s ess on shea a e, and he iscosi y cu es as he dependence o iscosi y on shea a e. All dependencies we e measu ed in he shea a e in e al o 5–35 s−1 . Fo all alloys, shea s ess and iscosi y inc eased non-linea ly wi h shea a e. F om his, i can be concluded ha all he alloys in es iga ed exhibi a ype o non- New onian beha io , i.e., shea hickening. Ma e ials 2023, 16, x FOR PEER REVIEW 5 o 13 he New onian o non-New onian beha io o he mel unde in es iga ion can be de e - mined. Fo New onian mel s, he shea s ess is di ec ly p opo ional o he shea a e, and he iscosi y depends only on he empe a u e, i.e., i is independen o he shea a e. In he case o non-New onian mel s, he iscosi y is dependen on he shea a e. Figu e 1 shows low and iscosi y cu es o all samples a 1550 °C. The low cu es a e p esen ed as he dependence o shea s ess on shea a e, and he iscosi y cu es as he dependence o iscosi y on shea a e. All dependencies we e measu ed in he shea a e in e al o 5– 35 s−1. Fo all alloys, shea s ess and iscosi y inc eased non-linea ly wi h shea a e. F om his, i can be concluded ha all he alloys in es iga ed exhibi a ype o non-New onian beha io , i.e., shea hickening. Figu e 1. Flow ( .c.) and iscosi y ( .c.) cu es o samples (A) 1 and 2, (B) 3 and 4, (C) 5 and 6, and (D) 7 and 8. The expe imen al da a o he low cu es ob ained a 1550 °C we e i ed wi h he He schel–Bulkley model [33] acco ding o Equa ion (1): 𝜏 = 𝜏0+ 𝑘𝛾󰇗𝑛 (1) whe e 𝜏 (Pa) is he shea s ess, 𝜏0 (Pa) is he yield s ess, 𝑘 (Pa·sn) is he consis ency index, 𝛾󰇗 [s−1] is he shea a e, and 𝑛 [-] is he low index. Non-linea leas squa es analysis in ol ing a gene alized educed-g adien op imi- za ion algo i hm [34] was used o op imize he model pa ame e s lis ed in Table 3. The i ing cu es a e shown in Figu e 2. Excellen ag eemen was eached be ween he expe - imen al and heo e ical da a, as e idenced by he alues o he co ela ion coe icien s and he e o sum o squa es (SSE). Figu e 1. Flow ( .c.) and iscosi y ( .c.) cu es o samples ( A ) 1 and 2, ( B ) 3 and 4, ( C ) 5 and 6, and (D) 7 and 8. The expe imen al da a o he low cu es ob ained a 1550 ◦ C we e i ed wi h he He schel–Bulkley model [33] acco ding o Equa ion (1): τ=τ0+k. γn(1) whe e τ (Pa) is he shea s ess, τ0 (Pa) is he yield s ess, k (Pa · s n ) is he consis ency index, . γ[s−1] is he shea a e, and n[-] is he low index. Non-linea leas squa es analysis in ol ing a gene alized educed-g adien op imiza- ion algo i hm [ 34 ] was used o op imize he model pa ame e s lis ed in Table 3. The i ing cu es a e shown in Figu e 2. Excellen ag eemen was eached be ween he expe imen al and heo e ical da a, as e idenced by he alues o he co ela ion coe icien s and he e o sum o squa es (SSE). Ma e ials 2023,16, 2656 6 o 13 Table 3. Op imized pa ame e s o he He schel–Bulkley model. Sample 103τ0(Pa) 103k(Pa·sn)nR2SSE 1 1.2 8.2 1.3 0.9989 0.0017 2 1.9 8.1 1.3 0.9994 0.0009 3 1.1 7.8 1.3 0.9995 0.0006 4 1.5 5.9 1.4 0.9999 0.0001 5 1.3 6.7 1.4 0.9994 0.0009 6 0.9 6.3 1.4 0.9998 0.0004 7 1.7 7.7 1.3 0.9989 0.0014 8 1.4 5.9 1.4 0.9998 0.0003 Ma e ials 2023, 16, x FOR PEER REVIEW 6 o 13 Table 3. Op imized pa ame e s o he He schel–Bulkley model. Sample 103 𝝉𝟎 (Pa) 103 𝒌 (Pa·sn) 𝒏 R2 SSE 1 1.2 8.2 1.3 0.9989 0.0017 2 1.9 8.1 1.3 0.9994 0.0009 3 1.1 7.8 1.3 0.9995 0.0006 4 1.5 5.9 1.4 0.9999 0.0001 5 1.3 6.7 1.4 0.9994 0.0009 6 0.9 6.3 1.4 0.9998 0.0004 7 1.7 7.7 1.3 0.9989 0.0014 8 1.4 5.9 1.4 0.9998 0.0003 Figu e 2. Flow cu es i ed by he He schel–Bulkley model (dashed lines deno e he i ing cu es); (A)–samples 1–4, (B)–samples 5–8. 3.3. Tempe a u e Dependence o Dynamic Viscosi y The empe a u e dependence o he dynamic iscosi y o he samples was expe i- men ally in es iga ed du ing he cooling p ocess, i.e., in he empe a u e in e al om he maximum empe a u e (1550 °C) o he solidi ica ion empe a u e. The ob ained depend- encies a e shown in Figu e 3A–D. As shown in he igu e, he dynamic iscosi y inc eases exponen ially wi h dec easing empe a u e, which ag ees wi h he A henius equa ion [35]. The de ails show he dependence o he dynamic iscosi y on empe a u e when he sample is in he liquid s a e. I can be a gued ha he e ec o chemical composi ion—Ni, C , and C con en s—is almos negligible in he in es iga ed concen a ion anges o C (0.924–4.796 w %), Ni (1.084–4.478 w %), and C (0.043–1.378 w %). Howe e , a sligh in- c ease in iscosi y wi h inc easing ch omium con en can be obse ed in Figu e 3B, whe e sample 3 wi h 0.924 w % ch omium had a iscosi y o 13.6 mPa a 1550 °C, while sample 4 wi h 4.796 w % ch omium had a iscosi y o 15.0 mPa a he same empe a u e. I is wo h no ing ha a simila e ec o ch omium was obse ed o e na y alloys con aining ch omium and nickel, bu he ch omium con en a ied in he o de o ens o pe cen [14,26]. A simila end can be obse ed o inc easing ca bon con en (Figu e 3C,D). Fo samples 5 (0.043 w % C) and 6 (1.563 w % C), con aining oughly he same nickel con en o abou 4.5 w %, he dynamic iscosi y alues a he maximum empe a u e we e 14.7 and 14.6 mPa, espec i ely. Addi ionally, o samples 7 (0.043 w % C) and 8 (1.378 w % C) wi h app oxima ely he same ch omium con en , he iscosi y inc eased sligh ly om a alue o 13.4 mPa o a alue o 14.5 mPa. A sligh dec ease in iscosi y can be obse ed wi h inc easing nickel con en (Figu e 3A), yielding iscosi ies o 16.0 mPa o sample 1 (1.084 w % Ni) and 15.2 mPa o sample 2 (4.478 w % Ni). In he same ein, Dubbe s ein Figu e 2. Flow cu es i ed by he He schel–Bulkley model (dashed lines deno e he i ing cu es); (A)–samples 1–4, (B)–samples 5–8. 3.3. Tempe a u e Dependence o Dynamic Viscosi y The empe a u e dependence o he dynamic iscosi y o he samples was expe i- men ally in es iga ed du ing he cooling p ocess, i.e., in he empe a u e in e al om he maximum empe a u e (1550 ◦ C) o he solidi ica ion empe a u e. The ob ained de- pendencies a e shown in Figu e 3A–D. As shown in he igu e, he dynamic iscosi y inc eases exponen ially wi h dec easing empe a u e, which ag ees wi h he A henius equa ion [ 35 ]. The de ails show he dependence o he dynamic iscosi y on empe a- u e when he sample is in he liquid s a e. I can be a gued ha he e ec o chemical composi ion—Ni, C , and C con en s—is almos negligible in he in es iga ed concen- a ion anges o C ( 0.924–4.796 w % ), Ni (1.084–4.478 w %), and C (0.043–1.378 w %). Howe e , a sligh inc ease in iscosi y wi h inc easing ch omium con en can be obse ed in Figu e 3B, whe e sample 3 wi h 0.924 w % ch omium had a iscosi y o 13.6 mPa a 1550 ◦ C, while sample 4 wi h 4.796 w % ch omium had a iscosi y o 15.0 mPa a he same empe a u e. I is wo h no ing ha a simila e ec o ch omium was obse ed o e na y alloys con aining ch omium and nickel, bu he ch omium con en a ied in he o de o ens o pe cen [ 14 , 26 ]. A simila end can be obse ed o inc easing ca bon con en (Figu e 3C,D). Fo samples 5 (0.043 w % C) and 6 (1.563 w % C), con aining oughly he same nickel con en o abou 4.5 w %, he dynamic iscosi y alues a he maximum empe a u e we e 14.7 and 14.6 mPa, espec i ely. Addi ionally, o samples 7 (0.043 w % C) and 8 (1.378 w % C) wi h app oxima ely he same ch omium con en , he iscosi y inc eased sligh ly om a alue o 13.4 mPa o a alue o 14.5 mPa. A sligh dec ease in iscosi y can be obse ed wi h inc easing nickel con en (Figu e 3A), yielding iscosi ies o 16.0 mPa o sample 1 (1.084 w % Ni) and 15.2 mPa o sample 2 (4.478 w % Ni). In he same ein, Dubbe s ein desc ibed a mode a e dec ease in iscosi y depending on he nickel con en o Fe–C –Mn–Ni alloys wi h 3–6 w % Ni [27]. Ma e ials 2023,16, 2656 7 o 13 Ma e ials 2023, 16, x FOR PEER REVIEW 7 o 13 desc ibed a mode a e dec ease in iscosi y depending on he nickel con en o Fe–C – Mn–Ni alloys wi h 3–6 w % Ni [27]. Figu e 3. Tempe a u e dependencies o iscosi y o he samples (A) 1 and 2, (B) 3 and 4, (C) 5 and 6, and (D) 7 and 8. 3.4. Resul s o SEM and EDX Analyses Samples wi h signi ican ly a ying ca bon con en s and he maximum amoun o al- loying elemen (C and Ni) we e es ed using SEM and EDX analyses in bo h he ini ial s a e and a e heological expe imen s (a e high- empe a u e es ing). Speci ically, sam- ples 5 (0.043 w % C; 4.465 w % Ni), 6 (1.563 w % C; 4.495 w % Ni), 7 (0.043 w % C; 4.863 w % C ), and 8 (1.378 w % C; 4.591 w % C ) we e in es iga ed o changes in in e nal s uc u e. The esul s o hese analyses a e shown in Figu es 4 and 5. Figu e 4A–D and 6A–D show he mic os uc u es o he samples wi h low ca bon con en , i.e., samples 5 and 7 (0.043 w % C). When compa ing he mic os uc u es o hese samples in he ini ial and emel ed s a es, i can be su mised ha no signi ican changes in hei in e nal s uc- u e occu ed du ing he heological measu emen s. In bo h samples, baini ic e i e o baini e is p esen in he ini ial and emel ed s a es. Sample 5 (4.465 w % Ni) con ains mino amoun s o pe li e and a coa se cemen i e ne wo k. Fo sample 7 (4.863 w % C ), baini ic e i e and baini e a e mo e e chable. In he cen e o his sample in he emel ed s a e, complex oxide inclusions (C o Mn oxides) we e de ec ed in he bulk g ain and along he g ain bounda ies (Figu e 5B). This was suppo ed by EDX analysis, he esul s o which a e shown in Table 4 and Figu e 6, con aining he mos ep esen a i e spec a o EDX spo mic oanalysis. The p esence o hese oxides is due o he o de o magni ude highe oxy- gen con en o his sample compa ed o he o he specimens. Figu es 4E–H and 5E–H show he mic os uc u e o samples 6 and 8 wi h a highe ca bon con en (1.563 and 1.378 w % C). In bo h cases, a dominan s uc u e o lamella pe li e is obse ed. Fo sample 6 Figu e 3. Tempe a u e dependencies o iscosi y o he samples ( A ) 1 and 2, ( B ) 3 and 4, ( C ) 5 and 6, and (D) 7 and 8. 3.4. Resul s o SEM and EDX Analyses Samples wi h signi ican ly a ying ca bon con en s and he maximum amoun o al- loying elemen (C and Ni) we e es ed using SEM and EDX analyses in bo h he ini ial s a e and a e heological expe imen s (a e high- empe a u e es ing). Speci ically, samples 5 (0.043 w % C; 4.465 w % Ni), 6 (1.563 w % C; 4.495 w % Ni), 7 (0.043 w % C; 4.863 w % C ), and 8 (1.378 w % C; 4.591 w % C ) we e in es iga ed o changes in in e nal s uc u e. The esul s o hese analyses a e shown in Figu es 4and 5. Figu es 4A–D and 6A–D show he mic os uc u es o he samples wi h low ca bon con en , i.e., samples 5 and 7 ( 0.043 w % C ). When compa ing he mic os uc u es o hese samples in he ini ial and emel ed s a es, i can be su mised ha no signi ican changes in hei in e nal s uc u e occu ed du ing he heological measu emen s. In bo h samples, baini ic e i e o baini e is p esen in he ini ial and emel ed s a es. Sample 5 (4.465 w % Ni) con ains mino amoun s o pe li e and a coa se cemen i e ne wo k. Fo sample 7 (4.863 w % C ), baini ic e i e and baini e a e mo e e chable. In he cen e o his sample in he emel ed s a e, complex oxide inclusions (C o Mn oxides) we e de ec ed in he bulk g ain and along he g ain bounda ies (Figu e 5B). This was suppo ed by EDX analysis, he esul s o which a e shown in Table 4and Figu e 6, con aining he mos ep esen a i e spec a o EDX spo mic oanalysis. The p esence o hese oxides is due o he o de o magni ude highe oxygen con en o his sample compa ed o he o he specimens. Figu es 4E–H and 5E–H show he mic os uc u e o samples 6 and 8 wi h a highe ca bon con en (1.563 and 1.378 w % C). In bo h cases, a dominan s uc u e o lamella pe li e is obse ed. Fo sample 6 (4.495 w % Ni), cemen i e pla es a e p esen Ma e ials 2023,16, 2656 8 o 13 in he ini ial s a e, including a ine cemen i e ne wo k excluded along g ain bounda ies. Howe e , a e heological es ing, only pla es o cemen i e a e p esen . The lamellae o pea li e appea ine a e he heological expe imen . In sample 8 ( 4.591 w % C ), globula islands o ledebu i e a e p esen in he ini ial s a e and a e al e ed in he emel ed s a e o la ge blocks o e icula ed ledebu i e along g ain bounda ies. Ma e ials 2023, 16, x FOR PEER REVIEW 8 o 13 (4.495 w % Ni), cemen i e pla es a e p esen in he ini ial s a e, including a ine cemen i e ne wo k excluded along g ain bounda ies. Howe e , a e heological es ing, only pla es o cemen i e a e p esen . The lamellae o pea li e appea ine a e he heological expe - imen . In sample 8 (4.591 w % C ), globula islands o ledebu i e a e p esen in he ini ial s a e and a e al e ed in he emel ed s a e o la ge blocks o e icula ed ledebu i e along g ain bounda ies. Figu e 4. Mic os uc u e o nickel sample 5 (A–D) wi h lowe ca bon con en and sample 6 (E–H) wi h highe ca bon con en ; le column—ini ial s a e, igh column— emel ed s a e; (A,B,E,F)— ligh mic oscopy, (C,D,G,H)–scanning elec on mic oscopy. Figu e 4. Mic os uc u e o nickel sample 5 ( A – D ) wi h lowe ca bon con en and sample 6 ( E – H ) wi h highe ca bon con en ; le column—ini ial s a e, igh column— emel ed s a e; ( A , B , E , F )—ligh mic oscopy, (C,D,G,H)–scanning elec on mic oscopy. Ma e ials 2023,16, 2656 9 o 13 Ma e ials 2023, 16, x FOR PEER REVIEW 9 o 13 Figu e 5. Mic os uc u e o ch omium sample 7 (A–D) wi h lowe ca bon con en and sample 8 (E– H) wi h highe ca bon con en ; le column—ini ial s a e, igh column— emel ed s a e; (A,B,E,F)— ligh mic oscopy, (C,D,G,H)—scanning elec on mic oscopy. Loca ions whe e EDX spo mic oanal- ysis was pe o med (inlay o Figu e 6B). Figu e 5. Mic os uc u e o ch omium sample 7 ( A – D ) wi h lowe ca bon con en and sam- ple 8 ( E – H ) wi h highe ca bon con en ; le column—ini ial s a e, igh column— emel ed s a e; (A,B,E,F)—ligh mic oscopy, ( C , D , G , H )—scanning elec on mic oscopy. Loca ions whe e EDX spo mic oanalysis was pe o med (inlay o Figu e 6B). Table 4. EDX poin analysis o oxide inclusions o sample 7. Spec um O Al C Mn Fe (w %) 1 29.2 6.6 31.5 20.3 12.6 2 29.7 7.3 32.6 21.0 9.4 3 31.9 8.9 32.6 21.3 5.3