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Material parameters in void growth model for G20Mn5QT cast steel at low temperatures
Construction and Building Materials 243 (2020) 118123
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Material parameters in void growth model for G20Mn5QT cast steel at low temperatures Yue Yin a,b, Shuai Li a, Qinghua Han a,b,⇑, Mengfei Li a a b
Department of Civil Engineering, Tianjin University, Tianjin 300072, China Key Laboratory of Coast Civil Structure Safety (Tianjin University), Ministry of Education, Tianjin 300072, China
h i g h l i g h t s Mechanical properties of G20Mn5QT cast steel at low temperatures were determined. Parameters in VGM/SMCS were calibrated for G20Mn5QT cast steel at low temperatures. VGM/SMCS are applicable for G20Mn5QT cast steel at low temperatures. Characteristic length of G20Mn5QT cast steel decreases with the drop of the temperature.
a r t i c l e
i n f o
Article history: Received 7 October 2019 Received in revised form 7 December 2019 Accepted 6 January 2020
Keywords: G20Mn5QT cast steel Low temperature Ductile fracture Void growth model Mechanical properties
a b s t r a c t With superior structural performances, G20Mn5QT cast steel has been extensively used in fabricating complex joints in steel constructions. Fracture failure of G20Mn5QT cast steel is then an important issue, especially for low-temperature situations. In this paper, mechanical properties of G20Mn5QT cast steel at low temperatures were studied by tensile coupon tests and Charpy impact tests. The effects of the low temperature on mechanical properties and the ductile-brittle transition temperature of G20Mn5QT cast steel were obtained based on the test results. The void growth model (VGM) and the stress modified critical strain (SMCS) model, which are two typical micromechanical fracture models, were calibrated for G20Mn5QT cast steel by experiments and complementary FEA on smooth notched tensile (SNT) specimens at four temperature levels, 20℃, 20℃, 40℃ and 60℃. For each temperature level, the material parameters in VGM and SMCS calculated based on test results of all six different specimens are in very good consistence. This consistency indicates the applicability of VGM and SMCS for predicting the ductile fracture of G20Mn5QT cast steel, even at the temperature of 60℃, which is much lower than the transition temperature of the material. The calibrated material parameters representing the resistance to ductile fracture of the material decrease linearly with the drop of the temperature. The characteristic length of G20Mn5QT cast steel was also determined by observation of fractured surfaces of test specimens with the scanning electron microscope, which has the tendency to decrease with the drop of the temperature. Ó 2020 Elsevier Ltd. All rights reserved.
1. Introduction Cast steel is an ideal solution for complex joints in steel constructions. With cast steel joints, geometric discontinuity can be avoided by smooth transition segments to reduce the stress concentration, and the welding can be arranged outside the joint region to minimize its adverse heat effects on the structural performance of the joints. Sometimes, cast steel joints are applied in regions of extreme environments such as low temperature. For ⇑ Corresponding author at: Department of Civil Engineering, Tianjin University, Tianjin 300072, China E-mail address: [email protected] (Q. Han). https://doi.org/10.1016/j.conbuildmat.2020.118123 0950-0618/Ó 2020 Elsevier Ltd. All rights reserved.
example, a large amount of cast steel joints was adopted in steel constructions in north China. If these joints were exposed outdoors, they would experience the minimum mean temperature as low as 40℃ in winter. This situation determines that these cast steel joints must have sufficient low-temperature ductility to ensure the safety of the structures. For steel joints and connections without sufficient ductility, the ductile fracture may occur under the action of monotonic loadings [1–6]. In the literatures, there are two typical micromechanical fracture models [7,8], void growth model (VGM) [9] and stress modified critical strain model (SMCS) [7], readily available for ductile fracture analysis of structural steels. These two models can give satisfactory results in ductile fracture prediction of various joints
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Y. Yin et al. / Construction and Building Materials 243 (2020) 118123
Fig. 1. Test setup and low-temperature environment.
Fig. 2. Temperature change process during a tension coupon test at 60℃.
Table 1 Mechanical properties of G20Mn5QT cast steel. Elongation
ry
ru
20%
300 MPa
500 ~ 650 MPa
and plastic strains in rigid plastic materials [8]. Since only the expansion of microvoids was considered, VGM and SMCS are applicable to ductile fracture prediction of materials with dominant tensile deformation, especially at the location of high-stress triaxiality. Compared with coupled micromechanical fracture models, for example, the GTN model [15,16], and those models applicable to ductile fracture caused by shear in low-stress triaxiality regimes [17–20], VGM and SMCS have an outstanding advantage that only one parameter is required for each model to define the resistance of materials to ductile fracture and provide simple and convenient fracture criteria. VGM and SMCS have been calibrated for different hot-rolled steels [21–27] through smooth notched tensile tests at ambient temperature. With the superior welding performance, G20Mn5QT cast steel [28] has been extensively used in steel constructions. Contents of sulphur and phosphorus in G20Mn5QT cast steel are strictly limited to 0.02% or under, which gives it the necessary plasticity and ductility for steel joints in different structural systems [29–32]. Material parameters in VGM and SMCS for G20Mn5QT cast steel at ambient temperature have also been calibrated and verified [33]. However, these material parameters are inapplicable to cast steel joints at low temperatures. Lots of research works [34,35] have proved the significant influence of the temperature on the mechanic properties, especially the ductility, of structural steels. The resistance of steels to ductile fracture at low temperatures
and connections under monotonic loadings [10–14]. VGM and SMCS are both uncoupled models, in which the growth rate of microvoids in the materials is calculated based on stress triaxiality
Fig. 3. The tension coupon.
Fig. 4. Nominal stress-strain curves by tensile coupon tests at different temperatures.
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describe the void growth quantitatively. The micromechanical fracture criterion can be expressed for VGM as
VGI ¼ Z
g¼
lnðR=R0 Þ ¼ c ecritical p
Z
ep
expð1:5T Þ dep > g
ð1Þ
0
expð1:5T Þdep
ð2Þ
0
where R is the radius of voids; R0 is the initial void radius; c is a constant; T is the stress triaxiality and expressed as T = rm/re (rm is the hydrostatic stress, and re is the von-Mises stress); qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dep ¼ ð2=3Þdeijp deijp is the incremental equivalent plastic strain;
ep is the equivalent plastic strain and ecritical is its critical value for p the initiation of the ductile fracture; g is a material parameter.
Fig. 5. True stress-plastic strain curves for G20Mn5QT cast steel at different temperatures.
may be much worse than that at ambient temperature [34,36,37]. It is then very desirable to calibrate the micromechanical fracture models for G20Mn5QT cast steel at low temperatures so that the ductile fracture of cast steel joints located in cold areas can be analyzed. In this paper, mechanical characteristics of G20Mn5QT cast steel at low temperatures were studied. Tensile coupon tests and Charpy impact tests were carried out on G20Mn5QT cast steel at different temperatures. Two micromechanical fracture models, VGM and SMCS, were calibrated for G20Mn5QT cast steel at four temperature levels by tests and complementary FEA on SNT specimens. The effects of low temperature on mechanical properties, Charpy impact toughness, and the calibrated fracture parameters were discussed for G20Mn5QT cast steel.
In many practical cases, with the increase of loading, the plastic strain rises rapidly while the stress triaxiality remains nearly a constant. If the variation of stress triaxiality is ignored, SMCS can be setup based on VGM. SMCS Index and a material parameter a were defined to express the fracture criterion of SMCS as shown in Eqs. (3) and (4).
SMCS Index ¼ ep expð1:5T Þ > a
ð3Þ
a ¼ ecritical expð1:5T Þ p
ð4Þ
The parameters g and a represent the resistance to ductile fracture of the material and can be calibrated through SNT tests and complementary FEA. The ductile fracture of steel is the behavior of a certain volume of materials. A length scale, termed as the characteristic length (l*) [21], was then defined to trigger the fracture of the material. The characteristic length of the material depends on its microstructure and is generally taken as the average size of microvoid colonies, which can be determined by scanning electron microscope (SEM) analysis of the fracture morphologies of the material. 3. Tension coupon tests
2. Micromechanical fracture criteria of VGM and SMCS model
3.1. Test setup and low-temperature environment
The ductile fracture of steel was considered as the result of nucleation, growth, and coalescence of microscopic voids in micromechanics of fracture. The relationship between the void growth and the combined effect of the stress triaxiality and the equivalent plastic strain has been established according to analytical derivations in references [8,38]. In VGM, the growth of microvoids controls the ductile fracture of materials. When voids grow to exceed the critical size, the ductile fracture occurs. Void growth index (VGI) was then defined to
All the tensile tests were conducted on an electronic universal testing machine with a capacity of 200kN. The test setup was shown in Fig. 1. In order to create a low-temperature environment, a cold chamber was manufactured with the injection of liquid nitrogen. The cold chamber was made up of two layers of the polyurethane board, with a thickness of 80 mm. In order to maximize the effect of thermal insulation, two layers of the polyurethane board were interlaced at the edge and corner of the cold chamber. The gaps between polyurethane boards were sealed with silica gel.
Table 2 Results of tension coupon tests at different temperatures. NO.
Temp (℃)
d0 (mm)
l0 (mm)
lf (mm)
df (mm)
E (GPa)
E(GPa)
fy (MPa)
f y (MPa)
fu (MPa)
f u (MPa)
d (%)
d(%)
w (%)
w(%)
1–1 1–2 1–3 2–1 2–2 2–3 3–1 3–2 3–3 4–1 4–2 4–3
20
12.50 12.48 12.47 12.49 12.51 12.50 12.48 12.51 12.51 12.49 12.50 12.51
50 50 50 50 50 50 50 50 50 50 50 50
63.60 63.52 63.14 62.30 62.52 63.02 61.85 62.21 62.05 60.46 60.82 61.52
8.50 8.34 8.28 8.61 8.42 8.55 8.86 8.75 8.50 9.64 9.52 9.46
202.5 210.2 208.5 220.2 218.6 216.5 227.1 225.4 223.5 243.5 251.8 247.6
207.1
327.6 335.2 328.7 346.3 347.5 348.8 349.6 357.6 356.8 397.1 388.3 370.4
330.5
585.3 588.2 583.9 611.0 608.1 606.2 615.6 614.2 618.2 631.2 632.5 633.1
585.8
27.2 27.0 26.3 24.6 25.0 26.0 23.7 24.4 24.1 20.9 21.6 23.0
26.8
53.8 55.3 55.9 52.5 54.7 53.2 49.6 51.1 53.8 40.4 42.0 42.8
55.0
20
40
60
218.4
225.3
247.6
347.5
354.7
385.3
608.4
616.0
632.3
25.2
24.1
21.9
53.5
48.2
41.7
4
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Fig. 6. Effect of the temperature on mechanical properties of G20Mn5QT cast steel.
Liquid nitrogen was injected into the chamber through a precise valve. Two PT100 thermocouples were mounted on each test specimen at two different locations to measure the real-time temperature of the specimen. The inflow of liquid nitrogen was controlled
by adjusting the valve so that the target temperatures could be obtained and maintained. Four temperature levels, TEMP = 20℃, 20℃, 40℃ and 60℃, were set for the tensile tests on G20Mn5QT cast steel. The thermocouples were connected to the acquisition equipment, and the temperature of the specimen could be monitored through a computer. An extensometer was put on the tension coupon in the cold chamber to measure the deformation and control the load rate. The temperature change process of a tensile specimen tested at 60℃ is shown in Fig. 2. The first 11 minutes is the cooling process, during which the specimen was cooled from ambient temperature to 60℃. In order to ensure the internal temperature of the specimen reach 60℃, the same as the external temperature, the target temperature (-60℃) was maintained for another 10 minutes. After that, the formal loading process began from the 21st minute.
3.2. Tension coupon tests
Fig. 7. The Charpy impact specimen.
With the superior performance in weldability, G20Mn5QT cast steel is very suitable for fabrication of complex steel joints. Mechanical properties of G20Mn5QT cast steel stipulated in reference [28] were listed in Table 1.
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Y. Yin et al. / Construction and Building Materials 243 (2020) 118123 Table 3 Charpy impact energy of G20Mn5QT cast steel at different temperatures. TEMP (℃)
Specimen NO.
20
CV1 CV2 CV3 CV4 CV5 CV6 CV7 CV8 CV9 CV10 CV11 CV12 CV13 CV14 CV15
0
20
40
60
Charpy impact energy (J) Ak (J)
Average
Stipulated in [28]
75.22 72.21 73.82 68.21 65.90 72.41 38.82 42.90 39.42 31.87 35.64 36.64 19.78 34.37 28.21
73.75
–
68.84
50 J
40.37
–
34.71
–
27.45
–
Fig. 8. The Charpy impact energy of G20Mn5QT cast steel at different temperatures.
were shown in Fig. 3. A total number of 12 tension coupons were machined for the tests at the four temperature levels. The tension coupons were put into the cold chamber and screwed into two end sleeves, which were clamped by the testing machine, as shown in Fig. 1(b). An extensometer was put on the tensile coupon in the cold chamber to measure the deformation of gage length. The loading rate was 1.0 mm/min, which was controlled through the deformation measured by this extensometer. Before the loading application, the upper chuck of the testing machine should be loosened to release the contractions of the coupons during the cooling process. Nominal stress-strain curves were determined by tension coupon tests, as illustrated in Fig. 4. Note that the extensometer was taken off before the deformation of the test coupon reached its measuring range. Consequently, the stress-strain relationship beyond e = 0.15% was not obtained directly by these tests. True stress-strain curves were determined based on the test data, as shown in Fig. 5. The diameters at the fractured surfaces of the test coupons were measured, and the true stress and strain were determined by Eqs. (5) and (6) for the fractured load.
2 rfracture ¼ F fracture = pdf =4 true
h
efracture ¼ ln d0 =df true
Fig. 9. The smooth notched tensile test specimen.
A 30 mm thick G20Mn5QT cast steel plate was cast for the manufacturing of test specimens in this paper. Mechanical properties of this cast steel plate at low temperatures were determined by tension coupon tests. The geometric details of the tension coupons
2 i
ð5Þ ð6Þ
in which, d0 and df is the diameter of the coupons before tests and at the fractured surface respectively. The true stress-strain curves were then extended linearly to the fracture of the coupons in Fig. 5, based on which relationships between the true stress and plastic strain was established for G20Mn5QT cast steel. Mechanical properties of G20Mn5QT cast steel determined by tensile coupon tests were summarized in Table 2, where it can be observed that all of them vary with the temperature, as shown in Fig. 6. The elastic modulus E, yield strength fy and ultimate strength fu increase almost linearly by 19.6%, 16.6% and 7.9% respectively with the drop of the temperature from 20℃ to 60℃; while the elongation d and reduction of cross section w decrease by 18.3% and 24.2% respectively. Obviously, the strength of G20Mn5QT cast steel increases and the ductility deteriorates at low temperatures. 4. Charpy impact toughness tests Charpy impact toughness tests were conducted for G20Mn5QT cast steel at 20℃, 0℃, 20℃, 40℃ and 60℃ respectively on a
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pendulum impact tester with a standard strike energy of 300 J. Fifteen Charpy impact specimens were machined, three for each temperature, from the G20Mn5QT cast steel plate. The Charpy impact specimen and its geometry details were shown in Fig. 7. Charpy impact specimens were cooled to a certain testing temperature in the mixture of ethyl alcohol and liquid nitrogen. Specimens were kept in the mixture long enough to make sure they were cooled completely. The temperature was monitored by PT100 thermocouple mounted on the test specimen. The mixture was placed very close to the test machine and the specimen was taken out of the mixture only after the test machine was ready. It took less than 5 seconds to take the Charpy impact specimen out of the cooling mixture, put it on the testing machine quickly and complete the test. The Charpy impact energies of G20Mn5QT cast steel at different temperatures were listed in Table 3. The Charpy impact energy obtained by tests at 0℃ meets the requirements in [28]. The variation of Charpy impact energy of G20Mn5QT cast steel with the temperature was illustrated in Fig. 8. An obvious decrease of the Charpy impact energy can be observed with the drop of the temperature, especially when the temperature reaches 0℃, which means the deterioration of the toughness of G20Mn5QT cast steel. Boltzmann function [39] was adopted to fit the relationship between the Charpy impact energy and the temperature, as shown in Fig. 8. The ductile-brittle transition temperature is 12.3℃, while the width of the temperature transition zone is 13.3 ℃.
5. Calibration of VGM and SMCS at different temperatures 5.1. Smooth notched tensile tests on G20Mn5QT cast steel Material parameters were calibrated for VGM and SMCS by SNT tests at four temperature levels, 20℃, 20℃, 40℃ and 60℃. Twenty-four SNT specimens were machined from the G20Mn5QT cast steel plate, as shown in Fig. 9. Three different notch radii (R = 1.5, 3.125 and 6.25 mm) were considered to provide different triaxial stress conditions. The tests were carried out on the electronic universal testing machine. The test setup was the same as the one severed for tension coupon tests shown in Fig. 1. After the temperature of the specimen in the cold chamber dropped to the test temperature, the uniform axial tensile load was applied and the specimen was stretched continuously until the fracture at the neck. The deformation measured by the extensometer was adopted to control the loading at the rate of 0.2 mm/min. Load versus deformation curves were illustrated for all test specimens in Figs. 10-12. Points with sudden slope change on these curves were identified as ductile fracture initiation. Two tests were conducted for each notch radius and each temperature, as shown in Table 4. Tensile loads Pf and specimen deformations Df at fracture initiation were obtained for all SNT specimens.
Fig. 10. Load-deformation curves obtained by tests and FEA for SNT specimens (R = 1.5 mm) at different temperatures.
Y. Yin et al. / Construction and Building Materials 243 (2020) 118123
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Fig. 11. Load-deformation curves obtained by tests and FEA for SNT specimens (R = 3.125 mm) at different temperatures.
5.2. SEM tests and characteristic length Fractographic features of the SNT specimens were studied through the scanning electron microscope (SEM). Typical micrographs of the fracture surfaces at different temperatures were presented in Figs. 13-16. During the ductile fracture, the coalescence and cleavage of microvoids generated microscopic plateaus and valleys, which can be easily distinguished from the micrographs. With the drop of the test temperature, the fracture surfaces tend to be more even, and less plastic deformation developed on fracture surfaces. It is generally accepted that, for particular materials, the characteristic length (l*) should be the size of a microvoid colony [21]. Measurement on the micrographs gave the characteristic length, as listed in Table 5, for G20Mn5QT cast steel at different temperatures. It should be noted that the obtained characteristic lengths for different temperatures are all at the order of 0.1 mm, the same as those of many other structural steels [21,23]. 5.3. FEA of smooth notched specimens under tension The nonlinear FEA of SNT specimens was conducted by the general FE software ABAQUS [40]. Axisymmetric plane models were established for all kinds of specimens, as shown in Fig. 17. Finite element models were discretized with the CAX4R element implemented in ABAQUS, which is a type of 4-node bilinear axisymmet-
ric element. In the notch region, ultra-fine mesh with element size being the characteristic length in Table 5 was adopted to capture the ductile fracture. Coarser meshes were adopted in regions far away from the notch to save the computational cost. In finite element analysis, the constitutive relationship of the material was set according to the results of the tension coupon tests at different temperatures as shown in Fig. 5 and Table 2. The Mises yield criterion was adopted to model the plastic behavior of the material. 5.4. Calibration of VGM and SMCS Material parameters in the two micromechanical fracture models were calibrated for G20Mn5QT cast steel at the four temperature levels, TEMP = 20℃, 20℃, 40℃ and 60℃, based on results of SNT tests and complementary FEA. The study on SNT specimens tested at the temperature of 20℃ was taken as an example to illustrate the calibration procedure. The distribution of the stress triaxiality and equivalent plastic strain over the critical section were obtained by FEA for the specimens with the three different notch radii, as shown in Fig. 18. The stress triaxiality is higher at the section center than on the surface. The equivalent plastic strain changes little over the section. VGI and SMCS Index were calculated over the critical section by Eqs. (1) and (3), as shown in Fig. 19. The maximum value of both indexes is at the center of the critical section, indicating that the
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Fig. 12. Load-deformation curves obtained by tests and FEA for SNT specimens (R = 6.25 mm) at different temperatures.
Table 4 Calibration of g and a for G20Mn5QT cast steel at different temperatures. Temp (℃)
Notch radius (mm)
Specimen NO.
Pf (kN)
Df (mm)
ecritical p
re (MPa)
rm (MPa)
g
g
a
a
20
1.5
20℃-1-1 20℃-1-2 20℃-2-1 20℃-2-2 20℃-3-1 20℃-3-2 20℃-1-1 20℃-1-2 20℃-2-1 20℃-2-2 20℃-3-1 20℃-3-2 40℃-1-1 40℃-1-2 40℃-2-1 40℃-2-2 40℃-3-1 40℃-3-2 60℃-1-1 60℃-1-2 60℃-2-1 60℃-2-2 60℃-3-1 60℃-3-2
24.20 22.11 22.42 21.78 18.20 19.17 23.35 24.81 22.50 22.15 19.39 15.96 25.62 24.10 22.21 22.38 19.67 21.64 27.16 24.74 24.57 24.54 23.21 23.66
0.77 0.80 0.96 1.00 1.32 1.35 0.68 0.71 0.85 0.91 1.17 1.25 0.71 0.72 0.79 0.83 1.13 1.15 0.65 0.60 0.70 0.75 1.12 1.13
0.2018 0.2176 0.3075 0.3275 0.3927 0.4042 0.1516 0.1670 0.2629 0.2938 0.3498 0.3860 0.1600 0.1650 0.2278 0.2461 0.3208 0.3290 0.1478 0.1284 0.1981 0.2186 0.3168 0.3207
703.04 710.71 754.22 763.93 795.48 801.05 695.18 698.78 721.19 728.40 741.47 749.94 705.60 707.22 728.04 734.09 758.84 761.57 731.23 717.48 751.66 760.01 799.90 801.50
949.03 955.97 755.14 759.93 623.94 627.03 963.14 986.10 800.14 812.15 664.00 674.94 961.22 968.20 768.27 780.13 645.27 648.27 963.15 916.40 761.97 781.24 661.97 663.55
1.51 1.67 1.46 1.59 1.41 1.46 0.97 1.09 1.13 1.29 1.12 1.26 1.02 1.05 0.92 1.01 0.98 1.01 0.92 0.79 0.77 0.87 0.95 0.97
1.52
1.37 1.51 1.36 1.47 1.32 1.37 0.91 1.01 1.05 1.19 1.05 1.17 0.95 0.99 0.87 0.95 0.93 0.95 0.88 0.75 0.74 0.83 0.91 0.92
1.40
3.125 6.25 20
1.5 3.125 6.25
40
1.5 3.125 6.25
60
1.5 3.125 6.25
1.14
1.00
0.88
1.06
0.94
0.86
Y. Yin et al. / Construction and Building Materials 243 (2020) 118123
Fig. 13. Micrograph of fractured surfaces at 20℃.
Fig. 14. Micrograph of fractured surfaces at 20℃.
Fig. 15. Micrograph of fractured surfaces at 40℃.
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Fig. 16. Micrograph of fractured surfaces at 60℃.
Table 5 Characteristic lengths for G20Mn5QT cast steel at different temperatures. TEMP
Specimen NO.
Characteristic length (mm)
20℃
20℃-1 20℃-2 20℃-3 Average 20℃-1 20℃-2 20℃-3 Average 40℃-1 40℃-2 40℃-3 Average 60℃-1 60℃-2 60℃-3 Average
0.207 0.215 0.221 0.214 0.199 0.187 0.206 0.197 0.177 0.165 0.160 0.167 0.133 0.145 0.140 0.139
20℃
40℃
60℃
strain was neglectable small. Then, the equivalent plastic strain kept rising with the load. However, the stress triaxiality remained almost unchanged. Therefore, it is acceptable that VGM can be simplified to SMCS by assuming the stress triaxiality is constant during the prediction of ductile fracture. These conclusions apply for the case at the temperature of 20℃, as well as the cases at other temperatures. The deformations of the specimens, Df, at the fracture obtained by SNT tests were as shown in Table 4. Apply these deformations to FE models of the corresponding test specimens and determine the equivalent plastic strain and stress triaxiality at the center of the critical section of each specimen by FEA. It can be seen that, for SNT specimens with the same notch radius, the equivalent plastic strains at the fracture decrease with the drop of the temperature. Then, g in VGM was calculated by Eq. (2), a in SMCS by Eq. (4), as listed in Table 4. Average values of g and a were calculated for all the four temperature levels, as listed also in Table 4. It can be seen that, for each temperature level, the values of g and a calculated based on test results of the six different specimens are all in very good consistence. The largest deviation between a calibrated value and the average is less than 15%. This indicates that VGM and SMCS are applicable for ductile fracture prediction even at the temperature of 60℃, which is much lower than the transition temperature of the material. Material parameters, g and a, have already been calibrated for G20Mn5QT cast steel at ambient temperature in reference [33]. The values of g and a are 0.99 and 1.05 respectively, which are all less than those listed in Table 4 for the temperature of 20℃. Note that the yield stress of the G20Mn5QT cast steel in reference [33] is 427 MPa, which is much larger than that in this paper. The divergence between the material parameters calibrated in this paper and the reference was then attributable to different mechanical properties of different batches of cast steels. In general, the higher the yield strength of the material, the worse the resistance to the ductile fracture.
Fig. 17. A typical finite element model for SNT specimens.
5.5. Ductile fracture prediction of SNT specimens with the calibrated VGM and SMCS
ductile fracture tends to initiate there. Variations of the stress triaxiality against the equivalent plastic strain were plotted for the three specimens in Fig. 20. The stress triaxiality increased sharply at the beginning of the loading process when the equivalent plastic
Ductile fracture of SNT specimens with notch radii 1.5, 3.125 and 6.25 mm was predicted with the calibrated VGM and SMCS at the four different temperatures. VGI and SMCS index at the center of the notch section were calculated based on FEA. The
Y. Yin et al. / Construction and Building Materials 243 (2020) 118123
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Fig. 18. Distribution of equivalent plastic strain and stress triaxiality over the critical section at 20℃.
Fig. 19. VGI and SMCS Index over the critical section at 20℃.
deformations at fracture were predicted for all specimens, as shown in Figs. 21–24. The predicted deformations at fracture (DFEM ) and those f obtained by tests (Dtest f ) were compared for all SNT specimens in Fig. 25. It can be seen that the predictions agreed well with test results and all data fell inside the 15% margin lines. The agreement verified the rationality of the micromechanical fracture models calibrated in this research. 5.6. Relationship between the calibrated material parameters and the temperature
Fig. 20. Relationship between stress triaxiality and equivalent plastic strain at the center of the critical section at 20℃.
All the calibrated g and a were plotted against the temperature as shown in Fig. 26. Both material parameters have the tendency to decrease with the drop of the temperature. This is consistent with the basic concept about the resistance of structural steels to the ductile fracture. The average values of the material parameters at the same temperature level were also plotted against the temperature in Fig. 26. It can be observed that both the average values of g in VGM and a
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Fig. 21. Prediction of ductile fracture of SNT specimens at 20℃.
Fig. 22. Prediction of ductile fracture of SNT specimens at 20℃.
Fig. 23. Prediction of ductile fracture of SNT specimens at 40℃.
Y. Yin et al. / Construction and Building Materials 243 (2020) 118123
Fig. 24. Prediction of ductile fracture of SNT specimens at 60℃.
Fig. 25. Errors between test results and prediction results.
Fig. 26. Calibrated value for g in VGM and a in SMCS.
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in SMCS decrease almost linearly with the drop of the temperature. Therefore, the relationships between the material parameters in the micromechanical fracture models and temperature were established with linear regression analysis, as shown in Eq. (7) for g in VGM, and Eq. (8) for a in SMCS.
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.
g ¼ g20 þ 0:0081 ðTEMP 20Þ
ð7Þ
Acknowledgement
a ¼ a20 þ 0:0072 ðTEMP 20Þ
ð8Þ
The authors are grateful for the support by the National Natural Science Foundation of China (No. 51525803).
Based on the proposed equations, material parameters in the two micromechanical fracture models for G20Mn5QT cast steel at different low-temperature levels can be determined for ductile fracture prediction conveniently.
6. Conclusions Structural steel tends to lose its ductility with the drop of temperature, which makes the fracture failure of steel an important issue for steel construction at low temperatures. In this paper, mechanical properties of G20Mn5QT cast steel at different low temperatures were studied by tension coupon tests and Charpy impact tests. The void growth model (VGM) and the stress modified critical strain (SMCS) model were calibrated for G20Mn5QT cast steel by tests and complementary FEA on SNT specimens at four temperature levels, 20℃, 20℃, 40℃ and 60℃. The following conclusions were obtained: (1) The elastic modulus, yield strength and ultimate strength of G20Mn5QT cast steel increase almost linearly by 19.6%, 16.6% and 7.9% respectively with the drop of the temperature from 20℃ to 60℃; while the elongation and reduction of cross section decrease by 18.3% and 24.2% respectively. (2) The Charpy impact energy of G20Mn5QT cast steel decreases significantly with the drop of the temperature, especially when the temperature is below 0℃, which means the deterioration of the toughness of G20Mn5QT cast steel. The ductile-brittle transition temperature is 12.3℃, while the width of the temperature transition zone is 13.3 ℃. (3) Material parameters, g in VGM and a in SMCS, were calibrated for G20Mn5QT cast steel at four temperature levels, 20℃, 20℃, 40℃ and 60℃. For each temperature level, the values of g and a calculated based on test results of all six different specimens are in very good consistence. This consistency indicates the applicability of VGM and SMCS for ductile fracture prediction even at the temperature of 60℃, which is much lower than the transition temperature of the material. The calibrated material parameters for G20Mn5QT cast steel decrease linearly with the drop of the temperature. (4) Fractographic features of the SNT specimens were studied through the scanning electron microscope (SEM). With the drop of the test temperature, the fracture surfaces tend to be more even, and less plastic deformation developed on fracture surfaces. Microscopic plateaus and valleys can be easily distinguished from the micrographs. The characteristic length of G20Mn5QT cast steel has the tendency to decrease with the drop of the temperature.
CRediT authorship contribution statement Yue Yin: Conceptualization, Methodology, Supervision, Writing - original draft, Writing - review & editing. Shuai Li: Methodology, Formal analysis, Investigation, Writing - original draft. Qinghua Han: Conceptualization, Project administration, Funding acquisition, Writing - review & editing. Mengfei Li: Investigation, Visualization, Writing - review & editing.
Declaration of Competing Interest
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Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Material parameters in void growth model for G20Mn5QT cast steel at low temperatures Yue Yin a,b, Shuai Li a, Qinghua Han a,b,⇑, Mengfei Li a a b
Department of Civil Engineering, Tianjin University, Tianjin 300072, China Key Laboratory of Coast Civil Structure Safety (Tianjin University), Ministry of Education, Tianjin 300072, China
h i g h l i g h t s Mechanical properties of G20Mn5QT cast steel at low temperatures were determined. Parameters in VGM/SMCS were calibrated for G20Mn5QT cast steel at low temperatures. VGM/SMCS are applicable for G20Mn5QT cast steel at low temperatures. Characteristic length of G20Mn5QT cast steel decreases with the drop of the temperature.
a r t i c l e
i n f o
Article history: Received 7 October 2019 Received in revised form 7 December 2019 Accepted 6 January 2020
Keywords: G20Mn5QT cast steel Low temperature Ductile fracture Void growth model Mechanical properties
a b s t r a c t With superior structural performances, G20Mn5QT cast steel has been extensively used in fabricating complex joints in steel constructions. Fracture failure of G20Mn5QT cast steel is then an important issue, especially for low-temperature situations. In this paper, mechanical properties of G20Mn5QT cast steel at low temperatures were studied by tensile coupon tests and Charpy impact tests. The effects of the low temperature on mechanical properties and the ductile-brittle transition temperature of G20Mn5QT cast steel were obtained based on the test results. The void growth model (VGM) and the stress modified critical strain (SMCS) model, which are two typical micromechanical fracture models, were calibrated for G20Mn5QT cast steel by experiments and complementary FEA on smooth notched tensile (SNT) specimens at four temperature levels, 20℃, 20℃, 40℃ and 60℃. For each temperature level, the material parameters in VGM and SMCS calculated based on test results of all six different specimens are in very good consistence. This consistency indicates the applicability of VGM and SMCS for predicting the ductile fracture of G20Mn5QT cast steel, even at the temperature of 60℃, which is much lower than the transition temperature of the material. The calibrated material parameters representing the resistance to ductile fracture of the material decrease linearly with the drop of the temperature. The characteristic length of G20Mn5QT cast steel was also determined by observation of fractured surfaces of test specimens with the scanning electron microscope, which has the tendency to decrease with the drop of the temperature. Ó 2020 Elsevier Ltd. All rights reserved.
1. Introduction Cast steel is an ideal solution for complex joints in steel constructions. With cast steel joints, geometric discontinuity can be avoided by smooth transition segments to reduce the stress concentration, and the welding can be arranged outside the joint region to minimize its adverse heat effects on the structural performance of the joints. Sometimes, cast steel joints are applied in regions of extreme environments such as low temperature. For ⇑ Corresponding author at: Department of Civil Engineering, Tianjin University, Tianjin 300072, China E-mail address: [email protected] (Q. Han). https://doi.org/10.1016/j.conbuildmat.2020.118123 0950-0618/Ó 2020 Elsevier Ltd. All rights reserved.
example, a large amount of cast steel joints was adopted in steel constructions in north China. If these joints were exposed outdoors, they would experience the minimum mean temperature as low as 40℃ in winter. This situation determines that these cast steel joints must have sufficient low-temperature ductility to ensure the safety of the structures. For steel joints and connections without sufficient ductility, the ductile fracture may occur under the action of monotonic loadings [1–6]. In the literatures, there are two typical micromechanical fracture models [7,8], void growth model (VGM) [9] and stress modified critical strain model (SMCS) [7], readily available for ductile fracture analysis of structural steels. These two models can give satisfactory results in ductile fracture prediction of various joints
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Y. Yin et al. / Construction and Building Materials 243 (2020) 118123
Fig. 1. Test setup and low-temperature environment.
Fig. 2. Temperature change process during a tension coupon test at 60℃.
Table 1 Mechanical properties of G20Mn5QT cast steel. Elongation
ry
ru
20%
300 MPa
500 ~ 650 MPa
and plastic strains in rigid plastic materials [8]. Since only the expansion of microvoids was considered, VGM and SMCS are applicable to ductile fracture prediction of materials with dominant tensile deformation, especially at the location of high-stress triaxiality. Compared with coupled micromechanical fracture models, for example, the GTN model [15,16], and those models applicable to ductile fracture caused by shear in low-stress triaxiality regimes [17–20], VGM and SMCS have an outstanding advantage that only one parameter is required for each model to define the resistance of materials to ductile fracture and provide simple and convenient fracture criteria. VGM and SMCS have been calibrated for different hot-rolled steels [21–27] through smooth notched tensile tests at ambient temperature. With the superior welding performance, G20Mn5QT cast steel [28] has been extensively used in steel constructions. Contents of sulphur and phosphorus in G20Mn5QT cast steel are strictly limited to 0.02% or under, which gives it the necessary plasticity and ductility for steel joints in different structural systems [29–32]. Material parameters in VGM and SMCS for G20Mn5QT cast steel at ambient temperature have also been calibrated and verified [33]. However, these material parameters are inapplicable to cast steel joints at low temperatures. Lots of research works [34,35] have proved the significant influence of the temperature on the mechanic properties, especially the ductility, of structural steels. The resistance of steels to ductile fracture at low temperatures
and connections under monotonic loadings [10–14]. VGM and SMCS are both uncoupled models, in which the growth rate of microvoids in the materials is calculated based on stress triaxiality
Fig. 3. The tension coupon.
Fig. 4. Nominal stress-strain curves by tensile coupon tests at different temperatures.
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Y. Yin et al. / Construction and Building Materials 243 (2020) 118123
describe the void growth quantitatively. The micromechanical fracture criterion can be expressed for VGM as
VGI ¼ Z
g¼
lnðR=R0 Þ ¼ c ecritical p
Z
ep
expð1:5T Þ dep > g
ð1Þ
0
expð1:5T Þdep
ð2Þ
0
where R is the radius of voids; R0 is the initial void radius; c is a constant; T is the stress triaxiality and expressed as T = rm/re (rm is the hydrostatic stress, and re is the von-Mises stress); qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dep ¼ ð2=3Þdeijp deijp is the incremental equivalent plastic strain;
ep is the equivalent plastic strain and ecritical is its critical value for p the initiation of the ductile fracture; g is a material parameter.
Fig. 5. True stress-plastic strain curves for G20Mn5QT cast steel at different temperatures.
may be much worse than that at ambient temperature [34,36,37]. It is then very desirable to calibrate the micromechanical fracture models for G20Mn5QT cast steel at low temperatures so that the ductile fracture of cast steel joints located in cold areas can be analyzed. In this paper, mechanical characteristics of G20Mn5QT cast steel at low temperatures were studied. Tensile coupon tests and Charpy impact tests were carried out on G20Mn5QT cast steel at different temperatures. Two micromechanical fracture models, VGM and SMCS, were calibrated for G20Mn5QT cast steel at four temperature levels by tests and complementary FEA on SNT specimens. The effects of low temperature on mechanical properties, Charpy impact toughness, and the calibrated fracture parameters were discussed for G20Mn5QT cast steel.
In many practical cases, with the increase of loading, the plastic strain rises rapidly while the stress triaxiality remains nearly a constant. If the variation of stress triaxiality is ignored, SMCS can be setup based on VGM. SMCS Index and a material parameter a were defined to express the fracture criterion of SMCS as shown in Eqs. (3) and (4).
SMCS Index ¼ ep expð1:5T Þ > a
ð3Þ
a ¼ ecritical expð1:5T Þ p
ð4Þ
The parameters g and a represent the resistance to ductile fracture of the material and can be calibrated through SNT tests and complementary FEA. The ductile fracture of steel is the behavior of a certain volume of materials. A length scale, termed as the characteristic length (l*) [21], was then defined to trigger the fracture of the material. The characteristic length of the material depends on its microstructure and is generally taken as the average size of microvoid colonies, which can be determined by scanning electron microscope (SEM) analysis of the fracture morphologies of the material. 3. Tension coupon tests
2. Micromechanical fracture criteria of VGM and SMCS model
3.1. Test setup and low-temperature environment
The ductile fracture of steel was considered as the result of nucleation, growth, and coalescence of microscopic voids in micromechanics of fracture. The relationship between the void growth and the combined effect of the stress triaxiality and the equivalent plastic strain has been established according to analytical derivations in references [8,38]. In VGM, the growth of microvoids controls the ductile fracture of materials. When voids grow to exceed the critical size, the ductile fracture occurs. Void growth index (VGI) was then defined to
All the tensile tests were conducted on an electronic universal testing machine with a capacity of 200kN. The test setup was shown in Fig. 1. In order to create a low-temperature environment, a cold chamber was manufactured with the injection of liquid nitrogen. The cold chamber was made up of two layers of the polyurethane board, with a thickness of 80 mm. In order to maximize the effect of thermal insulation, two layers of the polyurethane board were interlaced at the edge and corner of the cold chamber. The gaps between polyurethane boards were sealed with silica gel.
Table 2 Results of tension coupon tests at different temperatures. NO.
Temp (℃)
d0 (mm)
l0 (mm)
lf (mm)
df (mm)
E (GPa)
E(GPa)
fy (MPa)
f y (MPa)
fu (MPa)
f u (MPa)
d (%)
d(%)
w (%)
w(%)
1–1 1–2 1–3 2–1 2–2 2–3 3–1 3–2 3–3 4–1 4–2 4–3
20
12.50 12.48 12.47 12.49 12.51 12.50 12.48 12.51 12.51 12.49 12.50 12.51
50 50 50 50 50 50 50 50 50 50 50 50
63.60 63.52 63.14 62.30 62.52 63.02 61.85 62.21 62.05 60.46 60.82 61.52
8.50 8.34 8.28 8.61 8.42 8.55 8.86 8.75 8.50 9.64 9.52 9.46
202.5 210.2 208.5 220.2 218.6 216.5 227.1 225.4 223.5 243.5 251.8 247.6
207.1
327.6 335.2 328.7 346.3 347.5 348.8 349.6 357.6 356.8 397.1 388.3 370.4
330.5
585.3 588.2 583.9 611.0 608.1 606.2 615.6 614.2 618.2 631.2 632.5 633.1
585.8
27.2 27.0 26.3 24.6 25.0 26.0 23.7 24.4 24.1 20.9 21.6 23.0
26.8
53.8 55.3 55.9 52.5 54.7 53.2 49.6 51.1 53.8 40.4 42.0 42.8
55.0
20
40
60
218.4
225.3
247.6
347.5
354.7
385.3
608.4
616.0
632.3
25.2
24.1
21.9
53.5
48.2
41.7
4
Y. Yin et al. / Construction and Building Materials 243 (2020) 118123
Fig. 6. Effect of the temperature on mechanical properties of G20Mn5QT cast steel.
Liquid nitrogen was injected into the chamber through a precise valve. Two PT100 thermocouples were mounted on each test specimen at two different locations to measure the real-time temperature of the specimen. The inflow of liquid nitrogen was controlled
by adjusting the valve so that the target temperatures could be obtained and maintained. Four temperature levels, TEMP = 20℃, 20℃, 40℃ and 60℃, were set for the tensile tests on G20Mn5QT cast steel. The thermocouples were connected to the acquisition equipment, and the temperature of the specimen could be monitored through a computer. An extensometer was put on the tension coupon in the cold chamber to measure the deformation and control the load rate. The temperature change process of a tensile specimen tested at 60℃ is shown in Fig. 2. The first 11 minutes is the cooling process, during which the specimen was cooled from ambient temperature to 60℃. In order to ensure the internal temperature of the specimen reach 60℃, the same as the external temperature, the target temperature (-60℃) was maintained for another 10 minutes. After that, the formal loading process began from the 21st minute.
3.2. Tension coupon tests
Fig. 7. The Charpy impact specimen.
With the superior performance in weldability, G20Mn5QT cast steel is very suitable for fabrication of complex steel joints. Mechanical properties of G20Mn5QT cast steel stipulated in reference [28] were listed in Table 1.
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Y. Yin et al. / Construction and Building Materials 243 (2020) 118123 Table 3 Charpy impact energy of G20Mn5QT cast steel at different temperatures. TEMP (℃)
Specimen NO.
20
CV1 CV2 CV3 CV4 CV5 CV6 CV7 CV8 CV9 CV10 CV11 CV12 CV13 CV14 CV15
0
20
40
60
Charpy impact energy (J) Ak (J)
Average
Stipulated in [28]
75.22 72.21 73.82 68.21 65.90 72.41 38.82 42.90 39.42 31.87 35.64 36.64 19.78 34.37 28.21
73.75
–
68.84
50 J
40.37
–
34.71
–
27.45
–
Fig. 8. The Charpy impact energy of G20Mn5QT cast steel at different temperatures.
were shown in Fig. 3. A total number of 12 tension coupons were machined for the tests at the four temperature levels. The tension coupons were put into the cold chamber and screwed into two end sleeves, which were clamped by the testing machine, as shown in Fig. 1(b). An extensometer was put on the tensile coupon in the cold chamber to measure the deformation of gage length. The loading rate was 1.0 mm/min, which was controlled through the deformation measured by this extensometer. Before the loading application, the upper chuck of the testing machine should be loosened to release the contractions of the coupons during the cooling process. Nominal stress-strain curves were determined by tension coupon tests, as illustrated in Fig. 4. Note that the extensometer was taken off before the deformation of the test coupon reached its measuring range. Consequently, the stress-strain relationship beyond e = 0.15% was not obtained directly by these tests. True stress-strain curves were determined based on the test data, as shown in Fig. 5. The diameters at the fractured surfaces of the test coupons were measured, and the true stress and strain were determined by Eqs. (5) and (6) for the fractured load.
2 rfracture ¼ F fracture = pdf =4 true
h
efracture ¼ ln d0 =df true
Fig. 9. The smooth notched tensile test specimen.
A 30 mm thick G20Mn5QT cast steel plate was cast for the manufacturing of test specimens in this paper. Mechanical properties of this cast steel plate at low temperatures were determined by tension coupon tests. The geometric details of the tension coupons
2 i
ð5Þ ð6Þ
in which, d0 and df is the diameter of the coupons before tests and at the fractured surface respectively. The true stress-strain curves were then extended linearly to the fracture of the coupons in Fig. 5, based on which relationships between the true stress and plastic strain was established for G20Mn5QT cast steel. Mechanical properties of G20Mn5QT cast steel determined by tensile coupon tests were summarized in Table 2, where it can be observed that all of them vary with the temperature, as shown in Fig. 6. The elastic modulus E, yield strength fy and ultimate strength fu increase almost linearly by 19.6%, 16.6% and 7.9% respectively with the drop of the temperature from 20℃ to 60℃; while the elongation d and reduction of cross section w decrease by 18.3% and 24.2% respectively. Obviously, the strength of G20Mn5QT cast steel increases and the ductility deteriorates at low temperatures. 4. Charpy impact toughness tests Charpy impact toughness tests were conducted for G20Mn5QT cast steel at 20℃, 0℃, 20℃, 40℃ and 60℃ respectively on a
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Y. Yin et al. / Construction and Building Materials 243 (2020) 118123
pendulum impact tester with a standard strike energy of 300 J. Fifteen Charpy impact specimens were machined, three for each temperature, from the G20Mn5QT cast steel plate. The Charpy impact specimen and its geometry details were shown in Fig. 7. Charpy impact specimens were cooled to a certain testing temperature in the mixture of ethyl alcohol and liquid nitrogen. Specimens were kept in the mixture long enough to make sure they were cooled completely. The temperature was monitored by PT100 thermocouple mounted on the test specimen. The mixture was placed very close to the test machine and the specimen was taken out of the mixture only after the test machine was ready. It took less than 5 seconds to take the Charpy impact specimen out of the cooling mixture, put it on the testing machine quickly and complete the test. The Charpy impact energies of G20Mn5QT cast steel at different temperatures were listed in Table 3. The Charpy impact energy obtained by tests at 0℃ meets the requirements in [28]. The variation of Charpy impact energy of G20Mn5QT cast steel with the temperature was illustrated in Fig. 8. An obvious decrease of the Charpy impact energy can be observed with the drop of the temperature, especially when the temperature reaches 0℃, which means the deterioration of the toughness of G20Mn5QT cast steel. Boltzmann function [39] was adopted to fit the relationship between the Charpy impact energy and the temperature, as shown in Fig. 8. The ductile-brittle transition temperature is 12.3℃, while the width of the temperature transition zone is 13.3 ℃.
5. Calibration of VGM and SMCS at different temperatures 5.1. Smooth notched tensile tests on G20Mn5QT cast steel Material parameters were calibrated for VGM and SMCS by SNT tests at four temperature levels, 20℃, 20℃, 40℃ and 60℃. Twenty-four SNT specimens were machined from the G20Mn5QT cast steel plate, as shown in Fig. 9. Three different notch radii (R = 1.5, 3.125 and 6.25 mm) were considered to provide different triaxial stress conditions. The tests were carried out on the electronic universal testing machine. The test setup was the same as the one severed for tension coupon tests shown in Fig. 1. After the temperature of the specimen in the cold chamber dropped to the test temperature, the uniform axial tensile load was applied and the specimen was stretched continuously until the fracture at the neck. The deformation measured by the extensometer was adopted to control the loading at the rate of 0.2 mm/min. Load versus deformation curves were illustrated for all test specimens in Figs. 10-12. Points with sudden slope change on these curves were identified as ductile fracture initiation. Two tests were conducted for each notch radius and each temperature, as shown in Table 4. Tensile loads Pf and specimen deformations Df at fracture initiation were obtained for all SNT specimens.
Fig. 10. Load-deformation curves obtained by tests and FEA for SNT specimens (R = 1.5 mm) at different temperatures.
Y. Yin et al. / Construction and Building Materials 243 (2020) 118123
7
Fig. 11. Load-deformation curves obtained by tests and FEA for SNT specimens (R = 3.125 mm) at different temperatures.
5.2. SEM tests and characteristic length Fractographic features of the SNT specimens were studied through the scanning electron microscope (SEM). Typical micrographs of the fracture surfaces at different temperatures were presented in Figs. 13-16. During the ductile fracture, the coalescence and cleavage of microvoids generated microscopic plateaus and valleys, which can be easily distinguished from the micrographs. With the drop of the test temperature, the fracture surfaces tend to be more even, and less plastic deformation developed on fracture surfaces. It is generally accepted that, for particular materials, the characteristic length (l*) should be the size of a microvoid colony [21]. Measurement on the micrographs gave the characteristic length, as listed in Table 5, for G20Mn5QT cast steel at different temperatures. It should be noted that the obtained characteristic lengths for different temperatures are all at the order of 0.1 mm, the same as those of many other structural steels [21,23]. 5.3. FEA of smooth notched specimens under tension The nonlinear FEA of SNT specimens was conducted by the general FE software ABAQUS [40]. Axisymmetric plane models were established for all kinds of specimens, as shown in Fig. 17. Finite element models were discretized with the CAX4R element implemented in ABAQUS, which is a type of 4-node bilinear axisymmet-
ric element. In the notch region, ultra-fine mesh with element size being the characteristic length in Table 5 was adopted to capture the ductile fracture. Coarser meshes were adopted in regions far away from the notch to save the computational cost. In finite element analysis, the constitutive relationship of the material was set according to the results of the tension coupon tests at different temperatures as shown in Fig. 5 and Table 2. The Mises yield criterion was adopted to model the plastic behavior of the material. 5.4. Calibration of VGM and SMCS Material parameters in the two micromechanical fracture models were calibrated for G20Mn5QT cast steel at the four temperature levels, TEMP = 20℃, 20℃, 40℃ and 60℃, based on results of SNT tests and complementary FEA. The study on SNT specimens tested at the temperature of 20℃ was taken as an example to illustrate the calibration procedure. The distribution of the stress triaxiality and equivalent plastic strain over the critical section were obtained by FEA for the specimens with the three different notch radii, as shown in Fig. 18. The stress triaxiality is higher at the section center than on the surface. The equivalent plastic strain changes little over the section. VGI and SMCS Index were calculated over the critical section by Eqs. (1) and (3), as shown in Fig. 19. The maximum value of both indexes is at the center of the critical section, indicating that the
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Fig. 12. Load-deformation curves obtained by tests and FEA for SNT specimens (R = 6.25 mm) at different temperatures.
Table 4 Calibration of g and a for G20Mn5QT cast steel at different temperatures. Temp (℃)
Notch radius (mm)
Specimen NO.
Pf (kN)
Df (mm)
ecritical p
re (MPa)
rm (MPa)
g
g
a
a
20
1.5
20℃-1-1 20℃-1-2 20℃-2-1 20℃-2-2 20℃-3-1 20℃-3-2 20℃-1-1 20℃-1-2 20℃-2-1 20℃-2-2 20℃-3-1 20℃-3-2 40℃-1-1 40℃-1-2 40℃-2-1 40℃-2-2 40℃-3-1 40℃-3-2 60℃-1-1 60℃-1-2 60℃-2-1 60℃-2-2 60℃-3-1 60℃-3-2
24.20 22.11 22.42 21.78 18.20 19.17 23.35 24.81 22.50 22.15 19.39 15.96 25.62 24.10 22.21 22.38 19.67 21.64 27.16 24.74 24.57 24.54 23.21 23.66
0.77 0.80 0.96 1.00 1.32 1.35 0.68 0.71 0.85 0.91 1.17 1.25 0.71 0.72 0.79 0.83 1.13 1.15 0.65 0.60 0.70 0.75 1.12 1.13
0.2018 0.2176 0.3075 0.3275 0.3927 0.4042 0.1516 0.1670 0.2629 0.2938 0.3498 0.3860 0.1600 0.1650 0.2278 0.2461 0.3208 0.3290 0.1478 0.1284 0.1981 0.2186 0.3168 0.3207
703.04 710.71 754.22 763.93 795.48 801.05 695.18 698.78 721.19 728.40 741.47 749.94 705.60 707.22 728.04 734.09 758.84 761.57 731.23 717.48 751.66 760.01 799.90 801.50
949.03 955.97 755.14 759.93 623.94 627.03 963.14 986.10 800.14 812.15 664.00 674.94 961.22 968.20 768.27 780.13 645.27 648.27 963.15 916.40 761.97 781.24 661.97 663.55
1.51 1.67 1.46 1.59 1.41 1.46 0.97 1.09 1.13 1.29 1.12 1.26 1.02 1.05 0.92 1.01 0.98 1.01 0.92 0.79 0.77 0.87 0.95 0.97
1.52
1.37 1.51 1.36 1.47 1.32 1.37 0.91 1.01 1.05 1.19 1.05 1.17 0.95 0.99 0.87 0.95 0.93 0.95 0.88 0.75 0.74 0.83 0.91 0.92
1.40
3.125 6.25 20
1.5 3.125 6.25
40
1.5 3.125 6.25
60
1.5 3.125 6.25
1.14
1.00
0.88
1.06
0.94
0.86
Y. Yin et al. / Construction and Building Materials 243 (2020) 118123
Fig. 13. Micrograph of fractured surfaces at 20℃.
Fig. 14. Micrograph of fractured surfaces at 20℃.
Fig. 15. Micrograph of fractured surfaces at 40℃.
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Fig. 16. Micrograph of fractured surfaces at 60℃.
Table 5 Characteristic lengths for G20Mn5QT cast steel at different temperatures. TEMP
Specimen NO.
Characteristic length (mm)
20℃
20℃-1 20℃-2 20℃-3 Average 20℃-1 20℃-2 20℃-3 Average 40℃-1 40℃-2 40℃-3 Average 60℃-1 60℃-2 60℃-3 Average
0.207 0.215 0.221 0.214 0.199 0.187 0.206 0.197 0.177 0.165 0.160 0.167 0.133 0.145 0.140 0.139
20℃
40℃
60℃
strain was neglectable small. Then, the equivalent plastic strain kept rising with the load. However, the stress triaxiality remained almost unchanged. Therefore, it is acceptable that VGM can be simplified to SMCS by assuming the stress triaxiality is constant during the prediction of ductile fracture. These conclusions apply for the case at the temperature of 20℃, as well as the cases at other temperatures. The deformations of the specimens, Df, at the fracture obtained by SNT tests were as shown in Table 4. Apply these deformations to FE models of the corresponding test specimens and determine the equivalent plastic strain and stress triaxiality at the center of the critical section of each specimen by FEA. It can be seen that, for SNT specimens with the same notch radius, the equivalent plastic strains at the fracture decrease with the drop of the temperature. Then, g in VGM was calculated by Eq. (2), a in SMCS by Eq. (4), as listed in Table 4. Average values of g and a were calculated for all the four temperature levels, as listed also in Table 4. It can be seen that, for each temperature level, the values of g and a calculated based on test results of the six different specimens are all in very good consistence. The largest deviation between a calibrated value and the average is less than 15%. This indicates that VGM and SMCS are applicable for ductile fracture prediction even at the temperature of 60℃, which is much lower than the transition temperature of the material. Material parameters, g and a, have already been calibrated for G20Mn5QT cast steel at ambient temperature in reference [33]. The values of g and a are 0.99 and 1.05 respectively, which are all less than those listed in Table 4 for the temperature of 20℃. Note that the yield stress of the G20Mn5QT cast steel in reference [33] is 427 MPa, which is much larger than that in this paper. The divergence between the material parameters calibrated in this paper and the reference was then attributable to different mechanical properties of different batches of cast steels. In general, the higher the yield strength of the material, the worse the resistance to the ductile fracture.
Fig. 17. A typical finite element model for SNT specimens.
5.5. Ductile fracture prediction of SNT specimens with the calibrated VGM and SMCS
ductile fracture tends to initiate there. Variations of the stress triaxiality against the equivalent plastic strain were plotted for the three specimens in Fig. 20. The stress triaxiality increased sharply at the beginning of the loading process when the equivalent plastic
Ductile fracture of SNT specimens with notch radii 1.5, 3.125 and 6.25 mm was predicted with the calibrated VGM and SMCS at the four different temperatures. VGI and SMCS index at the center of the notch section were calculated based on FEA. The
Y. Yin et al. / Construction and Building Materials 243 (2020) 118123
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Fig. 18. Distribution of equivalent plastic strain and stress triaxiality over the critical section at 20℃.
Fig. 19. VGI and SMCS Index over the critical section at 20℃.
deformations at fracture were predicted for all specimens, as shown in Figs. 21–24. The predicted deformations at fracture (DFEM ) and those f obtained by tests (Dtest f ) were compared for all SNT specimens in Fig. 25. It can be seen that the predictions agreed well with test results and all data fell inside the 15% margin lines. The agreement verified the rationality of the micromechanical fracture models calibrated in this research. 5.6. Relationship between the calibrated material parameters and the temperature
Fig. 20. Relationship between stress triaxiality and equivalent plastic strain at the center of the critical section at 20℃.
All the calibrated g and a were plotted against the temperature as shown in Fig. 26. Both material parameters have the tendency to decrease with the drop of the temperature. This is consistent with the basic concept about the resistance of structural steels to the ductile fracture. The average values of the material parameters at the same temperature level were also plotted against the temperature in Fig. 26. It can be observed that both the average values of g in VGM and a
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Y. Yin et al. / Construction and Building Materials 243 (2020) 118123
Fig. 21. Prediction of ductile fracture of SNT specimens at 20℃.
Fig. 22. Prediction of ductile fracture of SNT specimens at 20℃.
Fig. 23. Prediction of ductile fracture of SNT specimens at 40℃.
Y. Yin et al. / Construction and Building Materials 243 (2020) 118123
Fig. 24. Prediction of ductile fracture of SNT specimens at 60℃.
Fig. 25. Errors between test results and prediction results.
Fig. 26. Calibrated value for g in VGM and a in SMCS.
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in SMCS decrease almost linearly with the drop of the temperature. Therefore, the relationships between the material parameters in the micromechanical fracture models and temperature were established with linear regression analysis, as shown in Eq. (7) for g in VGM, and Eq. (8) for a in SMCS.
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.
g ¼ g20 þ 0:0081 ðTEMP 20Þ
ð7Þ
Acknowledgement
a ¼ a20 þ 0:0072 ðTEMP 20Þ
ð8Þ
The authors are grateful for the support by the National Natural Science Foundation of China (No. 51525803).
Based on the proposed equations, material parameters in the two micromechanical fracture models for G20Mn5QT cast steel at different low-temperature levels can be determined for ductile fracture prediction conveniently.
6. Conclusions Structural steel tends to lose its ductility with the drop of temperature, which makes the fracture failure of steel an important issue for steel construction at low temperatures. In this paper, mechanical properties of G20Mn5QT cast steel at different low temperatures were studied by tension coupon tests and Charpy impact tests. The void growth model (VGM) and the stress modified critical strain (SMCS) model were calibrated for G20Mn5QT cast steel by tests and complementary FEA on SNT specimens at four temperature levels, 20℃, 20℃, 40℃ and 60℃. The following conclusions were obtained: (1) The elastic modulus, yield strength and ultimate strength of G20Mn5QT cast steel increase almost linearly by 19.6%, 16.6% and 7.9% respectively with the drop of the temperature from 20℃ to 60℃; while the elongation and reduction of cross section decrease by 18.3% and 24.2% respectively. (2) The Charpy impact energy of G20Mn5QT cast steel decreases significantly with the drop of the temperature, especially when the temperature is below 0℃, which means the deterioration of the toughness of G20Mn5QT cast steel. The ductile-brittle transition temperature is 12.3℃, while the width of the temperature transition zone is 13.3 ℃. (3) Material parameters, g in VGM and a in SMCS, were calibrated for G20Mn5QT cast steel at four temperature levels, 20℃, 20℃, 40℃ and 60℃. For each temperature level, the values of g and a calculated based on test results of all six different specimens are in very good consistence. This consistency indicates the applicability of VGM and SMCS for ductile fracture prediction even at the temperature of 60℃, which is much lower than the transition temperature of the material. The calibrated material parameters for G20Mn5QT cast steel decrease linearly with the drop of the temperature. (4) Fractographic features of the SNT specimens were studied through the scanning electron microscope (SEM). With the drop of the test temperature, the fracture surfaces tend to be more even, and less plastic deformation developed on fracture surfaces. Microscopic plateaus and valleys can be easily distinguished from the micrographs. The characteristic length of G20Mn5QT cast steel has the tendency to decrease with the drop of the temperature.
CRediT authorship contribution statement Yue Yin: Conceptualization, Methodology, Supervision, Writing - original draft, Writing - review & editing. Shuai Li: Methodology, Formal analysis, Investigation, Writing - original draft. Qinghua Han: Conceptualization, Project administration, Funding acquisition, Writing - review & editing. Mengfei Li: Investigation, Visualization, Writing - review & editing.
Declaration of Competing Interest
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