Flow Stress and Damage Behavior of C45 Steel over a range of Temperatures and Loading Rates

Transcription

1 Jounal of Engineeing teials an Technology. Reiv June 9, 216; mai post Dembe 2, 216. oi:1.1115/ ight (c) 216 by ASME Flow Stess an Damage Behavio of C45 Steel ove a ange of Tempeatues an Loaing Rates Fai H. Ab1, Mohamma H. Saffaini 1, Akum Abul-Latif2 an Geoge Z. Voyiajis3 Depatment of Civil Engineeing, Ameican Univesity of Shajah, UAE. 1 fab@aus.u Univesité Pais 8 IUT e Temblay-en-Fan, Dépatement GIM 3 ue e la Râpeie, Temblay-en-Fan 3 Depatment of Civil an Envionmental Engineeing, Louisiana State Univesity, USA 2 Abstact: This eseach aims to eibe the behavio of C45 steel an povie bette unestaning of the themo-mechanical uctile failue that occus ue to accumulation of mico-cacks an vois along with plastic efomation to enable pope stuctual esign; an hen povie bette seviability. A seies of quasi-static tensile tests ae conuct on C45 steel at a ange of tempeatues between 298 K an 923 K fo stain ates up to.15s-1. Dop hamme ynamic tests ae also pefom consieing iffeent masses an heights to stuy the mateial esponse at highe stain ates. Scanning electon micoo (SEM) images ae taken to quantify the ensity of mico-cacks an vois of each factu specimens which ae ne to efine the evolution of intenal efects using an enegy-bas amage moel. The coupling effect of amage an plasticity is incopoat to accuately efine the constitutive elation that can simulate the iffeent stuctual esponses of this mateial. Goo coelation was obsev between the popos moel pictions an expeiments paticulaly at egions whee ynamic stain aging is n pesent. Keywos: C45 steel; Tempeatue; Rate; nstitutive Moeling; Damage Downloa Fom: on 12/27/216 Tems of Use:

2 Jounal of Engineeing teials an Technology. Reiv June 9, 216; mai post Dembe 2, 216. oi:1.1115/ ight (c) 216 by ASME 1. Intouction ny eseach stuies an expeiments have been cai out in the past few ecaes to stuy the mateial behavio at elevat tempeatues an stain ates. Steel, in paticula, is one of the mateials that have been extensively stui fo that pupose ue to its wie use in the inusty. Reseaches have been tying to unestan an quantify expeimentally the paametes which eibe the themomechanical behavio of steel [1-8] incluing its amage behavio [9-12], an meically by eveloping constitutive equations to eibe the flow stess of iffeent types of mil an high stength steel [13-23]. The inteest of this eseach is to stuy the themomechanical behavio of C45 steel at elevat tempeatues an quasi-static stain ates. Steel supplies ae poviing C45 mainly to buil tools, machines, o stuctues that sustain impact loaing, shap cutting ges, coosion, bittle factue, an to povie high pefoman an welability. Also, this type of steel is known fo its wea esistan an ability fo quenching an tempeing. ny eseaches have ti in the past ecaes to cay out expeiments an analysis to stuy iffeent pespectives of C45 steel [24-34]. These stuies wee atteming to unestan the behavio of C45 steel in tems of fomability, effect of iffeent kins of posses such as heat teatment an cooling, Nano-stuctual behavio une impact loaing, istotion une cooling effect, behavio of the mateial when expos to lubication an coosion pection posses, vibation effect, fiction an wea popeties, sufa oughness, an machinability. Howeve, the latue lacks eseach elat to investigating the flow stess of C45 steel an its amage evolution. The cuently inceasing use of this type of steel as stuctual elements in the offshoe stuctues nessities the ne to stuy its constitutive behavio fo esign puposes. This eseach aims to fill this gap by conucting expeimental tests to investigate the stess-stain behavio of C45 steel une iffeent combinations of tempeatues an stain ates. In aition, Scanning Electon Micoo (SEM) images ae utiliz to quantify the ensity of mico-cacks an vois at factue. The SEM esults will be utiliz the evolution of mico-cacks an vois thoughout the inelastic i N it efomation using an enegy-bas amage moel [9]. Downloa Fom: on 12/27/216 Tems of Use:

3 Jounal of Engineeing teials an Technology. Reiv June 9, 216; mai post Dembe 2, 216. oi:1.1115/ ight (c) 216 by ASME 2. Expeimental Tests Results an Diussions The pesent expeimental pogam consies quasi-static tests at oom an high tempeatues, op-hamme tests at oom tempeatues an SEM images at factue. The mateial specimens wee mafactu fom thick stuctual C45 steel plate. The chemical composition of C45 steel us in this stuy is shown in Table 1. Table 1 Chemical composition of C45 steel nstituent C Mn Si S P Cu Ion ss % Bal Quasi-static tests at oom an high tempeatues Tensile coupon tests at oom tempeatue an thee iffeent stain ates of.15,.15, an.15 s -1 wee conuct using a Univesal Testing chine (UTM) with 1 kn capacity. Two specimens with the geomety shown in Figue 1 wee test fo each case. Figue 1: Geomety of the tensile test specimens at oom tempeatue with an aveage with w = 12 mm, thickness t = 1 mm an gauge length L = 57 mm. The measu stesses an stains wee eco an convet into tue stesses an tue stains as pesent in Figue 2. i N it Downloa Fom: on 12/27/216 Tems of Use:

4 Jounal of Engineeing teials an Technology. Reiv June 9, 216; mai post Dembe 2, 216. oi:1.1115/ ight (c) 216 by ASME s-1.15 s s Tue Tue 8 Figue 2: Tue stess-tue stain cuves at oom tempeatue fo iffeent stain ates As shown in Figue 2, the yiel stesses along with the ultimate stesses ae inceasing with the incease of the stain ate which is a typical ten of steel. It can also be nic that stain haening ten is simila egaless of the loaing ate an the main iffeen is the yiel point. In he wo, the stess stain cuves will be almost ientical if the yiel point is the same. The incease in yiel stess is intepet physically as the esistan of initial islocation by the Peiels baies povi by the latti itself [16]. The quasi-static tensile tests wee exten to investigate the mechanical esponse of C45 steel at highe tempeatues. Fo that pupose, thee tempeatues of 523 K, 723 K, an 923 K at two quasi- static loaing ates wee consie. The themal tests wee conuct using a UTM coupl with a heat chambe to apply the ne tempeatues. Two oun specimens with the geomety shown in Figue 3 wee test fo each themal test. Downloa Fom: on 12/27/216 Tems of Use:

5 Jounal of Engineeing teials an Technology. Reiv June 9, 216; mai post Dembe 2, 216. oi:1.1115/ ight (c) 216 by ASME Figue 3: Geomety of the tensile test specimens at high tempeatues with an aveage iamete of 6 mm an gauge length of 39 mm. The tue stess-tue stain cuves fo these high tempeatue tests ae shown in Figues 4 an 5 fo stain ates of.15s-1 an.15s-1, espectively K Tue K.8.1 Tue 8 Figue 4: Tue stess-tue stain cuves at high tempeatues fo stain ate of.15s-1 Downloa Fom: on 12/27/216 Tems of Use:

6 Jounal of Engineeing teials an Technology. Reiv June 9, 216; mai post Dembe 2, 216. oi:1.1115/ ight (c) 216 by ASME K K Tue K Tue Figue 5: Tue stess-tue stain cuves at high tempeatues fo stain ate of.15s-1 It can be nic fom Figue 4 fo stain ate of.15s-1 that the stesses ae geneally eceasing with the incease of tempeatue. The iffeen in the stain haening between tempeatues of 523 K an 723 K is inceasing with stain. Also, the plastic egion at tempeatue of 923 K is emaining ae en as athemal stesses [16] almost flat, which inicates that the stain haening at this high tempeatue level is iminish, an the The same obsevations can be mae on the tue stess-tue stain cuves shown in Figue 5 fo themal tensile tests pefom at stain ate of.15s-1. Howeve, it is clealy shown that the stesses fo the specimen at tempeatue of 723 K ae highe than the stesses at 523 K. Such a jump in the stess value is attibut to what is call the ynamic stain aging (DSA) phenomenon that is usually encounte in high stength fe an austen steel an at tain combinations of tempeatues an stain ates. It can be uc fom the above stess stain esults that the themal flow stess of C45 steel is mainly contoll by the yiel stess fo the ange of quasi static ates consie. The stain haening, on the he han, is mainly elat to the athemal pat of the flow stess at egions whee the DSA is inactive. Such behavio is simila to the flow stess of most of bcc metals an fe steel [16]. Downloa Fom: on 12/27/216 Tems of Use:

7 Jounal of Engineeing teials an Technology. Reiv June 9, 216; mai post Dembe 2, 216. oi:1.1115/ ight (c) 216 by ASME Dynamic Aging (DSA) coing to Wang et al. [35], ynamic stain aging is basically a phenomenon that occus ue to the inteaction between iffusing solute atoms an mobile islocations in the mateial. It usually occus afte citical stain at specific egime of stain ate an tempeatue. The authos stat that the ange of tempeatues at which this phenomenon occus is between 2% an 5% of the melting tempeatue. The effect of DSA can be expess in the mateial as seat flow, negative stain ate sensitivity, an peaks o plateaus on flow stess/tempeatue pls. Fo C45 steel, the DSA behavio can be clealy nic when the stesses vaiations with tempeatue ae plt fo iffeent stain levels as shown in Figue 6 an Figue 7 fo the lowe an highe stain ates consie. The peaks/jumps in the flow stess ae clealy nic at tempeatue of 523 K an patially at tempeatue 723 K fo stain ate of.15s-1 an at tempeatue of 723 K fo stain ate of.15s =.1 =.5 =.2 Yiel Point Tempeatue ( K) 1 2 Figue 6: Stess vaiations against tempeatue fo stain ate.15s-1 at vaious stain levels Downloa Fom: on 12/27/216 Tems of Use:

8 Jounal of Engineeing teials an Technology. Reiv June 9, 216; mai post Dembe 2, 216. oi:1.1115/ ight (c) 216 by ASME =.1 =.5 =.2 Yiel Point Tempeatue ( K) Figue 7: Stess vaiation against tempeatues fo stain ate.15s -1 at vaious stain levels 2.2. Dop hamme test The op hamme test is us to etemine the ynamic behavio of a sample at a stain ate in the oe of 12 s 1. Duing the test, a mass falls fom a given height on a sample tansfeing the pential enegy in the mass into kinetic enegy in the sample. Two cylinical specimens with a iamete of 8 mm an a height of 16 mm (Figue 8) wee test at oom tempeatue using two iffeent hamme masses of 28 kg an 56 kg opp fom heights of 4 m an 2 m espectively. This was one to ensue the same enegy fo two loaing ates equivalent to 39s-1 an 55s-1. Figue 8: Geomety of the op hamme test specimens Downloa Fom: on 12/27/216 Tems of Use:

9 Jounal of Engineeing teials an Technology. Reiv June 9, 216; mai post Dembe 2, 216. oi:1.1115/ ight (c) 216 by ASME The op hamme tests ae cai out using a ynamic loa ll of 2 tons an a lase beam isplament tansu as well as a 5g acleomete. These instuments ae connect to an acquisition chain that ensues the simultaneous ecoing of fo, isplament an acleation. In aition, two pholls ae us to assue the synchonization of the acquisition of these essential ata. The position of these pholls epesents one of the pincal ifficulties elat to the synchonization of the collect expeimental ata. The ata ecoing ne filteing especially the impact fo. The inetial effects ae assum negligible sin the impact velocities ae elatively low (lowe than 3 m/s) [36]. A filteing poss egaing the impact fo is achiev using the so call Chebyshev filte. Theefoe, the axial stess an stain ae comput via the filte impact fo an isplament, an convet into tue stess an tue stain, espectively as shown in Figue Hamme ss 28Kg Fom 4m Height - Tue Hamme ss 56Kg Fom 2m Height - Rate = 39s Tue.4.6 Figue 9: Tue stess-tue stain cuves fo op hamme test at stain ates of 39s-1 an 55s-1 It is ifficult to ientify a clea point which efines the yiel of the mateial an its flow stess behavio at such a test setup. This can be clealy nic in Figue 9 whee the cuves ae inceasing until they achieve the ultimate stess an then stat to eboun. The main iffeen between bh loaing enaios is the ultimate point achiev in which the ultimate stesses inceas with the incease of the stain ate Scanning Electon Micoo (SEM) Downloa Fom: on 12/27/216 Tems of Use:

10 Jounal of Engineeing teials an Technology. Reiv June 9, 216; mai post Dembe 2, 216. oi:1.1115/ ight (c) 216 by ASME This pat of the expeimental pogam is inten to chaacteize the mateial amage by possing the SEM images to estimate the ensity of mico cacks at factue. Fo each loaing conition, the factu sufa of each specimen afte each test was polish using a gine polish machine. A cut though the sample is ne to get clea factu sufas taking into consieation that the cut shoul be pefom slowly in oe n to heat the sample an to get a clea factu sufa without changing the mechanical popety of the sample, easing the cacks insie the sample, o even causing any futhe cacks [37]. Figue 1 pesents a sample of SEM images fo factu (b) (a) specimens at a stain ate of.15s-1 an vaious tempeatues. (c) () Figue 1: SEM images of factu amag sufas at iffeent tempeatues fo stain ate of.15s-1, a) T = 298 K, b) T = 523 K, c) T = 723 K, an ) T = 923 K Downloa Fom: on 12/27/216 Tems of Use:

11 Jounal of Engineeing teials an Technology. Reiv June 9, 216; mai post Dembe 2, 216. oi:1.1115/ ight (c) 216 by ASME The quantification esults fo the mateial amage in tems of ensity of mico-cacks an vois ae pesent in Figue 11. The ensity of cacks an vois was calculat by analyzing the SEM images by etecting the contast between the pixels which contain cacks an the pixels that on t contain cacks. In oe to obtain a goo aveage cack ensity, five to seven iffeent aeas on the factu sufa wee select an analyz [37]. The esults pesent in Figue 11 clealy explain the inceasing patten of the amage values with the incease of tempeatue an stain ates. These esults ae utiliz to ientify the mateial constants fo an enegy-bas amage moel as will be iuss.2 Damage Ф Damage Ф.8 T = 298 K T = 523 K T = 723 K T = 923 K.25 T = 298 K.1 next Rate Rate nstitutive Moeling Figue 11: Damage Ф at factue fo each ate of efomation at all tempeatues A coupl amage-plasticity constitutive moeling was consie in this stuy to eibe the flow stess of C45 steel. This was one by integating the enegy bas amage moel into the JC moel to accuately caue the stess stain behavio of C45 steel. The con of effective stess which elates the unamag an amag state of the mateial was us consieing isopic amage vaiable ϕ as shown in Eq. (1). In this case, the effective flow stess was calculat using the empiical elationsh of = σ Johnson-cook (JC moe) an the evolution of amage will be etemin accoing to Ab et al [9]. σ 1 ϕ (1) Downloa Fom: on 12/27/216 Tems of Use:

12 Jounal of Engineeing teials an Technology. Reiv June 9, 216; mai post Dembe 2, 216. oi:1.1115/ ight (c) 216 by ASME Whee σ is the effective stess in the boy which is calculat using the JC elationsh, ϕ is the amage facto, an σ is the stess of the amag boy Enegy-bas amage evolution moel As explain ealie, Ab et al. [8] evelop an enegy-bas moel that is capable of eibing the amage evolution in steel using the pincles of contium amage mechanics. The moel eibes the amage as the incease in the issat enegy of the mateial. The moel is expess as a function of the issat enegy atio to the tal issat enegy an the amage at factue as shown in equation (2): α Up ϕ = ϕ f (U ) (2) PT Whee ϕ is the amage at the point of inteest uing the efomation poss, ϕf is the amage at factue which is measu using SEM images (Figue 1), Up is the coesponing issat enegy at this point of inteest, UPT is the tal issat enegy, an the exponent α is a constant that etemines the ten of amage evolution thoughout the efomation poss. Sin most steel ten to have simila amage evolution ten, the value of the exponent α fo C45 steel is assum equal to 2. simila to the one obtain by Ab et al. [9]. The issat plastic enegy can be etemin using equation (3), whee σ an ε ae the tue ε (3) 𝑈𝑝 = p σεp stess an tue stain, espectively Figue 12 pesents the amage evolution esults fo C45 steel fo all loaing combinations consie. The amage gows with the incease of stain ate ex fo the case at tempeatue of 723 K. This coul be attibut to the stain aging phenomenon encounte that leas the mateial to gain moe stength at this loaing combination of tempeatue an stain ate. Also, the stain aging can be nic affecting the amage evolution at a tempeatue of 523 K. Oveall, the esults seem to be easonable an they seem to follow the ten that the high stength steel follows at these conitions [8]. Downloa Fom: on 12/27/216 Tems of Use:

13 Jounal of Engineeing teials an Technology. Reiv June 9, 216; mai post Dembe 2, 216. oi:1.1115/ ight (c) 216 by ASME It can also be nic fom Figue 12 that the amage effect stats to gow on highe ale at a tain stain point fo each case. At the beginning, the amage evolution is almost constant until a tain stain point at which the amage stats to gow faste, leaing to the egaation of the mateial. This is because the issat plastic enegy, which is epesent by the aea une the stess-stain cuve, is inceasing with stain until it eaches a value of high atio compa to the tal enegy. At that s s K.15s s-1.15s K.2.15s Damage Ф.1.15s-1.15s K s-1 Damage Ф 298 K Damage Ф Damage Ф.1 point, the amage effect stats to be nic clealy. Figue 12: Damage ϕ evolution in the mateial fo iffeent stain ates an tempeatues 3.2. Flow stess using JC moel ny flow stess moels have been evelop to eibe the mateials nonlinea behavio when expos to high stain ates an tempeatues. Some ae empiical o semi-empiical elations, while hes ae physically-bas shaing the same pupose of eibing the change in mechanical popeties of mateials when they expeien the accumulation of plastic efomation. They seve the pupose of poucing the mateial tue stess-tue stain cuves une iffeent loaing conitions. These moeling Downloa Fom: on 12/27/216 Tems of Use:

14 Jounal of Engineeing teials an Technology. Reiv June 9, 216; mai post Dembe 2, 216. oi:1.1115/ ight (c) 216 by ASME cons come fom the fact that the mechanical esponse epens on the ate of efomation as well as the evolving tempeatue. In this pape, the JC moel which was popos by Johnson an ok in 1983 [23] is consie to pict the flow stess of C45 steel. It is an empiical elation that eibes the flow stess in tems of stain, stain ate, an tempeatue as given by Eq. (4): σ = [A + B(ε p ) n ] [1 + C ln ( ἑ ) ] [1 ( T T ef ) m ] (4) ἑ o T melt T ef whee σ is the equivalent stess, ε p is the plastic stain, ἑ is the stain ate, ἑ o is the efeen stain ate, T is the tempeatue of the sample, T melt is the melting tempeatue of the mateial, T ef is the efeen tempeatue, A is the yiel stess of the mateial at a efeen efomation conitions, B is the stain haening constant, C is the stain ate stengthening coefficient, n is the stain haening constant, an m is the themal softening coefficient. The JC mateial constants fo C45 steel obtain using the expeimental esults pesent ealie ae list in Table 2. Table 2: JC paametes Paamete ε o (s -1 ) T ef ( K) T melt ( K) A (MPa) B (MPa) n C m Value In geneal, the JC moel shows acable compaisons at tain stain values an ealistically caues the nonlinea ten of C45 steel ove the ange of tempeatues an stain ates consie. Howeve, some eviation can be nic in egions whee the stain aging is active. Figue 13 shows a vey goo compaison between the stess-stain esults pict by the JC moel an expeiments at oom tempeatue. The coupl JC-Damage moel was capable of picting the values an tens of the stesses up to factue fo the thee iffeent loaing ates. On the he han, the moel was unable to caue the ynamic stain aging phenomenon encounte at tempeatues of 523 K an 723 K as clealy shown in Figues 14 an 15. As mention ealie, ynamic stain aging phenomenon is a vey i N it complicat poss an; theefoe, a physical-bas constitutive tem that is able to caue this incease in stength at the micostuctual level is equi. The DSA effect becomes active when the aging time is equal to the waiting time of mobile islocations which in tun inceases the obstacle stength by tain amount (i.e., jump) [15]. Theefoe, in oe to pict this stess incease, an Downloa Fom: on 12/27/216 Tems of Use:

15 Jounal of Engineeing teials an Technology. Reiv June 9, 216; mai post Dembe 2, 216. oi:1.1115/ ight (c) 216 by ASME aitional mathematical expession involving the DSA physical chaacteization is equi. Fo this eason, it is fai to say that the C45 mateial constants obtain in this stuy fo the JC moel is moe applicable at oom tempeatue conitions s EXPERIMENT Moel s c) b) a) EXPERIMENT Moel s Expeiment Moel Figue 13: Stess-stain cuves at T = 298 K fo stain ates of a).15s-1, b).15s-1, an c).15s-1 Downloa Fom: on 12/27/216 Tems of Use:

16 Jounal of Engineeing teials an Technology. Reiv June 9, 216; mai post Dembe 2, 216. oi:1.1115/ ight (c) 216 by ASME K Expeiment Moel Expeiement Moel b) a) 723 K 923 K 2 1 Expeiment c) a) Expeiment Moel b) Expeiment Moel K K 523 K 8 Figue 14: Stess-stain cuves fo stain ate.15s-1 at a) T = 523 K, b) T = 723 K, an c) T = 923 K Expeiment Moel c) Figue 15: Stess-stain cuves fo stain ate.15s-1 at a) T = 523 K, b) T = 723 K, an c) T = 923 K Downloa Fom: on 12/27/216 Tems of Use:

17 Jounal of Engineeing teials an Technology. Reiv June 9, 216; mai post Dembe 2, 216. oi:1.1115/ ight (c) 216 by ASME 3.3. Effect of amage. This section is inten to show an example of the effect of incluing the enegy-bas amage evolution on the oveall stess-stain esponse by iect compaison of the expeimental esults with JC moel piction with an without incluing the amage evolution. The compaison was conuct fo loaing enaios whee the moel cau the behavio almost sucssfully; i.e., n affect by the ynamic stain aging phenomenon. Hen, loaing enaios at oom tempeatue an 923 K fo loaing ates of.15s-1 an.15s-1 wee consie in this compaison as shown in Figue 16. The integation of the enegy bas amage moel into the JC equation suc in cauing the mateial.15s-1 at T = 298 K 6 4 EXPERIMENT Moel - Without Damage Moel - With Damage Expeiment Moel - Without Damage Moel - With Damage b) s-1 at T = 923 K 2 1 Expeiment Moel - Without Damage Moel - With Damage Expeiment Moel - Without Damage Moel - With Damage 2 c).24.15s-1 at T = 923 K a).15s-1 at T = 298 K softening behavio. ) Figue 16: mpaison between expeimental esults, JC moel, an coupl plasticity-amage JC moel fo a) ate =.15s-1 at T = 298 K, b) ate =.15s-1 at T = 298 K, c) ate =.15s-1 at T = 923 K, ) ate =.15s-1 at T = 923 K Downloa Fom: on 12/27/216 Tems of Use:

18 Jounal of Engineeing teials an Technology. Reiv June 9, 216; mai post Dembe 2, 216. oi:1.1115/ ight (c) 216 by ASME nclusion The C45 steel is inceasingly being us as stuctual mateial in the oil an gas inusty. The mateial esponse to typical loaing conitions expeienc in such envionment nes to be test an evaluat. Hen, a compehensive assessment of the themo-mechanical esponse of this type of high stength steel is timely an nessay fo esign puposes. This eseach stui the themo-mechanical behavio of C45 stuctual steel bas on the esults of a seies of expeimental tests that wee conuct at iffeent levels of tempeatues (298 K 923 K) at stain ates. The coesponing tue stess-tue stain esults wee utiliz to ientify the mateial constants fo constitutive moeling which is equi to unestan quantitatively the efomation behavio of this mateial. Scanning electon micoo (SEM) was utiliz to unestan the micostuctue of the mateial an measue the intenal mico-cacks an vois fo C45 steel at factue fo each test conition. The SEM esults wee then implement in an enegy-bas amage moel to efine the evolution of amage thoughout the efomation poss. The amage moel was integat into the JC plasticity moel to eibe the flow stess of C45 steel. The following conclusions can be awn: - The quasi-static tests esults at high tempeatues eveal the typical egaation ten of the themal stesses with tempeatue incease. Howeve, ynamic stain aging (DSA) took pla at tain combination of tempeatues an stain ates. The DSA is usually chaacteiz by the suen jump in the themal stess vaiation with tempeatue. This DSA phenomenon was clealy obsev at 523 K fo the case of.15s -1 stain ate an at 723 K fo the highe ate. - The yiel stess inceas with the incease of stain ate an eceas with tempeatue ex in the egions whee the DSA is active. On the he han, the stain haening was foun to be almost ate-inepenent at oom tempeatue. Howeve, the ate epenency behavio of the mateial inceas with tempeatue. - A constitutive eiion of C45 steel is equi to simulate the flow stess of the mateial. In this eseach, the empiical elation of JC constitutive moel was select to eibe the i N it mateial esponse. The DSA effects; howeve, wee n cau by this moel. - The enegy-bas amage moel cau the amage evolution within the micostuctue of the mateial an the failue moe beyon the ultimate point. Downloa Fom: on 12/27/216 Tems of Use:

19 Jounal of Engineeing teials an Technology. Reiv June 9, 216; mai post Dembe 2, 216. oi:1.1115/ ight (c) 216 by ASME The application of this eseach outcome is limit to the loaing conitions consie in the pesent expeimental pogam to get accuate esults. Any he enaios inten to be implement shall consie futhe expeimental tests an exploation. Also, the DSA phenomenon shoul be stui futhe in oe to unestan its effect on the mateial esponse. To caue such effect, a physicalbas constitutive moel shoul be evelop to accuately eibe the plasticity behavio of C45 steel. The moel shoul be able n only to aess the plastic efomation that is attibut to the mion of islocations but also to inclue the plastic flow in the ange of tempeatues an stain ates whee iffusion an ceep ae ominant, i.e., the egions whee DSA is active. i N it Downloa Fom: on 12/27/216 Tems of Use:

20 Jounal of Engineeing teials an Technology. Reiv June 9, 216; mai post Dembe 2, 216. oi:1.1115/ ight (c) 216 by ASME Refeens: 1. S. Nemat-Nasse, W. Guo, Themomechanical esponse of HSLA-65 steel plates: expeimental an moeling, Mechanics of teial, vol. 37, no. 5, pp , y Celentano, Diego J., an Jean-Louis Chaboche. 'Expeimental An Numeical Chaacteization Of Damage Evolution In Steels'. Intenational Jounal of Plasticity (27): S. Nemat-Nasse an W. Guo, Themomechanical esponse of DH-36 stuctual steel ove a wie ange of stain ates an tempeatues, Mechanics of teials, vol. 35, no. 11, pp , Guo, Wei-Guo, an Sia Nemat-Nasse. 'Flow Stess Of Nitonic-5 Stainless Steel Ove A Wie Range Of Rates An Tempeatues'. Mechanics of teials (26): Nemat-Nasse, Sia, Wei-Guo Guo, an Davi P. Kihl. 'Themomechanical Response of AL-6XN Stainless Steel ove a Wie Range of Rates An Tempeatues'. Jounal of the Mechanics an Physics of Solis 49.8 (21): Su, J. et al. 'Plastic Behavio An nstitutive Relations Of DH-36 Steel Ove A Wie Spectum Of Rates An Tempeatues Une Tension'. Mechanics of teials 65 (213): Vaynman, S. et al. 'Effect Of Rate An Tempeatue On Mechanical Popeties An Factue Moe Of High Stength Pecitation Haen Feitic Steels'. Scia teialia 55.4 (26): Roh, I., H. Nahme, an K. Thoma. 'teial Chaacteization An nstitutive Moelling Of Ductile High Stength Steel Fo A Wie Range Of Rates'. Intenational Jounal of Impact Engineeing 31.4 (25): Ab, Fai H., Ail K. Al-Tamimi, an Reem M. Al-Himaiee. 'Chaacteization an Moeling of Ductile Damage in Stuctual Steel at Low an Intemiate Rates'. Jounal of Engineeing Mechanics (212): B. Daas, F. Ab, S. Pevaiz an A. Abu-Latif, "Analysis of amage in 583 alumim alloy efom at iffeent stainates", teials Scien an Engineeing: A, vol. 568, pp , 213. i N it 11. Chae, D., an D.A. Koss. 'Damage cumulation An Failue Of HSLA-1 Steel'. teials Scien an Engineeing: A (24): Al-Himaiee, Reem je, Fai Hami Ab, an Ail K. Al-Tamimi. 'Damage Evolution In Stuctual Steel At Diffeent Loaing nitions'. KEM (211): Downloa Fom: on 12/27/216 Tems of Use:

21 Jounal of Engineeing teials an Technology. Reiv June 9, 216; mai post Dembe 2, 216. oi:1.1115/ ight (c) 216 by ASME 13. F. Ab an F. kaem, 'mpaisons of nstitutive Moels fo Steel Ove a Wie Range of Tempeatues an Rates', J. Eng. te. Technol., vol. 134, no. 2, p. 211, D. Go, R. Gaett, J. Binget, S. Chen an G. Gay, 'The mechanical theshol stess constitutivestength moel eiion of HY-1 steel', Metall an t Tans A, vol. 31, no. 8, pp , F. Ab, S. Ranganathan an M. Sey, 'nstitutive moeling of nitogen-alloy austenitic stainless steel at low an high stain ates an tempeatues', Mechanics of teials, vol. 77, pp , Fai H. Ab, nstitutive moeling of the mechanical behavio of high stength feitic steel fo static an ynamic applications, Mechanics of Time- Depenent teials Jounal, vol. 14, pp , B. Banejee, 'The Mechanical Theshol Stess moel fo vaious tempes of AISI 434 steel', Intenational Jounal of Solis an Stuctues, vol. 44, no. 3-4, pp , Lee, Y et al. 'A Stuy Fo The nstitutive Equation Of Cabon Steel Subject To Lage s, High Tempeatues An High Rates'. Jounal of teials Possing Technology (22): F. Ab, F. kaem an G. Voyiajis, "Dynamic Localizations in HSLA-65 an DH-36 Stuctual Steel at Elevat Tempeatues", J. Eng. te. Technol., vol. 135, no. 2, p. 217, F. kaem an F. Ab, "Nonlinea fin element moeling of ynamic localizations in high stength steel columns une impact", Intenational Jounal of Impact Engineeing, vol. 52, pp , F. Ab, "On the iffeens of ynamic localizations between iffeent types of metals", IJMSI, vol. 4, no. 234, p. 215, G. Voyiajis an F. Ab, "Tansient localizations in metals using micostuctue-bas yiel sufas", Moelling an Simulation in teials Scien an Engineeing, vol. 15, no. 1, pp. S83- S95, G.R. Johnson, W.H. ok, A constitutive moel an ata fo metals subject to lage stains, high stain ates an high, Poings of the 7thIntenational Symposium on Ballistics, , etiev 29. i N it Downloa Fom: on 12/27/216 Tems of Use:

22 Jounal of Engineeing teials an Technology. Reiv June 9, 216; mai post Dembe 2, 216. oi:1.1115/ ight (c) 216 by ASME 24. Chen, Haifeng, Jinyuan Tang, an Wei Zhou. 'An Expeimental Stuy Of The Effects Of Ultasonic Vibation On Gining Sufa Roughness Of C45 Cabon Steel'. Int J Av f Technol (213): 'Influen of Heating Rate on Sobitic Tansfomation Tempeatue of Tempeing C45 Steel'. Achives of Founy Engineeing 11.Special Issue 2/211 (211): Kemouche, G, an C Langlae. 'Mechanical Nano-Stuctuation Of A C45 Steel Une Repeat Nomal Impacts'. IOP nfeen Seies: teials Scien an Engineeing 63 (214): Kól, S. et al. 'Fiction An Wea Popeties Of Titanium An Oxiis Titanium In Dy Sliing Against Haen C45 Steel'. Jounal of teials Possing Technology (24): Leppet, Taeusz. 'Effect Of oling An Lubication nitions On Sufa Topogaphy An Tuning Poss Of C45 Steel'. Intenational Jounal of chine Tools an factue 51.2 (211): gnaboo, I. et al. 'Inuction Heat Teatment Of A ISO C45 Steel Ba: Expeimental An Numeical Analysis'. mputational teials Scien 35.2 (26): Michalik, Pete et al. 'Monitoing Sufa Roughness Of Thin-Wall mponents Fom Steel C45 chining Down An Up Milling'. Measuement 58 (214): Rajanna, K., B. Pathiaj, an B.H. Kolste. 'Some Stuies On The Influen Of Stess Ratio An Test Tempeatue On X-Ray Factogaphy Obsevations In C45 Steel Specimens'. Engineeing Factue Mechanics 54.4 (1996): SeeamaRy, T.V. et al. 'chinability Of C45 Steel With Deep Cyogenic Teat Tungsten Cabie Cutting Tool Insets'. Intenational Jounal of Refactoy Metals an Ha teials 27.1 (29): Szkoo, M. 'Relationsh Between Micostuctue Of Lase Alloy C45 Steel An Its Cavitation Resistan'. Jounal of teials Possing Technology (25): Yan, P.X et al. 'Post Boonizing Ion Implantation of C45 Steel'. Appli Sufa Scien (22): T. Wang, J. Jonas, H. Qin an S. Yue, "Effect of ynamic stain aging on the efomation an twinning behavio of a Mg 2Zn 2N alloy", teials Scien an Engineeing: A, vol. 645, pp , 215. i N it Downloa Fom: on 12/27/216 Tems of Use:

23 Jounal of Engineeing teials an Technology. Reiv June 9, 216; mai post Dembe 2, 216. oi:1.1115/ ight (c) 216 by ASME 36. Callaine C. R. an English R. W., ate an inetia effect in the collapse of the two types of enegy-absobing stuctue, Intenational Jounal of Mechanical Scien: vol. 26, pp , Saffaini, M. "Themo-Mechanical Behavio Of C45 Steel Ove A Range Of Tempeatues An Loaing Rates", ste thesis, Ameican Univesity of Shajah, 216. i N it Downloa Fom: on 12/27/216 Tems of Use: