Full-field temperature measurement of stainless steel specimens subjected to uniaxial tensile loading at various strain rates

ma e ials A icle Full-Field Tempe a u e Measu emen o S ainless S eel Specimens Subjec ed o Uniaxial Tensile Loading a Va ious S ain Ra es K zysz o ˙ Zaba 1,* , Tomasz T zepieci´nski 2, S anisla Rusz 3, Sand a Puchle ska 1and Maciej Balce zak 1   Ci a ion: ˙ Zaba, K.; T zepieci´nski, T.; Rusz, S.; Puchle ska, S.; Balce zak, M. Full-Field Tempe a u e Measu emen o S ainless S eel Specimens Subjec ed o Uniaxial Tensile Loading a Va ious S ain Ra es. Ma e ials 2021,14, 5259. h ps://doi.o g/10.3390/ma14185259 Academic Edi o s: Qing Liu and Jiangshan Zhang Recei ed: 28 June 2021 Accep ed: 7 Sep embe 2021 Published: 13 Sep embe 2021 Publishe ’s No e: MDPI s ays neu al wi h ega d o ju isdic ional claims in published maps and ins i u ional a il- ia ions. Copy igh : © 2021 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/). 1Depa men o Me al Wo king and Physical Me allu gy o Non-Fe ous Me als, Facul y o Non-Fe ous Me als, AGH—Uni e si y o Science and Technology, al. Adama Mickiewicza 30, 30-059 C acow, Poland; [email p o ec ed] (S.P.); [email p o ec ed] (M.B.) 2Depa men o Manu ac u ing and P oduc ion Enginee ing, Facul y o Mechanical Enginee ing and Ae onau ics, Rzeszow Uni e si y o Technology, al. Pows . Wa szawy 8, 35-959 Rzeszów, Poland; [email p o ec ed] 3Depa men o Mechanical Technology, Facul y o Mechanical Enginee ing, VŠB—Technical Uni e si y o Os a a, 17 lis opadu 15, CZ 708 33 Os a a–Po uba, Czech Republic; s anisla [email p o ec ed] *Co espondence: [email p o ec ed] Abs ac : This a icle p esen s a s udy on he e ec o s ain a e, specimen o ien a ion, and plas ic s ain on he alue and dis ibu ion o he empe a u e o dog-bone 1 mm- hick specimens du ing hei de o ma ion in uniaxial ensile es s. Full- ield image co ela ion and in a ed he mog aphy echniques we e used. A i anium-s abilised aus eni ic 321 s ainless s eel was used as es ma e ials. The dog-bone specimens used o uniaxial ensile es s we e cu along he shee me al olling di ec ion and h ee s ain a es we e conside ed: 4 × 10 −3 s −1 , 8 × 10 −3 s −1 and 16 × 10 −3 s −1 . I was ound ha inc easing he s ain a e esul ed in he in ensi ica ion o hea gene a ion. High-quali y eg ession models (Ra > 0.9) de eloped o he aus eni ic 321 s eel e ealed ha sample o ien a ion does no play a signi ican ole in he hea gene a ion when he sample is plas ically de o med. I was ound ha a he momen o o ma ion o a necking a he highes s ain a e, he maximum sample empe a u e inc eased mo e han ou imes compa ed o he ini ial empe a u e. A syne gis ic e ec o he s ain ha dening exponen and yield s ess e ealed ha hea is gene a ed mo e apidly owa ds small alues o s ain ha dening exponen and yield s ess. Keywo ds: digi al image co ela ion; mechanical p ope ies; s ainless s eel; empe a u e; he mo i- sion; uniaxial ensile es 1. In oduc ion Me als and hei alloys ha e a c ys alline s uc u e, which is cha ac e ised by a egula a angemen o a omic co es. Technical me als ob ained by con en ional me allu gical me hods ha e a polyc ys alline s uc u e [ 1 , 2 ]. This means ha me als a e made up o g ains cha ac e ised by app oxima ely he co ec c ys al s uc u e. Polyc ys alline ma e ials consis o g ains wi h a ious o ien a ions. Fo many polyc ys alline ma e ials, he g ain o ien a ions a e andom be o e any wo king (de o ma ion) o he ma e ial is unde aken. The e o e, e en i he indi idual g ains a e aniso opic, he p ope y di e ences end o a e age ou and, o e all, he ma e ial is iso opic. When a ma e ial is o med, he g ains a e usually dis o ed and elonga ed in one o mo e di ec ions which makes he ma e ial aniso opic [3]. In me als subjec ed o plas ic wo king, he mos impo an de ec s o he c ys al la ice a e disloca ions and g ain bounda ies. S ain ha dening—ha dening o a ma e ial wi h de o ma ion— esul s om in e ac ion and mul iplica ion o disloca ions du ing plas ic de o ma ion. G ain bounda ies ha e a much g ea e in luence on he mechanical p ope ies o me als han disloca ions [ 4 , 5 ]. The high ene gy le el o g ain bounda ies de e mines Ma e ials 2021,14, 5259. h ps://doi.o g/10.3390/ma14185259 h ps://www.mdpi.com/jou nal/ma e ials Ma e ials 2021,14, 5259 2 o 15 he occu ence o many phenomena, such as con inuous mobili y o bounda ies leading o g ain g ow h and lowe co osion esis ance [ 6 – 8 ]. G ain bounda ies also ha e a s ong in luence on he duc ili y o me als. The deg ee o s ain ha dening o ma e ials by g ain e ining is desc ibed by he Hall–Pe ch ela ionship [ 9 , 10 ] acco ding o which he yield s eng h o he ma e ial inc eases wi h he deg ee o g ain e inemen . On he one hand, g ain bounda ies inhibi he ee mo emen o disloca ions du ing g ain de o ma ion while pa icipa ing in he p ocess o ma e ial s eng hening and in he o ma ion o he de o ma ion ex u e [ 1 ]. On he o he hand, he g ain bounda ies a e he main a ea o pe manen de o ma ion du ing c eep o supe plas ic low. The de o ma ion o he ma e ial (elas ic o plas ic) occu s unde he in luence o a load applied o i . Elas ic de o ma ion disappea s when he load is emo ed. Plas ic de o ma ion emains a e he ma e ial is unloaded. The e a e wo main mechanisms o plas ic de o ma ion: he gliding mo ion o disloca ions and de o ma ion winning [ 11 , 12 ]. The gliding mo ion does no occu simul aneously in all possible planes and di ec ions o slip. De o ma ion occu s g adually, s a ing om he sliding planes and di ec ions p io i ised in ela ion o he di ec ion o he applied load. Du ing de o ma ion, he numbe o ac i e slip planes and ee disloca ions ha a e gene a ed du ing de o ma ion inc eases. Fu he plas ic de o ma ion equi es he applica ion o g ea e s ess in o de o ini ia e new disloca ions [ 13 – 15 ]. The p ocess by which s ess inc eases wi h de o ma ion is called wo k ha dening. Plas ic de o ma ion is also accompanied by hea gene a ion due o he in e nal esis ance o he ma e ial, which can be de ec ed a he mic os uc u e scale when loading he ma e ial [16,17]. The in es iga ion o hea gene a ion and dissipa ion du ing plas ic de o ma ion was e lec ed in scien i ic esea ch. Bodelo e al. [ 18 ] applied in a ed (IR) coupled ull- ield measu emen s o obse e he he e ogenei ies o kinema ic and he mal da a a he g ain scale o aus eni ic s ainless s eel. Specimens we e subjec ed o a cyclic loading. I was ound ha he empe a u e was signi ican ly a ec ed by di usion and his obse a ion ends o con i m ha empe a u e may no be used as a damage indica o . Boulange e al. [ 19 ] ha e ocused on he de e mina ion o hea sou ces om a empe a u e ield p o ided by an IR came a. They sepa a ely iden i ied he dissipa i e and he mo-elas ic hea sou ces. The mal ull- ield measu emen s om in a ed he mog aphy we e used o s udy he Po e in-Le Cha elie e ec [ 20 ]. The empe a u e ield p o ided insigh s in o he dynamics o band o ma ion and mo ion. The non-con ac op ical me hods o he measu emen o empe a u e displacemen in- clude ideo ex ensome e s [ 21 ], lase speckle co ela ion [ 22 ], in e e ome y me hods [23–25] and empe a u e-calib a ed CCD came as [ 26 ]. In addi ion o IR he mog aphy, he o he echnique ha allows empe a u e changes o be coupled wi h s ains is digi al image co e- la ion (DIC), in which digi al images o an objec be o e and a e de o ma ion a e cap u ed using a non-con ac op ic and ma e ial-independen measu ing ins umen , and hen hey a e subjec o co ela ion analysis [ 23 , 24 , 27 ]. High-speed DIC allows de o ma ion and dam- age mechanisms o be analysed in a quan i a i e manne [ 28 ]. DIC was used o ob ain s ain ields and o in es iga e he p opaga ion o he Lüde s band in s eel specimens subjec ed o he uniaxial ensile es [ 29 ]. The s ain s a es associa ed wi h localised necking and di use s ains a e also in es iga ed. Resul s show ha he c oss-sec ion o a ensile specimen mus be ega ded as a s uc u e, no as an elemen a y olume o ma e ial which is subjec ed o he uni o m load. The esul s o in es iga ions o Hung and Voloshin [ 30 ] indica ed ha o he uni o m ension es , DIC is a e y con enien and e icien ool o he measu emen o in-plane s ain measu emen . Feng and Xue [ 31 ] applied in a ed he mog aphy es s and DIC es s o he display o he he mal ield du ing mechanical ensile es s o 3D p in ed bol s. Cholewa e al. [ 32 ] de eloped he me hod o calib a ed in a ed he mal came as wi h a s e eo- ision DIC sys em applicable o scales o leng hs bo h la ge and small. ˙ Zaba e al. [ 33 ] used DIC and IR he mog aphy o ind he ela ionship be ween yield s ess and he Taylo –Quinney coe icien and hei change wi h he s ain a e du ing he s e ching o nickel-based supe alloys. A coupled he mog aphy and DIC sys em was calib a ed using a Ma e ials 2021,14, 5259 3 o 15 se ies o one sided hea exposu e expe imen s pe o med on loaded sandwich composi es. In a ed he mog aphy and DIC measu emen s a e no applicable o expe imen s wi h low conduc i i y ma e ials o discon inuous ma e ials [ 33 , 34 ]. Maynadie , e al. [ 35 ] de eloped an in a ed image co ela ion sys em equipped wi h a single IR came a o measu e simul a- neous he mal ields and de o ma ion. The disad an age o he p oposed me hod is ha his echnique equi es he use o a special coa ing o displacemen measu emen using he single came a. Ch ysochoos e al. [34] p oposed DIC and he mog aphy measu emen s o he de e mina ion o he mechanical ene gy and hea sou ces in ol ed a local scale du ing a he e ogeneous ensile es . The modynamic analysis o he ene gy balance showed he in luence o he dissipa ed mechanism on he s ess–s ain esponse. Many o s udies ake place a a mac oscopic scale wi h he measu emen o he a e age empe a u e o he ma e ial [ 36 , 37 ]. Meanwhile, due o he g ain s uc u e o polyc ys alline me als and he occu ence o a ious plas ic de o ma ion mechanisms, he empe a u e o he body subjec ed o loading is no uni o m. The way o explain his phenomenon is o ake ull- ield measu emen s. In his pape , he coupled IR and DIC measu emen s we e conduc ed o assess he he momechanical esponse o s ainless s eel s ip samples subjec ed o ensile load a di e en s ain a es. An analysis o a iance (ANOVA) was used o gain in o ma ion abou he ela ionship be ween he s ain ha dening phenomenon, yield s ess, sample o ien a ion in espec o he shee olling di ec ion, s ain a e, and plas ic s ain o he specimen and empe a u e. 2. Ma e ials and Me hods 2.1. Ma e ial The esea ch ma e ial was a i anium-s abilised aus eni ic s ainless s eel, 321 (AMS 5510). S eel 321 is a s eel wi h good o mabili y, weldabili y and esis ance o in e g anula co osion ha is mainly used in he chemical and a ia ion indus ies. The hickness o he shee s was 1 mm. The es samples we e cu om he shee in h ee di ec ions: he olling di ec ion (RD), a an angle o 45 ◦ o he RD and pe pendicula o he RD. The dimensions o es samples (Figu e 1) we e in acco dance wi h he ASTM E8/E8M–11 s anda d [ 38 ]. The equi emen s o he chemical composi ion o he es s eel a e shown in Table 1and a e in acco dance SAE AMS 5510 [39]. Ma e ials 2021, 14, x FOR PEER REVIEW 3 o 16 change wi h he s ain a e du ing he s e ching o nickel-based supe alloys. A coupled he mog aphy and DIC sys em was calib a ed using a se ies o one sided hea exposu e expe imen s pe o med on loaded sandwich composi es. In a ed he mog aphy and DIC measu emen s a e no applicable o expe imen s wi h low conduc i i y ma e ials o discon inuous ma e ials [33,34]. Maynadie , e al. [35] de eloped an in a ed image co ela ion sys em equipped wi h a single IR came a o measu e simul aneous he mal ields and de o ma ion. The disad an age o he p oposed me hod is ha his echnique equi es he use o a special coa ing o displacemen measu emen using he single came a. Ch ysochoos e al. [34] p oposed DIC and he mog aphy measu emen s o he de e mina ion o he mechanical ene gy and hea sou ces in ol ed a local scale du ing a he e ogeneous ensile es . The modynamic analysis o he ene gy balance showed he in luence o he dissipa ed mechanism on he s ess–s ain esponse. Many o s udies ake place a a mac oscopic scale wi h he measu emen o he a e age empe a u e o he ma e ial [36,37]. Meanwhile, due o he g ain s uc u e o polyc ys alline me als and he occu ence o a ious plas ic de o ma ion mechanisms, he empe a u e o he body subjec ed o loading is no uni o m. The way o explain his phenomenon is o ake ull- ield measu emen s. In his pape , he coupled IR and DIC measu emen s we e conduc ed o assess he he momechanical esponse o s ainless s eel s ip samples subjec ed o ensile load a di e en s ain a es. An analysis o a iance (ANOVA) was used o gain in o ma ion abou he ela ionship be ween he s ain ha dening phenomenon, yield s ess, sample o ien a ion in espec o he shee olling di ec ion, s ain a e, and plas ic s ain o he specimen and empe a u e. 2. Ma e ials and Me hods 2.1. Ma e ial The esea ch ma e ial was a i anium-s abilised aus eni ic s ainless s eel, 321 (AMS 5510). S eel 321 is a s eel wi h good o mabili y, weldabili y and esis ance o in e g anula co osion ha is mainly used in he chemical and a ia ion indus ies. The hickness o he shee s was 1 mm. The es samples we e cu om he shee in h ee di ec ions: he olling di ec ion (RD), a an angle o 45° o he RD and pe pendicula o he RD. The dimensions o es samples (Figu e 1) we e in acco dance wi h he ASTM E8/E8M–11 s anda d [38]. The equi emen s o he chemical composi ion o he es s eel a e shown in Table 1 and a e in acco dance SAE AMS 5510 [39]. Figu e 1. Dimensions (in mm) o he samples o he ensile es . Table 1. Chemical composi ion o 321 s eel (w .%) [39]. C (max.) Si Mo Mn (max.) P + S (max. C Ni Ti (max.) N (max.) Fe 0.08 0.25–1.00 0.75 2.0 0.04 P 0.03 S 17.0–19.0 9.0–12.0 0.7 0.1 balance Figu e 1. Dimensions (in mm) o he samples o he ensile es . Table 1. Chemical composi ion o 321 s eel (w .%) [39]. C (Max.) Si Mo Mn (Max.) P + S (Max.) C Ni Ti (Max.) N (Max.) Fe 0.08 0.25–1.00 0.75 2.0 0.04 P 0.03 S 17.0–19.0 9.0–12.0 0.7 0.1 balance 2.2. Uniaxial Tensile Tes Dog-bone samples (Figu e 1) we e s e ched in a uniaxial ensile es machine Zwick/Roell Z100 (Figu e 2). Th ee di e en s ain a es we e used in he in es iga ions: 4 × 10 −3 s −1 , 8×10−3s−1and 16 ×10−3s−1. The es s we e ca ied ou a a empe a u e o 24 ◦C. Ma e ials 2021,14, 5259 4 o 15 Ma e ials 2021, 14, x FOR PEER REVIEW 4 o 16 2.2. Uniaxial Tensile Tes Dog-bone samples (Figu e 1) we e s e ched in a uniaxial ensile es machine Zwick/Roell Z100 (Figu e 2). Th ee di e en s ain a es we e used in he in es iga ions: 4 × 10–3 s−1, 8 × 10−3 s−1 and 16 × 10−3 s−1. The es s we e ca ied ou a a empe a u e o 24 °C. Figu e 2. Tes s and. 2.3. Digi al Image Co ela ion Technique The digi al image co ela ion A amis sys em (GOM, B aunschweig, Ge many) was used o de e mine he cha ac e o he de o ma ion o he sample in a non-con ac manne du ing he s e ching p ocess o samples. The measu ing sys em consis s o wo essen ial componen s. The i s is a scanne , consis ing o wo high- esolu ion digi al came as (Fig- u e 2) posi ioned in ela ion o each o he in such a way as o be able o build a spa ial image. The second elemen o he se is a compu e wi h special so wa e o he nume ical p ocessing o images. P ope su ace p epa a ion o he samples is necessa y o DIC analysis. Fi s , he samples a e co e ed wi h whi e pain , and hen a andom pa e n o con as ing black spo s is applied. The selec ion o he size o he spo s depends on he size o he es objec and he op ical p ope ies o he measu ing appa a us. The measu emen p ocess consis s in aking a se ies o images o he sample by wo came as in successi e s ages o loading. Co ela ion o images om hese came as makes i possible o de e mine he posi ion o each pixel by gi ing hem coo dina es in a h ee-dimensional coo dina e sys em. Then he images a e di ided in o so-called de o ma ion g ids, each o which con ains a unique pa - e n o do s [40]. The ini ial se up becomes he e e ence s ep. Due o he de o ma ion o he shee su ace, he spo s in each elemen o he mesh change hei posi ion in ela ion o each o he , which makes i possible o calcula e he ull ield de o ma ion in ela ion o he e e ence posi ion. Howe e , in o de o make such an analysis possible, he sys em di ides he measu emen a ea in o ields o a ixed size called ace s. Local s ains a e ob ained om he o mula: 𝜺𝒆𝒏𝒈 =𝐥𝐢𝐦 𝒍→𝟎 𝒍𝒊𝒏 +∆𝒍𝒅 𝒍𝒊𝒏 −𝟏∙𝟏𝟎𝟎% (1) whe e lin is he ini ial dos ance be ween wo neighbou ing ace s and Δld is he dis ance inc ease du ing uniaxial ensile es . The dimension o s anda d ace is 21 × 21 pixels. The second cha ac e is ic alue is he dis ance be ween he cen es o adjacen ace s. The A amis sys em o e s many bene- i s, such as: • a s able solu ion o ull- ield analyses o es objec s o jus a ew millime e s up o s uc u al componen s o se e al me es in size, Figu e 2. Tes s and. 2.3. Digi al Image Co ela ion Technique The digi al image co ela ion A amis sys em (GOM, B aunschweig, Ge many) was used o de e mine he cha ac e o he de o ma ion o he sample in a non-con ac manne du ing he s e ching p ocess o samples. The measu ing sys em consis s o wo essen ial componen s. The i s is a scanne , consis ing o wo high- esolu ion digi al came as (Figu e 2) posi ioned in ela ion o each o he in such a way as o be able o build a spa ial image. The second elemen o he se is a compu e wi h special so wa e o he nume ical p ocessing o images. P ope su ace p epa a ion o he samples is necessa y o DIC analysis. Fi s , he samples a e co e ed wi h whi e pain , and hen a andom pa e n o con as ing black spo s is applied. The selec ion o he size o he spo s depends on he size o he es objec and he op ical p ope ies o he measu ing appa a us. The measu emen p ocess consis s in aking a se ies o images o he sample by wo came as in successi e s ages o loading. Co ela ion o images om hese came as makes i possible o de e mine he posi ion o each pixel by gi ing hem coo dina es in a h ee-dimensional coo dina e sys em. Then he images a e di ided in o so-called de o ma ion g ids, each o which con ains a unique pa e n o do s [ 40 ]. The ini ial se up becomes he e e ence s ep. Due o he de o ma ion o he shee su ace, he spo s in each elemen o he mesh change hei posi ion in ela ion o each o he , which makes i possible o calcula e he ull ield de o ma ion in ela ion o he e e ence posi ion. Howe e , in o de o make such an analysis possible, he sys em di ides he measu emen a ea in o ields o a ixed size called ace s. Local s ains a e ob ained om he o mula: εeng =lim l→0lin +∆ld lin −1·100% (1) whe e l in is he ini ial dos ance be ween wo neighbou ing ace s and ∆ l d is he dis ance inc ease du ing uniaxial ensile es . The dimension o s anda d ace is 21 × 21 pixels. The second cha ac e is ic alue is he dis ance be ween he cen es o adjacen ace s. The A amis sys em o e s many bene i s, such as: • a s able solu ion o ull- ield analyses o es objec s o jus a ew millime e s up o s uc u al componen s o se e al me es in size, •i is a ma e ial-independen and non-con ac measu ing sys em, • i pe o ms high-p ecision measu emen s wi h a 3D measu emen esolu ion in he sub-mic ome e ange, •i is a high- esolu ion o poin -based and ull- ield measu emen s. Ma e ials 2021,14, 5259 5 o 15 2.4. In a ed (IR) The mal Mapping The su ace empe a u e o he samples du ing he s e ching was measu ed using a high-sensi i i y IR Fli T640 came a (Fli Sys ems AB, An enn ägen 6, 187 66 Täby, Sweden). The measu emen s o empe a u e we e co ela ed wi h he measu emen o s ain using he A0A amis sys em. Non-in asi e dis ance measu emen was pe o med wi h an accu acy o he mog aphic measu emen s in he ange o +/ − 2 ◦ C. The p incipal pa ame e s o he Fli T640 came a a e lis ed in Table 2. Table 2. Pa ame e s o a Fli T640 came a. Pa ame e Uni Value Resolu ion pixel 2048 ×1536 Measu ing ange ◦C−40 ÷+2000 Re esh a e Hz 30 The mal sensi i i y mK 30 2.5. Analysis o Va iance Quad a ic mul idimensional ANOVA was used o de e mine he ela ionship be ween ma e ial p ope ies (s ain ha dening exponen , yield s ess, sample o ien a ion), p ocess pa ame e s (s ain a e and pe cen age s ain) and he maximum empe a u e appea ing in he sample du ing he s e ching p ocess. The alues o he s ain ha dening exponen we e de e mined by app oxima ing ue s ess- ue s ain cu es using he well known Hollomon’s powe law. ANOVA is a s a is ical me hod o examining obse a ions ha depend on one o mo e ac o s ac ing simul aneously. Due o he di e en nume ical anges o he da a, hey we e no malised o he ange [ − 1, +1] [ 41 ]. The min-max no malisa ion was applied by means o a linea unc ion b inging he da a o a new in e al (Coded Low, Coded High). Explana o y a iables should be independen o each o he . The inpu da a we e i ed wi h a polynomial, and he in luence o indi idual a iables on he quali y o he model was checked using backwa d elimina ion. The minimum and maximum alues o he inpu a iables o samples made o 321 shee a e p esen ed in Table 3. In e media e alues o inpu pa ame e s we e coded p opo ionally in he ange [−1, +1]. Table 3. Fac o s and le els o analysis o a iance (ANOVA) o s e ching o specimens o 321 s eel. Pa ame e Name Uni Type Minimum Maximum A S ain ha dening exponen - Nume ic 0.35 0.392 BYield s ess MPa Nume ic 341 367 CS ain a e s−1Nume ic 4×10−316 ×10−3 DSample o ien a ion deg. Nume ic 0 90 EPe cen age s ain % Nume ic 12 117.7 The eg ession models ha we e buil we e subjec ed o signi icance es s. The me hod o backwa d elimina ion o a iables was used in he analysis. I is a a iable selec ion p ocedu e in which all he a iables a e en e ed in o he eg ession equa ion and hen emo ed sequen ially. The a iable wi h he lowes pa ial co ela ion wi h he dependen a iable is conside ed o emo al i s . I i mee s he elimina ion c i e ia, i is emo ed. The basis o emo ing o lea ing a gi en a iable in he model is he calcula ion o Fishe F s a is ics. The independen a iable wi h he highes p obabili y co esponding o he Fishe pa ame e F is emo ed om he model i he p obabili y pis su icien ly high ( ypically p= 0.10). A e he i s a iable is emo ed, he nex one o be emo ed is he Ma e ials 2021,14, 5259 6 o 15 one ha has he smalles pa ial co ela ion wi h he dependen a iable. The p ocedu e exi s when he e a e no o he a iables in he equa ion ha mee he emo al c i e ia. The signi icance o he eg ession model a a le el o α = 0.05 is de e mined based on he a iance due o he e ec o a ac o and he a iance due o he e o e m. 3. Resul s and Discussion 3.1. Expe imen al In es iga ions Figu e 3shows he e olu ion o he su ace empe a u e o he samples cu along he shee olling di ec ion o he 321 s eel du ing i s s e ching wi h di e en s ain a es. I is clea ly isible ha e en wi hin he ange o p opo ional de o ma ions he zone wi h he highes empe a u e is loca ed app oxima ely a he cen al poin be ween he g ippe s o he es ing machine. As a esul o hea con ec ion caused by in e nal ic ion o he ma e ial, an inc ease in he empe a u e o he samples was also obse ed in he pa ha is g ipped whe e no plas ic de o ma ion occu s. Inc easing he s ain a e esul ed in he in ensi ica ion o hea gene a ion. A he momen o he o ma ion o a necking a he highes s ain a e, he maximum sample empe a u e inc eased by mo e han 4 imes compa ed o he ini ial empe a u e. Simila conclusions can be d awn o he samples cu a an angle o 45◦wi h espec o RD and pe pendicula o RD (Figu e 4). Only pa o he mechanical ene gy is con e ed in o hea in he de o ma ion p ocess. The emainde is s o ed in he mic os uc u e o he ma e ial inc easing he in e nal ene gy o he ma e ial. The o al ene gy spen on de o ming an elas ic-plas ic ma e ial is equal o he wo k unde aken on elas ic ( e e sible) de o ma ion and pe manen (plas ic) de o ma- ion. Mo eo e , he ene gy consumed on plas ic de o ma ion is di ided in o hea dissipa ed in he o ming p ocess and ene gy s o ed in he ma e ial [ 42 – 44 ]. The e olu ion o he mic os uc u e du ing de o ma ion depends on he ype o ma e ial, he ini ial empe a u e and he loading si ua ion [ 45 , 46 ]. Changing he de o ma ion me hod usually leads o a pa ial o comple e econs uc ion o he disloca ion sys ems o med in he p e ious s ages o de o ma ion and he o ma ion o new sys ems [ 47 , 48 ]. The in e ac ion o he la ice de ec s is ela ed o he o e lapping o hei s ess ields. I he o e lap o s ess ields caused by de ec s educes he ene gy o he sys em, hen wi h a speci ic ac i i y o he espec i e slip sys ems, hese de ec s will o m con igu a ions complian wi h he p inciple o ene gy minimisa ion [49,50]. The plas ici y ma gin measu ed as he di e ence be ween ul ima e ensile s ess and ield s ess is mo e p onounced in he case o 321 s eel han o 17-4PH s eel. Figu e 5show he e ec o pe cen age s ain on he change in he maximum empe a- u e o he specimens o 321 s eel. These dependencies, de e mined by he de e mina ion coe icien R 2 , show a linea end wi h a high co ela ion alue R 2 > 0.93. In he case o he sample made om 321 s eel cu a an angle o 45 ◦ es ed a a s ain a e o 16 ×10−3s−1 , he las poin co esponds o he ad anced s age o sample necking. The e o e, he R 2 - alue o ha case is abou 0.9484 (Figu e 5c). In gene al, he highe he s ain a e he s eepe he end lines. The samples made o 321 s eel show aniso opic ea u es, which a e pa icula ly isible a a s ain a e o 8 × 10 −3 s −1 (Figu e 5b). T end lines o samples cu a di e en angles a e inclined a di e en angles wi h espec o he abscissa axis. T ue s ess-s ain cu es o 321 s eel de e mined a a ious s ain a es a e shown in Figu e 6. T ue s ain is de ined as ε : ε =lnl l0(2) whe e land l0a e he cu en and ini ial gauge leng hs, espec i ely. Ma e ials 2021,14, 5259 7 o 15 Ma e ials 2021, 14, x FOR PEER REVIEW 7 o 16 Figu e 3. In a ed (IR) he mog aphy images and digi al image co ela ion cha s o 321 s eel samples cu along he shee olling di ec ion, es ed a he ollowing s ain a es: (a) 4 × 10−3 s−1, (b) 8 × 10−3 s−1and (c) 16 × 10−3 s−1. Figu e 3. In a ed (IR) he mog aphy images and digi al image co ela ion cha s o 321 s eel samples cu along he shee olling di ec ion, es ed a he ollowing s ain a es: (a) 4 ×10−3s−1, (b) 8 ×10−3s−1and (c) 16 ×10−3s−1. Ma e ials 2021,14, 5259 8 o 15 Ma e ials 2021, 14, x FOR PEER REVIEW 8 o 16 Figu e 4. IR he mog aphy images and digi al image co ela ion cha s o 321 s eel samples cu pe pendicula o he olling di ec ion (RD), es ed a he ollowing s ain a es: (a) 4 × 10−3 s−1, (b) 8 × 10−3 s−1and (c) 16 × 10−3 s−1. Figu e 5 show he e ec o pe cen age s ain on he change in he maximum empe - a u e o he specimens o 321 s eel. These dependencies, de e mined by he de e mina ion coe icien R2, show a linea end wi h a high co ela ion alue R2 > 0.93. In he case o he sample made om 321 s eel cu a an angle o 45° es ed a a s ain a e o 16 × 10−3 s−1, he las poin co esponds o he ad anced s age o sample necking. The e o e, he R2- alue o ha case is abou 0.9484 (Figu e 5c). In gene al, he highe he s ain a e he s eepe he end lines. The samples made o 321 s eel show aniso opic ea u es, which a e pa - icula ly isible a a s ain a e o 8 × 10−3 s−1 (Figu e 5b). T end lines o samples cu a di e en angles a e inclined a di e en angles wi h espec o he abscissa axis. T ue s ess-s ain cu es o 321 s eel de e mined a a ious s ain a es a e shown in Figu e 6. T ue s ain is de ined as ε : Figu e 4. IR he mog aphy images and digi al image co ela ion cha s o 321 s eel samples cu pe pendicula o he olling di ec ion (RD), es ed a he ollowing s ain a es: ( a ) 4 × 10 −3 s −1 , (b) 8 ×10−3s−1and (c) 16 ×10−3s−1. Ma e ials 2021, 14, x FOR PEER REVIEW 9 o 16 𝜺𝒕=𝒍𝒏𝒍 𝒍𝟎 (2) whe e l and l0 a e he cu en and ini ial gauge leng hs, espec i ely. Figu e 5. In luence o s ain on empe a u e o 321 s eel samples es ed a he ollowing s ain a es: (a) 4 × 10−3 s−1, (b) 8 × 10−3 s−1 and (c) 16 × 10−3 s−1. Figu e 6. T ue s ess- ue s ain cu es o 321 s eel de e mined a he ollowing s ain a es: (a) 4 × 10−3 s−1, (b) 8 × 10−3 s−1 and (c) 16 × 10−3 s−1. 3.2. Analysis o Va iance (ANOVA) o 321 S eel Samples A quad a ic model con aining only s a is ically signi ican elemen s was chosen o i he expe imen al da a. The empe a u e esponse su ace o he 321 s eel specimens is gi en by: 𝑻=𝟕𝟔.𝟕𝟏−𝟏𝟖.𝟓𝟔𝑨−𝟏𝟎.𝟎𝟐𝑩−𝟒.𝟏𝟗𝑪+𝟒.𝟕𝟏𝑫+𝟒𝟖.𝟔𝟏𝑬−𝟒.𝟗𝟕𝑨𝑩 +𝟗.𝟓𝟖𝑨𝑪+𝟖.𝟐𝟕𝑨𝑫−𝟑𝟏.𝟒𝟏𝑨𝑬−𝟏𝟐.𝟗𝟗𝑩𝑪−𝟏𝟑.𝟏𝑩𝑬 −𝟐𝟏.𝟑𝟓𝑪𝑬−𝟏.𝟐𝟐𝑫𝑬+𝟏𝟑.𝟑𝟔𝑬𝟐 (3) The signi icances o he in luence o he indi idual ma e ial pa ame e s as well as he condi ions o he s e ching p ocess and hei in e ac ion in he eg ession model we e de e mined on he basis o he ANOVA. The quali y o i o he model ob ained o he alues measu ed o a gi en esea ch plan (Equa ion (3)) was hen de e mined on he basis o he de e mina ion coe icien s R2 and he F es . The signi icance o he model is con- i med by an F- alue o 53.30 (Table 4). This model can, he e o e, be used o p edic em- pe a u e alues based on ma e ial de o ma ion. The p obabili y ha such a la ge F- alue can esul om da a noise is only 0.01%. The p obabili y alues p o E, AE, CE, E2 ha a e less han 0.0500 p o e ha hese ac o s a e s a is ically signi ican . The pa ame e s he emo al o which will no educe Figu e 5. In luence o s ain on empe a u e o 321 s eel samples es ed a he ollowing s ain a es: ( a ) 4 × 10 −3 s −1 , (b) 8 ×10−3s−1and (c) 16 ×10−3s−1. Ma e ials 2021,14, 5259 9 o 15 Ma e ials 2021, 14, x FOR PEER REVIEW 9 o 16 𝜺𝒕=𝒍𝒏𝒍 𝒍𝟎 (2) whe e l and l0 a e he cu en and ini ial gauge leng hs, espec i ely. Figu e 5. In luence o s ain on empe a u e o 321 s eel samples es ed a he ollowing s ain a es: (a) 4 × 10−3 s−1, (b) 8 × 10−3 s−1 and (c) 16 × 10−3 s−1. Figu e 6. T ue s ess- ue s ain cu es o 321 s eel de e mined a he ollowing s ain a es: (a) 4 × 10−3 s−1, (b) 8 × 10−3 s−1 and (c) 16 × 10−3 s−1. 3.2. Analysis o Va iance (ANOVA) o 321 S eel Samples A quad a ic model con aining only s a is ically signi ican elemen s was chosen o i he expe imen al da a. The empe a u e esponse su ace o he 321 s eel specimens is gi en by: 𝑻=𝟕𝟔.𝟕𝟏−𝟏𝟖.𝟓𝟔𝑨−𝟏𝟎.𝟎𝟐𝑩−𝟒.𝟏𝟗𝑪+𝟒.𝟕𝟏𝑫+𝟒𝟖.𝟔𝟏𝑬−𝟒.𝟗𝟕𝑨𝑩 +𝟗.𝟓𝟖𝑨𝑪+𝟖.𝟐𝟕𝑨𝑫−𝟑𝟏.𝟒𝟏𝑨𝑬−𝟏𝟐.𝟗𝟗𝑩𝑪−𝟏𝟑.𝟏𝑩𝑬 −𝟐𝟏.𝟑𝟓𝑪𝑬−𝟏.𝟐𝟐𝑫𝑬+𝟏𝟑.𝟑𝟔𝑬𝟐 (3) The signi icances o he in luence o he indi idual ma e ial pa ame e s as well as he condi ions o he s e ching p ocess and hei in e ac ion in he eg ession model we e de e mined on he basis o he ANOVA. The quali y o i o he model ob ained o he alues measu ed o a gi en esea ch plan (Equa ion (3)) was hen de e mined on he basis o he de e mina ion coe icien s R2 and he F es . The signi icance o he model is con- i med by an F- alue o 53.30 (Table 4). This model can, he e o e, be used o p edic em- pe a u e alues based on ma e ial de o ma ion. The p obabili y ha such a la ge F- alue can esul om da a noise is only 0.01%. The p obabili y alues p o E, AE, CE, E2 ha a e less han 0.0500 p o e ha hese ac o s a e s a is ically signi ican . The pa ame e s he emo al o which will no educe Figu e 6. T ue s ess- ue s ain cu es o 321 s eel de e mined a he ollowing s ain a es: ( a ) 4 × 10 −3 s −1 , (b) 8 ×10−3s−1and (c) 16 ×10−3s−1. 3.2. Analysis o Va iance (ANOVA) o 321 S eel Samples A quad a ic model con aining only s a is ically signi ican elemen s was chosen o i he expe imen al da a. The empe a u e esponse su ace o he 321 s eel specimens is gi en by: T=76.71 −18.56A−10.02B−4.19C+4.71D+48.61E−4.97AB +9.58AC +8.27AD −31.41AE −12.99BC −13.1BE −21.35CE −1.22DE +13.36E2(3) The signi icances o he in luence o he indi idual ma e ial pa ame e s as well as he condi ions o he s e ching p ocess and hei in e ac ion in he eg ession model we e de e mined on he basis o he ANOVA. The quali y o i o he model ob ained o he alues measu ed o a gi en esea ch plan (Equa ion (3)) was hen de e mined on he basis o he de e mina ion coe icien s R 2 and he F es . The signi icance o he model is con i med by an F- alue o 53.30 (Table 4). This model can, he e o e, be used o p edic empe a u e alues based on ma e ial de o ma ion. The p obabili y ha such a la ge F- alue can esul om da a noise is only 0.01%. Table 4. Resul s o analysis o a iance o he eg ession model o 321 s eel samples. Sou ce Sum o Squa es Deg ees o F eedom Mean Squa e F-Value p-Value Meaning Model 8991.31 14 642.24 53.30 <0.0001 signi ican A—s ain ha dening exponen 26.04 1 26.04 2.16 0.1723 - B—yield s ess 39.77 1 39.77 3.30 0.0993 - C—s ain a e 0.5708 1 0.5708 0.0474 0.8321 - D—sample o ien a ion 13.38 1 13.38 1.11 0.3167 - E—plas ic s ain 989.76 1 989.76 82.14 <0.0001 - AB 1.11 1 1.11 0.0920 0.7679 - AC 9.23 1 9.23 0.7664 0.4019 - AD 22.41 1 22.41 1.86 0.2025 - AE 171.00 1 171.00 14.19 0.0037 - BC 4.45 1 4.45 0.3696 0.5568 - BE 36.85 1 36.85 3.06 0.1109 - CE 758.38 1 758.38 62.94 <0.0001 - DE 2.40 1 2.40 0.1992 0.6649 - E266.37 1 66.37 5.51 0.0409 - Residual 120.49 10 12.05 - - - Co To al 9111.80 24 - - - - The p obabili y alues p o E,AE,CE,E 2 ha a e less han 0.0500 p o e ha hese ac o s a e s a is ically signi ican . The pa ame e s he emo al o which will no educe he quali y o he model include, in e alia, C,AB,BC,DE. Due o he sa is ac o y alue o he