Investigation on Uniaxial Tensile Instability of USIBOR1500 Steel Sheets at Elevated Temperature

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1 94 CHINESE JOURNAL OF MECHANICAL ENGINEERING Vo. 23,aNo.,a200 DOI: 0.390/CJME , avaiabe onine at Investigation on Uniaxia Tensie Instabiity of USIBOR500 Stee Sheets at Eevated Temperature MIN Junying, *, LIN Jianping, TIAN Haobin 2, SUN Guohua, and XU Zhou Coege of Mechanica Engineering, Tongji University, Shanghai 20804, China 2 Coege of Mechanica and Eectrica Engineering, Shanghai Second Poytechnic University, Shanghai 20209, China Received February 7, 2009; revised September 2, 2009; accepted September 22, 2009; pubished eectronicay February 20, 200 Abstract: In the sheet forming process with stretch, diffuse instabiity and ocaized instabiity usuay occur in the process one after another. The necking rate has a great impact on the instabiity process and the forming imits of the rate sensitive materia, such as USIBOR500 stee sheets at eevated temperature. The avaiabe reports about this stee mainy focus on hot uniaxia tensie, martensitic transformation and forming process, but there are few investigations on instabiity behavior and forming imits. Based on Inoue Kachiro s fow stress constitutive mode at eevated temperature, combined with Swift s diffuse instabiity rue and Hi s ocaized instabiity rue, the reation is theoreticay deduced between the diffuse necking rate aong with the ocaized necking rate and the exponent of strain rate sensitivity together with the strain rate in the case of the USIBOR500 stee sheets at eevated temperature. According to the time temperature characteristics of the hot stamping process, tensie tests of the stee sheets were carried out on Geebe3800, and the stress strain curves were obtained at different temperatures and different strain rates. Then the vaues of the exponent of strain rate sensitivity and the hardening exponent were obtained through fitting the curves by east squares. The tests aso heped to provide the distribution aws of the major strain of the specimens and the uniform strains as we as the necking width. The uniform strains obtained from the tests are matched we with the theoretica cacuations. Key words: USIBOR500, uniaxia tensie, instabiity, uniform strain, necking rate Introduction * Mechanica properties and forming imits are especiay important in hot forming of sheet meta, and the necking, as a typica phenomenon of the oca deformation, is one of the indications of mechanica properties []. Since the stee is rate sensitive at eevated temperature, the investigations on the diffuse instabiity and ocaized instabiity of USIBOR500 stee sheet under uniaxia tension at eevated temperature is significant. In the sheet forming process with stretch, the diffuse instabiity, namey the diffuse necking, first occurs and then the ocaized instabiity, namey the ocaized necking, occurs unti fracture. Three forming imit curves(flcs) can be obtained by regarding the diffuse instabiity, the ocaized instabiity and the fracture as imits respectivey. The FLC from the diffuse instabiity is the owest and safest, but the beginning of the diffuse instabiity is difficut to be determined in experiments. The FLC from the ocaized instabiity and the FLC form fracture are commony used [2]. The difference between the FLCs from the ocaized instabiity and diffuse * Corresponding author. E-mai: dabao_070@hotmai.com This project is supported by New Energy Vehice Specia Project of Shanghai Science & Technoogy Piar Program of China (Grant No. 08DZ50305) instabiity is reativey great for rate sensitive materia, and the necking rate has a great infuence on this difference. The ower the necking rate is, the greater the distance is. According to Ref. [3], the necking rate is a critica factor of the tensie stabiity and aso directy affects the eongation. The necking rate was investigated eariest by HART [4], since then, more and more schoars have been interested in the research on the necking rate [5 7]. The investigation into the mechanica properties of the hot forming technoogy of USIBOR500 utrahigh strength stee has aroused the interest of many schoars, and there has been many reports about tensie tests of the stee at high temperature [8 0]. However, these investigations have not invoved the necking behavior. In the foowing sections, based on Inoue Kachiro s fow stress constitutive mode at eevated temperature, the reation is theoreticay deduced between the diffuse necking rate aong with ocaized necking rate and the exponent of strain rate sensitivity m together with the strain ratee& in the present study, and tensie tests of USIBOR500 stee sheets at eevated temperature were performed on Geebe3800. The necking behavior of the stee sheets is investigated at different temperatures and different strain rates. The distribution aws of the major strain of the specimens and uniform strain as we as necking widths wi be aso obtained from experiments.

2 CHINESE JOURNAL OF MECHANICAL ENGINEERING 95 2 Uniaxia Tensie Instabiity Anaysis of USIBOR 500 Stee Sheets 2. Theoretica anaysis of instabiity Inoue Kachiro used Eq. () to mode thes -e reation of metas we at high temperature: D A& A D& e =- D & e - & e = - & e. D e After differentia of Eq. (2), we obtain (7) Ds De D& e = n + m. (8) s e & e n m æb ö s = ke & e exp ç, è T ø () According to the condition of Swift s diffuse instabiity [], there is where σ is the true stress, ε is the true strain,e& is the strain rate, T is temperature, and k, n, m, b are materia constants. Since the process of pastic instabiity is finished quicky, namey, the temperature variation is very sma during the pastic instabiity, here we suppose the temperature varies itte, and T is a constant. Then Eq. () can be simpified as n m s = K e & e, (2) Ds = s. De After insertion of Eq. (9) into Eq. (8), we obtain n - D & e e = & e. De m (9) (0) where K = kgexp( b / T ). Due to that the voume is unchanged in the pastic deformation, there is Ag = constant, (3) where A is the cross-section area, and is the ength of the sheet meta. After derivative to time of both sides of Eq. (3), we can obtain According to true strain formua, there is A& =- A &. (4) e = n. After derivative, e& can be expressed as foows: 0 After insertion of Eq. (0) into Eq. (7), we can rewrite Eq. (7) as foows: n - m- D A& = m e & e. () According to the theory of Hi s ocaized instabiity [], the hardening rate of the materia equas the reduction rate of its thickness, there is the foowing expression: Ds s i i Dt =- t, (2) where t is the thickness of the sheet meta, in uniaxia tensie due to s = s, D t =D =- t + r i e i = e, e3 D e and then Eq. (2) can be expressed as, & e æ ö dç n dt dt gdt. de è 0 ø d = = = = & (5) Ds = e. (3) s + r After insertion of Eq. (3) into Eq. (8), we obtain After insertion of Eq. (5) into Eq. (4), we can rewrite & A as A& =-A &. (6) Assuming the cross-section area is A+ at the necking pace, where is a negative vaue, it can be obtained after differentia of Eq. (6): e D & e & eæ n ö = ç -. D e mè+ r eø Substituting Eq. (4) into Eq. (7), we can obtain n - m- D A& + r = m e & e. (4) (5)

3 96 MIN Junying, et a: Investigation on Uniaxia Tensie Instabiity of USIBOR500 Stee Sheets Yat Eevated TemperatureY 2.2 Discussion According to HART s rue [4], if the vaue of the cross-section area difference does not increase during deformation, namey, the necking rate is ess than or equa to 0: D &A 0, (6) then the deformation is stabe; when the diffuse instabiity occurs, namey the diffuse necking begins, the necking rate is greater than 0: Tabe. Chemica composition of USIBOR 500 Aoy eements Content w/% C Mn.2 0 P S Si A Ti B Cr D &A > 0. After insertion of Eq. (6) into Eq. (), we can obtain the foowing equation: Fig.. Sketch of specimen used in tests ṉ e D =, m (7) where ε D is just the uniform strain and the condition of the diffuse instabiity when it occurs. We can find out the reationship among the diffuse necking rate, m, n, and e& from Eq. (). m has greater effect on the diffuse necking rate due to that m is ess than, and the diffuse necking rate varies inversey with m but directy to the strain rate. As the same, when the ocaized instabiity occurs, the expression D&A / performs as the ocaized necking rate. Substituting Eq. (6) into Eq. (5), we can obtain the foowing equation: n( + r) el =, - m( + r) (8) where ε L is just the strain condition of the ocaized instabiity when it occurs. We aso can find out the reationship among the ocaized necking rate, m, n, ande& from Eq. (5). m has greater effect to the ocaized necking rate due to that m is ess than, and the ocaized necking rate varies inversey with m but directy to the strain rate. 3 Uniaxia Tensie Tests of USIBOR 500 Stee Sheets at Eevated Temperature 3. Specimens The sheet meta used in tests is USIBOR500 stee sheets produced by Arceor. Its chemica composition is shown in Tabe. Its thickness is.7 mm, and it aso has roing state. The dimensions of the specimens are shown in Fig.. Since the materia USIBOR500 exhibits no significant dependence on the roing direction at eevated temperature, we ony use the specimens whose ength direction is in the roing direction. 3.2 Testing equipment Geebe3800 thermo-mechanica simuation system is chosen in tests. 3.3 Testing approach Two thermocoupes shoud be spot-weded to the midde of the specimens in advance. Then the specimens are fixed to the camping apparatuses of the machine and the uniaxia hot tensie tests are to be carried out. The deformation is performed in isotherma conditions. The testing temperature fow is: heating specimens to 900 with a cooing rate of 5 /s, and preserving heat for about 5 min for soaking austenitization, then cooing the specimens to the testing temperature with 80 /s and hoding for 5 s, after that performing isotherma tensie tests ti fracture, at ast cooing fast to the room temperature. Since the bainite transference wi occur beow 650 [2], the testing temperatures are respectivey set as 700, 800, 900 and the materia is in austenite state, where the specimens whose testing temperature is 900 have no cooing after austenitization. Then the width h of the specimens are measured from the break per mm aong the ength direction, and the minor strain e2 can be cacuated by e 2 = n( h / h0 ), and the major strain e can aso be cacuated by e =- ( r+ ) ge2 / r in uniaxia tensie, where r is the coefficient of thickness anisotropy. Its vaue can be seen from Ref. [3]. Then we can obtain the major strain distribution of the specimens. 4 Resuts and Anaysis 4. Stress-strain curves at eevated temperature Fig. 2 shows the true stress-strain curves at different temperatures when strain rates are 0.02/s, 0.2/s, /s, respectivey. We can obtain Tabe 2 by using of Inoue

4 CHINESE JOURNAL OF MECHANICAL ENGINEERING 97 Kachiro s fow stress constitutive mode and the east squares. 4.2 Major strain distribution of specimens and anaysis of the pastic instabiity LI, et a [4], have theoreticay eucidated that there is no absoutey uniform strain in uniaxia tensie in their investigation on the pastic instabiity. DU, et a [5], have described the necking deformation with two indexes of the imit strain and the necking width, where the necking width is determined as foows: given a sma vaue θ, twice of x N corresponding to the point, where the incuded ange of tangent and X-axis is θ, is the necking width, and ε N is the uniform strain (see Fig. 3). Fig. 3. Sketch of the major strain distribution Strain Fig. 2. Tabe 2. Infuence of the temperature on stress-strain curves at different strain rates Vaues n and m at different temperatures and strain rates Materia constant rate e& /s n m n m n m It can be seen from Tabe 2 how the temperature and the strain rate affect the vaue n and m. The vaue n decreases with the increasing of the temperature and the strain rate, but the vaue m increases Infuence of the temperature on the uniaxia tensie instabiity of the stee sheets Fig. 4 shows the major strain distributions of specimens at different temperatures whene& equas to 0.2/s. According to the uniform strain of Eq. (7), inserting the vaue n and m in Tabe 2 into it, we can see that the vaues of the theoreticay cacuated uniform strains get we with the vaues measured from tests (see Fig. 5). It can be seen from Figs. 4 and 5, when the strain rate is constant, the imit strain and necking width increase when the temperature increases, but the uniform strain decreases, where the necking width at 700, 800 and 900 are 4 mm, 8 mm and 28 mm, respectivey, and we can see from specimen photos that the break is aso narrow and thin. This is coincident with the resuts of theoretica anaysis in the section 2.2, because according to Tabe 2, the vaue is greater when the temperature is higher, and the diffuse necking rate wi be ower in accordance with Eq. (). The deformation is more sufficient, and the necking region of the specimens is onger and narrower. The ocaized necking rate wi be ower in accordance with Eq. (5), and the break of the specimens wi be narrow and thin, and the rate of section shrinkage is greater Infuence of the strain rate on the uniaxia tensie instabiity of the stee sheets Fig. 6 shows the major strain distributions of specimens when the testing temperature is 800 and the strain rates are 0.02/s, 0.2/s, /s, respectivey.

5 98 MIN Junying, et a: Investigation on Uniaxia Tensie Instabiity of USIBOR500 Stee Sheets Yat Eevated TemperatureY Fig. 6. Major strain distribution at different strain rates and specimen photos Inserting the vaue n and m in Tabe 2 into Eq. (8), we can see that the vaues of the theoreticay cacuated uniform strain go we with the vaues measured from tests too (see Fig. 7). Fig. 7. Uniform strain of the theoreticay cacuations and measured vaues Fig. 4. Major strain distributions at different temperatures and the specimen photos Fig. 5. Uniform strains of the theoretica cacuations and measured vaues It can be seen from Figs. 6 and 7, when the testing temperature is constant, the imit strain decreases with increasing of the strain rate, but the uniform strain increases, and we can see from specimen photos that the break is wide and thick. This is coincident with the resuts of the theoretica anaysis in the section 2.2 too, because a greater strain rate is beneficia to the uniform deformation. According to Eq. (), the diffuse necking rate wi be greater and the necking region of the specimens becomes short and wide. The ocaized necking rate wi be aso greater in accordance with Eq. (5) and the break of the specimens, whose rate of section shrinkage is smaer, wi be wide and thick.

6 CHINESE JOURNAL OF MECHANICAL ENGINEERING 99 5 Concusions () Based on Inoue Kachiro s fow stress constitutive mode at eevated temperature, combined with Swift s diffuse instabiity rue and Hi s ocaized instabiity rue, the reation is theoreticay deduced between the diffuse necking rate aong with the ocaized necking rate and the exponent of strain rate sensitivity m together with strain ratee& of the USIBOR500 stee sheets. It indicates that the diffuse and ocaized necking rates are in inverse reation to the exponent of strain rate sensitivity, but proportiona to the strain rate; (2) According to the time-temperature characteristics of hot stamping process, tensie tests of USIBOR500 stee sheets were carried out on Geebe3800, and the stress-strain curves were obtained in a strain rate range (0.2 /s) and a temperature range ( ). The vaues of the exponent of strain rate sensitivity and the hardening exponent in the corresponding test conditions were obtained through fitting the curves by east squares. (3) The distribution aws of the major strain of the specimens and the uniform strains as we as the necking widths were aso obtained, when the strain rate is 0.2/s but the temperature range is and when the temperature is 800 whie the range of e& is 0.02 /s. The theoreticay cacuated uniform strains go we with the vaues measured from tests. (4) According to the two indexes describing the necking deformation raised by DU, et a, the imit strain and the necking width, as we as the characteristic of the break, the testing resuts indicate that, when the strain rate is constant, the imit strain and the necking width increase with the temperature, but the uniform strain decreases, and the rate of section shrinkage is greater; when the temperature is unchanged, the uniform strain increases with the strain rate, but the imit strain and the rate of section shrinkage reduce. References [] WANG Xuebin, YANG Mei, PAN Yishan. Anaysis of necking under condition of uniaxia tension of ow-carbon stee specimen based on gradient-dependent pasticity[j]. Journa of Pasticity Engineering, 2002, 9(3): (in Chinese) [2] SUO Zhongin. Mechanica anaysis on necking diffusion in uper pastic tension deformation[j]. Journa of Changchun University of Science and Technoogy (Nationa Science Edtion), 2006, 29(2): (in Chinese) [3] LIANG Bingwen, CHEN Xiaodai, WANG Zhiheng. Forming properties of sheet meta[m]. Beijing: China Machine Press, 996. (in Chinese) [4] HART E W. Theory of the tensie test[j]. Acta Metaurgic, 967, 5: [5] HUANG Z Q, LEE L. Dynamic necking of an eastic-pastic cyinder under uniaxia stretching[j]. Inter. Journa of Soids and Structures, 984, 20: [6] JOUVE D. Dynamic pastic necking instabiities for a biaxiay pued pate[c]//proceedings of the 8th Internationa Conference on Mechanica and Physica Behaviour of Materias under Dynamic Loading, EURODYMAT 2006, Dijon, France, Sep. 4, 2006: [7] HITOSHI M. Criterion and mode of the forming imit in sheet forming[j]. Journa of Materia Processing Technoogy, 992, 3(3): [8] MERKLEIN M, LECHLER J, GEIGER M. Characterization of the fow properties of the quenchenabe utra high strength stee 22MnB5[J]. CIRP Annas-Manufacturing Technoogy, 2006, 55(): [9] NADERI M, BLECK W. An investigation into martensitic transformation in hot stamping process[j]. Computationa Methods and Experiments in Materias Characterization III, WIT Transactions on Engineering Sciences, 2007, 57: [0] TURETTA A, BRUSCHI S, GHIOTTI A. Investigation of 22MnB5 formabiity in hot stamping operations[j]. Journa of Materia Processing Technoogy, 2006, 77( 3): [] HU Shiguang, CHEN Hezheng. Engineering anaytic of sheet meta forming[m]. Beijing: Beijing University of Aeronautics and Astronautics Press, (in Chinese) [2] BERND-ARNO B, PHILLIPP O. Consideration of phase transformations in numerica simuation of press hardening[j]. Stee Research Internationa, 2007, 78(0 ): [3] MERKLEIN M, LECHLER J, GODE V, et a. Mechanica properties and pastic anisotropy of the quenchenabe high strength stee 22MnB5 at eevated temperatures[c]//proceedings of the 2th Internationa Conference on Sheet Meta, Paermo, Itay, Apr. 4, 2007: [4] SUOBEN, CUI Lingjiang, YU Lianzhong, et a. A study on the pastic instabiity in uniaxia tesion of sheet meta[j]. Forging & Stamping Technoogy, 989, : 5 9. (in Chinese) [5] DU Song, HU Shiguang. Construction of equiibrium equation and determination of uniaxia tensie strain distribution[j]. Forging & Stamping Technoogy, 987, 4: 2 8. (in Chinese) Biographica notes MIN Junying, born in 986, is currenty a PhD candidate in Coege of Mechanica Engineering, Tongji University, China. His research interests incude sheet meta forming and autobody ight-weighting. E-mai: dabao_070@hotmai.com LIN Jianping, born in 958, is currenty a professor and a PhD supervisor in Coege of Mechanica Engineering, Tongji University, China. His research interests incude sheet meta forming and autobody ight-weighting. E-mai: jpin58@tongji.edu.cn TIAN Haobin, born in 975, is currenty an associate professor in Coege of Mechanica and Eectronic Engineering, Shanghai Second Poytechnic University, China. Her research interest incudes sheet meta forming. E-mai: haobint@hotmai.com SUN Guohua, born in 983, is currenty a master candidate in Coege of Mechanica Engineering, Tongji University, China. His research interest incudes sheet meta forming. E-mai: yefeng-sober@63.com XU Zhou, born in 985, is currenty a master candidate in Coege of Mechanica Engineering, Tongji University, China. His research interest incudes sheet meta forming. E-mai: cambrejr@26.com