The fatigue stress amplitude of the welded cross plate-hollow sphere joint (WCPHSJ) in a grid structure varies due to the random loading produced by suspending cranes. A total of 14 specimens considering three different types of WCPHSJs were prepared and tested using a specially designed test rig. Four typical loading conditions, “low-high,” “high-low,” “low-high-low,” and “high-low-high,” were first considered in the tests to investigate the fatigue behavior under variable load amplitudes, followed by metallographic analyses. The experimental and metallographic analysis results provide a fundamental understanding on the fatigue fracture form and fatigue mechanism of WCPHSJs. Based on the available data from constant-amplitude fatigue tests, the variable-amplitude fatigue life of the three types of WCPHSJs was estimated using the Miner rule and Corten-Dolan theory. Since both accumulative damage theories yield virtually same damaging results, the Miner rule is hence suggested to estimate the fatigue life of WCPHSJs.
The grid structure (Figure
A coal cleaning plant in Shanxi, China.
Welded hollow spherical joint.
Previous studies focused on the static behavior and ultimate bearing capacity of WHSJs under axial loading and/or in-plane bending. Han et al. [
The research on the constant-amplitude fatigue performance of the WHSJs in a grid structure is relatively limited, mostly carried out in China. Lei [
Appendix 3 of ANSI/AISC 360-16 [
The fatigue accumulative damage theory is mainly used to estimate the fatigue life of a member or connection, in which the Miner rule is most common. The probability-based Miner rule was proposed to study the fatigue damage of concrete specimens and riveted joints [
Variable-amplitude fatigue study on WHSJs is even more limited. Consequently, current steel design specifications do not have a specific fatigue provision for WHSJs in a grid structure and only suggest that experimental verification should be performed. It is therefore essential to study further the fatigue of such joints in a gird structure. In this paper, both experimental and theoretical analyses on variable-amplitude fatigue behavior of WCPHSJs in a grid structure under random repeated loads are described and discussed along with a more reasonable estimation method for fatigue life.
The repeated loads caused by the suspended cranes at the WCPHSJs in a grid structure are random and complex. As such, a load spectrum should be used in the fatigue test of suspended joints. However, acceptable standard fatigue load spectrum has not become available due to limited studies. In this study, a simplified fatigue load spectrum reflecting the random loads was adopted to perform the fatigue tests of WCPHSJs.
The conducted tests include three types of details designed to represent the actual fatigue details of a grid structure with suspended cranes. They are labeled as KQ-4, KQ-5, and KQ-7, as shown in Figure
Fatigue details of the specimens. (a) KQ-4, (b) KQ-5, and (c) KQ-7.
Geometrical characteristics of the specimens (unit: mm).
Specimen label | Tested number |
|
|
|
Connection type |
---|---|---|---|---|---|
KQ-4 | 5 |
|
|
|
Butt weld |
KQ-5 | 7 |
|
|
|
Butt weld |
KQ-7 | 2 |
|
|
|
Fillet weld |
The circular tube, welded hollow sphere, cross plate, and cover plate were fabricated from Q235B steel. The sphere meets the requirement of JG/T 11-2009 [
The test rig (Figures
Central loading condition.
Unilateral loading condition.
Based on the test rig, the variable-amplitude fatigue tests of WCPHSJs were completed through a reasonably arranged loading sequence applicable to constant-amplitude fatigue tests. Four typical loading conditions including “low-high,” “high-low,” “high-low-high,” and “low-high-low” were considered in the tests to investigate the fatigue behavior under variable load amplitudes. Two particular loading conditions were also considered, as described in the following.
The Swiss made AMSLER fatigue test machine was used to simulate the constant- and variable-amplitude fatigue loads on specimens during the test. The heaviest load applied to the specimen was generated by the 1000 kN hydraulic pressure servo fatigue machine at the frequency of 6.67 Hz. The loading cycle followed a controlled smooth sine wave.
The variable-amplitude fatigue test was performed on WCPHSJ specimens. A reasonable definition of fatigue failure is necessary in order to analyze the fatigue test results. In this study, the observed through sphere wall fatigue crack is taken as the failure criterion to record the fatigue cycle number for the specimen [
Based on the test rig and predetermined load program, 3 types for a total of 14 specimens were tested under different variable-amplitude loads. The test results are summarized in Table
The variable-amplitude fatigue test data of WCPHSJ under program block.
Specimen label |
|
|
|
|
|
Stress histogram of variable-amplitude fatigue |
---|---|---|---|---|---|---|
KQ-4-1 | 26.38 | 3.09 | 23.29 | 12.97 | 0.117 |
|
28.37 | 3.29 | 25.08 | 44.35 | 0.116 | ||
29.36 | 3.39 | 25.97 | 19.24 | 0.115 | ||
KQ-4-3 | 32.35 | 3.68 | 28.67 | 19.05 | 0.114 |
|
28.37 | 3.29 | 25.08 | 107.37 | 0.116 | ||
26.38 | 3.09 | 23.29 | 124.87 | 0.117 | ||
25.38 | 2.99 | 22.39 | 27.89 | 0.118 | ||
KQ-4-5 | 24.38 | 2.89 | 21.49 | 161.48 | 0.118 |
|
32.35 | 3.68 | 28.67 | 12.11 | 0.114 | ||
KQ-4-7 | 23.39 | 2.79 | 20.60 | 49.60 | 0.119 |
|
24.38 | 2.89 | 21.49 | 50.30 | 0.118 | ||
25.38 | 2.99 | 22.39 | 10.68 | 0.118 | ||
KQ-4-8 | 25.38 | 2.99 | 22.39 | 25.03 | 0.118 |
|
26.38 | 3.09 | 23.29 | 53.07 | 0.117 | ||
28.37 | 3.29 | 25.08 | 44.35 | 0.116 | ||
29.36 | 3.39 | 25.97 | 21.56 | 0.115 | ||
34.83 | 3.93 | 30.90 | 14.04 | 0.113 | ||
KQ-5-4 | 35.33 | 3.53 | 31.80 | 40.0 | 0.1 |
|
37.02 | 3.70 | 33.32 | 18.41 | 0.1 | ||
KQ-5-6 | 36.17 | 3.62 | 32.55 | 40.0 | 0.1 |
|
37.86 | 3.79 | 34.07 | 40.0 | 0.1 | ||
39.54 | 3.95 | 35.59 | 40.0 | 0.1 | ||
41.22 | 4.12 | 37.10 | 40.0 | 0.1 | ||
42.90 | 4.29 | 38.61 | 13.03 | 0.1 | ||
KQ-5-10 | 33.65 | 3.37 | 30.28 | 40.0 | 0.1 |
|
35.33 | 3.53 | 31.80 | 25.05 | 0.1 | ||
KQ-5-12 | 42.22 | 4.22 | 38.00 | 40.0 | 0.1 |
|
44.44 | 4.44 | 40.00 | 40.0 | 0.1 | ||
46.67 | 4.67 | 42.00 | 24.75 | 0.1 | ||
KQ-5-15 | 31.97 | 3.20 | 28.77 | 40.00 | 0.1 |
|
33.65 | 3.37 | 30.28 | 40.00 | 0.1 | ||
35.33 | 3.53 | 31.80 | 40.00 | 0.1 | ||
38.70 | 3.87 | 34.83 | 8.24 | 0.1 | ||
KQ-5-19 | 25.38 | 2.54 | 22.84 | 40.0 | 0.1 |
|
26.38 | 2.64 | 23.74 | 40.0 | 0.1 | ||
28.37 | 2.84 | 25.53 | 40.0 | 0.1 | ||
29.36 | 2.94 | 26.42 | 14.05 | 0.1 | ||
KQ-5-20 | 35.33 | 3.53 | 31.80 | 40.0 | 0.1 |
|
37.02 | 3.70 | 33.32 | 40.0 | 0.1 | ||
38.70 | 3.87 | 34.83 | 40.0 | 0.1 | ||
40.38 | 4.04 | 36.34 | 40.0 | 0.1 | ||
42.33 | 4.23 | 38.10 | 52.87 | 0.1 | ||
KQ-7-10 | 25.38 | 2.99 | 22.39 | 131.83 | 0.118 |
|
24.38 | 2.89 | 21.49 | 161.48 | 0.118 | ||
32.35 | 3.68 | 28.67 | 178.96 | 0.114 | ||
KQ-7-12 | 23.39 | 2.79 | 20.60 | 49.6 | 0.119 |
|
24.38 | 2.89 | 21.49 | 50.3 | 0.118 | ||
25.38 | 2.99 | 22.39 | 40.6 | 0.118 | ||
26.38 | 3.09 | 23.29 | 39.94 | 0.117 |
According to the analysis of broken specimens, all 3 different specimen types appear to display a similar fatigue failure mode; namely, the fatigue crack initiated on the edge of the weld toe at the joint between the cross plate and the sphere and then propagating circumferentially around the sphere to a diameter equal to the cross plate width. The typical failure mode of the specimens is shown in Figure
Failure mode of specimen KQ-4-1.
Metallographic analysis is an important tool for detecting the fracture form of a material or member and provides the relevant fatigue fracture details. It can also provide the important information of crack initiation, crack propagation, and final fracture. Scanning electron microscope (TESCAN Mira3 LMH) was used to observe the precise fatigue fracture form and features. Through the constant-amplitude fatigue tests on specimens KQ-4 and KQ-5, macroscopic and microscopic metallographic analyses were made to determine the fatigue fracture mechanism of WCPHSJs.
Typical fatigue fracture surfaces for specimens KQ-4-5/7 and KQ-5-4 are described as follows. Figures
Macrofracture surface of KQ-4-5(I).
Macrofracture surface of KQ-4-5(II).
The two initial crack sources in KQ-4-5 fatigue fracture surfaces were magnified by about 40 times (Figures
Microfracture surface of KQ-4-5(I) magnified by 40 times.
Microfracture surface of KQ-4-5(II) magnified by 41 times.
Microfracture surface of KQ-4-5(I) magnified by 500 times.
Microfracture surface of KQ-4-5(II) magnified by 500 times.
Figure
Macrofracture surface of KQ-4-7.
Microfracture surface of KQ-4-7 magnified by 60 times.
Microfracture surface of KQ-4-7 magnified by 2000 times.
The initial crack sources in KQ-5-4 fatigue fracture surfaces were magnified by 20 times (Figures
Macrofracture surface of KQ-5-4.
Microfracture surface of KQ-5-4 magnified by 20 times.
Microfracture surface of KQ-5-4 magnified by 200 times.
Microfracture surface of KQ-5-4 magnified by 500 times.
Table
A total of 19 valid constant-amplitude fatigue test data covering 5 types (KQ-4, KQ-5, KQ-6, KQ-7, and KQ-8, as shown in Table
Geometrical characteristics of the constant-amplitude fatigue specimens (unit: mm).
Specimen label | Tested number |
|
|
|
Connection type |
---|---|---|---|---|---|
KQ-4 | 3 |
|
|
|
Butt weld |
KQ-5 | 6 |
|
|
|
Butt weld |
KQ-6 | 2 |
|
|
|
Butt weld |
KQ-7 | 7 |
|
|
|
Fillet weld |
KQ-8 | 1 |
|
|
|
Fillet weld |
Constant amplitude S-N data: lg(
The test results of welded cross plate-hollow sphere joints under constant amplitude load.
Specimen label |
|
|
|
|
|
|
|
---|---|---|---|---|---|---|---|
KQ-4-2 | 35.31 | 3.97 | 31.34 | 1.50 | 100.47 | 6.00 | 0.113 |
KQ-4-4 | 25.38 | 2.99 | 22.39 | 1.35 | 104.03 | 6.02 | 0.118 |
KQ-4-6 | 23.39 | 2.79 | 20.60 | 1.31 | 200 | 6.30 | 0.119 |
KQ-5-1 | 26.92 | 3.03 | 23.89 | 1.38 | 90.27 | 5.96 | 0.113 |
KQ-5-2 | 48.96 | 14.69 | 34.27 | 1.53 | 65.41 | 5.82 | 0.300 |
KQ-5-3 | 43.52 | 13.05 | 30.47 | 1.48 | 62.71 | 5.80 | 0.300 |
KQ-5-8 | 46.54 | 4.65 | 41.88 | 1.62 | 46.11 | 5.66 | 0.100 |
KQ-5-13 | 95.6 | 47.8 | 47.8 | 1.68 | 15.72 | 5.20 | 0.500 |
KQ-5-18 | 49.08 | 4.91 | 44.17 | 1.65 | 23.70 | 5.37 | 0.100 |
KQ-6-14 | 57.7 | 28.8 | 28.8 | 1.46 | 106.37 | 6.03 | 0.500 |
KQ-6-17 | 65.3 | 32.7 | 32.7 | 1.51 | 72.8 | 5.86 | 0.500 |
KQ-7-1 | 32.35 | 3.68 | 28.66 | 1.46 | 87.27 | 5.94 | 0.114 |
KQ-7-2 | 23.39 | 2.79 | 20.60 | 1.31 | 196.44 | 6.29 | 0.119 |
KQ-7-4 | 31.35 | 3.58 | 27.77 | 1.44 | 131.60 | 6.12 | 0.114 |
KQ-7-6 | 30.36 | 3.49 | 26.87 | 1.43 | 47.59 | 5.68 | 0.115 |
KQ-7-11 | 28.37 | 3.29 | 25.08 | 1.40 | 30.10 | 5.48 | 0.116 |
KQ-7-13 | 28.37 | 3.29 | 25.08 | 1.40 | 77.27 | 5.89 | 0.116 |
KQ-7-14 | 26.38 | 3.09 | 23.29 | 1.37 | 94.54 | 5.98 | 0.117 |
KQ-8-1 | 54.40 | 16.33 | 38.08 | 1.58 | 30.94 | 5.49 | 0.300 |
Referring to Table
The calculated result form based on the two theories.
Specimen label | Total fatigue damage, |
|
---|---|---|
Miner’s rule | Corten-Dolan theory | |
KQ-4-1 | 0.65 | 0.65 |
KQ-4-3 | 2.15 | 2.19 |
KQ-4-5 | 0.96 | 0.99 |
KQ-4-7 | 0.52 | 0.52 |
KQ-4-8 | 1.32 | 1.35 |
KQ-5-4 | 1.20 | 1.21 |
KQ-5-6 | 4.83 | 4.88 |
KQ-5-10 | 1.14 | 1.15 |
KQ-5-12 | 4.48 | 4.50 |
KQ-5-15 | 2.20 | 2.24 |
KQ-5-19 | 0.92 | 0.92 |
KQ-5-20 | 5.95 | 6.00 |
KQ-7-10 | 3.98 | 4.03 |
KQ-7-12 | 0.95 | 0.96 |
Miner’s rule states that fatigue failure occurs when
The exponent
Table
Table
During the variable-amplitude fatigue test, under the four different multistress random loading modes, the
Based on the variable-amplitude fatigue tests, metallographic analyses, and linear cumulative damage theory, the following key findings are offered: (1) The metallographic analysis shows that the unavoidable initial welding defects caused by the surface processing may lead to a fatigue failure at the joint. Fatigue failure generally occurs at the weld toe location where severe stress is concentrated. For welded cross plate-hollow sphere joints, fatigue cracks generally initiate at the weld toe and then propagate circumferentially around the sphere to a diameter equivalent to the width of the cross plate until fatigue fracture. (2) The analyses of the variable-amplitude fatigue tests indicate that the (3) The four adopted loading conditions can efficiently simulate the variable-amplitude fatigue tests, but the difference between the actual and test loading conditions appears to be distinct. Hence, it is suggested that a more representative fatigue loading spectrum be developed in the future.
The authors declare that they have no conflicts of interest.
The authors are grateful to the financial supports provided by the Natural Science Foundation of China (NSFC) through Grant no. 51578357, the Natural Science Foundation of Shanxi Province of China through Grant no. 2015011062, and Talent Training Program in the postgraduate joint training base of Shanxi Province of China through Grant no. 2016JD11.