1 Introduction

For modern multi-storey and industrial buildings, arenas as well as high-rise buildings with architecturally sophisticated design and increasing requirements, the use of structural components made of high-strength structural steels is appealing and has increased significantly in recent years, as the good strength-to-weight ratio of high-strength steels can contribute to reduced static cross sections and the resource efficiency of steel structures. For structures with fire safety requirements, however, the utilization of high-strength and ultra-high-strength steels is currently still hampered by a lack of experimentally verified knowledge about the material behavior in case of fire. In particular, there is a lack of expertise on mechanical material behavior under natural fire conditions and models to take into account the entire fire process, including the cooling phase and the post-fire strength.

The temperature-dependent material behavior of high-strength steels has been investigated in the past within the framework of several research projects. In particular, the focus was on investigations on the behavior of steels with nominal strengths up to 460 N/mm2 [1,2,3,4,5,6,7], as these are already established in the construction industry. Experimental results are also available on the material behavior of high-strength steels up to grade S690 [8,9,10,11,12,13]. For these high-strength steels, it was found that similar degradations in material properties existed as for mild steels. The reduction factors of the European fire design according to EN 1993-1-2 [14] are therefore able to represent the material behavior of high-strength structural steels sufficiently accurate. Within the scope of the revision of the European structural standards, the application limits of the constitutive model according to EN 1993-1-2 for fire scenarios with continuously increasing temperatures have therefore already been extended to structural steels up to and including S700 [15]. The behavior of ultra-high-strength steels with nominal strengths fy > 700 N/mm2 is also recently studied [8, 16, 17]. For an analogous extension of the application limits of part 1–2 of Eurocode 3 to ultra-high-strength steels, however, further experimental results on the temperature- and rate-dependent material behavior is essential.

In the context of modelling the constitutive behavior of high-strength and ultra-high-strength steel structures in fire, it can be assumed that, in contrast to earlier findings for mild steels [20, 21, 29,30,31], there is no reversible material behavior for quenched and tempered high-strength steels due to the manufacturing process. This fact is supported by a study on the material properties of high-strength bolts (grade 8.8 bolts) in the cooling phase of fires by F. Hanus [18] as well as a study by Wang et al. on the behavior of Q690D steel during cooling [19] and investigations of Chen et al. [22] on steel of grade G550. Some recent studies on the post-fire strength of high-strength steels [23,24,25,26,27,28] also showed that initial high-strength steels exhibit strength degradations after fire. This has led to the fact that in the upcoming second generation of the European structural fire design standard [15], the explicit allowance to consider the well-known temperature-dependent stress–strain relationships for the cooling phase of natural fire scenarios was limited to structural steels up to and including S500.

Therefore, this paper presents a comprehensive experimental study on the constitutive material behavior, which includes not only high-strength (S690QL) but also ultra-high-strength (S960QL) quenched and tempered steels in the case of natural fire scenarios under identical test conditions and takes into account in particular both the material behavior in the cooling phase and the residual strength of the material. Within the framework of the comprehensive experimental study, that comprises natural fire and post fire tests, the impact of the maximum temperature during heating on the constitutive behavior in the cooling phase of the high-strength and ultra-high-strength steels is investigated and compared to the respective behavior of grade S355 J2 + N mild steel. Finally, a constitutive material model for high- and ultra-high-strength structural steels under natural fire conditions is developed and compared to the test results of the present study as well as to results from few existing studies from literature.

2 Materials and Methods

The experimental study consists of an extensive tensile test program to investigate the temperature-dependent mechanical material behavior of high-strength steels in the cooling phase of natural fire scenarios (physically based fire curve). For the material characterisation, so called natural fire and post fire tests on small scale specimens made of high-strength (HSS) and ultra-high-strength (UHSS) quenched and tempered structural steels S690QL and S960QL were carried out. In addition, tests were conducted on test specimens made of a mild steel of grade S355 J2 + N for comparison purposes. The specimens were heated to predefined maximum temperatures Tu using an electric furnace and subsequently they were left to cool down to specified test temperatures Tt. The maximum temperatures of the tests were Tu = 400°C, 550°C, 700°C, 900°C in order to cover the temperature ranges relevant for structural steel in terms of both structural fire engineering and material technology. Analogous to the maximum temperatures, the test temperatures were set to Tt = 700°C, 550°C, 400°C, 20°C. When the test temperature was reached after the heating and cooling process, tensile tests were performed under steady state temperature conditions using a closed-loop-feedback strain-control system with a high-precision extensometer.

Each test combination of maximum and test temperature was performed twice to verify the reproducibility and reliability of the test performance. In case of significant deviations between both tests of the same configuration, which however did not occur in the study, a third test would have been performed.

2.1 Test Setup

A combined test setup consisting of an electromechanical universal testing machine with a maximum load capacity of 250 kN (manufacturer SCHENCK) and an electric furnace (manufacturer KÖNN) was used for the tensile tests. Figure 1a shows the test setup schematically and in Figure 1b, the open furnace and the testing machine as well as the high-temperature extensometer, which was used to control and measure the elongation of the specimens during the tensile tests, can be seen.

Figure 1
figure 1

(a) Schematic illustration of the installation of the specimens and the extensometer in the furnace and (b) combined test setup of furnace and testing machine

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The furnace has three independent controllable heating zones in vertical direction with a maximum temperature of 1200°C for each zone. The air temperature inside the furnace was measured by three mantle thermocouples, type N (D = 3.0 mm). For the present study, the heating of the furnace was controlled by three additional mantle thermocouples, type N (D = 1.5 mm), which were positioned directly on the surface of the test specimens. In Figure 2a, the positions of the thermocouples on the specimens are marked. The decisive thermocouple for the heat control of the furnace was the one in the middle of the measuring length of the specimens.

Figure 2
figure 2

(a) Geometry of the test specimens and (b) position of the samples in thickness direction of the plate material of I) the HEA 100 flanges, II) 12 mm plates and III) 40 mm plates

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A vertical opening is provided at the front of the furnace so that a strain measurement can be made using a temperature-resistant strain sensor. In the present study, the strain of the test specimens was measured with a high-temperature extensometer from manufacturer MAYTEC with two ceramic rods, which were placed directly on the specimens surface. The measured strain also served as feedback variable for the closed-loop feedback control during the strain-rate controlled tensile tests.

The specimens were placed in the furnace, respectively in the universal testing machine, using a high-temperature resistant coupon holder made of a nickel-based superalloy with a maximum load capacity of 50 kN at a test temperature of 1100°C.

2.2 Test Specimens

For the natural fire tests, dog-bone shaped specimens were manufactured from the flange plates of a HEA 100 section with a nominal thickness of 8 mm made of mild steel S355 J2 + N as well as from plate material made of HSS of grade S690QL and UHSS of grade S960QL. In case of the HSS and UHSS, plate material with an initial thickness of 12 mm and 40 mm was examined. In each case, material from the same batches as the test specimens in [4] and [8] was used, the results of which thus provide the basis for the respective temperature-dependent mechanical material behavior of the test specimens investigated in the current study during the heating phase. The analysis of these previous test results [8] revealed that different degradation processes can be observed in the core and peripheral material of 40 mm plates at elevated temperatures. It was found that the initial quenching and tempering process of the plate material affects the material behavior as the peripheral material has a higher initial strength but is slightly more sensitive to temperature than the core material. Therefore, also in the present study specimens were extracted from the core and peripheral material of the 40 mm plate material. As can be seen in Figure 2b, the test specimens from the 12 mm plates as well as the specimens from mild steel were each taken from the core material only. The following abbreviations are used to indicate the tested materials:

  • M1.1: S690QL, 12 mm

  • M1.2C: S690QL, 40 mm core material

  • M1.2P: S690QL, 40 mm peripheral material

  • M2: S355 J2 + N, HEA100 flange

  • M3.1: S960QL, 12 mm

  • M3.2C: S960QL, 40 mm core material

  • M3.2P: S960QL, 40 mm peripheral material

The geometry of the specimens was chosen according to the requirements of the test setup and is presented in Figure 2a. The specimens had a total length of L = 170 mm. The gauge length of the extensometer was set to L0 = 45 mm. The smallest cross section with A0 = 6 × 9 mm was present in the range of the gauge length. The thickness of the specimens was selected to t = 6 mm according to the smallest plate thickness of the initial plate material (M2, t = 8 mm) considering a post-treatment by grinding without significant material loss on the specimens. Further, a geometry with two fillet radii was selected. The first fillet radius of R1 = 15 mm served the form-fitted installation in the coupon holder while the second radius of R2 = 10 mm was chosen to ensure that the fracture of the specimens occured within the gauge length.

2.3 Test Procedure

For the natural fire tests as well as the post fire tensile tests of the present study, a test procedure consisting of five successive phases was defined. The test procedure is shown schematically in Figure 3 by (a) the time-force and (b) the time–temperature relationship.

Figure 3
figure 3

(a) Time-force and (b) time–temperature relationship of the test procedure

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In the first phase of the test, a specimen was subjected to five strain-rate controlled loading and unloading cycles with a maximum applied load corresponding to 80% of the nominal yield stress. The temperature was kept ambient during the first phase. The loading and unloading cycles were performed to ensure the centrical alignment of the specimen in the testing machine and to determine the Young’s modulus at ambient temperature.

The second phase comprised the heating of the specimen. During this phase, a small constant tensile force of Fhold = 0.5 kN was applied in a force-controlled manner to allow and measure the (free) thermal expansion of the specimen, while the specimen was heated at a constant heating rate of dT/dt = 15°C/min. The specimen temperature thus reached the specified maximum temperature Tu after 30 to 60 min. The temperature was then kept constant for 30 min to ensure that the entire cross-section of the specimen reached the target temperature.

In phase 3 of the procedure the specimen was cooled down to the test temperature Tt under natural ventilation conditions, i.e. the heating device of the furnace was switched off, but no additional cooling medium (water or similar) was used to cool the specimen. To avoid damage of the test setup, the furnace remained closed throughout the entire cooling process. The holding load Fhold = 0.5 kN continued to be applied during the cooling.

Once the target temperature Tt was reached, the mechanical loading of the tensile tests was carried out in the subsequent phases 4 and 5, during which the test temperature Tt was kept constant. In phase 4 the loading was realised strain-rate controlled with a constant strain rate of dε/dt = 1%/min using a closed-loop feedback control system via the high-temperature extensometer. Two elastic unloading–reloading cycles at predefined total strain levels of εtot = 0.8% and εtot = 2.0% were performed. After the second unloading step, the specimen was loaded beyond the tensile strength. In order to avoid damage of the extensometer by the sudden rupture of the specimen or too large deflection of the ceramic rods, the extensometer was removed at a force reduction of 15% based on the maximum achieved load.

At this point, for the fifth and final phase, the test was switched to a displacement-controlled loading with a constant velocity of v = 0.8 mm/min via the crosshead displacement of the testing machine until the rupture of the specimen.

2.4 Test Evaluation

Stress–strain curves were obtained directly from the natural fire and post fire tests at the various defined test temperatures. From these, material properties were determined according to the following evaluation methodologies:

The effective yield stresses at 0.5%, 1.5% and 2% total strain, fy,0.5,θ, fy,1.5,θ and fy,2.0,θ, were read out at the intersection between a vertical line at the specified total strain values and the stress–strain curves. The Young’s modulus Eθ was obtained as the scope of the initial almost linear part of the curves in the range between 0.1∙fy,2.0,θ and 0.3∙fy,2.0,θ. In addition, the proof stress fy,0.2,θ at 0.2% plastic strain was determined by using an offset-method with respect to the Young’s modulus Eθ. The proportional limit fp,θ was identified at the point of the stress–strain curve, where the relative deviation of the measured strain from the linear-elastic initial straight line, Δε/εel, exceeded 2%. The tensile strength ft,θ was specified as the maximum reached stress value. Moreover, the elastic strain at fracture, εu,θ, was determined at the rupture point, which marks the end of the fifth phase of the test using an offset-method related to the Young’s modulus Eθ. In tests with high test temperatures of Tt ≥ 700°C, a precise point of fracture could no longer be identified in some cases due to the high deformation capacity of the material. The specimens elongated in those cases until the stress reached almost zero level. In the following evaluations, the values of εu,θ for those cases are not provided.

3 Results and Discussion

In this section, the results of the tests for the material characterisation on series M1 (S690QL), M2 (S355 J2 + N) and M3 (S960QL) are presented. The temperature-dependent material behavior was investigated on the basis of experimentally determined stress–strain curves from natural fire tests as well as reduction factor-temperature relationships for material properties, which were derived from the stress–strain response.

3.1 Stress–Strain Response

Figures 4, 5, 6 show the stress–strain curves of the natural fire tests separately for each test series, i.e. for the various steel grades investigated; and Tables 1, 2, 3, 4, 5, 6 and 7 contain the temperature-dependent material properties, which were derived from the stress–strain curves. The material properties thereby are mean values of two tests with the same test combination of maximum temperature and test temperature and the stress strain curves each correspond to the first of the two tests. The structure of the graphs in Figures 4, 5, 6 will be explained using Figure 4 for mild steel S355 J2 + N of series M2 as an example. Figure 4a to d show the stress–strain curves, which were obtained from the natural fire tests at the various predefined test temperatures Tt after previous heating to higher maximum temperatures Tu. The coloring of the curves indicates the respective maximum temperatures Tu. The orange curves are accordingly assigned to tests during cooling after heating to Tu = 900°C. The results of tests with a maximum temperature of Tu = 700°C are colored grey, and for maximum temperatures of Tu = 550°C and Tu = 400°C the colors are green and dark blue respectively. The stress–strain curves are depicted in each case for the strain range up to 2% total strain (left) as well as up to 15% (right). The test temperatures Tt successively decrease from Figure 4a to d. Therefore, the stress–strain curves in Figure 4a correspond to the highest test temperature of Tt = 700°C and Figure 4d represents the stress–strain curves of the post fire tests at Tt = 20°C. Additionally, Figure 4d contains the initial stress–strain curve at ambient temperature (black). In case of the HSS (Figure 5) and UHSS (Figure 6), comparative tests of material with an initial plate thickness of 12 mm and 40 mm are shown. The stress–strain curves, which are plotted with solid lines, are assigned to 12 mm plate material (M1.1, M3.1), the dashed lines represent the results of the peripheral material of 40 mm plates (M1.2P, M3.2P) and the dotted lines belong to the core material of the 40 mm plates (M1.2C, M3.2C).

Figure 4
figure 4

Stress–strain curves of natural fire tests on series M2 at test temperatures of (a) Tt = 700°C, (b) Tt = 550°C, (c) Tt = 400°C and (d) Tt = 20°C

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Figure 5
figure 5

Stress–strain curves of natural fire tests on series M1 at test temperatures of (a) Tt = 700°C, (b) Tt = 550°C, (c) Tt = 400°C and (d) Tt = 20°C

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Figure 6
figure 6

Stress–strain curves of natural fire tests on series M3 at test temperatures of (a) Tt = 700°C, (b) Tt = 550°C, (c) Tt = 400°C and (d) Tt = 20°C

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Table 1 Material Properties from Natural Fire Tests on Series M2
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Table 2 Material Properties from Natural Fire Tests on Series M1.1
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Table 3 Material Properties from Natural Fire Tests on Series M1.2C
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Table 4 Material Properties from Natural Fire Tests on Series M1.2P
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Table 5 Material Properties from Natural Fire Tests on Series M3.1
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Table 6 Material Properties from Natural Fire Tests on Series M3.2C
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Table 7 Material Properties from Natural Fire Tests on Series M3.2P
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The curves with equal test temperature Tt and maximum temperature Tu represent the results of steady state tests at elevated temperatures, in which no cooling took place before the mechanical loading of the specimens in the tensile tests. In the case of the mild steel S355 J2 + N of series M2 (Figure 4) the results of steady state tests correspond to the study presented in [4], and for the HSS of series M1 (Figure 5) and the UHSS of series M3 (Figure 6), the steady state test results were taken from [8]. As a reminder, it should be noted again that in both reference studies exactly the same plate material was used to prepare the test specimens and also the test procedure was the same as in the current study.

The initial stress–strain curve of series M2 at ambient temperature (Figure 4d) shows the characteristic behavior of structural steel with a linear-elastic increase at the beginning of the test, followed by a distinct yield plateau and subsequent hardening up to tensile strength. As can be seen in Figures 5d and 6d, the initial stress–strain curves of HSS of series M1 and of UHSS of series M3 at ambient temperature also exhibit a distinct proportional limit with a clear change from the linear-elastic range to the beginning of plastic flow and also a hardening range is obvious. However, in case of the HSS of series M1.2, it can be noted that the initial absolute strength values of series M1.2C are lower than those of the series M1.2P. Thus, the core part of the thicker plates was not hardened to the same extent as the peripheral part throughout the quenching and tempering process when the plate material was produced. This is not the case for the investigated UHSS of series M3.2, since the initial curves of M3.2P and M3.2C almost coincide.

At elevated test temperatures, the stress–strain curves of all investigated materials show non-linear material behavior without a distinct yield plateau. This can be observed for both, the heating and cooling phase. In particular at test temperatures of Tt > 400°C, the strengths of the materials—as expected—are significantly reduced compared to the initial values at ambient temperature, and the stress–strain curves are considerably below the respective reference curves.

For normal-strength structural steel, it is generally assumed that the material behavior in the cooling phase of a fire is completely reversible and therefore the material model according to the current Eurocode is applicable for mild steels for the cooling phase and post fire range as well as the heating phase. Several studies in the past have shown that the material properties of mild steels largely recover after high temperatures [29,30,31]. The stress–strain curves in Figure 4 largely confirm this assumption. Up to a maximum temperature of Tu = 550°C in the heating phase, it appears that the strength of series M2, which was reduced by high temperatures during the heating process, increases again to the initial value in the cooling phase. Thus, there is complete reversibility. For maximum temperatures of Tu = 700°C, a slight strength degradation can be seen in post-fire tests. For test specimens exposed to a maximum temperature of Tu = 900°C, however, the stress strain curves at the various test temperatures were found to remain below those of all other maximum temperatures and the post fire strength was lower compared to the initially measured values. From these results it can be concluded that even for mild steels, the material behavior in the cooling phase and the post-fire strength are negatively affected by very high maximum temperatures, which do not necessarily occur in natural fire scenarios. It can be assumed that in such cases, where the A1-phase transformation temperature in the range of 725°C is exceeded in the heating phase, the phase composition of the microstructure of the steel does not exactly recover during cooling under natural ventilation conditions.

The stress–strain curves in Figure 5 show that there is also a (partial) recovery of the material behavior of the HSS of series M1 during the cooling phase; however, the curves also show that the maximum temperature Tu during the heating phase affects the material behavior during and after the cooling process. Higher maximum temperatures Tu during tests with the same test temperatures Tt lead to lower material strengths during the cooling phase. For maximum temperatures of Tu = 700°C, the post-fire strengths of the materials M1.1 and M1.2 are significantly reduced compared to the initial values. Furthermore, after heating to Tu = 900°C and subsequent cooling to Tt = 20°C, the initial strengths of the HSS were lost, and a material with characteristic strength values of a mild steel was present. It can be assumed that the fine-grained predominantly austenitic microstructure of the initial HSS, which was obtained through the quenching and tempering process during production, is transformed into a coarser-grained structure consisting of mostly ferrite and pearlite phases as a result of the carbon precipitation. This results in a material with lower strength, in cases where the A1-phase change-temperature was exceeded, followed by slow cooling under natural ventilation conditions.

However, Figure 5d also shows that the stress–strain curves in the initial linear elastic region are in agreement for all the maximum temperatures Tu investigated, and thus the reversibility of the stiffness and Young‘s modulus of the series M1 was independent of the maximum temperature.

The mechanical behavior during cooling of the investigated UHSS of series M3 was similar to that of the HSS of series M1. In Figure 6, a partially reversible material behavior is also observed, with the recovery of the material strength depending on the maximum temperature of the heating phase.

After heating to Tu = 900°C and subsequent cooling to Tt = 20°C, the absolute strength values of materials of series M1.1, M2 and M3.1 were of the same order of magnitude. This supports the hypothesis of a change in microstructure due to high temperatures in the heating phase and cooling under natural ventilation conditions, which led to a changed material behavior of the HSS and UHSS compared to the initial state at ambient temperature and similar behavior of the mild steel and high-strength steels.

3.2 Material Properties

3.2.1 Young’s Modulus

Figure 7 compares the development of the Young’s modulus Eθ during the cooling phase by means of the reduction factor-temperature relationships for the three investigated steel grades. The reduction factors were derived from the Young’s modulus Eθ, which was obtained from the stress–strain curves of natural fire tests at the various test temperatures Tt. By relating the temperature-dependent values of Eθ to the respective initial values E20°C at ambient temperature and plotting the reduction factors with respect to the test temperature Tt, sorted after the maximum temperature Tu, the development of the Young’s modulus and its dependence on Tu during the cooling process is visualized. The graphs of Figure 7 are to be read from right to left respectively, corresponding to the decrease of the test temperature Tt during the cooling process.

Figure 7
figure 7

Reduction factor-temperature relationships of natural fire tests for the Young’s modulus Eθ of (a) series M2, (b) series M1 and c series M3

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The mild steel of series M2 (Figure 7a) fully recovers its initial stiffness regardless of the maximum temperature Tu reached during the heating phase. The reduction factor-temperature relationships of different maximum temperatures almost coincide and reach a value of about Eθ/E20°C = 1.0 at ambient temperature. Only in cases with very high maximum temperatures of Tu = 900°C a slight decrease of the Young’s modulus of approximately 5% can be seen at a test temperature of Tt = 20°C. Therefore, the effect of the heating process and the maximum temperature are negligible for the development of the Young’s modulus in the cooling phase under natural ventilation conditions for mild steel.

For the HSS of series M1 (Figure 7b), the development of the Young’s modulus during cooling also did not depend on the maximum temperature Tu and, moreover, was almost the same for all materials of series M1. The stiffness of series M1 was fully reversible. In case of the UHSS in Figure 7c, however, the reduction factor-temperature relationships of the Young’s modulus show that complete reversibility of stiffness was present only up to a maximum temperature of Tu = 700°C, and slight stiffness losses occurred in the post-fire range for a very high maximum temperature of Tu = 900°C.

Overall, it can be concluded that the maximum temperature Tu of the heating phase has a negligible effect on the development of the stiffness of mild steels as well as of quenched and tempered HSS and UHSS during the cooling phase of a natural fire. The temperature dependent relative development of the stiffness of the investigated materials is qualitatively concurrent. For all materials investigated, the reduction factor-temperature relationships show an almost complete recovery of the Young’s modulus during the cooling process.

3.2.2 Effective Yield Strength

Figure 8 shows the reduction factor-temperature relationships of the effective yield strength at 2% total strain fy,2.0,θ for the series M2 (a), series M1 (b), and series M3 (c). The relationships between reduction factors and temperature in Figure 8a illustrate that the strength fy,2.0,θ of series M2 recovered to a large extent during the cooling process and regained the initial values when the maximum temperature of the heating phase did not exceed Tu = 700°C. However, after a temperature exposure of Tu = 700°C, slight strength losses occured at Tt = 400°C and at post-fire conditions with Tt = 20°C. Very high maximum temperatures of Tu = 900°C led to a reduction in the post-fire strength, and only about 70% of the initial value was reached.

Figure 8
figure 8

Reduction factor-temperature relationships of natural fire tests for the effective yield strength fy,2.0,θ of (a) series M2, (b) series M1 and c series M3

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For the HSS of series M1 (Figure 8b) and the UHSS of series M3 (Figure 8c), it was found that the maximum temperature Tu of the heating phase had a significant effect on the strength development during cooling. Higher maximum temperatures Tu resulted in greater reduction and lower recovery of the strength values during and after the cooling process. For low and medium maximum temperatures with Tu ≤ 550°C, the strength values recovered completely to the greatest extent possible. For maximum temperatures of Tu = 700°C, about 80% of the original strength for the studied HSS was recovered, and for Tu = 900°C, only 40–60% of the original value of fy,20°C was recovered.

Furthermore, small differences in the reduction factors for fy,2.0,θ of the materials with different plate thicknesses can be seen in Figure 8b for series M1 after exposures to high maximum temperatures. In particular, for tests with Tu = 900°C, the relative development of the core material of the 40 mm plate material (M1.2C) differed from both the peripheral material (M1.2P) and the 12 mm plate material (M1.1). The relative development of the strength of the core material M1.2C is apparently more favourable during the cooling process than the strength developments of the other two studied materials. This is due to the fact that the absolute value of the initial strength fy,20°C of M1.2C was lower compared to M1.1 and M1.2P, and as the temperature increases during the heating phase of the tests, the absolute strength values of the different materials converge, so that the ratios to the respective initial values show greater differences.

The reduction factor-temperature relationships of series M3 given in Figure 8c show that M3.1 and M3.2 exhibited almost similar development of behavior during cooling in cases with maximum temperatures up to Tu = 700°C. However, high maximum temperatures of Tu = 900°C led to an unexpected behavior of series M3.2, since the post-fire strengths of series M3.2 was almost equal to the respective initial values, while the post-fire strength of series M3.1 was—as expected—reduced to approximately 40% of the initial value. An explanation for this behavior could be provided by micrographs for the analysis of the microstructure of the materials, which, however, are not part of the present study.

3.2.3 Tensile Strength

The reduction factor-temperature relationships for the tensile strength ft,θ of natural fire tests are presented in Figure 9. The dependence of the strength development on the maximum temperature Tu, which was already found for the effective yield strength fy,2.0,θ of HSS and UHSS, also occured for the tensile strength ft,θ of series M1 and M3 (Figure 9b and c). The initial values of tensile strengths were reached in cases with Tu ≤ 550°C. Higher maximum temperatures during the heating phase had a negative effect on the development of the tensile strength. After a temperature exposure of Tu = 700°C, on average only about 80% of the initial tensile strengths of series M1 and M3 were achieved. For a maximum temperature of Tu = 900°C, the reduction in tensile strength was even greater.

Figure 9
figure 9

Reduction factor-temperature relationships of natural fire tests for the tensile strength ft,θ of (a) series M2, (b) series M1 and (c) series M3

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For the case of the mild steel of series M2, Figure 9a shows that the tensile strength recovered fully for maximum temperatures of Tu ≤ 550°C. At higher maximum temperatures, there was a slight decrease in strength recovery. However, the strength losses were less pronounced than for M1 and M3.

4 Comparative Study

The constitutive material model regularly used for structural fire design purposes and specified in the European standard EN 1993-1-2 [14] for describing the material behavior of structural steel at elevated temperatures in case of fire was developed on the basis of the investigations in [32, 33] for normal-strength steels and is based on the general assumption that the mechanical material behavior of mild steels is completely reversible after an exposure to fire. According to the model, the same reduction factors for the material properties can be applied for identical temperatures in the heating and cooling phases of natural fire scenarios. Various studies, in particular [6, 16] and [8], have shown that the use of the given reduction factors also leads to a sufficiently accurate description of the temperature-dependent material behavior of HSS during the heating-up and full-fire phases. Therefore, as part of the revision of Eurocodes and the development of the second generation of the fire design Part 1–2 of Eurocode 3, it was decided to extend the application range of prEN 1993-1-2:2022 [15] up to and including high-strength steels of grade S700. The application of the given constitutive material model is thus valid for fire scenarios with steadily increasing temperatures. For the cooling phase of natural fires, the explicit approval of the application of the model remains limited for the time being to steel grades up to S500 due to the lack of results of systematic investigations so far. The present study, which was presented in the previous sections, shows that the assumption of a complete reversibility of the mechanical material behavior for both HSS and UHSS in the cooling phase of natural fire scenarios is not valid, since a dependence of the strength development during the cooling process on the maximum temperature, reached in the heating phase, was observed. This leads to the obvious assumption that the common structural fire design model provides inaccurate and sometimes unconservative design results for HSS and UHSS in the cooling phase of natural fires. In the following subsections, the test results of both the presented natural fire tests and post-fire tests are compared to the constitutive material model of prEN 1993-1-2:2022 as well as the rare results available in the literature.

4.1 Material Behavior During the Cooling Phase

Figure 10 shows the comparison of reduction-factors for (a) the Young’s modulus and (b) the yield strength from own natural fire tests on material M1.1 and from a study of Hanus [18] regarding the material behavior of high-strength steel bolts (grade 8.8) during the cooling phase of natural fires as well as from a study of Wang et al. [19] on high-strength steel Q690 and a study on the mechanical behavior of G550 steel during cooling from Chen et al. [22]. It appears in Figure 10a, that Wang et al. [19] and Chen et al. [22]—in accordance with the current test results—discovered an almost full reversibility of the stiffness and the Young’s modulus of HSS during cooling to about 80% in [19] respectively about 100% in [22] of the initial values in cases with maximum temperatures below 900°C. The reduction factor-temperature relationships of Q690 and G550 are close to the ones of the material M1.1. Very high maximum temperatures of Tu = 900°C lead to a reduction of the Young’s modulus of the investigated Q690 and G550 in the post fire range. A similar effect was noticed in the current study in case of material M3 (see Figure 7).

Figure 10
figure 10

Comparison of reduction factors from natural fire tests on M1.1. to data from literature [18, 19, 22] for (a) the Young’s modulus and (b) the yield strength

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Figure 10b shows that the tests on grade 8.8 bolts [18] support the findings of the present study, as the reduction factors almost coincide with the results of the natural fire tests on material M1.1. The recovery of the yield strength of grade Q690 steel from [19] was less affected by the maximum temperature. Even for very high maximum Temperatures Tu, the reduction factors for the yield strength in the cooling phase were greater than those in the present experimental campaign and the results for grade 8.8 bolts. For medium maximum temperatures up to 600°C, the initial strengths were achieved at test temperatures Tt of 400°C; at lower test temperatures, the reduction factors were even greater than 1.0, which means that the strength in the cooling phase and the post-fire strength were higher than the initial strength. The study on G550 steel [22] on the other hand also shows that the recovery of the yield strength during cooling is strongly affected by high maximum temperatures of the heating phase as the reduction factor- relationships for Tu ≥ 600°C are significantly below the ones with lower maximum temperatures. Further, the reduction factor-temperature relationships from tests with maximum temperatures 600°C ≤ Tu ≤ 800°C are close to each other. Thus, the results on G550 steel for maximum temperatures Tu of 600°C to 800°C show a behavior during the cooling phase that differs significantly from the results of the present study and the results of [18] and [19]. The results of the post-fire tests also differ from the results of a broad database (Table 8). Whether the differences are due to the composition and microstructure of the steel or to differences in the test procedure cannot be assessed on the basis of the available data.

Table 8 Overview of Post-Fire Tests from Literature
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Figure 11a compares the reduction factors for the Young’s modulus Eθ of natural fire tests of the present study and from [18, 19] and [22] to the reduction factors kE,θ given in the Eurocode 3 for identical test temperatures. The results of all investigated materials of the present study, i.e. S355 J2 + N (M2), S690QL (M1) and S960QL (M3), are included.

Figure 11
figure 11

Statistical evaluation of the deviations between reduction factors from test results and according to Eurocode 3 for a the Young’s modulus and b the effective yield strength

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Figure 11a (left) reveals that the Eurocode 3 reduction factors for the Young’s modulus lead to conservative design results of the investigated materials in the cooling phase. Figure 11a (right) shows the statistical evaluation of the relative deviations between the test data and the normative reduction factors kE,θ. The deviations between the test results and the normative reduction factors are slightly greater for UHSS (M3) than for HSS (M1) and mild steel (M2). This occurs in particular in cases with high maximum temperatures of Tu = 700°C and Tu = 900°C. The mean value of the relative deviations between the test results and the reduction factors kE,θ is \(\bar{\text{x}}\)= 18.9% for mild steel, 5% for HSS and 24.1% for UHSS. However, it can be concluded that the reduction factor-temperature relationship for the Young’s modulus of the Eurocode is suitable to accurately describe the stiffness behavior of mild steel as well as HSS and UHSS during the cooling phase of natural fire scenarios.

Figure 11b (left) compares the temperature dependent reduction-factors for the effective yield strength from the natural fire tests and the reduction factors ky,θ of the Eurocode 3. The reduction factors of the Eurocode partially overestimate the strength values of HSS and UHSS during cooling. The reduction factors of the investigated mild steel of series M2 are also lower compared to the normative values, but the scatter and the mean deviation of the values is smaller than for HSS and UHSS. The overestimation of the strength values results from the assumption of complete reversibility of the material behavior, which does not take into account a dependence of the strength development during cooling on the maximum temperature of the heating phase. The statistical evaluation of the relative deviations between reduction factors for fy,2.0,θ from natural fire tests and ky,θ in Figure 11b (right) confirms that the mechanical material behavior of HSS and UHSS cannot be described accurately by the Eurocode model, since the average deviations are \(\bar{\text{x}}\)= − 94% for HSS and \(\bar{\text{x}}\)= − 52.6% for UHSS. For mild steel, the average deviation between test results and normative values is \(\bar{\text{x}}\)= − 31.4% and results in particular from tests with very high maximum temperatures of Tu = 900°C.

4.2 Post Fire Material Behavior

The reduction factors for the Young’s modulus and the effective yield strength of the post fire tests of the present study with respect to the maximum temperatures Tu are compared to test data from literature [11, 13, 24,25,26,27,28] in Figure 12. Table 8 gives an overview of the studies from which the data was extracted.

Figure 12
figure 12

Comparison of post fire reduction factor-temperature relationships for (a) the Young’s modulus and (b) the effective yield strength and statistical evaluation of the relative deviations between test results and the values of (c) kE,θ and (d) ky,θ of the Eurocode 3

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Figure 12a confirms that the assumption of complete recovery of stiffness and Young’s modulus of mild steels and of HSS is largely appropriate. In tests on UHSS from the literature [24, 28], stiffness losses occurred in the post-fire behavior after exposures to very high maximum temperatures.

The relative deviations between the test results and the assumption of complete reversibility, i.e. kE,θ = 1.0, are evaluated in Figure 12c. The Young’s modulus in the post-fire range is mostly independent from the maximum temperature Tu of the heating phase. The average deviations between test results and kE,θ = 1.0 are small for mild steels with \(\bar{\text{x}}\)= − 3.4% as well as for HSS with \(\bar{\text{x}}\)= -2.8% and UHSS with \(\bar{\text{x}}\)= − 5.0%.

In Figure 12b, the effective yield strengths of the post-fire tests (Tt = 20°C) of the present study are compared to test data from the literature. For HSS and UHSS with 460 ≤ fy,nom ≤ 700 N/mm2 and fy,nom > 700 N/mm2, respectively, the initial strength is almost completely recovered up to a maximum temperature of Tu = 550°C. The reduction factor-temperature relationships of the effective yield strength show that the residual strengths in these cases increase to almost the initial value. For higher maximum temperatures, however, the material strength does not recover completely. For very high maximum temperatures of Tu = 900°C, the residual strength was reduced up to 40% of the initial strength.

Figure 12d illustrates that the assumption of a complete strength reversibility is valid for the fire design of mild steels, since the relative deviations between the test results and the assumption of ky,θ = 1.0 are small with a mean value of \(\bar{\text{x}}\)= -4.5%. However, for HSS and UHSS, ky,θ = 1.0 is not appropriate in cases with high maximum temperatures during the heating phase. The deviations between the measured values and a full recovery are higher than for mild steels with \(\bar{\text{x}}\)= -18.8% for HSS and \(\bar{\text{x}}\)= − 20.3% for UHSS.

5 Predictive Equations

The comparative study of the previous section has evidenced that an adoption of the temperature-dependent constitutive model for structural steel according to prEN 1993-1-2:2022 [15], originally developed in the context of mild steels and ISO fire exposure, can lead to unconservative design results for high-strength steels during the cooling phase of natural fire scenarios and post-fire strength prediction. Hence, an adaption of the constitutive material model is required for a safe structural fire design of high-strength steel structures. The objective of the present study was to develop a consistent and comprehensive stress–strain response model for the application to high-strength and ultra-high-strength steels in the cooling phase of natural fires. In particular, the focus was on a user-friendly and practical model. Accordingly, the existing constitutive model of part 1–2 of Eurocode 3 [14] was used as a basis and modified and extended, respectively, by simple approaches.

The model proposed in the present study essentially consists of the stress–strain-relationship and reduction factors given in EN 1993-1-2 for structural steel at elevated temperatures, plus a novel reduction factor for the proportional limit and the effective yield strength in the cooling phase. For the heating phase of natural fires, the Eurocode model is used for HSS and UHSS without modifications based on the results in [8]. A modification of the model is made for the cooling phase to account for the dependence of the material behavior on the maximum temperature in the heating phase. A novel reduction factor g(Tu) for the effective yield strength and the proportional limit during cooling is proposed, which depends on the maximum temperature Tu during heating. The stiffness in the elastic range and the Young‘s modulus are adopted unchanged from the temperature-dependent material properties for the heating phase. In view of a possible implementation in future generations of standards and ease of use, simple bilinear equations were chosen for the novel reduction factor and, moreover, the same reduction factor was chosen to modify the effective yield strength fy,2.0,θ and the proportional limit fp,θ. The effective yield strength and the proportional limit of HSS and UHSS during cooling should be calculated by Equations. (1–3). Figure 13 shows the reduction factor-temperature relationships for HSS and UHSS in the cooling phase of natural fires according to Equations. (1–3). The reduction factors are sorted by the maximum temperatures Tu and plotted as a function of the test temperatures Tt.

Figure 13
figure 13

Proposed reduction factors for (a) the effective yield stress and b the proportional limit for HSS and UHSS in the cooling phase of natural fire scenarios

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yield stress:

$${f}_{y,\theta ,c}={f}_{y,\theta }\bullet g\left({T}_{u}\right)={f}_{y,20^\circ C}\bullet {k}_{y,\theta }\bullet g\left({T}_{u}\right)$$
(1)

proportional limit:

$${f}_{p,\theta ,c}={f}_{p,\theta }\bullet g\left({T}_{u}\right)={f}_{y,20^\circ C}\bullet {k}_{p,\theta }\bullet g\left({T}_{u}\right)$$
(2)

with:

$${T}_{u}\le 500^\circ C:g\left({T}_{u}\right)=\mathrm{1,0}$$
$${T}_{u}>500^\circ C:g\left({T}_{u}\right)=\mathrm{1,75}-\mathrm{1,5}\bullet {T}_{u}\bullet {10}^{-3}$$
(3)

where, ki,θthe reduction factors for material properties at elevated temperatures according to EN 1993–1-2; fy,θ,cthe effective yield stress in the cooling phase of natural fire scenarios; fp,θ,cthe proportional limit in the cooling phase of natural fire scenarios; g(Tu)the reduction factor to determine fy,θ,c and fp,θ,c in the cooling phase of natural fire scenarios depending on the maximum temperature Tu [°C].

Figure 14 compares the analytical stress–strain curves according to the proposed material model with the experimentally determined stress–strain curves from (i) our own post-fire tests of series M1.1 and series M3.1 of the present study (Figure 14a and b) and (ii) independent post-fire tests from the literature for S690QL from [26] (Figure 14c) and for tests on 8.8 bolts from [18] (Figure 14d). The proposed model leads in each case to an appropriate approximation of the experimentally determined post fire material behavior, although the analytical model is of a simple character. The post fire curves of the HSS of series M1.1 and the UHSS of series M3.1, as well as the curves from the literature, are sufficiently accurate represented in the context of a structural fire design. However, the consideration of the maximum temperature for the calculation of the post-fire strength is necessary for the characterisation of the measured material behavior of various high-strength steels.

Figure 14
figure 14

Comparison between stress–strain curves from post fire tests with Tt = 20°C and analytical stress–strain curves based on the developed material model for (a) series M1.1, (b) series M3.1, (c) S690QL from [26] and (d) 8.8 bolts of [18]

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Figure 15 shows an example of the comparison of stress–strain curves derived using the proposed material model and from natural fire tests of series M1.1 (a) and series M3.1 (b) as well as test results of Q690 from [19] (c) and of 8.8 bolts from [18] (d). The proposed simple-to-apply model leads to a good approximation of the measured curves. The shape of the stress–strain-relationship, which is described by an ellipse equation according to Part 1–2 of Eurocode 3, does not correspond to the exact curvature of the measured stress–strain curves. Nevertheless, the model agrees well with the test results, especially in the range of small strains. Therefore, for reasons of user-friendliness, the curvature of the existing model was not changed in the present study.

Figure 15
figure 15

Comparison between stress–strain curves from natural fire tests and analytical stress–strain curves based on the developed material model for (a) series M1.1, (b) series M3.1, (c) Q690 from [19] and (d) 8.8 bolts from [18]

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The proposed reduction factor-temperature relationships for the effective yield strength ky,θ (a) and the proportional limit kp,θ (b) of HSS and UHSS in the cooling phase of natural fires are compared in Figure 16 with the experimental results of materials of series M1 and M3, i.e. S690QL and S960QL. The left graphs show the test results in relation to the proposed reduction factors. The right graphs show the statistical analysis of the relative deviations between the test results and the proposed reduction factors. The measured values of the effective yield strength agree well with the experimentally determined values (Figure 16a). The average deviation between the model values and the test results is -31% for the effective yield strength of HSS and 0,9% for the UHSS of series M3. The scatter in the relative deviations is larger for HSS with a standard deviation of s = 83%. For UHSS it is much smaller with s = 24,9%. However, compared to the original model of Eurocode 3 (without modifications), the application of the proposed reduction factor to take into account the maximum temperature Tu leads to a significant improvement of the description of the strength development during cooling. In case of the proportional limit there is no experimental data from natural fire tests provided in literature. Therefore only the data from the present tests on series M1 and M3 are taken into account for the evaluation in Figure 16b. The prediction accuracy of the proportional limit (Figure 16b) has an average deviation between proposed values and test results of 3.1% for M1 and 5.0% for M3, which is sufficiently accurate in the context of structural fire design. In summary, the influence of the maximum temperature on the stress–strain response of HSS and UHSS can accurately be considered by simple-to-apply reduction factors.

Figure 16
figure 16

Statistical evaluation of the deviations between reduction factors from test results and model values for (a) the effective yield strength and (b) the proportional limit

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6 Summary and Conclusions

An extensive natural fire tensile test program has been carried out to investigate both the mechanical properties in the cooling phase of natural fire scenarios and the post-fire strength of high- (S690QL) and ultra-high-strength quenched and tempered steels (S960QL) that are increasingly used in construction industry due to their material-efficiency and their good strength-to-weight ratio. The program has provided novel fundamental knowledge on the high-temperature and post-fire constitutive behavior of such steels, focusing on the thus far unstudied impact of maximum temperature on material properties in the cooling phase. Furthermore, a systematic comparative study has been performed on the basis of the present test program and a most comprehensive yet rare experimental database on natural fire and post-fire tests from the literature. This study has assessed the possibility of easily adapting existing elevated-temperature code models for the heating phase also for high and ultra-high strength steels in the cooling phase of natural fire scenarios. Finally, an easy-to-apply analytical material prediction model for structural fire design purposes of high- and ultra-high-strength steel structures has been proposed.

With respect to future modeling of elevated-temperature constitutive behavior of high- and ultra-high-strength quenched and tempered steels in advanced structural fire design considering natural fire scenarios, the following conclusions and recommendations are drawn from the present experimental and theoretical study:

The general assumption of complete reversibility of the material behavior of mild steels during cooling was largely confirmed by the results of the comparative tests on specimens made of S355 J2 + N. For such steels, therefore, the same temperature-dependent constitutive models for the heating and cooling phases of fires can be used. The post-fire strength and deformation capacity after fire exposure are largely in agreement with the corresponding initial strength and deformation values. Only for very high maximum temperatures significantly above the A1-phase change temperature are minor strength losses to be expected after fire exposure.

For quenched and tempered high-strength and ultra-high-strength steels, on the other hand, there is no complete reversibility of the constitutive material behavior. Maximum temperatures in the range of the A1-phase transformation temperature and above significantly influence the stress–strain behavior in the cooling phase of natural fire scenarios and the post-fire strength of these steels. An accurate prediction of the strength must take the maximum steel temperature during fires into account. However, the stiffness in the elastic range and the Young’s modulus are not affected by the maximum temperature, irrespective of the steel grade and the product thickness, and reversible behavior is present in this respect.

The European structural fire design model can be easily adapted with a simple reduction factor to adequately account for the influence of the maximum temperature during the heating phase on the stress–strain response in the cooling phase of natural fires and the post-fire strength. The proposed model can accurately reflect both the results of the present study's experiments and the rare results from the literature. The presented investigations and the proposed analytical model provide an essential basis for the further development of advanced structural fire design and the amendment of the European design models.

It has been shown that the consideration of the altered material behavior of HSS and UHSS is necessary for an accurate estimation of the structural fire behavior of steel structures in natural fires including the cooling phase and the post fire behavior.