Ultra-low cycle fatigue prediction of Q345qC steel at different … · 2019-09-09 · Ultra-low...

The 2019 World Congress on Advances in Structural Engineering and Mechanics (ASEM19)Jeju Island, Korea, September 17 - 21, 2019

Ultra-low cycle fatigue prediction of Q345qC steel at different stress triaxiality

Shuailing Li1) and *Xu Xie2)

1), 2) College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China

2) [email protected]

ABSTRACT Steel structures may experience the ultra-low cycle fatigue (ULCF) damage due to cyclic large strain, when subjected to strong earthquake action. In this paper, tests on circular notched specimens were conducted, and the scanning electron microscopy studies were carried out on the fractured surfaces. The ULCF prediction model, the cyclic void growth model (CVGM), was calibrated at high and moderate stress triaxiality. The relationship between the damage degradation parameter of CVGM model and stress triaxiality was established. Based on the calibrated CVGM model, ULCF assessment was performed on circular notched specimens. The results show that the fracture mechanism of “void nucleation, growth and coalescence” was observed. At high stress triaxiality, void dilation is dominant, and void growth gradually transitions elongation with stress triaxiality decreasing. The equivalent plastic strain to ULCF fracture initiation predicted by the calibrated CVGM model agreed well with the experimental results. Keywords: Ultra-low cycle fatigue; Cyclic void growth model; High stress triaxiality; Moderate stress triaxiality; Q345qC steel 1. INTRODUCTION Ultra-low cycle fatigue (ULCF) damage in steel bridge piers and beam-column connections was observed in site investigations after the 1994 Northridge earthquake in California and the 1995 Kobe earthquake in Japan (Miller 1998, Nakashima et al. 1998, Subcommittee on Investigation of Seismic Damage of Steel Structure 2000). The tests in laboratory also confirmed the phenomenon of ULCF (Tateishi et al. 2008, Ge et al. 2007, 2013). Unlike traditional high cycle and low cycle fatigue, ULCF generally undergoes large plastic strain leading to ductile fracture initiation after a few reverse loading cycles (typically less than 100). Ductile fracture is initiated by void nucleation, followed by void growth (dilation or elongation), and finally void coalescence causing a ductile crack (Anderson 2005). The crack initially expands under cyclic loading, and catastrophic failure occurs in a brittle mode (Kuwamura and Yamamoto 1997).

1)

Graduate Student 2)

Professor


Therefore, ULCF fracture initiation can be considered to be a limit state in structural steel members, and it need to be verified in the seismic design of steel structures.

Ductile fracture initiation is dependent on the stress state and hardening property of material matrix, especially the process of void growth and coalescence (McClintock 1968). The stress state is usually characterized by stress triaxiality (T= σh/σe), defined as the ratio of the hydrostatic stress (σh) and the Mises stress (σe). It has been observed that at high stress triaxiality (T > 0.70), void dilation is dominant, and at moderate stress triaxiality (0.33< T < 0.70), void elongation is dominant in the process of void growth (Danas et al. 2012, Kiran et al. 2014). At low or negative stress triaxiality (T < 0.33), other forms of void growth and coalescence mechanisms have been reported in the literature (Bron et al. 2004). Additionally, it has been indicated that at low stress triaxiality, the lode angle parameter has a great effect on the behavior of void growth and coalescence except for stress triaxiality (Barsoum et al. 2011, Danas et al. 2012, Kiran et al. 2014). However, at high and moderate stress triaxiality, the ductile fracture is dominant by the void growth and coalescence, and the effect of load angle parameter can be neglected.

In the literature, some models were proposed to predict ULCF in metals. Tateishi et al. (2007) developed a ULCF prediction model that consider damage due to cyclic loading and static loading. A unified expression is proposed to predict ULCF life where an exponential function and additional material parameter are introduced (Xue 2008). Ge et al. (2012) proposed a damage index-based method to predict ULCF fracture initiation in steel structures based on Coffin-Manson formula and Miner’s rule. However, it is worth noting that the above empirical models are derived based on experimental results in uniaxial strain condition, and micromechanics-based models have been proposed to ULCF fracture initiation under multiaxial strain condition in recent years. Huang et al. (2013) applied the micromechanics damage model to investigate the crack initiation and propagation of beam-to-column weld joints. Tong et al. (2016) investigated the ULCF behavior of beam-to-column joints based on continuous damage mechanics model. But the above models have too many material parameters, and calibration task is difficult owing to the coupling effect among parameters. Kanvinde and Deierlein (2007) proposed the cyclic void growth model (CVGM) for ductile fracture initiation of structural steels, which has only two materials parameters, and the effectiveness of CVGM model is confirmed in material specimens (Kanvinde and Deierlein 2008). Additionally, the CVGM model was also applied to access ULCF fracture initiation in steel members. Myers et al. (2009) investigated the ULCF fracture initiation of steel column baseplate connections with the CVGM model. Fell et al. (2010) investigated fracture behaviour induced by inelastic cyclic buckling of steel braces. Zhou et al. (2013) conducted the ULCF fracture initiation prediction of beam-to-column connection by using the CVGM model. Generally, the CVGM model has a reasonable prediction accuracy in the above research. However, the calibration value of CVGM model damage degradation parameter has a significant impact in ULCF prediction, and it is shown that the value is related to the magnitude of stress triaxiality in the previous study (Li et al 2019). Therefore, it is significant to determine the relationship between damage degraded parameter and stress triaxiality.

In order to determine the relationship between CVGM model damage degraded parameter and stress triaxiality, tests on circular notched specimens were carried out.


The ULCF fracture mechanism at different triaxiality was investigated using scanning electron microscopy (SEM). Based on experimental results and finite element analysis (FEA), the CVGM model was calibrated, and empirical formula between damage degradation parameter and stress triaxiality was proposed. Finally, the prediction accuracy of calibrated CVGM model was evaluated. 2. CYCLIC VOID GROWTH MODEL Based on the Rice-Tracey void growth theory (Rice and Tracey 1969), Kanvinde and Deierlein (2006) proposed the void grow model (VGM) to predict ductile fracture of structural steels under monotonic loading. According to VGM criterion, fracture can be predicted to occur when the following mathematical expression is satisfied.

0

e x p ( 1 . 5 ) 0c r i tp

pT d

(1)

where crit

p is the equivalent plastic strain at the instant of fracture, T indicates the

stress triaxiality, (2 / 3) .p p

p ij ijd d d denotes the equivalent plastic strain increment.

represents material parameter, determined by calibration to circular notched specimens tensile tests and corresponding FEA.

For cyclic loading, the sign of the stress triaxiality changes during the loading history. It should be noted that if the stress triaxiality is positive, the void will grow, and conversely the void will shrink. The critical void size under cyclic loading is determined by a degraded function of its counterpart under monotonic loading due to the accumulated damage. The CVGM model for predicting ULCF can be expressed as follows (Kanvinde and Deierlein 2007):

2 2

1 1

exp 1.5 d exp 1.5 d / exp accum

p p CVGM p

tensile compressive

T T f

(2)

Where ε1 and ε2 are the equivalent plastic strain at the beginning and end of the tensile

and compressive excursions, respectively.accum

p denotes damage variable that is the

cumulative equivalent plastic strain at the beginning of last tensile cycle. λCVGM is the damage degradation parameter that can be calibrated through the circular notched specimens cyclic tests and FEA.

It should be noted that the ULCF fracture initiation is not the behaviour at a material point but involves a critical volume of material. Therefore, the characteristic length is defined to reflect the length scale, which can be evaluated by SEM (Kanvinde and Deierlein 2004). ULCF fracture initiates only when CVGM model is satisfied at the characteristic length of the material. 3. EXPERIMENT 3.1 Material and specimens

The Q345qC steel is used in this paper and its mechanical properties are presented in Table 1 (Li et al. 2019). The circular notched specimens with different


notch radii were designed and manufactured, and the dimensions are shown in Figure 1.

Table 1. Mechanical properties of Q345qC steel.

E (MPa) σy(MPa) σu (MPa) A (%)

198,221 351.10 508.57 40.60

Note: E indicates elastic modulus; σy and σu denote the yield strength and ultimate strength respectively; A represents elongation ratio.

Figure 1. The dimensions of specimens (unit: mm). 3.2 Experiment programme

The twelve uniaxial tensile specimens and seventy two cyclic specimens were tested to calibrate CVGM model parameters. Additionally, thirty four specimens were also tested to evaluate the prediction accuracy of CVGM model. The MTS 880 (MTS Systems Corporation, Eden Prairie, MN, USA) was used, as shown in Figure 2. The gauge length of extensometer is 50mm, and two types of strain control loading pattern was adopted, which is shown in Figure 3. In CTF loading, the specimens were cycled at constant strain amplitude until fracture occurs. The C-PTF loading entails cycling for five cycles at specified strain amplitudes, followed by a monotonic tensile fracture. The cyclic loading protocol of specimens is presented in Table 2 and Table 3.

Figure 2. Test setup.

(a) CTF (b) C-PTF

180

50 5080

25

R12.5

R=1.80, 2.50, 3.75, 4.50, 6.00,

7.50,10.0, 15.0, 20.0, 30.0 or 60.0

15

7.5

Loading cycles

Str

ain

Loading cycles

Str

ain


Figure 3. Loading pattern. 3.3 Experimental results

For monotonic tensile loading, Figure 6 presents experimental force-displacement curves of specimens, where the sudden drop point of the slope of curves is defined as the instant of fracture initiation (Kanvinde and Deierlein 2006). The fracture

displacement f of tensile specimens is presented in Table 4. It can be observed that

the fracture toughness of Q345qC steel increases with the notch radius of specimens increasing.

For cyclic loading, the experimental force-displacement curves of specimens are presented in Figure 7, where the sudden drop point of the slope of the last tensile cycle corresponds to the instant of ULCF fracture initiation (Kanvinde and Deierlein 2007). Table 2 and 3 show the experimental results for calibrating model parameters and evaluating model prediction accuracy, respectively. The number of ULCF failure cycles of all specimens is within 25 cycles.

Table 2. The experimental results of specimens for calibrating model parameters.

Notch size R (mm)

No. Loading Loading Strain Cycles to

fracture initiation

1.80

BMC-1 C-PTF [0,0.0050] 6 BMC-2 C-PTF [0,0.0050] 6 BMC-3 C-PTF [0,0.0100] 6 BMC-4 C-PTF [0,0.0100] 6

2.50 BMC-5 C-PTF [0,0.0050] 6

3.75

BMC-6 CTF [0,0.0125] 14 BMC-7 CTF [0,0.0125] 14 BMC-8 CTF [0,0.0150] 8 BMC-9 CTF [0,0.0150] 9 BMC-10 CTF [0,0.0160] 7 BMC-11 CTF [0,0.0160] 8 BMC-12 CTF [0,0.0170] 5 BMC-13 CTF [0,0.0175] 6

4.50

BMC-14 CTF [0,0.0130] 14 BMC-15 CTF [0,0.0130] 14 BMC-16 CTF [0,0.0130] 15 BMC-17 CTF [0,0.0135] 13 BMC-18 CTF [0,0.0135] 13 BMC-19 CTF [0,0.0150] 10 BMC-20 CTF [0,0.0150] 11 BMC-21 CTF [0,0.0200] 5 BMC-22 CTF [0,0.0200] 5

5.00

BMC-23 C-PTF [0,0.0100] 6 BMC-24 C-PTF [0,0.0100] 6 BMC-25 CTF [0,0.0180] 8 BMC-26 CTF [0,0.0180] 8

6.00 BMC-27 CTF [0,0.0150] 14 BMC-28 CTF [0,0.0150] 14


BMC-29 CTF [0,0.0200] 7 BMC-30 CTF [0,0.0200] 7

7.50

BMC-31 C-PTF [0,0.0100] 6 BMC-32 C-PTF [0,0.0100] 6 BMC-33 CTF [0,0.0150] 21 BMC-34 CTF [0,0.0150] 25 BMC-35 CTF [0,0.0200] 11 BMC-36 CTF [0,0.0200] 12 BMC-37 CTF [0,0.0225] 6 BMC-38 CTF [0,0.0225] 7 BMC-39 CTF [0,0.0250] 7 BMC-40 CTF [0,0.0250] 8 BMC-41 CTF [0,0.0300] 4 BMC-42 CTF [0,0.0300] 6

10.0

BMC-43 C-PTF [0,0.0100] 6 BMC-44 C-PTF [0,0.0100] 6 BMC-45 C-PTF [0,0.0200] 6 BMC-46 C-PTF [0,0.0200] 6

15.0

BMC-47 C-PTF [0,0.0100] 6 BMC-48 C-PTF [0,0.0100] 6 BMC-49 CTF [0,0.0200] 20 BMC-50 CTF [0,0.0200] 23 BMC-51 CTF [0,0.0250] 11 BMC-52 CTF [0,0.0250] 12 BMC-53 CTF [0,0.0350] 5 BMC-54 CTF [0,0.0350] 6

20.0

BMC-55 CTF [0,0.0250] 13 BMC-56 CTF [0,0.0250] 16 BMC-57 CTF [0,0.0350] 7 BMC-58 CTF [0,0.0350] 7

30.0

BMC-59 CTF [0,0.0300] 14 BMC-60 CTF [0,0.0300] 14 BMC-61 CTF [0,0.0350] 8 BMC-62 CTF [0,0.0350] 9 BMC-63 CTF [0,0.0400] 6 BMC-64 CTF [0,0.0400] 7

60.0

BMC-65 C-PTF [0,0.0200] 6 BMC-66 C-PTF [0,0.0200] 6 BMC-67 CTF [0,0.0300] 18 BMC-68 CTF [0,0.0300] 19 BMC-69 CTF [0,0.0350] 12 BMC-70 CTF [0,0.0350] 13 BMC-71 CTF [0,0.0400] 8 BMC-72 CTF [0,0.0400] 8

Note: For example, [0, 0.0300] refers to a specimen cycled between strain 0 and 0.0300.


Table 3. The experimental results of specimens for verifying model accuracy.

Notch size R (mm) No. Loading Loading Strain Cycles to

fracture initiation

1.80

BMC-73 CTF [0,0.0100] 16 BMC-74 CTF [0,0.0100] 18 BMC-75 CTF [0,0.0125] 8 BMC-76 CTF [0,0.0125] 10 BMC-77 CTF [0,0.0130] 6 BMC-78 CTF [0,0.0135] 7 BMC-79 CTF [0,0.0140] 4 BMC-80 CTF [0,0.0140] 4 BMC-81 CTF [0,0.0150] 5 BMC-82 CTF [0,0.0150] 6 BMC-83 CTF [0,0.0180] 3 BMC-84 CTF [0,0.0180] 3

3.75


4.50 BMC-89 C-PTF [0,0.0050] 6 BMC-90 C-PTF [0,0.0050] 6

7.50 BMC-91 C-PTF [0,0.0150] 6 BMC-92 C-PTF [0,0.0150] 6

15.0


20.0 BMC-97 C-PTF [0,0.0100] 6 BMC-98 C-PTF [0,0.0100] 6

30.0


60.0

BMC-103 CTF [0,0.0250] 20

BMC-104 CTF [0,0.0250] 24

BMC-105 CTF [0,0.0350] 10

BMC-106 CTF [0,0.0350] 11

3.4 SEM analysis

In order to study the effect of stress triaxiality on microscopic fracture mechanism, the fracture surfaces of cyclic specimens with different notch radii were observed by using SEM. The SEM observation results of specimens are illustrated in Fig 4. As can been in Figure 4, a typical ductile fracture mechanism (void nucleation, growth and coalescence) was observed. At high stress triaxiality, the dimple is large and shallow; at moderate stress triaxiality, the dimple is small and deep. This is may be because that


void dilation is dominant at higher stress triaxiality, and the void growth gradually transitions elongation with stress triaxiality decreasing (Danas et al. 2012, Kiran et al. 2014).


Figure 4. SEM observation of specimens: (a) BMC-1 (b) BMC-14 (c) BMC-23 (d) BMC-31 (e) BMC-43 (f) BMC-47 (g) BMC-99 and (h) BMC-65. 4. CALIBRATION OF CVGM MODEL

To calibrate the CVGM model parameters, the FEA was carried out to obtain

stress-strain data at the location of fracture initiation. Due to the axisymmetry of the specimen geometry and loading pattern, a half axisymmetric two-dimensional model with reduced integration element CAX8R was built using ABAQUS 6.14. Figure 5 presents the finite element model of the circular notched specimen (R=3.75), and the element size in the notched area is about 0.20mm, which is equal to the characteristic length value of Q345qC steel (Liao 2018). Because of the significant changes of stress triaxiality during tests, the average stress triaxiality is introduced as shown in Eq. (3):

1

( )dp p

f

T T

(3)

where εf denotes the equivalent plastic strain at the instant of fracture initiation, and T(εp) represents the loading history of stress triaxiality.

Figure 5. Axisymmetric finite element model of circular notched specimen(R =3.75mm).

In the tensile loading simulation of circular notched specimens, the true stress-

plastic strain relation of Q345qC steel was employed (Li et al. 2019). Figure 6 presents the comparison of simulated force-displacement curves with experimental curves of

specimens, and a good agreement is obtained. The average stress triaxialityT of all

Element size in notch *area 0.20l mm


tensile specimens is calculated according to Eq. (3) and shown in Table 4. It can be seen that the larger stress triaxiality, the smaller fracture toughness of Q345qC steel.

Based on the fracture displacementf and stress-strain data at the center of net

section, η was calibrated, as shown in Table 4. It can be inferred that the value of η is independent of the magnitude of stress triaxiality.

Figure 6. Comparison of force-displacement curves obtained by tests and FEA under tensile loading.

Table 4. Calibration results of monotonic void growth capacity

Notch size No. f /mm T η

1.80 BM-1 1.17 1.20 2.05

BM-2 1.21 1.22 2.10

3.75 BM-3 1.64 0.89 1.92

BM-4 1.80 0.92 2.10

7.50 BM-5 3.00 0.69 2.20

BM-6 3.18 0.68 2.38

15.0 BM-7 3.48 0.60 1.98

BM-8 3.59 0.60 2.09

30.0 BM-9 4.35 0.54 1.96

BM-10 4.35 0.54 1.97

60.0 BM-11 5.05 0.49 1.78

BM-12 5.32 0.50 1.98

Mean value 2.04

Cov/% 7.09

Similarly, in the FEA of circular notched specimens under cyclic loading, the

Lemaitre-Chaboche hybrid hardening model (Lemaitre 1990) was employed, including isotropic and kinematic hardening. The true stress-plastic strain curve of Q345qC steel

0 1 2 3 4 5 6 70

5

10

15

20

25

30

35

40

45

FEA(BM-7) FEA(BM-9) FEA(BM-11)

Test(BM-1)

FEA(BM-1)

Test(BM-3)

FEA(BM-3)

Test(BM-5)

FEA(BM-5)

Test(BM-7) Test(BM-9) Test(BM-11)

Displacement(mm)

Fo

rce(

kN

)


is used to simulate the kinematic behavior, and the isotropic hardening is described by Eq. (4).

0

0 1 exp pQ b (4)

where 0 is the size of initial yielding surface; Q is the maximum change value of

yielding surface; b is changing rate of yielding surface size with plastic strain

developing. Based on the best fit between the test and FEA curves, Q and b were

determined. The comparison of force-displacement curves of partial specimens from tests and FEA is presented in Figure 7, where test curves agree well with FEA curves. Additionally, the other specimens have similar results.

Figure 7. Comparison of force-displacement curves obtained by tests and FEA under cyclic loading.

The stress-strain data of specimens at the center of net section was extracted

based on FEA. The damage degradation parameter λCVGM was calibrated at different

average stress triaxialities T according to the exponential function in Eq. (2). The experimental data scatter plot and the fitted curves are shown in Figure 8. It can be observed that the damage degradation parameter λCVGM is not a material constant, which varies with the stress triaxiality.

0.0 0.3 0.6 0.9 1.2 1.5 1.8

-40

-30

-20

-10

0

10

20

30

40

Fo

rce(

kN

)

Displacement(mm)

Test

FEA

Fracture initiation

0.0 0.3 0.6 0.9 1.2 1.5 1.8

-40

-30

-20

-10

0

10

20

30

40

Displacement(mm)

Fo

rce(

kN

)

Test

FEA

Fracture initiation

0 1 2 3 4 5 6 7 8 90.0

0.2

0.4

0.6

0.8

1.0

1.2

Experimental data Fitted curve

accumulated

p

f

exp( 0.13. ) accumulated

pf

0 1 2 3 4 5 6 7 80.0

0.2

0.4

0.6

0.8

1.0

1.2


accumulated

p

f


pf


(a) 0.66T (b) 0.72T

(c) 0.66T (d) 0.72T

(e) 0.86T (f) 0.90T

(g) 1.00T (h) 1.07T



pf

0 1 2 3 4 5 6 7 8 90.0

0.2

0.4

0.6

0.8

1.0

1.2

f

accumulated

p0 1 2 3 4 5 6 7 8 9 10 11

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Experimental data

Fitted curve

accumulated

p

f


pf

0 1 2 3 4 5 6 7 8 9 100.0

0.2

0.4

0.6

0.8

1.0

1.2



pf

accumulated

p

f



pf

0 1 2 3 4 50.0

0.2

0.4

0.6

0.8

1.0

1.2

accumulated

p

f


accumulated

p

f


pf

0 1 2 3 4 50.0

0.2

0.4

0.6

0.8

1.0

1.2

0 1 2 3 4 50.0

0.2

0.4

0.6

0.8

1.0

1.2


pf

Experimental data

Fitted curve

accumulated

p

f


(i) 1.13T

Figure 8. Scatter plot and fitted curve of damage degradation parameter for Q345qC steel.

The damage degradation parameter λCVGM versus average stress triaxiality is

presented in Figure 9, and a quadratic function relationship is obtained ( 0.50 0.90T ).

When the stress triaxiality is higher ( 0.90T ), the damage degradation parameter

tends to a constant value, and it is consistent with the original CVGM model where the damage degradation parameter is regarded as a material constant at high stress triaxiality.

Figure 9. The damage degradation parameter versus average stress triaxiality. 5. EVALUATION OF THE ACCURACY OF CVGM MODEL

In order to evaluate the prediction accuracy of the above calibrated CVGM model,

thirty four circular notched specimens are tested, and its experimental results are

shown in Table 3. The experimental resultsexperimental

p and prediction resultsanalytical

p at the

instant of ULCF fracture initiation are compared, as listed in Table 5, and plotted against each other in Figure 10. The relative error γ is calculated. As shown in Table 5 and Figure 10, good agreement is obtained between the predicted results and

0 1 2 3 4 50.0

0.2

0.4

0.6

0.8

1.0

1.2

Experimental data

Fitted curve

accumulated

p

fexp( 0.12. ) accumulated

pf

0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

21.72 2.56 1.00T T

2 0.88R

CVGM

T


experimental results at different stress triaxiality. As presented in Table 5, the prediction errors of most specimens are within 25%, and for a small part of specimens, the errors are larger than 25%, which may be owing to the contingency of experimental results and some assumptions in the CVGM model. In general, the average value of prediction errors is 12.0%, and the result is encouraging. Therefore, the CVGM model considering the effect of stress triaxiality on damage degradation parameter can accurately predict ULCF at high and moderate stress triaxiality.

Figure 10. Comparisons of experimental and FEA results.

Table 5. Equivalent plastic strain predicted by CVGM model and tests.

Notch size/mm

Specimen experimental

p analytical

p γ T λCVGM

1.80

BMC-73 3.47 3.99 15.0% 1.41 0.11 BMC-74 3.71 3.99 7.5% 1.42 0.11 BMC-75 1.79 2.13 19.0% 1.36 0.11 BMC-76 2.35 2.13 9.4% 1.39 0.11 BMC-77 1.70 1.80 5.9% 1.34 0.11 BMC-78 1.50 1.87 24.7% 1.33 0.11 BMC-79 1.32 1.66 25.8% 1.31 0.11 BMC-80 1.67 1.66 0.6% 1.34 0.11 BMC-81 1.08 1.45 34.3% 1.29 0.11 BMC-82 1.10 1.45 31.8% 1.29 0.11 BMC-83 1.03 1.02 1.0% 1.26 0.11 BMC-84 1.01 1.02 1.0% 1.26 0.11

3.75

BMC-85 0.71 0.87 22.5% 0.88 0.07 BMC-86 0.72 0.87 20.8% 0.89 0.08 BMC-87 1.19 1.71 43.7% 0.97 0.11 BMC-88 1.61 1.71 6.2% 1.00 0.11

4.50 BMC-89 0.75 0.94 25.3% 0.83 0.05 BMC-90 0.80 0.94 17.5% 0.83 0.05

7.50 BMC-91 2.26 2.25 0.4% 0.78 0.04 BMC-92 2.30 2.25 2.2% 0.78 0.04

15.0 BMC-93 1.96 2.02 3.1% 0.60 0.08

analy

tica

l

p

experimental

p

Margin lines25%

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10


BMC-94 2.07 2.02 2.4% 0.61 0.07 BMC-95 3.81 3.96 3.9% 0.68 0.05 BMC-96 4.66 3.96 15.0% 0.69 0.05

20.0 BMC-97 1.46 1.50 2.7% 0.50 0.15 BMC-98 1.47 1.50 2.0% 0.50 0.15

30.0

BMC-99 1.35 1.41 4.4% 0.53 0.12 BMC-100 1.39 1.41 1.4% 0.53 0.12 BMC-101 3.25 4.06 24.9% 0.56 0.10 BMC-102 4.12 4.08 1.0% 0.57 0.10

60.0

BMC-103 7.16 7.66 7.0% 0.53 0.12 BMC-104 8.91 7.66 14.0% 0.54 0.12 BMC-105 4.42 5.04 14.0% 0.51 0.14 BMC-106 5.05 5.04 0.2% 0.51 0.14

Mean value 12.0%

Note: experimental

p indicates the equivalent plastic strain at the instant of experimentally

observed ULCF, analytical

p denotes the equivalent plastic strain at the instant of predicted

ULCF fracture initiation. exp

exp

analytical erimental

p p

erimental

p

, represents relative error between

experimental and predicted results. 6. CONCLISIONS

In this paper, the experimental study and numerical simulation on ultra-low cycle

fatigue of Q345qC steel at different stress triaxiality were conducted. The CVGM model

parameters of Q345qC were calibrated, and the model prediction accuracy was

evaluated. Based on the above studies, the following conclusions can be drawn:

(1) The experimental results of circular notched specimens under tensile loading

show that the fracture toughness of Q345qC steel decreases with the stress

triaxiality increasing. The model parameter η for Q345qC steel was calibrated

at high and moderate stress triaxiality, which is independent on the magnitude

of the stress triaxiality. The calibration value η can be used to predict fracture

initiation under tensile loading.

(2) The SEM observation results show that ULCF fracture initiation of Q345qC

steel exhibits a typical mechanism of “void nucleation, growth and

coalescence”. The dimples are larger and shallower at high stress triaxiality

compared to that at moderate stress triaxiality. As the stress triaxiality

decreases, the void growth gradually transitions from dilation to elongation.

(3) The damage degradation parameters of CVGM model for Q345qC steel at

different stress triaxiality were obtained, and the quadratic function

relationship between damage degradation parameter and average stress


triaxiality was established. When the average stress triaxiality is relatively

larger, the damage degradation parameter value is constant, which is

consistent with the original CVGM model.

(4) It is shown that the equivalent plastic strain to ULCF fracture initiation

predicted by the calibrated CVGM model agrees well with the experimental

results. The improved CVGM model that considers the effect of stress

triaxiality on damage degradation parameter has a wider application range of

stress triaxiality compared to original models.

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