Mechanical properties of normal strength mild steel and high strength steel S690 in low temperature relevant to Arctic environment

Materials and Design 61 (2014) 150–159

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Mechanical properties of normal strength mild steel and high strength steel S690 in low temperature relevant to Arctic environment Jia-Bao Yan, J.Y. Richard Liew ⇑, Min-Hong Zhang, Jun-Yan Wang Department of Civil and Environmental Engineering, National University of Singapore, E1A-07-03, 1 Engineering Drive 2, Singapore 117576, Singapore

a r t i c l e

i n f o

Article history: Received 22 February 2014 Accepted 19 April 2014 Available online 1 May 2014 Keywords: Arctic environment High strength steel Mild steel Low temperature Mechanical properties

a b s t r a c t The development of Arctic oil and gas fields requires low temperature high strength steel materials that can resist critical loads in extreme environments. This paper investigates the mechanical properties such as stress–strain curves, elastic modulus, yield strength, ultimate tensile strength, and fracture strain of normal mild steel and high strength S690 steel to be used in low temperatures relevant to arctic environment. Tensile tests are carried out on steel coupons at different temperatures ranging from 80 °C to +30 °C in a cooling chamber. The influences of the low temperatures on the mechanical properties of mild steel and high strength steel are compared and their differences are discussed. Regression analyses are also carried out on the test data to develop empirical formulae to predict the elastic modulus, yield strength, and ultimate strength of the steels at ambient low temperatures. Finally, design formulae are recommended and their accuracies are further confirmed by the test data including those from the literature. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction To meet the increasing demand of oil and gas, the exploration activities of hydrocarbon reserves increased significantly in recent decades in the Arctic due to the 13% of the world’s undiscovered oil and gas in the Arctic Circle [1]. However, due to the harsh cold climate and continuous formation of ice sheets in these regions, the design and operation of the Arctic offshore structures face immense engineering challenges. The structures are constantly subjected to high dynamic loading from huge mass of moving iceberg driven by wind and sea currents, which may cause catastrophic damage to the structures. Moreover, the structures are exposed to the low temperatures that may affect the performances of construction materials used in the structures. Consequently, the design and feasibility of an offshore structure in the Arctic are often controlled by the ice environment. Many concepts of offshore drilling structures have been proposed and some have been used for the explorations of oil and gas in the Arctic e.g. artificial island, caisson retained island and mobile caisson [2]. A concept of flower conical gravity based structure with external steel-concrete-steel sandwich composite ice resisting walls was proposed for Arctic oil and gas platform as shown in Fig. 1 [3–5]. Normal mild steel (NMS) and high strength ⇑ Corresponding author. Tel.: +65 65162154; fax: +65 67791635. E-mail address: [email protected] (J.Y.R. Liew). http://dx.doi.org/10.1016/j.matdes.2014.04.057 0261-3069/Ó 2014 Elsevier Ltd. All rights reserved.

steel (HSS) were considered for the steel-concrete-steel (SCS) sandwich ice resistant walls to resist the severe ice contact pressure and provide protections. Recently, the interest of using the HSS with a nominal yield strength equal to or above 460 MPa is increasing in the buildings and offshore structures [6–16]. The material properties of the HSS S460, S690 under or post fire were investigated by Qiang et al. [6–8]. The influences of the processing and chemical compositions on the mechanical properties of the HSS have been studied [9–11]. Rajendran et al. [12] and Ashur et al. [13] have studied the creep life prediction and environmental cracking of the HSS, respectively. The residual stress studies in the HSS used for the steel construction have been carried out by Lee et al. [14] and Wang et al. [15]. All these studies were focused on the application of the HSS in the steel constructions [14–16]. From these engineering activities, it can be seen that the HSS exhibits many advantages over NMS, e.g. reduced weight of steel used, higher tensile strength, enhanced toughness and ductility, and better corrosion resistance and weldability due to the thinner plates used. Since the mechanical properties are important to the strength of the constructions and influenced by the environmental and processing elements, the influences of most challengeable environment element i.e. the low temperatures on the mechanical properties of the steels need to be considered for the prediction and evaluation of the structural performance of the Arctic offshore structures. The temperature in the Arctic can vary from about 70 °C to +30 °C depending on the location and time of the year. Along the

J.-B. Yan et al. / Materials and Design 61 (2014) 150–159

151

Outer steel skin

Concrete core Inner steel skin

Fig. 1. Conical arctic offshore platform using steel-concrete-steel sandwich systems.

coast in the Arctic, the temperature varies between 30 °C and 40 °C from December to February [17–20]. The winter temperature in some extreme conditions at Verkhoyansk Siberia near the Arctic can be as low as 72 °C [20]. On the other hand, the temperature in the summer on the land occasionally exceeds 30 °C [17–20]. There is limited information available on the mechanical properties of the NMS and HSS within the temperature range of 80 °C to +30 °C. Mechanical properties of the hot rolled steel reinforcements for the reinforced concrete structures at the cryogenic temperature were studied by Elices et al. [21]. Their experiments investigated strengths of the steel at 20 °C, 80 °C, and 180 °C. From the tests, it was observed that the strengths of the hot rolled steel were increased as the temperature decreased. The influence of the low temperature on the ductility of the hot rolled steel bars was less significant compared with that of the cold stretched steel bars. Lahlou et al. [22] observed that the mild steel reinforcement exhibited significant loss in the ductility whereas the strength and elastic modulus were increased at cryogenic temperatures of 195 °C. From these literatures, it seems that the mechanical properties of the mild steel under low temperature from 0 °C to 80 °C have not been thoroughly studied. Moreover, there are limited studies on the mechanical properties of the HSS S690 under the low temperature. Therefore, it is of importance to investigate the stress–strain behavior of the NMS and HSS under the low temperatures relevant to the Arctic environment. This paper presents a study on the mechanical properties of the NMS and HSS under the low temperatures encountered in the arctic region. The tensile behavior of 29 NMS coupons and 12 HSS coupons were determined at various low temperatures from 80 °C to +30 °C. Mechanical properties including the stress–strain curves, elastic modulus, yield and ultimate tensile strengths, and fracture strain were obtained from these tensile tests. From the results, the influences of the low temperatures on the mechanical properties were discussed. Based on the information, regression analyses were carried out to develop empirical formulae for prediction purposes. The accuracy of these formulae was also discussed and evaluated. 2. Experimental program This experimental study comprises tensile tests of 29 mild steel (NMS) coupons and 12 high strength steel (HSS) S690 coupons at

various temperatures from 80 °C to +30 °C (Table 2). The temperature range was selected to simulate the Arctic environment. 2.1. Mild steel and high strength steel specimens The HSS is a type of quenched and tempered structural steel with excellent forming and weldability [23]. The chemical compositions of the mild and high strength steels are given in Table 1. The chemical compositions of the three HSS with different thicknesses vary slightly. Comparing the chemical compositions of the mild and high strength steels, it seems that the HSS generally has lower sulfur, phosphate, chromium, molybdenum, nickel, copper and nitrogen content, but higher silicon and manganese content. The lower sulfur content permits greater lamellar tearing resistance, better notch impact toughness, better weldability but lower machinability, whereas the lower nitrogen content reduces the probability of blue brittleness [8,23]. Specimens used in the tensile tests were fabricated in compliance with ASTM: A370-13, and their sizes are shown in Fig. 2. All the specimens were cut from the NMS plates or HSS plates using a high pressure water jet cutting machine to minimize heating during the cutting. In addition, the ends of the specimens were enlarged according to ASTM: A370-13 in order to fit the specimens to the test equipment. 2.2. Test equipment and procedure The tensile tests were conducted using a 100-ton MTS loading system equipped with a low temperature chamber as shown in Fig. 3. The testing machine was a servo hydraulic system with displacement-control. Loading rates specified in the ASTM: A370-13 were used for the tensile tests at 80 °C, 60 °C, 40 °C, 20 °C, 0 °C, and +30 °C. Liquid nitrogen was used to achieve the low testing temperatures. The low temperature chamber had an automatic control system which combines several fans and an electromagnetic valve to achieve even temperature in the chamber. Four thermocouples were placed at different locations in the chamber to monitor the temperature and to control the inflow of the liquid nitrogen. The steel coupon was installed to the testing machine through two-pin connections. The bottom pin connector was installed to a steel cylinder that was fixed to the frame of the test rig. The tensile force was transferred from the load cell to the steel coupon

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Table 1 Chemical composition of the mild steel and HSS. Chemical composition

C (%)

Si (%)

Mn (%)

S (%)

P (%)

Cr (%)

Mo (%)

Nb (%)

MSt4 MSt8 MSt12 HSS(RQT701)

0.14 0.15 0.15 0.14

0.26 0.31 0.29 0.44

0.96 0.84 1.02 1.44

0.019 0.020 0.022 0.003

0.023 0.024 0.024 0.011

0.11 0.09 0.08 0.02

0.007 0.007 0.008 0.003

– – – 0.032

MSt4 MSt8 MSt12 HSS(RQT701)

Ti (%) – – – 0.029

V (%) – – – 0.049

Ni (%) 0.06 0.07 0.06 0.02

Cu (%) 0.38 0.33 0.38 0.029

N (%) 0.007 0.011 0.008 0.003

B (%) – – – 0.002

Al (%) – – – 0.035

CE (%) – – – –

Table 2 Quantities of the steel coupons used in the tensile test. Steel type

t (mm)

MSt4 MSt8 MSt12 HSS

4 8 12 12

Bi ¼

Temperature 30 °C

0 °C

20 °C

40 °C

60 °C

80 °C

2 2 1 2

2 2 2 2

2 1 1 2

1 2 2 2

2 2 2 2

1 1 1 2

MS = mild steel; HSS = high strength steel RQT701.

Unit: mm

D26

R=Radius D=Diameter

hðV=AÞ h½twl=ð2tl þ 2wlÞ htw=2ðt þ wÞ ¼ ¼ k k k

ð1Þ

where w = width of the steel coupons used in this report; t = thickness of the steel coupons; V = volume of the steel coupons, m3; A = external area of the steel coupons, m2; l = length of the specimen, m; k = thermal conductivity, 33 W/(m K); h = surface coefficient of convective heat transfer, herein 24 W/(m2 K) was used for steel in the air. If Bi < 0.1, the LPM method can be used. In this report, for steel coupons with thickness t = 4, 8, and 12 mm, the Bi indexes are 0.0013, 0.0018, 0.0023, respectively, and hence the LPM method can be used. (2) The minimum time required for cooling down of the steel coupon can be calculated by

  T  T1 hA ¼ exp s T0  T1 qcV

*The thickness t of the steel coupon is as the raw materials, t=4, 8, and 12mm for NMS, t=12mm for HSS

(a) Dimension of the steel coupon

(b) Steel coupons Fig. 2. Steel coupons for the tensile tests.

through the top pin connection. Three thermocouples were attached to each specimen to measure its temperature. After the steel specimen had been fixed for testing in the low temperature chamber, it was cooled down to the specified test temperatures, and this took time. After the testing temperature was achieved in the chamber, the minimum time required to achieve the same temperature of the specimen may be estimated by the Lumped Parameter Method (LPM) [24] as follows: (1) For the LPM method, the Bi index needs to be calculated to check if it is applicable to the steel coupons

ð2Þ

where T is the anticipated temperature of the steel coupon; T1 the temperature set for the cooling chamber; T0 the initial temperature of steel coupon before cooling down; q the density of the material; c the specific head capacity; V the volume of the material and A the external area of the steel coupons. Using Eqs. (1) and (2), the minimum time required to cool down a specimen to the lowest testing temperature of 80 °C was estimated to be 1200 s (20 min). The starting time of the tensile test was determined according to the minimum cooling time calculated above and the temperature measurement from the thermocouples attached to the test coupon. During the cooling process, the steel coupon was free to move to release the contraction stress caused by the low temperatures. Two strain gauges were attached to each specimen to measure its strain during the test. Since the strain gauges were usually damaged in the post yield range, extensometer was also used to measure the strain, especially after the yield point of the steel specimen was reached. All the information was recorded by a data logger and controlled by a linked PC control system.

3. Results and discussion Results on the stress–strain curves, elastic modulus, yield strength, ultimate tensile strength, and fracture strain of the steel materials determined at 80 °C, 60 °C, 40 °C, 20 °C, 0 °C, +30 °C (the corresponding readings in kelvin are 193 K, 213 K, 233 K, 253 K, 273 K, and 303 K) are presented in this section and discussed.

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100ton MTS Loading system

Insulation Tensile force from the load cell

Chamber with tempertature controller

Frame Load Cell Liquid Nitrogen

Steel coupon Extensometer

Thermolcouples

Data Adquisition system Fig. 3. Tensile test setup of steel coupons under low temperature.

3.1. Stress–strain curves The stress–strain curves obtained from the tensile tests for the NMS and HSS specimens at various temperatures are shown in Fig. 4a–d. For the NMS specimens, the stress firstly increases linearly to the yield strength. This is followed by a yield plateau with strength hardening process until it reaches the ultimate tensile strength. After that, necking is observed just before the fracture of the test specimen. From Fig. 4(a)–(c), it can be observed that as the temperature decreases, the yield strength, ultimate tensile strength, and fracture strain are increased. From Fig. 4(d), it is observed that the stress–strain curves of the HSS specimens under various temperature levels are different from those of the NMS specimens. Compared with the stress–strain curves of the NMS specimens, the HSS specimens exhibit lower fracture strain (fracture strain reduced from 0.35 to 0.27), much higher yield and ultimate tensile strengths, larger necking part after achieving the ultimate tensile strength in the stress strain curves compared with the hardening part. It can also be observed that as the temperature decreases the fracture strain and yield and ultimate tensile strengths are increased. 3.2. Elastic modulus The elastic modulus of the steels at various low temperatures was determined from the stress–strain curves according to ASTM: A370-13 as shown in Fig. 5, and the results are presented in Table 3. Ratio of the elastic modulus at low temperature EsT to the elastic modulus at room temperature (30 °C) Esa is presented in Table 3 to evaluate the increase of the elastic modulus due to the reduction in temperature. The effects of the low temperatures on the ratio of the elastic modulus IET = EsT/Esa of the NMS and HSS coupons are shown in Fig. 6. The followings are observed based on the comparison of the test data: (1) The elastic modulus of steel was generally increased somewhat with the reduction in steel temperature. (2) Low temperatures seem to have more significant effect on the elastic modulus of the NMS than the HSS with thickness plate of 12 mm. This might be due to their different production process, chemical compositions, and microstructures. The low temperatures had more significant influence on the elastic moduli of the 12-mm thick NMS coupons than those with 4 mm and 8 mm coupons. For example, with the reduction in temperature from 30 °C to 80 °C, the

4 mm NMS coupons exhibited average increase of about 7%, whereas the 12 mm thick NMS coupons exhibited average increase of about 24%. 3.3. Yield strength and ultimate tensile strength The yield strength fy and ultimate tensile strength fu of the steel coupons were determined according to ASTM: A370-13 and the results are presented in Table 3. For the stress–strain curves exhibit typical sharp-kneed diagram, the ‘Autographic Diagram Method’ was used to determine the yield strength. This method is applicable to the NMS coupons of 4 mm and 8 mm thicknesses. For the stress–strain curves without sharp-kneed diagram, the 0.2% offset method was used to determine the yield strength which is for the 12 mm thick NMS and HSS specimens. The ratio of the yield strength at low temperatures fyT to the yield strength at room temperature fya (IfyT = fyT/fya) are also given in Table 3, and plotted against temperature as shown in Fig. 7. Similar ratio on the ultimate tensile strength was presented in Table 3 and shown in Fig. 8. From the results, it is observed that: (1) The yield strength and ultimate tensile strength of the steel are generally increased with the decrease in temperature. (2) The low temperatures seem to have less significant effect on the HSS than the NMS specimens. For the 4 mm, 8 mm, 12 mm thick NMS and 12 mm HSS specimens, the yield strengths were increased by 21%, 12%, 13%, and 8%, respectively, while the ultimate tensile strengths were increased by 18%, 14%, 13%, and 9%, respectively, with the reduction in the temperature from +30 °C to 80 °C. (3) The low temperatures had more significant effect on the yield strength and ultimate tensile strength of the NMS specimens with the thicknesses of 4 mm and 8 mm than those of the 12 mm thick NMS and HSS coupons. (4) The ultimate tensile strength of the NMS and HSS exhibits higher correlation to the low temperature compared with those of the elastic modulus and yield stress. This can be judged from the correlation coefficients in Fig. 8 (R2 = 0.94, 0.91, 0.69, and 0.96 for 4 mm, 8 mm, 12 mm NMS and 12 mm HSS) in comparison to those in Figs. 6 and 7. 3.4. Fracture strain Typical failure modes of the NMS and HSS coupons at various low temperatures are shown in Fig. 9. It can be seen that necking

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500

Stress (MPa)

400 300 200 100 0 0.00

t4 +30C t4 -20C t4 -60C 0.10

t4- 0C t4 -40C

0.20

0.30

0.40

Strain

(a) Stress-strain curves of the 4 mm thick mild steel specimens 600

Stress (MPa)

450

300

150

0 0.00

t8 +30C t8 -40C t8 -80C

t8 -0C t8 -60C

4. Analysis and discussion

600

In order to develop mathematical relationships between the mechanical properties of the steel (including elastic modulus Es, yield strength fy, and ultimate tensile strength fu) and the temperature T, multiple regression analyses were carried out. All the 41 tensile tests were included in the regression analyses. The temperature increasing factors for IE, Ify, and Ifu are defined as follows, and are used to evaluate the increasing ratios of the Es, fy, and fu under the low temperatures with reference to room temperature.

450

IE ¼

EsT Esa

ð3Þ

Ify ¼

fyT fya

ð4Þ

Ifu ¼

fuT fua

ð5Þ

0.10

0.20

0.30

0.40

Strain

(b) Stress-strain curves of the 8 mm thick mild steel specimens

Stress (MPa)

750

300 150 0 0.00

t12 +30C t12 -20C t12 -60C 0.10

0.20

t12 -0C t12 -40C t12 -80C 0.30

0.40

Strain

(c) Stress-strain curves of the 12-mm thick mild steel specimens 1000 800

Stress (MPa)

occurs in the NMS and HSS steel coupons. This implies no brittle failure of the specimens. Elongation was recorded by the extensometer, and the elongation at the fracture point of the steel specimen eF obtained from the stress–strain curve was used as a measure of ductility of the steel specimens (Table 3). It should be noted that if the necking was located out of the measuring zone of the extensometer, the measured fracture strain value was generally much smaller than the real one. These values were therefore not included in Table 3. The influence of the temperatures on eF is plotted in Fig. 10. The fracture strain eF increases with the decrease in temperature. This finding was consistent with that reported by Ehlers and Østby [25]. The average fracture strains for the 4 mm, 8 mm, 12 mm NMS and HSS were increased only by about 3%, 11%, 10%, and 4.5%, respectively, with the reduction in the temperature from 30 °C to 80 °C. It should be mentioned, however, that the correlations between the eF and temperature are quite low as shown in Fig. 10 (R2 = 0.17, 0.12, 0.32, 0.11 for NMS-4, -8, -12, and HSS-12 respectively). This implies weak correlation of the fracture strain to the temperature and significant variation of the data for both the NMS and HSS. Thus, the effect of the low temperature on the fracture strain will not be studied further.

600 400 200 0 0.00

Ht12 +30C Ht12 -20C Ht12 -60C 0.10

Ht12 -0C Ht12 -40C Ht12 -80C 0.20

0.30

where,IE, Ify, Ifu is the increasing factors for elastic modulus, yield strength, and ultimate tensile strength, respectively; EsT, fyT, fuT the elastic modulus, yield strength, and ultimate tensile strength of steel specimen at temperature T, respectively; Esa, fya, fua the elastic modulus, yield strength, and ultimate tensile strength of steel specimen at room temperature, respectively. General exponential models were assumed for the analysis that consider the influence of different variables including temperature T, thickness of the steel plate t, and the strength and elastic modulus of the steels at the room temperature fya, fua, Esa as shown in Eqs. (3)–(5), respectively. Among these three variables, temperature T is the main variable which should be included in each assumed model. The assume exponential models are

IE ¼ atb T c Edsa

ð6Þ

d Ify ¼ at b T c fya

ð7Þ

d Ifu ¼ at b T c fua

ð8Þ

Strain

(d) Stress-strain curves of 12 mm thick HSS Fig. 4. Stress–strain curves of the high-strength steel specimens under low temperatures.

In order to make linear regression analyses, logarithmic transformations were made to these three models in Eqs. (6)–(8).

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900

500

fy

fy Stress (MPa)

Stress (MPa)

400 300 200

Es

600

Es

300

1

1

100 0

0

0.0

1.0

2.0 Strain (%)

3.0

0

0.2

0.4 Strain (%)

0.6

0.8

Fig. 5. Determination of the elastic modulus and yield strength.

Table 3 Tensile test results and predictions. No.

Specimen

t (mm)

T (K)

Es (GPa)

fy (MPa)

fu (MPa)

eF

IET

IEP by Eq. (9)

IfyT

IfyP by Eq. (10)

IfuT

IfuP by Eq. (11)

1 2 3 4 4 6 7 8 9 10 11 12 13 14 14 16 17 18 19 20 21 22 23 24 24 26 27 28 29 30 31 32 33 34 34 36 37 38 39 40 41

t4+30-1 t4+30-2 t4-0-1 t4-0-2 t4-20-1 t4-20-2 t4-40-1 t4-60-1 t4-60-2 t4-80-1 t8+30-1 t8+30-2 t8-0-1 t8-0-2 t8-20-1 t8-40-1 t8-40-2 t8-60-1 t8-60-2 t8-80-1 t12+30-1 t12-0-1 t12-0-2 t12-20-1 t12-40-1 t12-40-2 t12-60-1 t12-60-2 t12-80-1 Ht12+30-1 Ht12+30-2 Ht12-0-1 Ht12-0-2 Ht12-20-1 Ht12-20-2 Ht12-40-1 Ht12-40-2 Ht12-60-1 Ht12-60-2 Ht12-80-1 Ht12-80-2

4.7 4.6 4.7 4.5 4.6 4.8 4.6 4.7 4.8 4.7 7.4 7.6 7.5 7.4 7.5 7.6 7.6 7.5 7.6 7.6 11.9 12.0 11.7 12.0 11.9 11.9 12.0 11.9 11.9 12.4 12.1 12.3 12.3 12.1 12.4 12.0 12.4 12.3 12.0 12.3 12.4

301 304 272 272 250 248 228 209 209 190 300 304 270 270 249 233 233 213 213 189 305 271 271 252 233 233 211 213 191 303 303 270 268 248 251 238 238 207 209 185 189

213 221 219 219 235 210 227 221 222 233 219 207 218 226 230 217 226 223 232 243 194 213 187 227 236 227 216 220 241 207 210 214 213 218 219 223 224 224 230 242 228

333 330 334 340 360 355 365 380 380 400 335 340 343 343 358 362 340 378 375 398 350 342 360 355 370 360 370 385 392 745 750 770 760 775 770 775 772 796 790 790 810

419 421 424 431 457 450 468 473 468 498 507 515 523 527 532 568 546 574 577 581 539 528 568 546 568 560 575 612 611 814 818 835 834 849 844 851 847 883 884 883 893

0.33 0.35 0.33 0.33 0.32 0.32 0.33 0.32 0.34 – 0.27 – 0.35 0.30 0.27 – 0.28 – – 0.33 – 0.30 0.27 0.34 0.33 0.32 0.33 0.31 0.33 0.22 0.22 0.25 0.23 0.22 0.21 0.25 0.23 0.25 0.23 0.23 0.24

0.98 1.02 1.01 1.01 1.08 0.97 1.05 1.02 1.02 1.07 1.03 0.97 1.02 1.06 1.08 1.02 1.06 1.05 1.09 1.14 1.00 1.10 0.96 1.17 1.21 1.17 1.11 1.13 1.24 0.99 1.01 1.03 1.02 1.05 1.05 1.07 1.07 1.07 1.10 1.16 1.09

0.98 0.98 1.01 1.01 1.03 1.03 1.05 1.07 1.07 1.09 1.00 0.99 1.02 1.02 1.04 1.06 1.06 1.08 1.08 1.11 1.06 1.09 1.09 1.11 1.13 1.13 1.16 1.15 1.18 0.99 0.99 1.02 1.03 1.05 1.04 1.06 1.06 1.09 1.09 1.12 1.12

1.00 1.00 1.01 1.03 1.09 1.07 1.10 1.15 1.15 1.21 0.99 1.01 1.02 1.02 1.06 1.07 1.01 1.12 1.11 1.18 1.01 0.99 1.04 1.03 1.07 1.04 1.07 1.11 1.13 1.00 1.00 1.03 1.02 1.04 1.03 1.04 1.03 1.06 1.06 1.06 1.08

1.01 1.00 1.04 1.04 1.07 1.07 1.11 1.14 1.14 1.18 1.00 0.99 1.03 1.04 1.06 1.09 1.09 1.12 1.12 1.17 0.97 1.01 1.01 1.04 1.07 1.07 1.10 1.10 1.14 1.00 1.00 1.01 1.02 1.03 1.03 1.03 1.03 1.05 1.05 1.07 1.07

1.00 1.00 1.01 1.02 1.09 1.07 1.11 1.13 1.11 1.18 0.99 1.01 1.02 1.03 1.04 1.11 1.07 1.12 1.13 1.14 1.00 0.98 1.05 1.01 1.05 1.04 1.07 1.14 1.13 1.00 1.00 1.02 1.02 1.04 1.03 1.04 1.04 1.08 1.08 1.08 1.09

1.00 1.00 1.04 1.04 1.06 1.07 1.10 1.13 1.13 1.16 0.99 0.98 1.02 1.02 1.05 1.07 1.07 1.10 1.10 1.15 0.98 1.02 1.02 1.04 1.07 1.07 1.10 1.10 1.14 1.01 1.01 1.03 1.03 1.05 1.04 1.05 1.05 1.08 1.08 1.10 1.10

t = thickness of the steel coupon; T = temperature, K; Es = elastic modulus; fy = yield strength; fu = ultimate tensile strength; eu = strain (or elongation) at the ultimate tensile strength; eF = Fracture strain; IET = experimental increment factor of elastic modulus as defined in Eq. (6); IEP = predicted increment factor of elastic modulus by Eq. (9); IfyT = experimental increment factor of yield strength as defined in Eq. (7); IfyP = predicted increment factor of yield strength by Eq. (10); IfuT = experimental increment factor of ultimate tensile strength as defined in Eq. (8); IfuP = predicted increment factor of ultimate tensile strength by Eq. (11).

There are several available approaches for the predictor subset selection e.g. forward selection, backward elimination, stepwise regression, and best subset method [26,27]. In this study, the best subset method was used to observe the significant predictors for the increasing factors of the elastic modulus, yield strength, and ultimate tensile strength at the Arctic low temperature. The main

objective of the subset selection is to select a proper subset of predictors from the chosen considered parameters to make a resulting regression model with good predicting ability [28–30]. In the best subset method, the correlation coefficient R2, Mallows Cp index, and standard error of the regression S were used to evaluate the best fitting model [31,32]. The correlation coefficient R2 commonly

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-90 1.4

-60

-30

0

30° C

HSS Item

R2

EsT/Esa

1.2

1.0

NMS-4

0.24

NMS-8

0.60

NMS-12 0.55 0.8

NMS-4 NMS-12

NMS-8 HSS-12

30°C

0°C

-20°C

-40°C

213

243

273

-80°C

(a) Failure of S690 under low temperature

HSS-12 0.88

0.6 183

-60°C

t=4 mm Mild Steel

303

Temperature (K) Fig. 6. Effect of low temperature on the elastic modulus.

- 90 1.3

- 60

- 30

0

30 ° C

Item

R2

30°C

fyT /fya

1.2

1.1

NMS-4

0.97

NMS-8

0.81

0°C

-20°C

-40°C

-60°C

-80°C

(b) Failure of 4-mm thick mild steel specimens under low temperatures t=8 mm Mild Steel

NMS-12 0.77 1.0

0.9 183

NMS-4 NMS-12 213

HSS-12

NMS-8 HSS-12 243

273

0.90

303

Temperature (K)

30°C Fig. 7. Effect of low temperature on the yield strength.

- 90 1.2

-30

- 60

0

-20°C

-40°C

-60°C

-80°C

(c) Failure of 8-mm thick mild steel specimens under low temperatures

30° C

t=12 mm Mild Steel Item

fUT/fUa

1.1

1.0

0.9 183

0°C

NMS-4

NMS-8

NMS-12

HSS-12

213

243

273

R2

NMS-4

0.94

NMS-8

0.91

NMS-12 0.69

30°C

HSS-12 0.96

(d) Failure of 12-mm thick mild steel specimens under low temperatures

0°C

-20°C

303

-40°C

-60°C

-

Fig. 9. Failure of the NMS.

Temperature (K) Fig. 8. Effect of low temperature on the ultimate tensile strength.

- 90 0.40

- 60

- 30

0

30°C

Item

R2

0.30

F

is a value less than 1.0 that means how much percent of the values can be explained by the regression model. Therefore, regression models with high R2 values will be preferred. Regarding the Mallows Cp index, for any model containing a subset of p predictors from the total number of n predictors p < n, variable subsets with lower Cp values (around p or less) are preferred [26,29–32]. Commonly, the predictor subset with the minimum Mallows Cp is the preferred subset model. The standard error of the regression S is used to evaluate the accuracy of the regression model. In addition to the above three evaluation criteria, the number of predictors in the equation also needs to be considered. The objective is to obtain a model with the lowest possible number of predictors that ‘‘adequately’’ describe the data. The regression analysis on IE, Ify, Ifu by using the best subset method were carried out on the mild steel specimens (NMS), high

0.20

NMS-4

0.17

NMS-8

0.12

NMS-12 0.32 0.10

NMS-4 NMS-12

0.00 183

213

NMS-8 HSS-12 243

273

HSS-12

0.11

303

Temperature (K) Fig. 10. Effect of low temperature on the fracture strain of steel specimens.

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J.-B. Yan et al. / Materials and Design 61 (2014) 150–159

strength steel specimens (HSS), and all the specimens (AS) comprising both the NMS and HSS specimens. Therefore, with the best subset method, various possible combinations of the predictors were considered. The regression results are presented in Tables 4–6, and observations are summarized as follows. (1) For the regression analyses on ln IE (Table 4), ln Ify (Table 5), and ln Ifu (Table 6), it can be seen that it is better to develop separate regression models for the NMS and HSS. (2) For the HSS S690, Models 6E (Table 4), 6fy (Table 5), and 6fu (Table 6) are recommended based on the above mentioned criteria. In these models only temperature T is considered. (3) From statistical point of view, Models 3E (Table 4), 3fy (Table 5), and 3fu (Table 6) seem to be preferred for the NMS. In Model 3E two parameters of temperature T and elastic modulus in room temperature Esa are considered, whereas in Models 3fy and 3fu, two parameters of temperature T and specimen thickness t are considered. When dealing with yield strength and ultimate tensile strength, Models 4fy (Table 5) and 4fu (Table 6) may also be considered from both statistical and physical meaning point of views. It should be noted that the NMS specimens with different thicknesses had different chemical compositions and mechanical properties. If these NMS specimens were made from the same steel and had the same mechanical properties, it is possible that only temperature T needs to be considered in prediction formulae. Based on the data and above discussion, Models 3E, 4fy, and 4fu are recommended. For these recommended models, coefficients a, b, c, and d in Eqs. (6)–(8) and R2 are summarized in Table 7. The recommended models to calculate the increasing factors IE, Ify, and Ifu for Es, fy, and fu are as follows: (1) For elastic modulus of the steel

EsT IE ¼ ¼ Esa

(

fyT ¼ fya

(

175:01E0:716 T 0:233 sa

for MS

4:03T 0:245

for HSS

0:509 0:339 133:60fya T

2:21T

0:139

ð9Þ

for NMS

ð10Þ

for HSS

Table 4 The best subset regression analysis of ln IEon ln t, ln T, and ln Esa. Material

NMS

HSS

AS

a

Material

NMS

HSS

AS

Model

n

R2

Mallows Cp

S

1E 2E

1 1

31.4 31.1

16.8 17.0

0.056 0.057

3E 4E 5E 6E

2 2 3 1

58.5 57.3 59.0 87.9

2.3 3.1 4.0 1.8

0.045 0.045 0.045 0.016

7E 8E 9E 10E

1 2 1 1

0.7 88.9 38.9 27.0

72.3 3.0 23.2 35.0

0.045 0.016 0.048 0.052

11E 12E 13E

2 2 3

62.4 51.3 62.5

2.0 13.0 4.0

0.038 0.043 0.039

ln t

ln T

ln Esa

Model

R2

n

Mallows Cp

S

ln t

1fy 2fy

1 1

80.5 2.3

8.6 143.0

0.025 0.056

3fy 4fy 5fy 6fy

2 2 3 1

85.3 84.7 85.5 89.9

2.3 3.3 4.0 1.1

0.022 0.022 0.022 0.008

x

7fy 8fy 9fy 10fy

1 2 1 1

0.0 89.4 66.9 6.2

81.4 3.0 18.6 120.4

0.026 0.009 0.029 0.049

x x

11fy 12fy 13fy

2 2 3

76.8 74.7 78.0

3.9 7.5 4.0

0.025 0.026 0.024

ln T x

ln fya

a

x

x

x x x x

x x

x x

x x x

x x x

x x

a Denotes considered predictors in the subset regression analysis; n, number of considered predictors; NMS = normal mild steel; HSS = high strength steel; AS = all specimens.

Table 6 The best subset regression analysis of ln Ifu on ln t, ln T, and ln fua. Material

NMS

HSS

AS

where Esa is the elastic modulus at room temperature, in GPa and T the temperature, in K, and 193 6 T 6 303 K. (2) For yield strength of the steel

Ify ¼

Table 5 The best subset regression analysis of ln Ifyon ln t, ln T, and ln fya.

Item

n

R2

Mallows Cp

S

1fu 2fu

1 1

81.7 1.7

8.2 153.6

0.022 0.053

3fu 4fu 5fu 6fu

2 2 3 1

85.7 84.6 86.2 95.8

2.9 4.9 4.0 2.7

0.021 0.021 0.021 0.007

7fu 8fu 9fu 10fu

1 2 1 1

0.4 96.5 75.5 4.0

247.4 3.0 16.4 172.2

0.033 0.007 0.024 0.047

x x

11fu 12fu 13fu

2 2 3

82.7 81.9 83.0

2.7 4.4 4.0

0.020 0.021 0.020

x

ln t

ln T

ln fua

xa x x x

x x x x

x x

x x x

x

x x x

x x

a Denotes considered predictors in the subset regression analysis; n, number of considered predictors; NMS = normal mild steel; HSS = high strength steel; AS = all specimens.

where fya is the yield strength at room temperature, in MPa and T the temperature, in K, and 193 6 T 6 303 K. (3) For ultimate tensile strength of the steel

fuT Ifu ¼ ¼ fua

(

0:082 0:320 10:22fua T

2:90T

0:185

for NMS for HSS

ð11Þ

xa x x x x x

x x x x

x x

x x x

x x

x x x

x x

Denotes considered predictors in the subset regression analysis; n, number of considered predictors; NMS = normal mild steel; HSS = high strength steel; AS = all specimens.

where fua is the ultimate tensile strength at room temperature, in MPa and T the temperature, in K, and 193 6 T 6 303 K. The developed models for the NMS shown in Eqs. 10 and 11were compared with test results by Ehlers and Østby [25], and the comparisons are shown in Fig. 11. It can be seen that the developed models offer reasonable predictions on the increasing factors for yield and ultimate strengths of the mild steel. The prediction error is increased with the reduction in temperature. At 0 °C and 30 °C, the models give good predictions for the strength increasing factors, whereas at 60 °C the models give prediction errors of about 2% for the increasing factors on the yield strength and ultimate strength. It should be noted, however, that the models underestimate the experimental results.

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J.-B. Yan et al. / Materials and Design 61 (2014) 150–159

Table 7 Regression analyses results by the recommended models. Steel type

Obtained coefficients for the parameters from the regression analysis a

Model IE ¼ at b T c Edsa NMS 175.01 HSS 4.03

Coefficient of correlation R2

Model number

b

c

d

0 0

0.233 0.245

0.716 0

0.59 0.88

3E 6E

0 0

0.339 0.139

0.509 0

0.85 0.90

4fy 6fy

0 0

0.320 0.185

0.082 0

0.85 0.96

4fu 6fu

d Model Ify ¼ atb T c fya

NMS HSS

133.60 2.21

d Model Ifu ¼ at b T c fua NMS 10.22 HSS 2.90

1.25

Test in Ref. [25]

1.20

Prediction

Ify /Ify0

1.15 1.10 1.05 1.00 0.95 0.90 0

-30

-60

-80 -90

Temperature (degree)

(a) Validation of models for yield strength 1.20

Prediction 1.15

Test in Ref. [25]

Ifu /Ifu0

1.10 1.05 1.00 0.95 0.90 0

-30

-60

-80

-90

Temperature (degree)

increments of the Es, fy, and fu were influenced by the thickness of the mild steel plate. For thinner steel plate of 4 mm thick, Es, fy, and fu increase by 7%, 13% and 13%, respectively; however, for thicker plate of 12 mm thick, the increments of Es, fy and fu are 24%, 21% and 18%, respectively. (2) For high strength S690 steel plates, the average Es, fy, fu and fracture strain values increased by 13%, 7%, 9%, and 4.5%, respectively when the temperature decreases from +30 °C to 80 °C. The influence of the low temperature on these mechanical properties of the high strength steel was less significant compared to those of the normal mild steel plates with the same thickness. (3) From the analysis of test data, the influence of the low temperature on the fracture strain of the mild steel is less than 11%. For high strength steel it is not more than 5%. Though the fracture strain increases as the temperature decreases from 80 °C to 30 °C, the fracture strains shows weak correlations to the temperatures. Therefore, from the statistic view, more test data are needed for the prediction of the relationship between the fracture strain and temperature. (4) Based on the test results, regression analyses were carried out. The considered key predictors were the types of the steel, mechanical properties at the room temperature, thickness of the steel specimens, and temperature. Finally, empirical formulae Eqs. (9)–(11) were developed and recommended to predict the mechanical properties of mild steel and high strength steel at low temperature, and their accuracies were further confirmed by the test data from the literature. So far the work is limited to mechanical properties of steel in cold temperature. Future work will be focused on brittle fracture of the high strength steel in low temperature arctic environment.

(b) Validations of model for ultimate strength Fig. 11. Validations of the developed models against test results in Ref. [25].

5. Conclusions This paper deals with the mechanical properties of the normal mild steel and high-strength S690 steel plates in low temperature Arctic environment. Tensile tests were carried out on 41 steel coupons in the cooling chamber with temperatures ranging from 80 °C to 30 °C. Formulae on necessary cooling time for the tensile tests in the cooling chamber were developed based on the Lumped Parameter Method. Based on the test results, the following conclusions were drawn: (1) For normal mild steel plates, the elastic modulus Es, yield strength fy, and ultimate tensile strength fu were increased when the temperature reduced from +30 °C to 80 °C. The

Acknowledgements The research described herein was funded by the Maritime and Port Authority of Singapore, and supported by the American Bureau of Shipping (ABS) and National University of Singapore under research project titled ‘‘Curved steel-concrete-steel sandwich composite for Arctic region’’ (Project No. R-302-501-002490).

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