Post-fire mechanical properties of stainless steel cables

Journal of Constructional Steel Research 172 (2020) 106177

Contents lists available at ScienceDirect

Journal of Constructional Steel Research

Post-fire mechanical properties of stainless steel cables Guojun Sun a,b,⁎, Shuo Xiao a, Yuan Yang c, Xiaohui Li d, Martin Mensinger c a

College of Architecture and Civil Engineering, Beijing University of Technology, Beijing 100124, PR China The Key Laboratory of Urban Security and Disaster Engineering, MOE, Beijing University of Technology, Beijing 100124, PR China c Department of Civil, Geo and Environmental Engineering, Technical University of Munich, Munich 80333, Germany d Beijing General Municipal Engineering Design & Research Institute Co., Ltd, Beijing 100082, PR China b

a r t i c l e

i n f o

Article history: Received 23 September 2019 Received in revised form 10 March 2020 Accepted 23 May 2020 Available online xxxx Keywords: Stainless steel cable Post-fire Mechanical properties Constitutive equation Experimental investigation

a b s t r a c t During the heating process of a fire test, most test specimens are in a stress-free state, while the components of the actual structures are often in a complex state of stress, particularly for pre-stressed members such as steel cables. To reflect the actual fire conditions of stainless steel cables and explore the effects of stress levels on the mechanical properties of stainless steel cables after high temperatures, this study examines the residual mechanical properties of a stainless steel cable after high temperatures. A fire test on stainless steel cables at different stress levels was conducted, and subsequently, the static tensile test at room temperature (30°C) was conducted for the specimens after firing and after natural air cooling. The elastic modulus, tensile strength, yield strength, fracture strain, and stress-strain curves of the stainless steel cables under different temperature-stress conditions were obtained. The mechanical properties of stainless steel cables after a high temperature were compared with those of carbon steel cables and other stainless steel materials. The equations to predict the mechanical properties of a stainless steel cable after a high temperature are provided, and it can provide a reference for the safety assessment and replacement of pre-stressed structures after a fire. © 2020 Elsevier Ltd. All rights reserved.

1. Introduction Owing to their aesthetic appearance, excellent corrosion resistance, and ease of maintenance and sustainability, stainless steel cables have been used in large-scale public buildings [1], such as the Gateway Arch, St. Louis, USA. Some scholars have studied the mechanical properties of steel cables and steel that have been exposed to high temperatures [2–4]. Thus, research on the safety of space structures is becoming essential, for which the fire resistance of pre-stressed space and structures has become a popular topic [5–8]. The cable is an essential component of pre-stressed space structures. Its mechanical properties and deformation evolution at high temperatures contribute significantly to fire resistance design and numerical simulation analysis of pre-stressed space structures. Different from the general steel structural components, the cable is fabricated from several steel wires twisted around a central steel wire in layers according to a certain twist distance [9]. Its mechanical properties are the comprehensive reflection of the cooperative work between the steel wires. Many predecessors have studied the mechanical properties of pre-stressing steel wires at high temperatures. In 1970, Harmathy [10] studied the ⁎ Corresponding author at: College of Architecture and Civil Engineering, Beijing University of Technology, Beijing 100124, PR China. E-mail address: [email protected] (G. Sun).

https://doi.org/10.1016/j.jcsr.2020.106177 0143-974X/© 2020 Elsevier Ltd. All rights reserved.

mechanical properties of A421 pre-stressing steel wire at high temperatures. In 1982, Holmes [11] conducted a series of steady-state and transient tests on a steel strand to determine its yield strength, ultimate strength, and elastic modulus at high temperatures. Mirmomeni [12] conducted a comprehensive test on the impact fire performance of 350 steel under well-defined conditions, proposed three different damage levels for the displacement corresponding to the ultimate stress, and observed that the strength and ductility of low carbon steel are closely related to the loading rate, pre-deformation history, and subsequent temperature. Amin [13] studied the mechanical properties of Grade 1200 ultra-high-strength steel (UHSS) steel under extreme cooling conditions, which are defined as cooling from fire temperatures using an extreme cooling rate or cooling from ambient state to sub-zero temperatures. Fatemeh [14] studied the mechanical behaviour of a Grade 1200 UHSS tube under a multi-phase loading scenario including fire and creep. The microstructural origin of accelerated softening in UHSS owing to creep strain was discussed. Fan [15] and Zhou [16] conducted high-temperature steady-state tests on 1860 MPa pre-stressed steel strands for concrete. Zhang [17] conducted a high-temperature tensile test on 1860-MPa single steel wires. The reduction equations of tensile strength, elasticity modulus, and yield strength of steel wires, as well as the stress-strain relationship at high temperatures, were provided. Du [18] selected 1 × 7 pre-stressing steel cables with a strength grade of 1860 MPa, commonly used in pre-stressing buildings, as the

2

G. Sun et al. / Journal of Constructional Steel Research 172 (2020) 106177

research object. Through steady-state tension tests, the reduction coefficients of mechanical properties such as proportional limit, elasticity modulus, nominal yield strength, and fracture strain of the cables at different temperatures were obtained and compared with the European code EN1992-1-2. The suggested values were compared. In recent years, developed countries such as the United States and those in Europe have successfully provided relevant suggestions on the mechanical properties of pre-stressed high-strength steel wires and strands in standards such as BS 5896-2012 [19], ASTM A416 [20], and ACI 216.114 [21]. EN1992-1-2 [22] indicates that the high-temperature mechanical properties of pre-stressed high strength steel wires and cables for pre-stressed concrete are also changed with temperature. Some scholars have conducted high-temperature tests and mechanical analyses of stainless steel [23–26]. There are few studies on the mechanical properties of stainless steel cables at high temperatures, which restricts the fire-resistance design and numerical simulation analysis of structures with stainless steel cables. Thus, post-fire residual mechanical properties of stainless steel cables were examined in this study. The main research contents conducted in this study are as follows. Twenty-seven stainless steel cables under different initial stress states of 0.3Fu(Fu is the breaking force of stainless steel cable)，0.5Fu, and 0.7Fu were exposed to different temperatures of up to 600 °C and then allowed to cool down to room temperature before they were tested for failure. The method of natural cooling in air was used in this study. The residual mechanical properties and stress-strain curve of stainless steel cables after being subjected to high temperatures were obtained. Equations for the ultimate strength, yield strength, elastic modulus, and fracture strain of stainless steel cables after undergoing high temperatures are proposed.

2. Experimental investigation 2.1. Test specimens Three types of stainless steel cables, φ14, φ20, and φ26, were investigated in this study. Stainless steel cables of φ14, φ20, and φ26 are composed of 19-, 37-, and 61-wires, respectively. The 19-wire stainless steel cable constituted twelve steel wires in the first layer and six in the second, encircling the core wire in three layers, (Fig. 1(a)). Similarly, Figs. 1 (b) and (c) show the 37- and 61-wire stainless steel cable arrangements, respectively. The wire material was high strength cold-drawn steel with a tensile strength of 1500 MPa. The diameter of all stainless steel cables was 2.9 mm. The twist distance of each layer of steel wire was invariable; thus, cables with different standard length had the

Table 1 Cross-sectional parameters and mechanical properties of stainless steel cables. Structure

n

D (mm)

d (mm)

S (mm2)

f (MPa)

Fu (kN)

1 × 19 1 × 37 1 × 61

10 10 10

14 20 26

2.9 2.9 2.9

125.5 244.4 402.9

1500

139 279 469

same twist characteristic. Considering the possible defects cable processing. The length of the standard pitch section of the specimen was set at 400 mm, which was greater than 1.0 times the length of the twist pitch of any layer of steel wire of the cable, which could reflect the twisted characteristics of the steel cable. The equivalent section area, S, of a stainless steel cable is the sum of the steel wire area of all components of the cable. Table 1 shows the section characteristics and mechanical properties of the stainless steel cable. The stainless steel cable in the test was composed of a stainless steel strand, two stainless steel anchorages, and a clamping round pole. The stainless steel strand was fabricated from 316 austenitic stainless steel (0Cr17Ni12Mo2), corresponding to European standard EN1.4401. Table 2 shows the chemical composition of the stainless steel cable. The diameter of the stainless steel cable did not exceed 40 mm. All the stainless steel was used to suppress the anchorage. The specific sample sizes are shown in Fig. 2. 2.2. Testing device The testing device comprised a SANS universal testing machine (with a capacity of 2000 kN). As shown in Fig. 1. The testing machine was checked using a legal measuring department before start-up. The heating equipment consisted of a high-temperature GW-1200B box and built-in circulating fan to ensure a uniform temperature in the furnace. The length of the furnace was 600 mm. The temperature could go up to 600 °C, and the deformation measuring system comprised two high-precision displacement sensors (PM11-R-50L) with a range of 50 mm and an extensometer with a gauge length of 400 mm, as shown Fig. 4. The tie rod and cable were connected via a special snap ring structure. Local protuberances were produced on the inner side of the snap ring to ensure that relative sliding did not occur between the cable and extensometer during the tensile test. Thus, the deformation of the cable could be effectively transmitted to the displacement sensors connected to the bottom of the extensometer (Fig. 3). Before the test, the temperature field distribution in the hightemperature furnace was tested via the gradient placement of a

Fig. 1. Cross-sectional schematics of the specimen. 1: clamping round pole; 2: stainless steel anchorage; 3: stainless steel strand.

G. Sun et al. / Journal of Constructional Steel Research 172 (2020) 106177 Table 2 Chemical constituents of the stainless steel cables. Constituent C C (%)

Si

P

S

Mn

Cr

Ni

Mo

≤0.08 ≤1.00 ≤0.035 ≤0.030 ≤2.00 16.0–18.5 10.0–14.0 2.0–3.0

thermocouple. The results indicated that the temperature difference between the sample and target temperature was within the standard range (within ±5 °C); therefore, the sample temperature could be considered to be uniform within the standard range. 2.3. Test loading system As the core member of a pre-stressed spatial structure, the cable is always under tension during service. However, in the existing tests for the mechanical properties of steel after high temperatures, most specimens are in the stress-free state during the heating process, which cannot reflect the actual fire conditions of the component in use. To reflect the fire conditions of stainless steel cables more accurately, we tested the mechanical properties of a stainless steel cable under stress at high temperatures. Meanwhile, to explore the effect of different initial pre-stressing levels

3

on the mechanical properties of stainless steel cables after a high temperature, three initial stress levels of 0.3F u , 0.5F u, and 0.7F u and fire temperatures of 200, 400, and 600 °C were set up in the test. Data on the mechanical properties of stainless steel strands indicated a strong stability at room and high temperatures in previous studies [27,28], and high-temperature test periods are long. Therefore, only one specimen was tested for each temperaturestress condition in the high-temperature test. To compare and analyse the mechanical properties of stainless steel cables under high and room temperatures, we also tested three specimens at room temperature for tensile strength. In total, thirty specimens were considered in this study. The number of samples and corresponding temperature-stress levels are shown in Table 3. The mechanical property test of stainless steel cables after high temperatures included the following three stages: heating the specimen under static loading, natural cooling, and static stretching. Before the formal test, to simulate the stainless steel cable extreme stretching procedure before delivery. At a loading speed of 10 MPa/s, a cable was uniformly loaded to 50% of the minimum cable breaking force (elastic tension stage) and subsequently, uniformly unloaded to 5% of the minimum cable breaking force. This process was repeated three times to eliminate the effect of each wire gap in the stainless steel cable on the test results. Subsequently, the specimens were loaded to the

Fig. 2. Detailed dimensions of the specimens.

4

G. Sun et al. / Journal of Constructional Steel Research 172 (2020) 106177

experimental specimens and the high-temperature furnace did not attain the same temperature at the same time; hence, the temperature was maintained for two hours. The furnace was then cooled naturally to room temperature in air. Finally, the displacement sensor was reset to zero, and the specimens were loaded at a uniform rate of 10 MPa/s (according to the provision of GB/T 242191-2009 for the determination of actual elastic modulus of steel wire ropes) until failure. The stressstrain curve was recorded using the test machine and the displacement sensor connected to the extension rod system during the test. The temperature control box was used to control and record the temperature change with time in the high-temperature furnace. The stress-strain curve, tensile strength, yield strength, elastic modulus, and fracture strain of the stainless steel cables under different temperature stress were obtained. 3. Test results and analysis 3.1. Testing phenomenon Fig. 3. Test setup of tensile test.

Fig. 4. Deformation measurement system.

Table 3 Number and corresponding temperature-stress conditions of specimens. Specimen number

T-f

1×19

1×37

1×61

1×19-0 1×19-1 1×19-2 1×19-3 1×19-4 1×19-5 1×19-6 1×19-7 1×19-8 1×19-9

1×37-0 1×37-1 1×37-2 1×37-3 1×37-4 1×37-5 1×37-6 1×37-7 1×37-8 1×37-9

1×61-0 1×61-1 1×61-2 1×61-3 1×61-4 1×61-5 1×61-6 1×61-7 1×61-8 1×61-9

30 °C 0.3Fu-200 °C 0.3Fu-400 °C 0.3Fu-600 °C 0.5Fu-200 °C 0.5Fu-400 °C 0.5Fu-600 °C 0.7Fu-200 °C 0.7Fu-400 °C 0.7Fu-600 °C

corresponding pre-stressing levels (0.3Fu, 0.5Fu, and 0.7Fu), the target temperature was set (200, 400, and 600 °C), and the hightemperature furnace was closed and heated up to the target temperature at the rate of 10 °C/min. During the heating process, the

Fig. 5 shows the stainless steel cable specimens after the fire test. The three types of stainless steel cables arranged from left to right and numbered 1–9. The corresponding temperature-stress conditions were 0.3Fu-200 °C, 0.3Fu-400 °C, 0.3Fu-600 °C, 0.5Fu-200 °C, 0.5Fu-400 °C, 0.5Fu-600 °C, 0.7Fu-200 °C, 0.7Fu-400 °C, and 0.7 Fu-600 °C. After the test, the lengths of the specimens after the high temperature were observed to increase compared with that of the original specimens. At the same stress level, the higher the temperature was, the larger the change in specimen length was. After each stainless steel cable underwent a high temperature and was cooled by air, the surface colour of stainless steel cable was darker than at room temperature; at 200 °C, it was light yellow and exhibited a metallic lustre. At 400 °C, it was golden yellow. At 600 °C, it appeared indigo blue. The change in the surface colour of the stainless steel cable after being cooled from fire could be used to determine the highest temperature of the stainless steel cable after the fire. The specimen 1 × 61-9 (0.7Fu-600 °C) was in a state of high temperature-high stress. As the temperature continued to increase, the deformation of the specimen developed extremely rapidly, leading to the ultimate breaking of the specimen. The cooled stainless steel cables were subjected to static tensile tests at room temperature; Fig. 6(a)–(c) show the respective failure modes of the three types of stainless steel cables. In the figure, the leftmost cable is the specimen not subjected to fire, which was used for comparative analysis of the difference in the mechanical properties of stainless steel cables subjected to high temperatures and those that were not. The cables were arranged from left to right from 1–9 corresponding to the temperature-stress conditions of 0.3Fu-200 °C, 0.3Fu-400 °C, 0.3Fu600 °C, 0.5Fu-200 °C, 0.5Fu-400 °C, 0.5Fu-600 °C, 0.7Fu-200 °C, 0.7Fu400 °C, and 0.7 Fu-600 °C. There were three failure modes in the test: stainless steel strands broken at the connection between the anchorage and stainless steel strand, the stainless steel strands sliding from the anchorage, and stainless steel strands broken in the middle. The figure indicates that when the fire temperature increased to 200 and 400 °C, the failure modes included the stainless steel strand breaking at the

Fig. 5. Specimens after experiencing elevated temperature.

G. Sun et al. / Journal of Constructional Steel Research 172 (2020) 106177

5

Fig. 6. Failure phenomenon of stainless steel cable specimens.

connection between the anchorage and stainless steel strands (1 × 19-1, 1 × 19-2, 1 × 19-5, 1 × 19-7, 1 × 19-8, 1 × 37-1, 1 × 37-2, 1 × 37-4, 1 × 61-2, 1 × 61-5, 1 × 61-1, and 1 × 61-8) and stainless steel strand sliding from the anchorage (1 × 37-5, 1 × 67-1, and 1 × 61-8). This indicated that when the cable’s temperature was lower than 400 °C, its mechanical properties did not significantly decrease compared with room

temperature, because the failure point of the cable was not where the fire affected the cable, but more often at the anchorage position with a complex stress state. Simultaneously, the heating-cooling process had a considerable effect on compression anchorage. After being subjected to a high temperature and cooled to room temperature, the cable’s holding force of the compression anchorage on the stainless steel strand

Fig. 7. Stress-strain curves of stainless steel cables after being subjected to high temperatures.

6

G. Sun et al. / Journal of Constructional Steel Research 172 (2020) 106177

Table 4 Post-fire nominal yield strength of stainless steel cables. No.

0 1 2 3 4 5 6 7 8 9

Combination condition

Ambient 0.3Fu-200 °C 0.3Fu-400 °C 0.3Fu-600 °C 0.5Fu-200 °C 0.5Fu-400 °C 0.5Fu-600 °C 0.7Fu-200 °C 0.7Fu-400 °C 0.7Fu-600 °C

fʹ0.2,T / MPa

fʹ0.5,T / MPa

fʹ1.0,T / MPa

1×19

1×37

1×61

1×19

1×37

1×61

1×19

1×37

1×61

1059 1144 1180 1260 1155 1291 1313 1293 1269 1261

1079 1170 1126 1266 1204 1171 1184 1122

958 995 906 964 1081 1016 1036 -

670 700 710 733 700 715 737 690 679 718

658 666 718 690 716 655 689 705

655 700 687 678 689 700 676 -

1070 1142 1175 1235 1145 1230 1271 1211 1199 1215

1071 1126 1150 1207 1191 1117 1150 1132

1008 1048 1002 1018 1103 1068 1070 -

Table 5 Reduction coefficient of post-fire nominal yield strength of stainless steel cables. NO.

0 1 2 3 4 5 6 7 8 9

Combination condition

Ambient 0.3Fu-200 °C 0.3Fu-400 °C 0.3Fu-600 °C 0.5Fu-200 °C 0.5Fu-400 °C 0.5Fu-600 °C 0.7Fu-200 °C 0.7Fu-400 °C 0.7Fu-600 °C

fʹ0.2,T / f0.2

fʹ0.5,T / f0.5

fʹ1.0,T / f1.0

1×19

1×37

1×61

1×19

1×37

1×61

1×19

1×37

1×61

1.00 1.08 1.11 1.19 1.09 1.22 1.24 1.22 1.20 1.19

1.00 1.08 1.04 1.17 1.12 1.09 1.10 1.04

1.00 1.04 0.95 1.01 1.13 1.06 1.08 -

1.00 1.05 1.06 1.09 1.04 1.07 1.10 1.03 1.01 1.07

1.00 1.01 1.09 1.05 1.09 1.00 1.05 1.07

1.00 1.07 1.05 1.04 1.05 1.07 1.03 -

1.00 1.07 1.10 1.15 1.07 1.15 1.19 1.13 1.12 1.14

1.00 1.05 1.07 1.13 1.11 1.04 1.07 1.06

1.00 1.04 0.99 1.01 1.09 1.06 1.06 -

decreased to an extent. In the tensile test at room temperature, the cable lost its bearing capacity due to the steel strand breaking from the compression anchorage too early. When the fire temperature was 600 °C, the failure modes included stainless steel strands breaking in the middle (1 × 19-6, 1 × 37-3, and 1 × 37-6) and stainless steel strands breaking at the connection between the anchorage and the strands (1 × 19-3, 1 × 37-9, 1 × 61-,3 and 1 × 61-9). The broken steel strands exhibited a clear necking phenomenon. This indicated that the strength of the cables may have decreased considerably after they were restored to room temperature from being heated at 600 °C, which was due to a large number of irrecoverable plastic strains produced by the decrease in material strength and creep at the high temperature. During the heating process, the effective cross-section of the cable in the furnace

Fig. 8. Definition of mechanical properties of stainless steel cables.

decreased. When the section decreased and the static tension test was conducted at room temperature, the internal force of this part of the stainless steel strand was larger; thus, it was the first to break in the presence of a fire. 3.2. Stress-strain curve Fig. 7 shows the stress-strain curves of three stainless steel cables after being subjected to high temperatures. The figure indicates that the stress-strain curves exhibited a lower proportional limit and no visible yield platform, which is a characteristic of stainless steel [29]. The failure modes of specimens 1 × 37-1, 1 × 37-5, 1 × 61-1, and 1 × 61-8 were stainless steel strands sliding from the anchorage. Thus,

Fig. 9. Variation in the yield strength of stainless steel cables after being subjected to elevated temperature.

G. Sun et al. / Journal of Constructional Steel Research 172 (2020) 106177 Table 6 Reduction coefficient of post-fire elastic modulus of stainless steel cables. NO.

0 1 2 3 4 5 6 7 8 9

Combination condition

Ambient 0.3Fu-200 °C 0.3Fu-400 °C 0.3Fu-600 °C 0.5Fu-200 °C 0.5Fu-400 °C 0.5Fu-600 °C 0.7Fu-200 °C 0.7Fu-400 °C 0.7Fu-600 °C

EʹT / MPa

7

Table 7 Reduction coefficient of the post-fire tensile strength of stainless steel cables. NO.

EʹT / E

1×19

1×37

1×61

1×19

1×37

1×61

134953 142261 145980 150700 141055 144678 151681 140223 141491 146272

132790 137963 138165 146299 136719 138986 146598 134114 139853 143614

133203 141472 143891 143406 138537 140969 143894 139434 143181 -

1.00 1.05 1.08 1.12 1.04 1.07 1.12 1.04 1.05 1.09

1.00 1.04 1.04 1.10 1.03 1.05 1.10 1.01 1.05 1.08

1.00 1.06 1.08 1.08 1.04 1.06 1.08 1.05 1.07 -

0 1 2 3 4 5 6 7 8 9 a

complete stress-strain curves were not obtained. In the fire stage, the temperature had a significant effect on the creep of the material [30]. The high-temperature creep and strength reduction led to some unrecoverable plastic deformation of stainless steel cable. After the stainless steel cables were subjected to fire and cooled to room temperature, they exhibited a strain hardening phenomenon, which is a prominent characteristic of stainless steel strands at high temperatures [31]. The yield strength increased higher than before the fire, but the tensile strength changed slightly.

Combination condition

ambient 0.3Fu-200 °C 0.3Fu-400 °C 0.3Fu-600 °C 0.5Fu-200 °C 0.5Fu-400 °C 0.5Fu-600 °C 0.7Fu-200 °C 0.7Fu-400 °C 0.7Fu-600 °C

fʹu,T (MPa)

fʹu,T / fu

1×19

1×37

1×61

1×19

1×37

1×61

1483 1482 1483 1525 1456 1510 1481a 1495 1493 1505

1449 1409 1542a 1485 1507a 1403 1416 1423

1332 1364 1407 1380 1305 1298 1377 -

1.00 1.00 1.00 1.03 0.98 1.02 1.00a 1.01 1.01 1.02

1.00 0.97 1.06a 1.02 1.04a 0.97 0.98 0.98

1.00 1.02 1.06 1.04 0.98 0.97 1.03 -

Represents the stainless steel strands broken in the middle.

No visible yield platform was observed in the stress-strain curve of the stainless steel cables. Referring to the method of mechanical property test results of stainless steel materials proposed by Gardner, the corresponding stress value of 0.2% residual strain was selected as the nominal yield strength of a stainless steel cable [32]. Considering that the method to determine the yield strength of stainless steel cables subjected to high temperatures has not been uniformly prescribed, some specifications have proposed to consider the stress value at 0.5 or 1.0% of the total strain in the stress-strain curve as the yield strength of the specimens [19]. Therefore, Table 4 also shows the stress values at 0.5 and 1.0% of the total strain for comparison. Table 5 shows the change in strength of f ‘0.2, T, f ‘0.5, T, and f ‘1.0, T with respect to the unburned specimens. The reduction coefficient of the yield strength of the stainless steel cables after the high temperature is the ratio of yield strength after high temperature to the yield strength of the unburned specimens. The mechanical properties of

stainless steel cables are defined in Fig. 8. As specimens 1 × 37-1, 1 × 37-5, 1 × 61-1, and 1 × 61-8 failed by their strands sliding prematurely during the tensile tests, and 1 × 61-9 was pulled during the fire stage, the static tensile at test room temperature could not be conducted for these five specimens. The yield strengths of the above five specimens after being subjected to high temperatures are not listed in Table 5. As Tables 4 and 5 show, fʹ0.5, T was closer to the proportional limit than fʹ0.2, T and fʹ1.0, T were. Therefore, fʹ0.5, T was adopted as the yield strength of the stainless steel cables, which seemed to be conservative. Fʹ1.0, T and fʹ0.2, T were similar, and the change in mechanical properties was similar after being subjected to high temperatures. Therefore, fʹ1.0, T, the stress value corresponding to 1.0% of the total strain, could be used as the yield strength of stainless steel cables after being subjected to high temperatures. Fig. 9 shows the change in yield strength of stainless steel cables after different temporal-stress couplings. The figure indicates that the yield strength of stainless steel cables after the fire increased. The increased range was less than 25%. For 1 × 19 stainless steel cable, at the same stress level, the higher the fire temperature, the more apparent the yield strength increase range was. When the fire temperature was 600 °C, the yield strength of stainless steel cables increased by approximately 20% compared with the room temperature. For 1 × 37 and 1 × 61 stainless steel cables, when the high temperature was between 30 and 400 °C, the yield strength gradually increased with temperature. When the temperature exceeded 400 °C, the yield strength decreased with increasing temperature, but it still increased as a whole, with the variation range in between 95 and 117%.

Fig. 10. Variation in the elastic modulus of stainless steel cables after being subjected to elevated temperatures.

Fig. 11. Variation in the tensile strength of stainless steel cable after being subjected to elevated temperatures.

3.3. Nominal yield strength

8

G. Sun et al. / Journal of Constructional Steel Research 172 (2020) 106177

Table 8 Reduction coefficients of post-fire fracture strains of the stainless steel cables. NO.

0 1 2 3 4 5 6 7 8 9 a

Combination condition

Ambient 0.3Fu-200 °C 0.3Fu-400 °C 0.3Fu-600 °C 0.5Fu-200 °C 0.5Fu-400 °C 0.5Fu-600 °C 0.7Fu-200 °C 0.7Fu-400 °C 0.7Fu-600 °C

εʹf,T

εʹf,T / εf

1×19

1×37

1×61

1×19

1×37

1×61

0.0288 0.0224 0.0176 0.0184 0.0193 0.0162 0.0204a 0.0198 0.0173 0.0162

0.0212 0.0190 0.0372a 0.0265 0.0330a 0.0179 0.0170 0.0154

0.0235 0.0292 0.0343 0.0310 0.0176 0.0181 0.0287 -

1.00 0.78 0.61 0.64 0.67 0.56 0.71a 0.69 0.60 0.56

1.00 0.89 1.69a 1.25 1.56a 0.84 0.80 0.73

1.00 1.24 1.46 1.32 0.75 0.77 1.22 -

Represents the stainless steel strands broken in the middle.

Fig. 12. Variation in the fracture strains of stainless steel cables after being subjected to elevated temperatures.

3.4. Elasticity modulus According to the method for the measurement of actual elastic modulus of steel wire ropes in the GB/T 24191-2009 standard, the elastic modulus of a stainless steel cable after a high temperature is calculated by determining the slope of the 10–30% section of the minimum breaking force of the cable. Table 6 shows the elastic modulus of stainless steel cables after being subjected to high temperatures and the reduction coefficient of the elastic modulus under different temperatures and stress conditions. The reduction coefficient of the elastic modulus of stainless steel cables after high temperatures was the ratio of the elastic modulus, EʹT, after the high temperature to the elastic modulus, E, of unburned specimens. 1 × 61-9 was broken at the stage of fire; as a result, it could not be subjected to the room-temperature static tensile test. Hence, its elastic modulus after high temperature could not be measured. Fig. 10 shows the change in the elastic modulus of stainless steel cables after different temporal-stress couplings. The figure indicates

that the elastic modulus of the stainless steel cables after high temperatures increased; this was because, after the high temperatures, the internal properties of stainless steel strands changed [33]. The overall trend of change was as follows: the initial stress level was the same and the elastic modulus of the stainless steel cables increased with increase in the high temperature. At the same high temperature, the elastic modulus of the stainless steel cables decreased with increase in the initial stress. 3.5. Tensile Strength The tensile strength of the stainless steel cables was calculated using the peak point of the stress value on the stress-strain curve, which reflected the maximum bearing capacity of the stainless steel cable after high temperatures. Table 5 shows the tensile strength and reduction coefficient of the tensile strength of stainless steel cables after high temperature. In the table, the stainless steel strands broken in the middle are marked by *. As specimens 1 × 37-1, 1 × 37-5, 1 × 61-1, and 1 × 61-8 failed by sliding prematurely in the tensile process of the test, the maximum stress values at the time of specimen failure are not listed in Table 7. The reduction coefficient of the tensile strength of stainless steel cables after being subjected to high temperatures was the ratio of tensile strength, fʹu, T, and the tensile strength, fu, of unburned specimens after being subjected to high temperatures. Fig. 11 shows the variation in the tensile strength of stainless steel cables being subjected to high temperatures. The figure indicates that whether the break position of the stainless steel cables was the connection between anchorage and stainless steel strands or in the middle of the strands, the tensile strength of the three types of stainless steel cable after the high temperature exhibited a slight difference compared with that before the fire. The variation range was basically between 97 and 107%, approximating to 100%. Therefore, when the fire temperature was less than 600 °C and initial stress less than 0.7Fu, the effects on the tensile strength of the stainless steel cables after the high temperature was negligible. The tensile strength of the stainless steel cables after high temperatures could be restored to the level of strength before the fire. 3.6. Fracture strains The fracture strain is the maximum strain at the moment of breaking of a stainless steel cable, which can reflect the plastic deformation capacity of the stainless steel cable to a certain extent and ensure a sufficient safety reserve of the structure. The tensile displacement of the

Table 9 Overview of the mechanical-properties test after being subjected to elevated temperatures. Experiment object

T (°C)

Initial stress state

Cooling mode

stainless steel cables Galfan-coated steel cables concrete steel cables 304 stainless steel

200~600 °C 100~500 °C 100~600 °C 100~600 °C

yes yes no no

Natural air cooling Natural air cooling Natural air cooling Natural air cooling

Fig. 13. Comparison of variation in yield strengths.

G. Sun et al. / Journal of Constructional Steel Research 172 (2020) 106177

Fig. 14. Comparison of variation in elastic modulus.

stainless steel strand was measured using the SANS universal testing machine, and the ratio of the tensile displacement to the original length of the stainless steel strands was the fracture strain. Table 8 shows the fracture strains and their reduction coefficients of the stainless steel cables after being subjected to high temperatures. The stainless steel strands broken in the middle are marked by *. The reduction coefficient of the fracture strain of the stainless steel cables being subjected to high temperatures was the ratio of the fracture strain, εʹf, T, after the high temperatures to the fracture strain, εf, at room temperature. As specimens 1 × 37-1, 1 × 37-5, 1 × 61-1, and 1 × 61-8 failed by sliding prematurely during the tensile test, the failure strains of these specimens when they failed are not listed in Table 8. Fig. 12 shows the variation in fracture strain of the stainless steel cables after high temperatures. The figure indicates that the fracture strains after high temperatures were related to the initial pre-stress levels in the fire stage and the processing levels of the cables. During the high temperature, due to the decrease in the strength of the stainless steel cables and high-temperature creep action producing an irreversible plastic deformation, the initial stress level was higher, the fire stage plastic deformation was greater, and during the cooling to room temperature, the fracture strain was also smaller. This phenomenon was deduced from the change in fracture strain of the 1 × 19 stainless steel cable specimen after high temperatures. Except for 1 × 19-6 (0.5 Fu-600 °C), the breaking position of this cable type occurred at the

9

connection between the anchorage and stainless steel strands with a relatively complex stress state, and the fracture strain decreased gradually with increase in fire temperature. After being subjected to high temperatures, the breaking position of the cable primarily included the following: (1) the position of connection between the anchorage and stainless steel strands, which was prone to stress concentration in the process of the static tensile test, leading to excessive stress on the steel wire and thus breaking; (2) in the middle of the stainless steel strands. This part was in the high-temperature furnace during the fire stage. Because of the decrease in material strength and high-temperature creep, a large number of irreversible plastic strains were produced, resulting in a decrease in the effective cross-section of the cables in the furnace. When the static tensile test was conducted at room temperature, the internal force of the stainless steel strands in the furnace was relatively large; hence, the destruction of the parts affected by the fire occurred first. When the fire temperature was 600 °C, the ductility of the cable increased considerably after the hot deformation [34]. The fracture strain of stainless steel cables subjected to a temperature of 600 °C increased considerably compared that of cables without fire and low fire temperatures. This phenomenon was apparent in the 1 × 37 gauge cable. The fracture positions of specimens 1 × 37-3 (0.3 Fu -600 °C) and 1 × 37-6 (0.5 Fu -600 °C) occurred in the middle of the stainless steel strands and the fracture strains after high temperatures exceeded that of the unburned specimens. However, the fracture strains of different cables were still discrete due to the effect of the manufacturing level. 4. Comparative analysis with carbon steel cable 4.1. Overview of mechanical properties test after high temperatures The difference in the mechanical properties of the stainless steel cables after high temperatures and carbon steel cables and other types of stainless steel materials after high temperatures were explored by treating stainless steel and Galfan-coated steel cables, pre-stressed steel strands in concrete structures [35] and 304 stainless steel [36] at high temperatures and analysing their mechanical properties. The mechanical properties of the pre-stressed strand [35] and 304 stainless steel [36] at high temperatures were compared. As Table 9 shows, the stainless steel and Galfan-coated steel cables were heated under a state of initial stress, while the pre-stressed steel strands for concrete and 304 stainless steel were heated under a state of no stress. Among them, the test data of 1 × 19 stainless steel cables with a stress state of 0.5Fu were selected to compare the gap between the stress-free and stress states. The comparison was made more appreciable by comparing the reduction coefficient of the mechanical properties. 4.2. Yield strength

Fig. 15. Comparison of variation in ultimate strength.

Fig. 13 shows the yield strength reduction coefficients obtained during the post-fire test. The figure indicates that the yield strength of the stainless steel cables increased gradually with temperature when the fire temperature did not exceed 600 °C. However, the yield strength of Galfan-coated steel cables initially increased and subsequently decreased after high temperatures. The yield strength of the concrete strands decreased gradually with increase in temperature, while the yield strength of 304 stainless steel at high temperature was virtually unchanged compared with that before the fire. The yield strength of the stainless steel cables and 304 stainless steel specimens did not decrease at high temperatures compared with ambient temperature, while the yield strength of Galfan-coated steel cables and pre-stressed steel strands for concrete exhibited a noticeable decrease after high temperatures, indicating that stainless steel has a better fire resistance than carbon steel. Meanwhile, the yield strength of both the stainless steel and Galfan-coated steel cables increased to a certain extent, while for the steel strand for concrete did not. Because both the former

10

G. Sun et al. / Journal of Constructional Steel Research 172 (2020) 106177

Fig. 16. Comparison between equation-predicted and test values of yield strength.

had specific initial stress in the fire stage, after high-temperature cooling, the specimens exhibited a certain degree of work hardening phenomenon, resulting in an increase in the yield strength compared with room temperature. When the ignition temperature exceeded 200 °C, the yield strength of the materials affected by the hightemperature action of steel gradually exceeded the positive effect of work hardening on the yield strength of Galfan-coated steel cables. The yield strength of Galfan-coated steel cables after being subjected to high temperatures gradually decreased with an increase in temperature. 4.3. Elasticity modulus Fig. 14 shows the reduction coefficients of elastic modulus obtained during the post-fire test. As the figure shows, when the fire temperature was lower than 600 °C, the elastic modulus of the four specimens obtained by the experiment did not decrease significantly. The elastic modulus of stainless steel cables and stranded steel wires used in concrete increased rather than decreased, and the elastic modulus of stranded steel wires coated with Galfan was the same after the experiment as before the fire. The elastic modulus reduction coefficient of 304 stainless steel specimens fluctuated significantly after the experiment. Table 9 indicates that the pre-stress of four different test

members were grouped, and then after the high-temperature test, Fig. 14 indicates that the elastic modulus reduction coefficient obtained by the four experiments was between 97 and 110%, regardless of whether the sample had initial pre-stress during heating. When the fire temperature was lower than 600 °C, the elastic modulus of the sample after cooling could be restored to the corresponding level before fire [36]. 4.4. Tensile Strength The reduction coefficients of tensile strength obtained by the test after high temperatures are shown in Fig. 15. The figure indicates that when the high temperature did not exceed 300 °C, the tensile strength of all four specimens could recover to the response size they had before being exposed to fire. When the fire temperature was between 300 and 600 °C, the tensile strengths of stainless steel cable and 304 stainless steel specimens hardly decreased. The tensile strength of Galfancoated steel cables and pre-stressed steel strands for concrete decreased noticeably. At 500 °C, after cooling, the tensile strength of the Galfancoated steel cables returned to 70% of that before the high temperature. When the steel strands of concrete were heated at 600 °C, their tensile strength after cooling could be restored to approximately 60% of that before the high temperature.

G. Sun et al. / Journal of Constructional Steel Research 172 (2020) 106177

11

Fig. 17. Comparisons between equation-predicted and test values of the elastic modulus.

4.5. Decrease in mechanical properties at high temperatures Through comparative analysis, the mechanical properties of stainless steel cables after high temperatures were observed to exhibit certain differences under different fire temperatures and initial pre-stress levels. However, post-fire mechanical properties of stainless steel cables were relatively different from that of Galfan-coated steel cables, steel strands for concrete, and stainless steel materials. The reduction equations of the yield strength, elastic modulus, tensile strength, and fracture strain of stainless steel cable under high temperatures are provided here, which can provide a reference for the safety assessment and post-disaster repair of pre-stressed spatial structures.

Fig. 18. Comparison between equation-predicted and test values of ultimate strength.

4.5.1. Yield strength The dispersion of yield strength of three types of stainless steel cables was relatively large after high temperature. The yield strength of the 1 × 19 stainless steel cables increased with temperature, while that of the 1 × 37 and 1 × 61 stainless steel cables initially increased and subsequently decreased. However, on the whole, when the temperature of the

12

G. Sun et al. / Journal of Constructional Steel Research 172 (2020) 106177

stainless steel cable did not exceed 600 °C, the yield strength after the fire increased compared with that before the fire. Based on the test results, the reduction equation of the yield strength of the stainless steel cable after being subjected to high temperatures are provided here: f 00:2,T =f 00:2 ¼ 0:826 þ 6:526  10−4 T þ 0:642μ − 9:407  10−7 T 2 − 0:607μ 2 þ 2:376  10−4 Tμ

ð1Þ

where fʹ0.2, T is the yield strength of a stainless steel cable after high temperature; fʹ0.2 is the yield strength (MPa) of a stainless steel cable before fire; T is fire temperature, where 200 °C ≤ T ≤ 600 °C; and μ is the ratio of force in the fire to the breaking force at room temperature. Fig. 16 shows the comparison between the formula-predicted value and the test results. 4.5.2. Elastic modulus The elastic modulus of three types of stainless steel cables changed similarly after high temperatures, increasing gradually with the increase in fire temperatures, and the reduction coefficient of the three types of stainless steel cables exhibited slight differences. The reduction equation of the elastic modulus of the stainless steel cable after being subjected to high temperatures is shown below:

E0T =E ¼ 0:957 þ 2:981  10−4 T þ 0:179μ − 6:691  10−8 T 2 − 0:183μ 2 − 1:152  10−4 Tμ

ð2Þ

where EʹT (MPa) is the elastic modulus of the stainless steel cable after being subjected to high temperatures, E is the elastic modulus of stainless steel cable before fire (MPa), T is fire temperature (200 °C ≤ T ≤ 600 °C), and μ is the ratio of force in fire to the breaking force at room temperature. The comparison between the formula-predicted value and the test results as shown in Fig. 17.

4.5.3. Tensile strength The variation in the tensile strength of stainless steel cables of three types was similar after high temperatures. When the temperature of the fire was lower than 600 °C, the tensile strength of stainless steel cables cooled to room temperature after being subjected to the high temperature exhibited a slight difference from that before the fire. The reduction equation of tensile strength is shown below. The comparison between the formula-predicted value and test results is shown in Fig. 18.

Fig. 19. Comparison between equation-predicted value and test value of the ultimate strain.

G. Sun et al. / Journal of Constructional Steel Research 172 (2020) 106177

f 0u,T = f u ¼ 1

ð3Þ

where fʹu, T (MPa) is the tensile strength of stainless steel cable after a high temperature (MPa), fu is the tensile strength (MPa) of stainless steel cable before the fire, and T is fire temperature (200 °C ≤ T ≤ 600 °C). 4.5.4. Fracture strain The fracture strains of the stainless steel cables varied significantly after high temperatures. To provide sufficient safety reserve for the design of structural fire resistance, we considered the lower limiting value of the fracture strain reduction coefficient of the stainless steel cable specimen for fitting. The fracture strain reduction equation of the stainless steel cable after high temperatures is shown below: ε0 f ,T =εf ¼ 1:085 − 0:002T þ 0:047μ þ 2:467  10−6 T 2 − 0:005μ 2 − 1:984  10−4 Tμ

ð4Þ

where εʹf, T is the fracture strain of the stainless steel cable after high temperature, ε f is the fracture strain of the stainless steel cable before fire, T is fire temperature (200 °C ≤ T ≤ 600 °C), and μ is the ratio of force in fire to the breaking force at room temperature. The comparison between the formula-predicted value and the test results is shown in Fig. 19. 5. Conclusions The mechanical properties of stainless steel cables after being subjected to high temperatures are examined in this paper. Stainless steel cables at different stress levels were tested under fire, and the specimens were naturally cooled by air to conduct static tension tests at room temperature. The variations in elastic modulus, tensile strength, yield strength, fracture strain, and stress-strain of stainless steel cables under different temperature-stress conditions were obtained. The mechanical properties of stainless steel cables after high temperatures were compared with Galfan-coated steel cables, pre-stressing strands for concrete, and stainless steel materials. The conclusions are as follows: (1) The mechanical properties of stainless steel cables will change after high temperatures, but the various procedures of various mechanical indexes are not the same. In general, when the fire temperature does not exceed 600 °C, the tensile strength of the stainless steel cable through air cooling can be restored at room temperature. The elastic modulus and yield strength increase slightly compared with that before the fire, and the increased range is within 20%. The fracture strain will gradually decrease with the increase in fire temperature. After a stainless steel cable is subjected to a high temperature of 600 °C, its fracture strain can only recover to 56% of that before the fire. Sufficient focus should be given to the safety assessment of the structural performance of the pre-stressed structure after a fire. (2) Compared with the heating process under the stress-free state, the stainless steel cables will exhibit irreversible plastic deformation under the thermo-mechanical coupling state. After being cooled to room temperature, stainless steel cables will exhibit a certain degree of cold work hardening, which causes their yield strength to increase and fracture strain to decrease. The thermomechanical coupling test method can be more accurate. The mechanical properties of the stainless steel cable after a high temperature are reflected immediately. (3) The mechanical properties of stainless steel cables after high temperatures are significantly different from those of Galfan-coated steel cables, pre-stressed steel strands for concrete, and 304 stainless steel, and the fire-resistant properties of stainless steel cables are significantly better than those of carbon steel cables. (4) The reduction equation of mechanical properties provided in this paper can better reflect the change in mechanical properties such as yield strength, tensile strength, elastic modulus, and fracture strain after high temperatures, which can provide a reference for the safety assessment and repair of pre-stressed structures after fires.

13

Notation E elastic modulus at room temperature EʹT elastic modulus at after high temperature T °C Eʹ0.2, T Tangent modulus at 0.2% proof stress at after high temperature T °C Fu minimum breaking force(kN) of stainless steel cable ε strain at room temperature εʹT strain at after high temperature T °C ε0.2 strain corresponding to f0.2 at room temperature εʹ0.2, T strain corresponding to f0.2 at after high temperature T °C εu strain corresponding to ultimate strength at room temperature εʹu, T strain corresponding to ultimate strength at after high temperature T °C εf fracture strain at room temperature εʹf, T fracture strain at after high temperature T °C f stress at room temperature fʹ T stress at after high temperature T °C fʹ0.2 0.2% proof strength at room temperature fʹ0.2,T 0.2% proof strength at high temperature T °C fʹ0.5 strength corresponding to 0.5% total strain at room temperature fʹ0.5, T strength corresponding to 0.5% total strain at after high temperature T °C fʹ1.0 strength corresponding to 1.0% total strain at room temperature fʹ1.0, T strength corresponding to 1.0% total strain at after high temperature T °C fu ultimate strength at room temperature fʹu, T ultimate strength at after high temperature T °C T the temperature in °C μ the ratio of force in fire to the breaking force at room temperature. Acknowledgment This work was sponsored by National Nature Science Foundation of China [grant number 51408016] and Scientific Research Program of Beijing Municipal Education Committee, China [grant number KM201710005017] References [1] N.R. Baddoo, Stainless steel in construction: a review of research, applications, challenges and opportunities, J. Constr. Steel Res. 64 (11) (2008) 1199–1206. [2] Wei Tan, Study on steel structure material performance under high temperature (fire) conditions, Industrial Architect. 30 (10) (2000) 61–6367. [3] J. Zhao, c. Experimental study on mechanical properties of steel at high temperature, Architect. Struct. 30 (4) (2000) 26–28(in Chinese). [4] Li Guoqiang, Chen Kai, Experimental study on material properties of Q345 steel under high temperature, Building Struct. 31 (1) (2001) 53–55. [5] Xu Yan, Zhao Jincheng, Experimental study and constitutive relationship of material properties of Q235 steel under different stress-temperature path, J. Shanghai Jiaotong Univ. 38 (6) (2004) 967–971. [6] Wang Yehua, Shen Zuyan, Li Yuanqi, Research progress on fire resistance of largespan spatial structure, Space Struct. 16 (2) (2010) 3–10. [7] Kong Qingkai, Wan Peng, Basic mechanical properties and finite element method simulation of steel strand, Sichuan Architect. 23 (1) (2003) 20–22. [8] Yuanqing Wang, Yuan Huanxin, Shi Yongyuan, Application and research status of the stainless steel structure, Steel Struct. 25 (2) (2010) 1–1218. [9] Zhang Yigang, Suduo Xue, Qingshan Yang, Large span space structure[M], China machine press, Beijing, 2014. [10] T.Z. Harmathy, W.W. Stanzak, High temperature tensile and creep properties of some structural and pre-stressing steel, Fire Test Performance (1970) 186–208. [11] M. Holmes, R.D. Anchor, G.M.E. Cook, et al., Effects of high temperatures on the strength properties of reinforcing and pre-stressing steel, J. Struct. Eng. 60 (1982) 7–13. [12] M. Mirmomeni, A. Heidarpour, X.L. Zhao, et al., Mechanical properties of partially damaged structural steel induced by high strain rate loading at high temperatures – An experimental investigation, Int. J. Impact Eng. 76 (2015) 178–188. [13] Heidarpour Amin, Zhao Xiao-Ling, R. Hutchinson Christopher, et al., Mechanical response of ultra-high strength (Grade 1200) steel under extreme cooling conditions, Construction and Building Materials 175 (Jun.30) (2018) 790–803.

14

G. Sun et al. / Journal of Constructional Steel Research 172 (2020) 106177

[14] Azhari Fatemeh, Heidarpour, et al. Effect of creep strain on mechanical behaviour of ultra-high strength (Grade 1200) steel subject to cooling phase of a fire.Construction and Building Materials,2017,136(Apr.1):18-30 [15] Fan Jin, Zhitao Lu, Experimental study on prestressed steel strands performance under high temperature action, Architect. Struct. 32 (3) (2002) 50(63). [16] Zhou Huanting, Li Guoqiang, Jiang Shouchao, Experimental study on mechanical properties of steel strands materials at high temperature, J. Sichuan Univ. 40 (5) (2008) 106–110. [17] Zhang haoyu, Zheng Wenzhong. Mechanical properties of low relaxation steel strand at high temperature of class 1860. Journal of Harbin Institute of Technology, 2007, 39(6): 861-865. [18] Y. Du, J.Z. Peng, J.Y. Richard Liew, et al., Mechanical properties of high tensile steel cables at high temperatures, Constr. Build. Mater. 182 (2018) 52–65. [19] BS 5896-2012, Specification for High Tensile Steel Wire and Strand for the Prestressing of Concrete, British Standards Institution, London, 2012. [20] ASTM, A416/A416M. Standard specification for steel strand, uncoated seven-wire for prestressed concrete, West Conshohocken, PA, ASTM International, 2012. [21] ACI/TMS 216.1-14, Code Requirements for Determining Fire Resistance of Concrete and Masonry Construction Assemblies, American Concrete Institute, Michigan, 2014. [22] EN1992-1-2 Eurocode 2, Design of Concrete Structures-Part 1.2: General RulesStructural Fire Design, European Committee for Standardization, Brussels, 2004. [23] Huang Yuner, Structure performance of cold-formed lean duplex stainless steel beams at high temperatures, Thin-Walled Struct. 129 (2018) 20–27. [24] K.H. Xiang Li, C.T. Kwok Lo, Post-fire mechanical and corrosion properties of duplex stainless steel: Comparison with ordinary reinforcing-bar steel, Constr. Build. Mater. 174 (2018) 150–158. [25] Wang Xingqiang, Zhong Tao, Song Tianyi, etc. Stress–strain model of austenitic stainless steel after exposure to high temperatures, J. Constr. Steel Res. 99 (2014) 129–139.

[26] Rong Chengxiao, Shi Gang, Zuo Yong, et al., Study on properties of structural steel after overheating, Steel Struct. 33 (233) (2008) 122–131. [27] Xuhong Qiang, Frans S.K. Bijlaard, Henk Kolstein, Post-fire mechanical properties of high strength structural steels S460 and S690, Eng. Struct. 35 (2012) 1–10. [28] Liang Zhaojia, Lu Wenliang, Xie Linger FangJiwei, Experimental study on performance change of high strength steel wire after high temperature treatment, Railway Construct. (05) (2016) 166–169. [29] Wang Yuanqing, Chang Ting, Shi Yongsheng, Yuan Huanxin, Liao Dongfan, Yang Lu, Constitutive relation test of austenitic stainless steel S31608, J. Univ. 53 (09) (2013) (1231-1234+1240). [30] Wang Jun, Cai Yue, Huang Dingye, Research and application of finite element analysis on high temperature creep test of prestressed reinforcement, Chin. J. Civil Eng. (11) (2004)(1-5+55). [31] Fan Sheng-Gang, Zheng Jiacheng, Sun Wenjuan, Xia Xinfeng, Liu Meijing, S30408 austenitic stainless steel high temperature mechanical properties experimental study, J. Eng. Mech. 4 (2017)(167-176 + 186). [32] L. Gardner, M. Ashraf, Structural design for non-linear metallic materials, Eng. Struct. 28 (6) (2006) 926–934. [33] Ji Xinhua Di Yuxian, Li Linan, Qin Yuwen, Chen Jinlong, Numerical simulation of macroscopic elastic modulus of nanomaterials, J. Mech. Strength (01) (2007) 16–19. [34] Liu Guimin, Ma Lili. Analysis of mechanical properties and microstructure of 316 austenitic stainless steel annealed in air and vacuum. Journal of mechanical strength,2007(01):139-142. [35] Fan Jin, Experimental study on properties of pre-stressed steel strands after high temperature, J. Nanjing Univ. Sci. Technol. 28 (2) (2004) 186–189. [36] Fan Shenggang, Zhang Jiahan, Meng Chang, Mechanical properties of austenitic stainless steel after high temperature cooling, J. Zhejiang Univ. 51 (12) (2017) 56–62.