Ultrahigh-strength steels at elevated temperatures

Abstract The main purpose of this research is to bring deeper understanding about the use of compression loaded ultrahigh-strength steel components at elevated operating temperatures. Another reason for this research is lack of design guidelines concerning ultrahigh-strength steels. This paper provides elevated temperature tensile test data for S700 and S960 ultrahigh-strength steels and discusses the implications of the data from the point of view of structural engineering based on Eurocode 3 design procedures. The experimental part of this paper consists of the tensile testing of two ultrahigh-strength steels grades at temperatures between room temperature and 1000 °C. The models for predicting the temperature reduction factors of Young's modulus, yield strength, ultimate strength and proportional limit are also proposed based on the test results. The obtained proportional limit values together with calculations exhibited that the capacities against buckling of S700 and S960 steels at elevated temperatures are weaker than assumed in Eurocode 3 and Tetmajer's theory for these steel grades. This is mainly due to the lower proportional limit values at room temperature than expected. However, the detected proportional limits do not decrease as fast as Eurocode 3 assumes while the operating temperature increases.


Introduction
During recent years, the upper limit of the strength range of commercially available structural steels has increased considerably [1]. However, this development has not been accompanied by developments in design rules, recommendations, engineering knowledge and fabrication experience regarding ultrahigh-strength steels. Due to the lack of design guidelines, the use of the ultrahigh-strength steels with yield strengths over 700 MPa is, however, uncommon, especially in civil engineering. However, there is some research regarding the use of ultrahigh-strength steels in load bearing structural components. For example, Nassirnia et al. [2] have examined hybrid hollow columns which consisting of ultrahigh-strength corner tubes and mild steel trapezoidal corrugated plates connecting them with yield strengths 1250 MPa and 262 MPa. The ultrahigh-strength columns have even 5.5 times greater compression force resistance compared with columns without corner tubes. Farahi et al. [3] have also examined the capacity of compression loaded concrete-filled double-skin tubular (CFDST) sections, where the corner tubes were fabricated of mild and ultrahighstrength steels (yield strengths 1247 and 305 MPa). The capacity of ultrahigh-strength section was almost double (5180 and 2675 kN) compared to mild steel section. The difference was mostly due to the strengths of tube materials, because the tested cross sections and concrete were similar. Based on these papers, the ultrahigh-strength steels can improve the structural performance considerably.
Ultrahigh-strength steels are increasingly used in automotive and mechanical engineering applications where weight reduction is important. However, in civil engineering, the consumption of these modern steels is low for many reasons, not least their higher cost per unit weight. The use of ultrahigh-strength steels leads to lighter structures because of their better weight-carrying capacity. In vehicle applications, when the structure is lighter, the relative payload can be increased, which decreases transportation emissions. In such cases, the use of high-strength steels leads to financial and environmental savings. For example, compared to conventional structural steel S355, ultrahighstrength steel with yield strength of 960 MPa can lead to a weight saving of up to 60% [4]. If the yield strength is doubled the thickness of a tensile loaded component can be halved, but the situation for compression loaded parts is more complicated as buckling can be the critical design aspect. The stability under a compressive load depends more on the geometry than the strength of the material. For this reason, it is important to study the effect of the mechanical properties of high and ultrahighstrength steels on the design of compression loaded structures.
The structural design process is based on design codes, like Eurocode EN 1993 (EC3), which deal with the common steel grades with yield strength varying from 235 MPa to 460 MPa. For example, Eurocode 3 only has an extension up to the strength level S700 [5], but these additional rules are so unfavourable that in practise they offer no advantages to S700 compared to S355 or S460. Steels with yield strengths between 460 MPa and 700 MPa are referred to as high-strength steels and are located in an extension to the Eurocode 3. Steel grades with yield strengths higher than 700 MPa, which may be referred as ultrahighstrength steels, are nowadays widely available and a need for upgrading standards is obvious. These ultrahigh-strength materials have excellent yield strength and strength-weight ratio, which are inevitable advantageous in structural steel members. Reduced yield strength to ultimate limit ratio and less studied proportional limit are material properties, which may have caused a challenge for developing commonly used design guidelines like Eurocodes. At present, design guidelines concerning the use of the ultrahigh-strength steels in structures are lacking in many standards. For this reason, it is important to ensure that the design standards are applicable for ultrahigh-strength steels. There can be really serious safety risks if the real material properties are worse than standard propose. The design guidelines and standards must always be on the conservative side to ensure the safe design. The aim of this research is to give basic information and understanding about ultrahigh-strength steels material properties and their effect on safe norm-based design procedures especially when operating temperatures are above room temperatures. The use of such steels must be based on knowledge of their material properties, which differ from those of conventional steels combined with a deep understanding about the Eurocode guidance rules.
Sajid and Kiran [6] have published a comprehensive summary of the mechanical properties of structural steels in a post-fire situation. They also tested the effect of cooling method on the post-fire properties of ASTM A572 steel (yield strength 389 MPa) with different stress concentration factors. The most considerable changes were observed when the temperature was above 600°C. They found that post-fire mechanical properties depend on the behaviour of the steel during heating and cooling, the improvement of properties is mostly due to martensite formation. The high strength of modern ultrahigh-strength steels is achieved for example by thermo-mechanical treatments such as controlled rolling and cooling or even water quenching [7], which produces at least a partially martensitic microstructure. Thus, heating by more than a few hundred degrees may decrease the strength properties considerably, due to tempering of the martensite. Qiang et al. have reported mechanical properties of ultrahigh-strength steel S960QL [8] and high strength steel S690QL [9] in temperatures between 20 and 700°C. According to Ref. [8,9], for the steel grades S960QL and S690QL, Q means quenching and tempering and L means low notch toughness testing temperature. The tests were performed using a Gleeble 3800 thermal-mechanical physical simulation system. The reduction factors of elastic modulus, yield strength and ultimate strength were reported and prediction models for the reduction factors were proposed. Maraveas et al. [10] have collected data concerning the elevated temperature and post-fire mechanical properties of structural steels with yield strengths in the range 503-1307 MPa. A model for the reduction factors of Young's modulus, yield strength and ultimate strength was also proposed. Chen et al. [11], Chiew et al. [12] and Xiong et al. [13] have studied different S690 steels at elevated temperatures up to 940°C , 1000°C and 800°C, respectively. Chen et al. and Xiong et al. were conducted both steady and transient state tests and Chiew et al. conducted only steady state tests. In [11] the yield strengths, Young's modulus and thermal elongations of S690Q (BISPLATE 80) and Grade 350 steels were presented and compared with standards. The main findings were that the yield strength, Young's modulus and thermal elongation are conservatively predicted in standards up to 1000°C compared with S690 steel. The Young's modulus values in standards for S690Q steel are between steady-and transient state test results. The reduction factors of yield strength and elastic modulus of high strength and mild steels were quite similar up to 540°C and above that the factors of higher strength steels decreases faster. In [12] the yield and tensile strengths and Young's modulus of reheated, quenched and tempered RQT-S690 steel were presented both elevated temperatures and in post fire situation. The main finding at elevated temperatures is that the steel lost most of its strength at temperature range between 400 and 600°C. In addition, it was found that the current fire design standards are unconservative for hardened steels at elevated temperatures. In [13] the thermal elongations, Young's modulus and effective strength of S690 TMCP (Thermo-Mechanically Controlled Processed) steel are presented and compared with S690 QT (Quenched and Tempered) steel. The tensile tests were performed with steady state method up to 800°C and transient state up to 600°C. They shown that the thermal elongation of TMCP steel was slightly greater above 400°C compared to QT steel, which is due to the differences of bainitic and martensitic microstructures. However, there were no noticeable differences in the reduction factors of elastic moduli of TMCP and QT steels. Xiong et al. [14] have studied also the mechanical properties of high strength RQT 701 steel at elevated temperatures up to 800°C. RQT 701 steel has a nominal proof strength of 740 MPa. They reported the reduction factors for Young's modulus and yield strength from steady state tests and for proportional limit from transient state tests also. In addition, the thermal elongations were presented. The main findings were that the Young's modulus from transient state tests were lower than those from steady state tests especially above 400°C. However, there were not considerable differences in yield strengths between steady state and transient state tests, so it is reasonable to utilize steady state test method for yield strength determination at elevated temperatures although transient state test takes better account of the effects of the creep.
In previous research, the effect of elevated temperature on the proportional limit was not considered, and tensile test results for S700 and S960 ultrahigh-strength structural steels above 700°C have not been reported previously. Qiang et al. [8,9] have reported the temperature reduction of Young's modulus, yield strength and ultimate strength for S960QL and S690QL steels, at temperatures up to 700°C. They have also done a comprehensive research of reductions in different design standards: BS5950, AISC, ASCE, AS4100 and EC3, so there is no need for re-comparison of reductions in the design standards. In Europe, Eurocode is the only allowed design standard, so this paper examines the suitability of ultrahigh-strength steels for Eurocode-based design. In addition, Azhari et al. [15][16][17] have reported yield and ultimate strength reductions under fire and after cooling conditions of 1200 grade steel up to 800°C. These type ultrahigh-strength steels are manufactured by extrusion or roll forming from plates and quenching and are typically used in automotive engineering for enhancing vehicle safety [18]. Heidarpour et al. [18] also proposed two-piece models for predicting the reduction factors of VHS steel for proof stress and ultimate strength up to 600°C. They show that the strength of ultrahighstrength (Grade 1200) steel decreases considerably after cooling down from 450°C and 600°C while that temperatures does not affect on the mild steels noticeably. This difference is mainly due to the different microstructures; ultrahigh-strength steel is martensitic and heating up to 600°C continues the tempering process while the strength is reduced [15]. In ref. [16] the main finding of heat-up tests was that the most of strength is deteriorated when test temperature is raised up to 800°C. The deterioration of yield and ultimate strengths was the fastest between 300 and 700°C and between 700°C and 800°C it was considerably slower. According to ref. [17], the water cooling after fire situation from 800°C gives about 60% higher ultimate tensile strength in comparison with air cooling. However, water cooling produces more brittle microstructure which may be due to martensite formation.
In this study, the structural steels S700 and S960 are tested in the temperature range 20-1000°C. The mechanical properties, elastic modulus, proportional limit, yield strength and ultimate strength, described above are determined based on elevated temperature tensile tests. The main purpose of this paper is to study the stability design and proportional limits of ultrahigh-strength steels at elevated temperatures.
Reduction factors as defined in Eurocode 3 were also defined and models for predicting the reduction factor for the proportional limit, Young's modulus, yield strength and ultimate strength are proposed on the basis of the model of Maraveas et al. [10]. Buckling stress limits based on measured proportional limits and the minimum proportional limits according to Eurocode 3 are determined for the design of compression loaded structural members. The development of design guidelines and recommendations is a long-term process requiring extensive testing and research. This publication contributes to the learning process and the development of design rules. This study also seeks to advance the protection of the environment by promoting the use of the ultrahigh-strength steels in engineering.

Experimental study
The aim of the material testing is to determine the effect of temperature on the mechanical properties of ultrahigh-strength steels. The most important mechanical properties are Young's modulus, the proportional limit, the yield strength and the ultimate tensile strength. In addition, the ultimate tensile strain is important property because it describes the ductility of the steel. Ultrahigh-strength steels typically do not have clear yield limit so the plastic strain of 0.2% corresponding to the yield strength is generally used. These properties are needed in structural engineering analysis as a function of temperature, especially in fire design or the strength and stability analysis of shell structures at elevated temperatures. The nature of these two limit states are different. In fire design, it is assumed that temperature rises as a function of time according to a standardized temperature-time curve under constant load. The most common loading history is the temperature-time curve given in the standard EN 13501-2 [19]. The strength and stability analysis of shell structures according to the standard EN 1993-1-6 [20] assumes that temperature is constant while load increases during the analysis.
Tensile properties can be determined by using either steady state or transient state testing. In steady state testing, the load is raised until the specimen breaks in the constant temperature. In transient testing, the temperature is raised under constant load until the specimen breaks, this method was applied for example in [21] with Gleeble 3800 system because transient test method can be more realistic in simulation of nature of fire situation and creep effects. However, the more easily applied steady state test seems to give the quite similar results with transient state test [8] and has been used in this study. In addition to this, the steady state test gives stress-strain curves directly. The steady state material testing method is, of course, suitable for the strength and stability analysis of shell structures due to the nature of the loading in the test and in practise as described above. The steady state testing was applied also in [15]. The realistic fire heat rate, creep or comparison of the test methods are not considered in this research. In addition, microstructural research was also excluded from this study. If there was creep during the heating period due to high temperature or preload, the creep effects are not included in the tensile test results, because the elongation measurement was started after heating and holding periods. This is shown in Fig. 3 where testing procedure is described. Possible creep during the tensile test was included in the test results but creep effects are not separated from the results. Tensile tests at high temperatures were performed according to the EN ISO 6892-2 [22], so all test results according to this standard may include creep effects.
Tensile tests were conducted according to the standards EN ISO 6892-1 [23] and EN ISO 6892-2 [22] for the room temperature and elevated temperature testing, respectively. The test materials were 6 mm thick plates of the commercially available steels Strenx 700 MC PLUS and Strenx 960 MC (EN 10149-2) from the SSAB company. The nominal mechanical properties and chemical compositions of the tested steels are shown in Table 1. The manufacturing process and high strength of the steels are based on thermomechanical rolling (TMCP) and direct quenching (DQ) after rolling process. This manufacturing process gives martensitic-bainitic microstructure for Strenx 960 MC and bainitic-ferritic microstructure for Strenx 700 MC PLUS [24,25].
Test specimens were water jet cut and machined to the dimensions given in Fig. 1. For test temperatures over 200°C a Zwick Z100 testing machine equipped with Maytec high-temperature tensile testing equipment was used while a Zwick temperature chamber was used for testing at 200°C. The main difference between the Zwick temperature chamber and the Maytec equipment is that the temperature chamber has longer extensometer arms. A view of the test device with the Maytec equipment is shown in Fig. 2. Both extensometer arms in the tests were clip-on type arms from Zwick Roell Group, which are mounted directly on the specimen. Extensometer was mounted automatically just before the tensile test start when the target temperature was reached. In that case the gauge length of 50 mm is constant at the beginning of the test. The same test specimen attachments, made of high temperature strength and oxidation resistant alloy (Inconel), were used in all tests to minimise the inaccurate specimen alignment. These attachments were made rotationally symmetric by turning and the specimens were fastened to attachments by central threads. In addition, during the fastening of the test specimens to attachments, the force sensor was observed; if the force value increases or decreases, it may be due to inaccurate specimen alignment.
Thermal expansion was noticed by keeping the preload constant during the heating period. Preload was 0.5 MPa, which causes tension force of 6.3 N, and it was kept constant by moving the crosshead of the test machine in line with thermal expansion. This was performed to compensate for the thermal expansion to avoid unwanted compression stress or -deformation in a test specimen, which could distort the test results. The test speeds were selected based on EN ISO 6892-1 [23] and EN ISO 6892-2 [22], where the test speeds for determination of strength and strain values are lower at higher temperatures. The tensile tests were displacement controlled with a strain rate of 0.008 1/s at room temperature and 0.0014 1/s at higher temperatures. The stress rate for the determination of Young's modulus was 30 MPa/s at room temperature. This stress rate is based on EN ISO 6892-1 [23] test method B, where the stress rate must be between 6 and 60 MPa/s when the nominal elastic modulus is over 150 GPa. According to [23], the stress rate 30 MPa/s corresponds to method A range 2 under certain conditions. Above room temperatures, the strain rate for Young's modulus determination of 0.0014 1/s was used. The strain rate for yield point Table 1 Chemical compositions (wt%) and specified mechanical properties of the studied steels.

Material
Chemical composition %  Table 2. At temperature range from room temperature to 200°C, the tests were controlled by extensometer. At higher temperatures, only the beginning of the tests were controlled based on extensometer. The extensometer was attached to the specimen after heating and holding periods, so the thermal expansion was also excluded from the test results. The maximum measurement travel of hot tensile test extensometer in tensile tests was 10 mm and extensometer had to be detached before fracture to avoid extensometer failure. After this point, the tensile tests were controlled based on cross head measurements. The maximum heating rate was set to 30°C/min but a typical heating rate was approximately 20°C/min. The furnace was heated by three separately controlled resistors, which were located in the upper, middle and lower part of the furnace. Temperature was measured with six detectors, three measuring the temperature of the air in the furnace and three measuring the temperature of the test specimen. The maximum deviation for the preselected test temperature was ±3°C, in accordance with the requirements of the standard EN 6892-2:2011 [22]. When the desired temperature was reached, the holding time before the start of tensile test was 120 s. This holding time was selected based on the strain values due to thermal expansion; tests were started when the strain values had stabilized. Relatively short holding time is due to small dimensions of the specimen (Fig. 1). The schematic presentation of high temperature tensile test procedure is shown in Fig. 3. The test temperatures were 20°C, 200°C, 400°C, 600°C, 800°C and 1000°C. Altogether 36 tests were performed, three at each test temperature. A typical sample before and after the tensile test is shown in Fig. 1, from which the large elongation is visible. Fig. 4 shows how the stressstrain curves were used to determine the various tensile properties studied. Young's modulus is the tangent modulus at the origin, the proportional limit is the limit stress corresponding to 0.002% plastic strain, yield strength is the limit stress corresponding to 0.2% plastic strain and the ultimate strength is the stress leading to failure in displacementcontrolled tension test. The determination of plastic elongation at maximum force Ag and plastic elongation at fracture A are shown also in Fig. 4. Proportional limit with strain of 0.002% was used because it is commonly used in technical applications [26]. BS 5950 [27] allows to use the strains of 0.2%, 1.5% and 2.0% for determination of elevated temperature yield strength (proof stress) of steel grades S275 to S355. In Eurocode 3 [28] the terms corresponding these strains are called yield strain, limiting strain for yield strength and ultimate strain. Yield Fig. 1. Test specimen dimensions according to EN 6892-1 and typical test specimen before and after testing. The tested specimen is S960 steel and test temperature was 800°C.   [29]. In ref. [29], equations for predicting yield strength, elastic modulus, ultimate strength and ultimate strain for cold-formed G550 and G450 steels were also proposed. At 970°C reduction factors with 0.2% and 2% strains are 0.022 and 0.027 for G550 steel, and 0.04 and 0.045 for G450 steel, correspondingly. This means the difference of a few MPa's, which is about the same size of typical deviation in tensile testing.

Fig. 5a
) shows examples of measured stress-strain curves for various temperatures. It is clear that the ultimate limits decrease considerably, while the total elongation increases as the temperature rises to 1000°C . Young's modulus, proportional limit, yield limit and ultimate limit are given in Fig. 5b) and Tables 3 and 4 as a function of temperature. Uniform and total elongation values are given in Fig. 5c) and Table 5. The values in Tables 3, 4 and 5 are averages of three test results. The values of stress properties are below 100 MPa at 1000°C and Young's modulus below 100 GPa at 800°C and 1000°C. Based on these values, the assumption of EC3 that the values at 1200°C are zero is accordance with the test results.
Steel must be sufficiently ductile that it can be utilized in the application of civil engineering where plastic analysis can be applied. Ductility is an important factor to show the plastic deformation ability of the material. The uniform and total elongations describe the ductility of steels on a general level. Uniform elongation (A gt ) is an elongation at maximum force in the tensile test when the stress is calculated based on the original cross section of tensile test specimen, as shown in Fig. 4. Necking of the test specimen starts when strain value reach uniform elongation and end when final fracture occurs at total elongation (A t ). Between the yield limit and uniform elongation, the material is strain hardened. If the load causes the elongation above uniform elongation, the permanent local deformation is visible. The percentage of strain hardening area of total elongation A gt,θa / A t,θa is shown in Fig. 5  d) and Table 5.
Generally, ductility shows the amount of absorbed energy or ability to deform plastically before fracture, and it is high when both the strength and strain of material are high before fracture. The uncomplicated way to assess ductility at elevated temperatures is the ratio of uniform elongation and uniform elongation of room temperature A gt,θa / A gt,θRT [16], the greater value means better ductility. The values of this ratio are shown in Fig. 5 d) and Table 5. Based on this ductility parameter, S960 has noticeably better ductility compared with S700 steel when temperature increases. Ductility of the steels seems to be quite similar up to 600°C, but above that the ductility of S960 increases to 5.5 when the value of S700 remains almost constant around 0.2. When Fig. 4. An example of the determination of the mechanical properties: Young's modulus E, proportional limit f p , yield strength f y , ultimate strength f u, proof elongation A y , uniform plastic elongation A g , uniform elongation A gt , plastic elongation after fracture A and total elongation at fracture A t . temperature increases, the percentage of strain hardening decreases and the same time the ductility parameter presented above decreases. This means that the behaviour of S700 steel is more brittle at high temperatures. Design standards such EC3, have the requirements according to ductility and in EC3 gives requirement where the ratio A gt / A y ≥ 15 [5,30], where A y is yield elongation as shown in Fig. 4. These ratios are also given in Table 5 showing that this requirement is meeting only 1000°C for S960 steel. This means that the application of ultrahighstrength structural steels in civil engineering needs more research work regarding to microstructure characterization to take account the higher strength steel grades.
Maraveas et al. [10] proposed two models for predicting the reduction factors of yield strength, ultimate strength and Young's modulus. They are based on a Gaussian fit (Eq. 1) and a sum of sines (Eq. 2). Models proposed by Maraveas et al. are based on steels with the yield strengths of 503 to 1307 MPa. In that case, the models tend to predict the mechanical properties of high and ultrahigh-strength steels widely.
where k p,θ is the reduction factor for the proportional limit, x is temperature (°C) and a i , b i and c i are fitting parameters. The original values for parameters a i , b i and c i are shown in Table 6 according to Maraveas et al. [10]. Qiang et al. [8] proposed models for predicting the reduction factors of Young's modulus, yield strength and ultimate strength of S960QL (quenched and tempered) ultrahigh-strength structural steel up to 700°C. The prediction models are based on tensile testing using a Gleeble 3800 system. The formula (Eq. 3) for predicting the Young's modulus is third degree equation and is applicable in temperature range 20-700°C: where k E,θ is the reduction factor for the Youngs modulus and θ is temperature (°C). The prediction formula for yield strength reduction is piecewise two-part equation (Eq. 4) and is based on steady state tests. Based on ref. [8], the yield strength reduction from transient state tests is more optimistic compared to steady state tests.
where k y,θ is the reduction factor for yield strength and θ is temperature (°C). The prediction formula for ultimate strength is also piecewise twopart equation (Eq. 5): In this study, we followed the same approach as Maraveas et al. [10] and developed new models based on the present test data and fitting with the aid of Matlab. The new models are based on Eqs. 1 and 2. Fitted curves and test results for proportional limit, yield strength, ultimate strength and Young's modulus are shown in Fig. 6. The fitting parameters for Eqs. 1 and 2 are shown in Table 7. The estimated R-square values of the resultant models and the sum of squares due to error (SSE) values are also shown. Based on the high R values and low SSE values (shown in Table 7), the Eqs. 1 and 2 with the parameters of Table 7 are able to describe the mechanical properties as the function of temperature   [8], it must be noticed that the tests in [8] were performed with Gleeble system. The choice of test equipment may have affect on test results and this may be one reason for differences; in this study the universal tensile testing machine was used. Qiang et al. [8] have also compared comprehensively the Young's modulus reduction according to design standards EC3, AISC and AS4100. Based on the Ref. [8], the reductions of EC3 and AISC standards do not differ from each other. The reduction of AS4100 is on optimistic side in comparison with EC3 and AISC. The models for yield and ultimate strength proposed in this study and models from literature and EC3 [8,10,18,20] are quite similar except for models proposed by Heidarpour et al. [18], as shown in Fig. 6. The reductions of yield and ultimate strengths according to Heidarpour et al. are significantly faster compared to other results. This may be due to higher steel grade (1200-1300 MPa) or different microstructure; the microstructure of VHS steel is completely martensitic according to Heidarpour et al. [18]. Martensite is generally more unstable when the temperature rises, which can cause faster reduction compared to ferritic microstructure, for example. The test results of S700 and S960 steels and prediction models for yield strength are below EC3 values up to 500°C, which means that EC3 is overoptimistic and may be unsafe for ultrahigh-strength steels in this temperature range. Based on Fig. 6, the models for yield and ultimate strengths proposed by Qiang et al. [8] and Maraveas et al. [10] represents the properties of tested S700 and S960 steels below 500°C . Above this, the difference between S960 and S700 steels is higher; the reduction of S960 steel is faster up to 1000°C. Between 500 and 1000°C the models proposed by Qiang et al. and Maraveas et al. are between the new models for yield and ultimate strengths of S700 and S960 ultrahigh-strength steels. In Ref. [8] the yield strength reductions from design standards EC3, BS5950, AISC, ASCE and AS4100 were compared comprehensively. The most of the test results of [8] are between reduction curves according to different standards. Based on this comparison, the yield strength reductions in EC3, BS5950 and AISC are really similar and on optimistic side when the values from ASCE are the most conservative up to 600°C . The reduction according to AS4100 is between previous standard. As shown in Ref. [8], only AISC gives the temperature reduction for ultimate strength. The reduction in this standard is optimistic in the temperature range of 20 to 400°C compared to the test results of S960QL steel. Between 400 and 600°C AISC describes the reduction of ultimate strength of S960QL steel.
The models for predicting the proportional limit reductions of S960 and S700 steels are compared to EC3 reduction with test results in Fig. 6. Based on Fig. 6 the reduction of EC3 is on conservative side compared to test results. The difference is noticeable between 100 and 800°C . Up to 500°C the reductions of S700 and S960 steels are similar but above this the reduction of S960 steel is faster.
Based on the comparison of proposed models and models from literature, the design standards can not describe mechanical properties of ultrahigh-strength steels at elevated temperatures accurately enough. The properties at elevated temperatures depends on steel grades, manufacturing process and microstructures. Thus, the specific models for predicting the behaviour of different ultrahigh-strength steels are needed. Based on the comparisons, the higher steel grade seems to have the faster temperature reduction of all reported material properties except Young's modulus. This is a major reason for the generation of new models for S700 and S960 steels. In the engineering design the accurate material models and behaviour are needed for reliable design results. Thus, the specific material model must be used in the design. For example, if the S700 MC PLUS or S960 MC steel is used in design, the corresponding material model must also be used. This study provides specific material properties of two different ultrahigh-strength steel grades in form of mathematical model based on material testing.

Discussion and comparing results to Eurocode 3 material properties
The observed reduction factors are compared with predicted values, Eurocode 3 [28] values and values from literature [8,10,16,31] in Fig. 7. The proportional limit and the yield strength reduction factors are also Table 7 Parameters for proposed prediction models of yield strength (k y ), ultimate strength (k u ) and Young's modulus (k E ) and proportional limit (k p ) for S700 and S960 steels. compared with those of S355 as given in reference [32]. The observed reduction factors of S700 steel are compared with the test results of the similar strength steels from literature [9,[11][12][13][14]31] in Fig. 8. Fig. 7a) show that the present values of Young's modulus were lower than those given in EC3; however, the temperature reduction factors are greater than those given in EC3 for both steels at  temperatures above 200°C. They are also higher than those obtained by Qiang et al. [8] and Maraveas et al. [10]. This means that the reductions of the Young's modulus of tested materials are not as dramatic as found in previous studies and assumed in standards. When comparing the test results of this study and results from [8], it must be noticed that the tests in [8] were performed with Gleeble system. The choice of test equipment may have affect on test results and this may be one reason for relatively low Young's modulus reduction factors of [8] in comparison with other test results as shown in Fig. 7a). However, Winful et al. [31] has reported even larger Young's modulus reduction factors between 200°C and 800°C for S700 MC high strength steel. The differences can be caused by different microstructures, the strain rates used, inaccurate specimen alignment or definition of Young's modulus, for example. However, based on the tests, the lower Young's modulus can be typical for these steels although the Young's modulus is generally assumed the same regardless of the steel grade. In any case, the reasons for the variation and differences of Young's modulus and the effect of temperature need further research. Generally, the Young's modulus of steels is about 210 GPa.

Tables 3 and 4, and
Tables 3 and 4, and Fig. 7b) show that the reduction factors for the proportional limit are generally greater than those given in EC3, so the deterioration of the proportional limit is not so considerable as given in EC3. The consequences of this are discussed in the case study described below. The reduction factors in EC3 are based on mild steels having a ferritic-based microstructure. The studied steels are bainiticferritic and martensitic-bainitic, which combined with higher strength seems to cause differences in proportional limit decrease. The proportional limit reductions of ultrahigh-strength steels at high temperatures were not reported in literature comprehensively, so this may need more accurate further research especially with regard to the effects of the microstructures. Tables 3 and 4, and Fig. 7c) show that, in the temperature range between 20°C and 500°C, the present yield strength reduction factors are lower than the EC3 values. Qiang et al. [8], Maraveas et al. [10] and Outinen and Mäkeläinen [32] have also found similar behaviour in this temperature range. However, Winful et al. [31] reported higher yield strength reduction factor values compared with EC3. In addition, Azhari et al. [16] has reported noticeably lower yield strength reduction factors for 1200 grade tube steel in comparison with EC3 and other literature values discussed here. This difference may be due to different steel grade. Based on the current test results and those from previous studies, it seems that the yield strength reduction factors up to 400°C in EC3 are over-optimistic. Tables 3 and 4 and Fig. 7d) show that the ultimate strength reduction factors are in good accordance with previous studies. Ultimate strength reduction factors for 1200 grade steel, according to Azhari et al. [16], are considerably lower compared to other values in Fig. 7d), which also may be due to different steel grade or microstructure. Differences of yield and ultimate strengths at 200°C can be caused by the need for large activation energy for dislocation, which appears as steps at stress-strain diagram and is called Cottrell's atmosphere [33]. In a few tensile tests, the steps in the stress-strain diagram were detected at 200°C, which may be caused by Cottrell atmosphere or blue brittleness. According to Miekk-oja's materials science text book (in Finnish), the steps in the stress-strain diagram are typically detected in tensile tests at temperature range 150°C -300°C [26].
As shown in Fig. 8a), the obtained reduction factors of Young's modulus of S700 steel in this paper are in good accordance with results from literature. Especially above about 300°C the obtained results of S700 steel are in the middle of the results from literature. In the temperature range of 20-300°C the Young's modulus reduction seems to be more conservative in comparison with other test results and Eurocode. In addition, the models proposed by Maraveas et al. [10] seems to predict the Young's modulus of S700 and similar structural steels with good accuracy. The test results of Qiang et al. [9] and Xiong et al. [13,14] are near to the EC3, while the results of Winful et al. [31] and Chen et al. [11] are on the optimistic side compared to the EC3 and test results of this paper. The results of Chiew et al. [12] are similar with the obtained properties of S700 steel above 500°C, below this, the reduction is too low for S700 steel of this study. Chiew et al. [12] has reported the proportional limit reduction as a function of temperature of S690 steel.
Based on Fig. 8b), the reduction of S690 steel is quite similar with S700 up to 400°C. Above that the reduction of S690 steel decreases more quickly and complies with the proportional limit reduction from Eurocode 3. The differences between S690 and S700 steels may be due to differences in manufacturing process and microstructures; S690 is made by reheating, quenching and tempering while S700 steel manufacturing is based on TMCP and DQ processes.
In Fig. 8c), the obtained reductions of yield strength are compared with other reductions of the S700, S690 and RQT 701 steels. Based on this Figure, the reductions of S690 and 701 steels are quite similar with obtained S700 results up to 400°C. However, the results of Qiang et al. [9] are on conservative side between 200 and 400°C. Above 400°C the obtained results of S700 are higher compared with results from Qiang et al., Chiew's et al. and Xiong's et al. [9,13,14] papers. It must be noticed that Chiew et al. and Xiong et al. have presented the yield strength reduction with the strains of 0.5%, 2.0% and 0.2%. The reduction of S690 present by Chen et al. [11] is quite similar with S700. In addition, models from Maraveas et al. [10] are in the middle of curves in Fig. 8c) which means that models proposed by Maraveas et al. [10] are suitable for this yield strength levels.
In Fig. 8d) the ultimate strength reduction of the test results of S700 steel is compared with the results of Chiew et al. [12], results of Qianq et al. [9] and Maraveas et al. [10] models. Up to 400°C the reductions of S690 is similar with other predictions, but above that the reduction Based on the tensile testing, the reductions of Young's modulus and proportional limit of S700 and S960 steels seem to be unconservative in comparison with Eurocode 3. In addition, the reductions of S700 and S960 steels are quite similar. This means that the proportional limits of TMCP and DQ manufactured high and ultrahigh-strength steels do not lose their elasticity and proportional limit so quickly than standards assumed. However, the yield strength reduction of high and ultrahighstrength steels begins immediately when temperature increases above room temperature. The tensile strength reduction begins at temperatures above 200°C. These results may limit the use of Eurocode because the prediction of it seems to be unconservative. Thus, the use of reduction according to Eurocode can lead to unsafe design in temperature range between 20 and 600°C. Similar results are shown also in literature as shown previously. This means that Eurocode and other design standards must be updated for higher strength steels.
As previously discussed, the good strength properties of the ultrahigh-strength steels are achieved by heat treatments giving at least partially bainitic or martensitic microstructures. The higher reduction of yield and ultimate strength in the temperature range 200°C -600°C can be caused by the softening of the martensite or bainite. Above the A 1 temperature (lower austenite transformation temperature, about 725°C), the principal microstructural component increasingly becomes austenite in all low-alloy steels and their behaviour is similar due to their similar microstructures. As the literature research of this paper shown, there are not comprehensive test results for the proportional limit and reduction of it for high and ultrahigh-strength steels. This paper provides the test data of proportional limits which are needed in structural design. In this paper, the tensile tests were performed using steady state testing method. This testing method does not consider creep effects, which may be important in many structures. The microstructures of 960 MC and S700 MC PLUS steels are martensiticbainitic and bainitic-ferritic, correspondingly, and these microstructures are generally unstable when operating temperature increases. This means that creep behaviour can become significant in structural stability especially in structures at elevated operating temperatures. For this reason, the research on the creep effects and microstructures of ultrahighstrength steels could be an important subject for further research.

Behaviour under compressive load -A case study
In Eurocode 3, the classification of cross-sections is given in part EN 1993-1-1 [30]. Four classes of cross-sections are defined, based on their resistance and rotation capacity. EN 1993-1-1 states: "Class 4 crosssections are those in which local buckling will occur before the attainment of yield stress in one or more parts of the cross-section". Determination of the reduction factor of tubular sections in class 4 cross-sections can be found in EN 1993-1-6 [20]. When the relative slenderness is between squash limit λ 0 and plastic limit λ p slenderness values, Eq. 8b is straight line with parameter η = 1. This relation is called Tetmajer's theory.
The example of the dependence of reduction factor χ on relative slenderness λ is described in the situation of the membrane buckling in Fig. 9. The reduction factor was calculated according to Eqs. (8, 8a, 8b and 8c) as described below, where α = 0.75 according to EN 1993-1-6 Annex D [34]. The curve was drawn without safety factors. The buckling stress can be determined with the reduction factor based on yield strength and suitable safety factors. The horizontal area in Fig. 9 corresponds the Eq. (8a), the descending straight corresponds Eq. (3b) and is called Tetmajer's theory and the parabolic curve corresponds Eq. (8c).
For the simplicity, here only the meridional direction is considered in the given equations. The characteristic buckling stress σ Rk and the reduction factor χ can be expressed as a function of the relative slenderness λ of the shell as follows: where χ ¼ 1; when λ ≤ λ 0 ; ð8aÞ where the meridional squash limit relative slenderness λ 0 = 0.20 corresponding to yield strength with reduction factor χ = 1 and the plastic range factor β = 0.60 corresponding to plastic limit relative slenderness λ p . When λ > λ p , the behaviour is entirely elastic. The characteristic buckling stress σ Rk may, instead of Eq. (8), alternatively be determined directly from σ Rk = α · σ Rcr , where α is the elastic imperfection reduction factor and σ Rcr is the elastic critical buckling stress [20]. At the point λ = λ p the reduction factor χ = 0.40 and the characteristic buckling stress σ Rk = 0.40 · f y < f p / γ, where f p is the proportional limit and γ is a suitable factor of safety, typically γ = 2.3. In Eurocode, Tetmajer's theory above is written using the definition of elastic behaviour limit according to Eq. 9: where α is the elastic imperfection reduction factor and β is the plastic range factor. Three fabrication tolerance quality classes are expressed, corresponding to specific elastic imperfection reduction factors α. In EN 1993-1-6 [20] the given tolerances are stricter than in the execution standard EN 1090. In this way, the relationship between the imperfection amplitudes and the evaluated resistance (the characteristic buckling stress σ Rk ) satisfy the definition of the proportional limit f p in Tetmajer's theory. In Eurocode 3, the buckling resistance of class 4 tubular sections can be expressed σ Rd = σ Rk / γ M1 where γ M1 is the value of the partial factor. The relevant value of γ M1 may be defined in the National Annex of Eurocodes or other upper level standards. It is recommended that the value of γ M1 should not be taken as smaller than γ M1 = 1.1, especially if the specific application standard does not exist.
In Eurocode EN 1993-1-1 the buckling resistance of members under compression depends on geometric imperfections described by imperfection reduction factor α, which is determined by a function of steel grade. In EN 1993-1-6 strength and stability of shell structures based on buckling stress σ Rk given in Eq. (8), where the values of parameters α, β, η and λ 0 should be taken from standard's Annex D and all these parameters are independent of yield strength f y . It is clear that such an approximation cannot be very accurate for all steel grades and might to lead to overestimate structures capacity. Therefore, the stress limitation for yield strength f y is needed to use in Eq. (8). In this paper, the limitations are given to S700 and S960 structural steels based on tensile testing.
Stress limitation method is a method, which limits the maximum allowable value of yield strength in determination of design strength. In EC3 the stress limitation is based on properties of S460-steel, and the same properties are assumed up to S700-grade steels [5]. The analysis is based on the stress limitation method of the Eurocode 3 and leads to requirements on the minimum allowed value of the material's proportional limit (Eq. 10): where f y,nom is the EC3 value of the yield strength at the given temperature, γ = 2.3 and β = 0.60. Using the measured proportional limit f p this leads to the stress limitation f y,limit (Eq. 11): where f p is the measured proportional limit. Measured and calculated values of these material parameters are shown in Table 7 and in Table 8 for S960 and S700 steels, where the reduction factor kf p and stress limitation values f y,limit and minimum values of proportional limit f p,min are also presented. The yield strength values of S960 and S700 at operating temperatures are also presented based on EC3 reduction factors from Tables 3 and 4. EC3 limit values are calculated by multiplying the nominal room temperature yield strength f y,nom by reduction factor EC3 k from Tables 3 and 4 at the temperature under consideration. The measured magnitudes of the proportional limit were lower than Tetmajer's theory and EC3 requirements, which are shown in Table 8 for  S960 and Table 9 for S700, where kf p < 1. In comparison of the obtained and calculated (Eq. 10) proportional limits, obtained proportional limit values are lower than calculated, except S700 proportional limit at 1000°C . This is due to the fact that the measured proportional limit of S700 at 1000°C is higher than EC3 assumed (see Fig. 7b) and the proportional limit of S960 at the same temperature is similar with EC3. In addition, Eq. (10) employs the proportional limit from EC 3 and Eq. 11 employs the obtained value. The obtained proportional limit values are 752 MPa and 566 MPa for S960 and S700, respectively, when the minimum values from Eq. 10 are 883 MPa and 644 MPa at room temperature. Low obtained proportional limit values lead to the yield strength limitations according to Eq. 11. In Eurocode stress limitation method, the yield strength limit f y,limit can be found as a minimum value of ratio kf p at the operating temperature. In Eurocode 3 the design yield strength is the same than nominal yield strength but based on the obtained proportional limit values, the yield strength limits must be lower; 817 MPa and 615 MPa for S960 and S700 steels, respectively. This means that obtained values for S960 and S700 are about 15% and 12% lower than it is assumed in Eurocode 3. Based on the analysis, Eurocode 3 seems to overestimate the capacity for buckling with S960 and S700 ultrahigh-strength steels and the updating of the standard is needed for high and ultrahigh strength steels.
Analysis shows that the kf p reduction factor values for S960-steel decreases monotonically when the temperature increases up to 800°C. However, at 1000°C reduction factor is almost double compared to factor at 800°C. This difference is due to the lower ratio of measured and calculated proportional limits. Measured proportional limit at 800°C is therefore lower than expected. The lowest kf p value is found at 800°C which leads to the stress limitation to 40 MPa. The obtained limit value for S700 grade is 498 MPa at 400°C and it is shown in Table 9. According to the examination, the capacities of S960 and S700 steels against buckling at elevated temperatures are worse than it is assumed in Eurocode 3. The capacities of S960 and S700 steels are 15-62% and 12-29% worse compared to Eurocode 3 based values. However, S700 at 1000°C has about 78% better capacity against buckling in comparison with Eurocode 3.
Shankar and Mayuram [35] showed with the aid of calculations that the transition from elastic-plastic to the fully plastic state depends on the yield strength and the strain hardening behaviour of the material. This may be one possible reason for the differences in proportional limits, because the proportional limit is the property that describes the transition between elastic and plastic area. S700 and S960 steel do not have well defined yield points so the determination of exact strain hardening area is impossible. Generally, aluminium and stainless steels have similar behaviour with the ultrahigh-strength steels of this study when the strain hardening is determined from nonlinear stress-strain curve above yield strength. The example of stress-strain -curve from the test of this study was shown in Fig. 4 where can be noticed that the tested steels do not have upper and lower yield points or plastic flow (yielding plateau) area. In addition, the tensile test results of ultrahigh-strength steels at 1000°C are difficult to compare because there are no test results from literature at this temperature, as shown above.
The ratio between yield strength and proportional limit for mild steel S355 and ultrahigh-strength steels S700 and S960 are shown as the function of test temperature in Fig. 10. The main differences between mild and high strength steels are the differences at room temperature and at 1000°C. At low temperatures the yield strengths of high strength steels are higher in relation to the proportional limit compared with mild steel. At 1000°C the difference is opposite. At these extremes the behaviour of S700 and S960 steels is similar, but between 400°C and 1000°C the ratio between yield strength and proportional limit of S700 steel is obviously higher. Fig. 10 shows that the proportional limit of different steel grades does not increase in the same proportion with yield strength at room temperature and below 600°C. It must be noticed that the mild steel S355 typically has the well-defined yield point and the yield strength of ultrahigh-strength steels in this paper is a proof stress at the strain value of 0.2%. In EC3 the expected ratio of yield strength and proportional limit is 1/0.4 = 0.25, as shown above, which is greatly higher in comparison with ratios of Fig. 10. This supposition of EC3 may be also cause of the special features of ultrahigh-strength steels as described in this paper.   It is clear that the different chemical compositions and manufacturing processes produces different microstructures, hardness and other properties, which have an influence on the mechanical behaviour of steels at different conditions. Generally, when the cooling rate of the carbon steel at manufacturing phase increases, the proportion of martensite increases and thus the strength of the steel is higher. However, martensite is more brittle and unstable in comparison with ferrite causing faster temperature reduction in mechanical properties as shown above. Ultrahigh-strength structural steels are typically manufactured based on thermomechanical controlled process combined with accelerated cooling; direct quenching or quenching and tempering. These processes produce at least partially martensitic microstructure. Depending on the steel grade, the amount of martensite or bainite varies, which leads to differences in mechanical behaviour. The steel grades in this study are Strenx 700 MC PLUS and Strenx 960 MC, which are bainitic-ferritic and martensitic-bainitic in their microstructures, respectively. These steels have different behaviour when the operating temperature increases. The differences between steel grades are typically the biggest when the microstructures are different; when the operating temperature rises to austenite transformation temperatures, the behaviour is more similar because of the presence of austenite. This study provides specific models for predicting the reduction of mechanical properties for these two ultrahigh-strength steel grades. The new model for predicting the proportional limit temperature reduction was proposed especially for buckling design.
Although, the Eurocode 3 has an extension up to S700 grade steels, there are no improvement for capacity against buckling of ultrahighstrength steels at elevated temperatures. In the EC3 design procedure, the question of the suitable stress limit or allowable design strength is problematic and depends on the design temperature of the application under consideration.

Conclusions
The steel grades S960 and S700 have been investigated and key material parameters needed for EC3 design procedures were determined as a function of temperature for the test temperatures 20, 200, 400, 600, 800 and 1000°C. Based on the tests and calculations, the following conclusions are drawn: -The measured proportional limits were lower than Tetmajer's theory assumes, but the proportional limits do not decrease so quickly than Tetmajer's theory and Eurocode 3 assumes, while the operating temperature increases. -Based on the proportional limits, the capacities against buckling of S960 and S700 steels are 15-28% and 12-29% lower at temperature range of 20-400°C than Eurocode 3 assumes. -The models for assessing the temperature reduction factors for proportional limit, Young's modulus, yield strength and ultimate strength were proposed for S700 and S960 steels.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.