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Ultra-low cycle fatigue fracture of tensile weld detail of typical steel beam-to-column connections
Accepted Manuscript Ultra-low Cycle Fatigue Fracture of Tensile Weld Detail of Typical Steel Beamto-column Connections Yue Yin, Lei Peng, Yuhang Wu, Qinghua Han, Lu Liu PII: DOI: Reference:
S0167-8442(16)30051-9 http://dx.doi.org/10.1016/j.tafmec.2016.07.003 TAFMEC 1723
To appear in:
Theoretical and Applied Fracture Mechanics
Received Date: Revised Date: Accepted Date:
4 March 2016 11 June 2016 11 July 2016
Please cite this article as: Y. Yin, L. Peng, Y. Wu, Q. Han, L. Liu, Ultra-low Cycle Fatigue Fracture of Tensile Weld Detail of Typical Steel Beam-to-column Connections, Theoretical and Applied Fracture Mechanics (2016), doi: http://dx.doi.org/10.1016/j.tafmec.2016.07.003
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Ultra-low Cycle Fatigue Fracture of Tensile Weld Detail of Typical Steel Beam-to-column Connections Yue Yin1,2, Lei Peng1, Yuhang Wu3, Qinghua Han1,2*, Lu Liu1 (1. Department of Civil Engineering, Tianjin University, Tianjin 300072, China; 2. Key Laboratory of Coast Civil Structure Safety (Tianjin University), Ministry of Education, Tianjin 300072, China 3. China Southwest Architectural Design and Research Institute Corp., Ltd, Chengdu 610041, China)
Abstract: Two micromechanical approaches, cyclic void growth model (CVGM) and improved cyclic void growth model (ICVGM), were employed for the prediction of ultra-low cycle fatigue (ULCF) fracture of the tensile weld detail of typical steel beam-to-column connections. Both symmetric and asymmetric fatigue loads were considered. The predicted fracture location and ULCF lifetime were compared with corresponding test results to verify the applicability of these two micromechanical criteria for ULCF analysis of steel connections. ULCF fracture under symmetric load predicted by both CVGM and ICVGM agreed very well with test results. For asymmetric load, ICVGM gave more accurate ULCF fracture prediction than CVGM. ULCF fracture caused by the artificial crack at the interface between the backing bar and the column flange was also studied with ICVGM. It was illustrated that the tip of the artificial crack is also a potential source of ULCF fracture and the ULCF fracture can be prevented by closing the artificial crack with a continuous fillet welds.
Keywords: Ultra-low cycle fatigue; fracture; micromechanical approaches; steel beam-to-column connections
*
Corresponding author. Tel.: +86-22-13821378765; Fax: +86-22-27404465; Email: [email protected]
Address: Department of Civil Engineering, Tianjin University, Tianjin, 300072, China
1. Introduction Site investigations after 1994 Northridge earthquake in American and 1995 Hyogoken Nanbu Earthquake in Japan showed that, the stress concentration region of welded beam-to-column connections would undergo large plastic strain ranges and fracture by very few load reversals, even less than dozens of cycles [1-2]. Different from conventional fatigue problems, this kind of fatigue fracture is much more like ductile fracture due to monotonic loading, the failure mechanism of which is the growth and coalescence of microvoids. This kind of fatigue failure is termed as ultra-low cycle fatigue (ULCF) fracture. For conventional high cycle or even low cycle fatigue problems, fatigue crack occurs under nominal linear elastic state. Miner’s cumulative damage rule [3] and Manson-Coffin’s relationship [4] can be adopted for fatigue life prediction. However, because ULCF fracture is caused by ductile crack initiation with large local plastic strains, Miner's rule and Manson-coffin's relationship may not be applicable any more
[5]
. New approach
is then needed to simulate the growth and coalescence of microvoids for ULCF fracture prediction. Ductile fracture under monotonic loading has been studied by Rice and Tracey [6] with void growth model (VGM) based on the assumption that ductile fracture occurs when the void ratio attains a critical size under plastic strains. Research works
[7-8]
on ULCF fracture of steel connections suggested that the underlying
mechanism of ULCF fracture is the growth and coalescence of microvoids, similar to the ductile fracture under monotonic loading. Kanvinde and Deierlein [9-10] extended the application of VGM and presented cyclic void growth model (CVGM) for ULCF fracture prediction and validated the accuracy of CVGM through tests and finite element analysis of 14 blunt notch compact fracture specimens and 4 dogbone specimens. Myers et al. [11] improved CVGM by redefining the damage measure D equal to the plastic strain accumulated only during previous compressive cycles, which was termed as ICVGM in this paper. Liao et al.
[12-13]
calibrated material
parameter in CVGM for Q345 steel [14] and successfully predicted the ULCF fracture of welded beam-to-column
connection and beam-to-column connection with welded flanges and bolted web by CVGM. Though the prediction of ULCF fracture with the above mentioned micromechanical approaches, CVGM and ICVGM, agreed with test results on some steel connections, it is still desirable to verify these approaches with more experimental outcomes and evaluate their accuracy and consistency for more types of details in steel connections. In this paper, micromechanical approaches, CVGM and ICVGM, were employed for ULCF fracture prediction of the tensile weld detail of typical beam-to-column connections. The predicted fracture location and ULCF lifetime were compared with corresponding test results
[15]
to verify the applicability of these two
micromechanical criteria for ULCF analysis of steel connections. ULCF fracture caused by the artificial crack at the interface between the backing bar and the column flange was also studied with ICVGM for typical beam-to-column connections.
2. Micromechanical approaches for ULCF failure Prediction 2.1 Cyclic Void Growth Model (CVGM) In CVGM, microvoids grow and coalesce during loading excursions. Fracture occurs when the void ratio attains a critical size. CVGM is extended from VGM, in which Rice and Tracey [6] define the void growth rate as
dR C exp 1.5T d R
d p
2 / 3 d ijp d ijp
p
(1) (2)
where R is average void radius; T is stress triaxiality and T m / e ( m is hydrostatic stress, which equals the average of the three principle stresses and plastic strain; C is a constant.
e is von Mises stress); d p is incremental equivalent
The fracture criterion of VGM can be expressed as a void growth index VGI monotonic reaching its critical critical value VGI monotonic , as shown in Eq. 3.
p
critical VGI monotonic = exp 1.5T d p VGI monotonic
(3)
0
critical where VGI monotonic is a material property and is dependent on the initial void radius R0 , critical value of
average void radius for fracture under monotonic loading Rcritical , constant C and is independent on stress and critical strain states. VGI monotonic can be calibrated by material tests.
In CVGM, cyclic loading and void shrinkage during negative triaxialities are considered. The void growth index for cyclic loading is expressed as VGI cyclic
p final
tensile cycles ( i .e.,T 0)
p initial
exp 1.5T d p
p final
compressive cycles ( i .e.,T 0)
p initial
exp 1.5T d
p
(4)
Ductile fracture occurs when the following inequality is satisfied. critical VGI cyclic VGI cyclic
(5)
critical The critical value of the cyclic void growth index VGI cyclic is defined as a reduction from its monotonic
critical counterpart VGI monotonic ,
critical critical VGI cyclic f D VGI monotonic
where function f D
(6)
reflects the material damage D accumulated during prior inelastic loading cycles.
Kanvinde and Deierlein [9] proposed the following functional form of f D ,
f D exp D D= paccumulated
(7) (8)
where is material parameter that defines the rate at which VGI cyclic degrades with respect to D , paccumulated equals to the equivalent plastic strain at the start of the most recent tensile excursion. The cyclic damage parameter can be determined using cyclic tests of the notched round bar specimens. critical VGI cyclic is back-calculated for each experiment by substituting the triaxialities and plastic strains (obtained by
nonlinear FEM) leading up to the measured failure point into Eqs. (4) and (5). The cyclic damage parameter can then be determined by fitting the exponential function of Eq. (6) to a scatter plot of the measured values of critical critical VGI cyclic / VGI monotonic and paccumulated
[10]
.
Note that a characteristic length l of the material must be defined for CVGM. Only when Inequality (5) is satisfied over the material characteristic length l , the predicted ductile fracture occurs. The characteristic
length l represents the minimum volume of material necessary for void coalescence based on inclusion
spacing and other aspects of the material microstructure. The most commonly used approach for determination of l is derived from the dimple diameter on the fracture surface. The dimple diameter is representative of the
intervoid spacing and can be measured from scanning electron micrographs of the fracture surface of the material
. In Ref. [12], the value of the characteristic length l was determined as the average size of the
[16]
plateaus and valleys based on 10 measurements from the scanning electron micrograph of the fracture surface of Q345 steel.
2.2 Improved Cyclic Void Growth Mode (ICVGM) Ductile fracture can be predicted accurately with CVGM for materials subjecting symmetric ULCF loading. However, there is obvious conflict in CVGM when asymmetric loading consisting of a large inelastic tensile cycle followed by a negligibly small inelastic compressive cycle is considered. On one hand, material damage D is defined as the accumulated equivalent plastic strain equaling to the sum of prior tensile portion and compressive portion. Due to the large amount of equivalent plastic strain from the tensile portion, the value of critical VGI cyclic reduces significantly during every cycle. On the other hand, with only negligibly small inelastic
compressive excursion in every load cycle, the loading excursion is similar with a monotonic loading and the critical value of VGI cyclic would reduce slightly. To solve this conflict, Myers, et al. [12] improved CVGM by redefining
the damage measure D accumulated only during the previous compressive cycles, as shown in Eq. 9.
D cp
p
(9)
compressive cycles ( i .e.,T 0)
3. ULCF fracture prediction for tensile weld details of typical beam-to-column connections 3.1 Brief introduction of tests conducted in reference [15] A total number of 20 specimens for the tensile weld detail of typical beam-to-column connections (as shown in Fig.1) were tested under monotonic tensile or cyclic load by Shi, et al. [15] of Tsinghua University, among which specimens SP-5B and SP-4B were tested under symmetric and asymmetric cyclic loads respectively. In this section, micromechanical approaches, CVGM and ICVGM, were employed for the ULCF fracture prediction of specimens SP-5B and SP-4B. The prediction was compared with corresponding test results to verify the applicability and accuracy of the micromechanical approaches. Specimens SP-5B and SP-4B are both made from Q345 steel. The configuration of the specimens is as shown in Fig. 2. Full penetration groove welds were adopted to connect the beam flange and beam web to the column flange. The welding details are as shown in Fig. 3. A quarter-circle-shaped access hole (R=30mm) was machined for the passing through of the beam flange welds. A backing bar was adopted for specimen SP-5B to improve the quality of the beam flange welds, which is common in practice. Specimen SP-5B was tested under symmetric cyclic axial load, which is determined in accordance with Specification of seismic test methods for Buildings JGJ101-1996 [17]. The loading procedure consisted of two phases, as shown in Fig. 4(a). The test was first conducted under load control with load increment of 200kN for every load levels until the first yield occurred. Then, the specimen was loaded cyclically under displacement control till the fracture of the specimen. The displacement increment was set to be 2Δy, where Δy is the axial displacement at the first yield. For each load level, the load cycled twice.
Specimen SP-4B was tested under asymmetric cyclic axial load, as shown in Fig. 4(b). At the tension side, the loading procedure was just the same as that for specimen SP-5B. While at the compression side, the test was conducted under load control and the maximum compression force was set to be -50kN for all load cycles after the first yield. And again, for each load level, the load cycled twice. Related test results are as shown in Table 1. Both specimens SP-5B and SP-4B fractured under ULCF load at the HAZ of the bottom end of the welds between beam web and column flange (location F in Fig. 2), just above the access hole. The experimental number of cycles to fracture was listed as 16 for specimens SP-5B and 31 for specimens SP-4B in Ref. [15] and can be counted from hysteretic curves obtained by tests. 3.2 Setup of finite element analysis model Finite element model was setup for the local region of specimens SP-5B and SP-4B with general finite element software ABAQUS
[18]
. In consideration of the symmetry of their configuration, only one-half of each
specimen needs to be modeled. Deposit metal of the welds connecting beam web and beam flange with column flange was included in the model, as well as the backing bar for specimen SP-5B, as shown in Fig. 5. 8-node solid element C3D8R implemented in ABAQUS was adopted for the model discretization. For all materials, the elastic modules is set to be E= 2.06 10 5MPa and the Poisson ratio =0.3. Tri-linear model was adopted for the stress-strain relationship and related material properties of the base metal and the deposit metal are as shown in Table 2. The plasticity behavior was modeled by Mises yield criterion and combined hardening criterion was adopted to simulate the plastic circulation flow of all materials. All the nodes on the right end surface of the finite element model were completely fixed. Nodes on the left end surface were coupled to reference point RP-1 at the centroid. All the degrees of freedom of RP-1 were restrained except the translation along the longitudinal direction. Cyclic loading as shown in Fig. 4(a) and (b) were applied on RP-1 along longitudinal direction for specimens SP-5B and SP-4B respectively.
Primary analysis showed that the maximum equivalent plastic strain occurs at location F, as shown in Fig. 5, which locates at the HAZ of the bottom end of the welds between beam web and column flange. This location was consistent with the fracture position of the test specimens. Ultra fine mesh was then adopted at this location to capture the ductile fracture caused by ULCF. The size of the mesh was smaller than 0.3mm, the average value of the characteristic length l of Q345 steel [12]. Hysteretic curves obtained by finite element analysis for specimens SP-5B and SP-4B, as shown in Fig. 6, agreed very well with the test results, which validated the rationality and reliability of the finite element models. The ULCF fracture of the two specimens can then be predicted based on the finite element models. 3.3 ULCF fracture prediction Micromechanical approaches, CVGM and ICVGM, were employed for ULCF fracture prediction of the tensile weld detail of typical beam-to-column connections in this section. Micromechanical fracture parameters in CVGM were calibrated in reference [12] for Q345 steel in HAZ and the deposited metal, as shown in Table 3. (1)ULCF fracture prediction by CVGM Equivalent plastic strain distribution for specimens SP-5B and SP-4B under the peak tension load is shown in Fig. 7. VGI cyclic values were calculated for elements around the stress concentration and it was found that the element with maximum equivalent plastic strain also has the highest VGI cyclic value. According to CVGM, ULCF facture will initiate at the location of this element, which locates at the HAZ of the bottom end of the welds between beam web and column flange, marked again as location F in Fig. 7. The fluctuation of VGI cyclic under cyclic tension and compression loadings was calculated for the critical element at location F by Eq. (4). The values of
critical VGI cyclic at the start of every tensile excursion were calculated
for the critical element at location F by Eq. (5), with the material accumulated damage D being calculated by Eq. (7).
ULCF fracture prediction for specimen SP-5B by CVGM is as shown in Fig. 8(a). The ULCF fracture occurs at the 15th load cycle. ULCF fracture prediction for specimen SP-4B by CVGM is as shown in Fig. 8(b). The ULCF fracture occurs at the 26th load cycle. (2) ULCF fracture prediction by ICVGM In ICVGM, the ULCF fracture was also predicted according to the value of VGI cyclic , which was calculated the same way as that in CVGM. Therefore, the initial facture was predicted to occur at the same location as that in CVGM, which was shown as location F in Fig. 7. The value of VGI cyclic under each tension and compression cycle was calculated by Eq. (4), and the value of
critical VGI cyclic at the start of the most recent tensile excursion was calculated by Eq. (5), with the material
accumulated damage D being calculated by Eq. (9). ULCF fracture predictions for specimens SP-5B and SP-4B by ICVGM are as shown in Fig.9. The ULCF fracture occurs at the 16th load cycle for specimen SP-5B and 33th load cycle for specimen SP-4B. ULCF lifetime predicted by the two micromechanical approaches was compared with corresponding test results in Table 4. ULCF fracture of specimen SP-5B predicted by both CVGM and ICVGM agreed very well with the test results. While, for specimen SP-4B, the prediction by CVGM is too conservative and ICVGM gave more accurate ULCF fracture prediction than CVGM, which proved better applicability of ICVGM for ULCF under asymmetric cyclic load.
4. Prediction of ULCF fracture caused by artificial crack 4.1 Artificial crack at the interface between the backing bar and the column flange In the construction of typical beam-to-column connections, backing bar is a common practice to improve the quality of the groove welds between the beam flange and the column flange. If the backing bar is not to be
removed after welding, the vertical unfused interface between the backing bar and the column flange, as shown in Fig. 10, acts as an open crack, which is known as artificial crack. Under earthquake actions, this artificial crack may extend along the interface between the deposited metal and the column flange and lead to ULCF fracture eventually [19]. ULCF fracture caused by the artificial crack is a typical failure mode observed in 1994 Northridge earthquake. In this section, specimen SP-5B and specimen SP-4B with a hypothetical backing bar were taken as case studies, and the ULCF fracture caused by the artificial crack was studied by ICVGM approach. 4.2 Finite element model with artificial crack detail Finite element models were setup for the local region of specimens SP-5B and SP-4B with artificial crack detail as shown in Fig. 10. The finite element models are almost the same as those in section 3.2, but with artificial crack configurated at the unfused interface between the backing bar and the column flange. Hard surface-to-surface contact was defined between the two surfaces of the artificial crack. Ultra fine mesh was discretized at the tip of the artificial crack to capture the ULCF fracture. The size of the mesh is smaller than the average value of the characteristic length l
of Q345 steel. The width and thickness of the backing bar are
20mm and 5mm respectively. Symmetric and asymmetric cyclic loads as shown in Fig. 4(a) and (b) were applied on specimens SP-5B and SP-4B respectively. 4.3 Prediction of ULCF fracture at the tip of the artificial crack by ICVGM Equivalent plastic strain distribution for specimens SP-5B and SP-4B under the peak tension load is shown in Fig. 11. VGI cyclic values were calculated for elements around the tip of the artificial crack and it was found that the element with maximum equivalent plastic strain also has the highest VGI cyclic value. The element locates just above the tip of the artificial crack in the root of the groove welds, shown as location FC in Fig. 11. According to ICVGM, ULCF facture will initiate at this location.
The fluctuation of VGI cyclic under cyclic tension and compression loadings was calculated for the critical element at location FC by Eq. (4). The values of
critical at the start of every tensile excursion were VGI cyclic
calculated for the critical element at location FC by Eq. (5), with the material accumulated damage D being calculated by Eq. (9). ULCF fracture prediction for specimens SP-5B and SP-4B by ICVGM is as shown in Fig. 12. The ULCF fracture occurs at the 21th and 35th load cycle respectively. Though ULCF lifetimes of specimens SP-5B and SP-4B at location Fc are all a little longer than those at the most dangerous location F, the tip of the artificial crack is still a potential source of ULCF fracture, to which close attention need to be paid in the construction of the connection. It should be noted that finer mesh with element size of l*/2 at the artificial crack tip was adopted for comparison analysis. It was found that there is little effect of the element size on the ULCF fracture prediction. The resulted number of cycles to fracture based on the finer mesh is only one cycle earlier than that based on the coarser mesh for specimen SP-5B. 4.4 Measures to eliminate ULCF fracture caused by the artificial crack Popov et al.
[18]
proposed two measures to eliminate the ULCF fracture caused by the artificial crack. A
direct method is to remove the backing bar using a carbon arc, and then apply fillet welds along the root of the groove welds between the beam flange and the column flange, which is expensive and may damage the main groove welds. The other measure is to place continuous fillet welds along the edge of the backing bar to close the artificial crack. With the fillet welds, the opening tendency of the artificial crack under tension load can be stopped. The efficiency of placing continuous fillet welds to close the artificial crack can be evaluated by comparing the values of VGI cyclic of the element at location FC before and after placing the fillet welds, as shown in Fig.
13. An obvious decrease of VGI cyclic can be observed with the existing of the fillet welds. During the cyclic loading, the VGI cyclic values are always less than the critical value,
critical , which means no ULCF fracture VGI cyclic
will occur in the artificial crack region any more. So, placing a continuous fillet welds along the backing bar is an efficient way to reduce the fracture possibility caused by the artificial crack, and the ductile of the beam-to-column connection can be improved.
5. Conclusion Two micromechanical approaches, cyclic void growth model (CVGM) and improved cyclic void growth model (ICVGM), were employed for the prediction of ultra-low cycle fatigue (ULCF) fracture of the tensile weld detail of typical steel beam-to-column connections. Following conclusions were obtained. (1) ULCF fracture location predicted by CVGM and ICVGM agreed well with corresponding test results. Further analysis showed that there are two potential sources of ULCF fracture in typical steel beam-to-column connections, one at the bottom end of the welds between beam web and column flange, and the other at the tip of the artificial crack between the backing bar and the column flange. (2) ULCF lifetime under symmetric load predicted by both CVGM and ICVGM agreed very well with test results. For asymmetric load, the prediction by CVGM is too conservative and ICVGM gave more accurate ULCF life prediction. (3) Placing a continuous fillet welds along the backing bar is an efficient way to reduce the fracture possibility caused by the artificial crack, and by doing so the ductile of the beam-to-column connection can be improved.
Acknowledgements The authors of this paper would like to express their appreciation for the financial support given by the National Natural Science Foundation of China (No. 51178307).
References: [1] Skiles JL, Campbell III HH. Why steel fractured in the Northridge Earthquake. Welding Journal, 1994, 73(11), 67- 71. [2] Kuwamura, H. Fracture of steel welded joints under severe earthquake motion. Proceedings of the 11th World Conference on Earthquake Engineering, Paper No. 466, 1996. [3] Miner MA. Cumulative damage in fatigue. Journal of Applied Mechanics, 1945, 12:159-164. [4] Manson SS. Fatigue: A complex subject-Some simple approximations. Journal of Experiment Mechanics, 1965, 5(7):193-226. [5] Tateishi K, Hanji T, Minami K. A prediction model for extremely low cycle fatigue strength of structural steel. International Journal of Fatigue, 2007, 29:887-896. [6] Rice JR, Tracey DM. On the ductile enlargement of voids in triaxial stress fields. Journal of the Mechanics and Physics of Solids, 1969, 17(3): 201-217. [7] Kuwamura H and Yamamoto K. Ductile crack as a trigger of brittle fracture in steel. Journal of Structural Engineering, ASCE, 1997, 123(6): 729-735. [8] Kuwamura H. Transition between fatigue and ductile fracture in steel. Journal of Structural Engineering, ASCE, 1997, 123(7): 864-870. [9] Kanvinde AM, Deierlein GG. Cyclic void growth model to assess ductile fracture initiation in structural steels due to ultra-low cycle fatigue. Journal of Engineering Mechanics, ASCE, 2007, 133(6):701-712. [10] Kanvinde AM, Deierlein GG. Validation of cyclic void growth model for fracture initiation in blunt notch and dogbone steel specimens. Journal of Structural Engineering, ASCE, 2008, 134(9):1528-1537. [11] Myers AT, Kanvinde AM, Deierlein GG, Baker JW. Probabilistic formulation of the cyclic void growth
model to predict ultra-low cycle fatigue in structural steel. Journal of Engineering Mechanics, ASCE, 2014, 140(6):1528-1537. [12] Liao FF. Study on micromechanical fracture criteria of structural steels and it applications to ductile fracture prediction of connections. Tongji University, Shanghai, 2012 (in Chinese). [13] Liao FF, Wang W, Chen YY. Extremely low cycle fatigue fracture prediction of steel connections under cyclic loading. Journal of Tongji University (Natural Science), 2014, 42(4):539-546, 617 (in Chinese). [14] GB50017-2014 Code for design of steel structure. China Planning Press, Beijing, 2014 (in Chinese). [15] Shi YJ, Xiong J, Wang YQ. Study on damage behavior of weld of beam-to-column connection in steel frame I: experiment. Journal of Building Structures, 2012, 33(3):48-55 (in Chinese). [16] Kanvinde AM, Deierlein GG. The void growth model and the stress modified critical strain model to predict ductile fracture in structural steels. Journal of Structural Engineering, ASCE, 2006, 132(12), 1907–1918. [17] JGJ 101-1996 Specification of test methods for earthquake resistant building. China Architecture & Building Press, Beijing, 1996 (in Chinese). [18] ABAQUS. Theory Manual Version 6.10. H.K.S, 2012. [19] Popov EP, Yang TS, Chang SP. Desgn of MRF connections before and after 1994 Northridge earthquake. Engineering Structures, 1998, 20:1030-1038.
Fig. 1 Location of tensile weld detail in typical beam-to-column connections
Fig. 2 Configuration of the test specimen for the tensile weld detail
(a) Weld between beam web and column flange
(b) Weld between beam flange and column flange
2000
4
Displacement Controll
1000
2
fy
0
3000
6 Load Controll
2000 1000
0
4
Diaplacement Controll
2
fy
-1000
-2
-1000
0 9 10 11 12 Nmax=-50kN -2
-2000
-4
-2000
-4
-6
-3000
0
1
2
3
4
5
6
7
8
9
0
10 11 12
-3000
0
1
2
3
4
5
6
7
8
Displacement/Δy
6 Load Controll
Load/kN
3000
Displacement/Δy
Load/kN
Fig. 3 Welding details of the specimen
-6
Loading Cycles
Loading Cycles
(a) Symmetric loading for specimen SP-5B
(b) Asymmetric loading for specimen SP-4B
Fig. 4 Cyclic loading procedures for tests on the tensile weld detail
Fig. 5 FE model for specimen SP-5B
1000 750 500 250 0 -250 -500 -750 -1000
1000
Load/kN
Load/kN
750 500 250 0 -250 -500
-3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3
Displacement/mm
(a) For specimen SP-5B
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
Displacement/mm
(b) For specien SP-4B
Fig. 6 Load-displacement curves by finite element analysis
(a) For specimen SP-5B
(b) For specimen SP-4B Fig. 7 Equivalent plastic strain distribution at location F under the peak tension load
(a) For specimen SP-5B
(b) For specimen SP-4B Fig. 8 ULCF fracture prediction by CVGM
(a) For specimen SP-5B
(b) For specimen SP-4B Fig. 9 ULCF fracture prediction by ICVGM
Fig. 10 FE model with artificial crack detail
(a) For specimen SP-5B
(b) For specimen SP-4B with a hypothetical backing bar Fig. 11 Equivalent plastic strain distribution at location Fc under the peak tension load
(a) For specimen SP-5B
(b) For specimen SP-4B with a hypothetical backing bar Fig. 12 Prediction of ULCF fracture caused by artificial crack by ICVGM
(a) For specimen SP-5B
(b) For specimen SP-4B with a hypothetical backing bar Fig. 13 Comparison of
VGI cyclic
values at Fc before and after placing the fillet welds
Table 1 Test results for specimens SP-5B and SP-4B Number of
Specimen No.
Fracture position
total cycles
SP-5B
16
the HAZ of the bottom end of the weld between
SP-4B
31
beam web and column flange
Table 2 Material properties for specimens SP-5B and SP-4B Yield
Ultimate
Yield strain
Ultimate
strength/MPa
strength/MPa
εy
strain εu
12
369.9
638.0
0.02
0. 2
Q345
10
438.0
638.0
0.02
0. 2
E5015
—
391.4
615.8
0.02
0. 2
Material
t/mm
Q345
Table 3 Material parameters of Q345 steel for CVGM
l /mm Material
critical VGI monotonic
Lower
Average
Upper limit
limit value
value
value
HAZ
2.53
0.33
0.072
0.329
0.671
Deposited metal
2.63
0.31
0.062
0.202
0.311
Table 4 Comparison of the predicted UCLF lifetime with corresponding test results Specimen No.
CVGM
ICVGM
Test results
SP-5B
15
16
16
SP-4B
26
33
31
Highlights: (1) ULCF fracture location was predicted by CVGM and ICVGM. the prediction agreed well with corresponding test results. (2) ULCF lifetime for symmetric loading predicted by both CVGM and ICVGM greed very well with corresponding test results. For asymmetric load, the prediction by CVGM is too conservative and ICVGM gave more accurate ULCF life prediction. (3) Artificial crack at the interface between the backing bar and the column flange is also a potential location of ULCF fracture. Placing a continuous fillet welds along the backing bar is an efficient way to reduce the fracture possibility.
S0167-8442(16)30051-9 http://dx.doi.org/10.1016/j.tafmec.2016.07.003 TAFMEC 1723
To appear in:
Theoretical and Applied Fracture Mechanics
Received Date: Revised Date: Accepted Date:
4 March 2016 11 June 2016 11 July 2016
Please cite this article as: Y. Yin, L. Peng, Y. Wu, Q. Han, L. Liu, Ultra-low Cycle Fatigue Fracture of Tensile Weld Detail of Typical Steel Beam-to-column Connections, Theoretical and Applied Fracture Mechanics (2016), doi: http://dx.doi.org/10.1016/j.tafmec.2016.07.003
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Ultra-low Cycle Fatigue Fracture of Tensile Weld Detail of Typical Steel Beam-to-column Connections Yue Yin1,2, Lei Peng1, Yuhang Wu3, Qinghua Han1,2*, Lu Liu1 (1. Department of Civil Engineering, Tianjin University, Tianjin 300072, China; 2. Key Laboratory of Coast Civil Structure Safety (Tianjin University), Ministry of Education, Tianjin 300072, China 3. China Southwest Architectural Design and Research Institute Corp., Ltd, Chengdu 610041, China)
Abstract: Two micromechanical approaches, cyclic void growth model (CVGM) and improved cyclic void growth model (ICVGM), were employed for the prediction of ultra-low cycle fatigue (ULCF) fracture of the tensile weld detail of typical steel beam-to-column connections. Both symmetric and asymmetric fatigue loads were considered. The predicted fracture location and ULCF lifetime were compared with corresponding test results to verify the applicability of these two micromechanical criteria for ULCF analysis of steel connections. ULCF fracture under symmetric load predicted by both CVGM and ICVGM agreed very well with test results. For asymmetric load, ICVGM gave more accurate ULCF fracture prediction than CVGM. ULCF fracture caused by the artificial crack at the interface between the backing bar and the column flange was also studied with ICVGM. It was illustrated that the tip of the artificial crack is also a potential source of ULCF fracture and the ULCF fracture can be prevented by closing the artificial crack with a continuous fillet welds.
Keywords: Ultra-low cycle fatigue; fracture; micromechanical approaches; steel beam-to-column connections
*
Corresponding author. Tel.: +86-22-13821378765; Fax: +86-22-27404465; Email: [email protected]
Address: Department of Civil Engineering, Tianjin University, Tianjin, 300072, China
1. Introduction Site investigations after 1994 Northridge earthquake in American and 1995 Hyogoken Nanbu Earthquake in Japan showed that, the stress concentration region of welded beam-to-column connections would undergo large plastic strain ranges and fracture by very few load reversals, even less than dozens of cycles [1-2]. Different from conventional fatigue problems, this kind of fatigue fracture is much more like ductile fracture due to monotonic loading, the failure mechanism of which is the growth and coalescence of microvoids. This kind of fatigue failure is termed as ultra-low cycle fatigue (ULCF) fracture. For conventional high cycle or even low cycle fatigue problems, fatigue crack occurs under nominal linear elastic state. Miner’s cumulative damage rule [3] and Manson-Coffin’s relationship [4] can be adopted for fatigue life prediction. However, because ULCF fracture is caused by ductile crack initiation with large local plastic strains, Miner's rule and Manson-coffin's relationship may not be applicable any more
[5]
. New approach
is then needed to simulate the growth and coalescence of microvoids for ULCF fracture prediction. Ductile fracture under monotonic loading has been studied by Rice and Tracey [6] with void growth model (VGM) based on the assumption that ductile fracture occurs when the void ratio attains a critical size under plastic strains. Research works
[7-8]
on ULCF fracture of steel connections suggested that the underlying
mechanism of ULCF fracture is the growth and coalescence of microvoids, similar to the ductile fracture under monotonic loading. Kanvinde and Deierlein [9-10] extended the application of VGM and presented cyclic void growth model (CVGM) for ULCF fracture prediction and validated the accuracy of CVGM through tests and finite element analysis of 14 blunt notch compact fracture specimens and 4 dogbone specimens. Myers et al. [11] improved CVGM by redefining the damage measure D equal to the plastic strain accumulated only during previous compressive cycles, which was termed as ICVGM in this paper. Liao et al.
[12-13]
calibrated material
parameter in CVGM for Q345 steel [14] and successfully predicted the ULCF fracture of welded beam-to-column
connection and beam-to-column connection with welded flanges and bolted web by CVGM. Though the prediction of ULCF fracture with the above mentioned micromechanical approaches, CVGM and ICVGM, agreed with test results on some steel connections, it is still desirable to verify these approaches with more experimental outcomes and evaluate their accuracy and consistency for more types of details in steel connections. In this paper, micromechanical approaches, CVGM and ICVGM, were employed for ULCF fracture prediction of the tensile weld detail of typical beam-to-column connections. The predicted fracture location and ULCF lifetime were compared with corresponding test results
[15]
to verify the applicability of these two
micromechanical criteria for ULCF analysis of steel connections. ULCF fracture caused by the artificial crack at the interface between the backing bar and the column flange was also studied with ICVGM for typical beam-to-column connections.
2. Micromechanical approaches for ULCF failure Prediction 2.1 Cyclic Void Growth Model (CVGM) In CVGM, microvoids grow and coalesce during loading excursions. Fracture occurs when the void ratio attains a critical size. CVGM is extended from VGM, in which Rice and Tracey [6] define the void growth rate as
dR C exp 1.5T d R
d p
2 / 3 d ijp d ijp
p
(1) (2)
where R is average void radius; T is stress triaxiality and T m / e ( m is hydrostatic stress, which equals the average of the three principle stresses and plastic strain; C is a constant.
e is von Mises stress); d p is incremental equivalent
The fracture criterion of VGM can be expressed as a void growth index VGI monotonic reaching its critical critical value VGI monotonic , as shown in Eq. 3.
p
critical VGI monotonic = exp 1.5T d p VGI monotonic
(3)
0
critical where VGI monotonic is a material property and is dependent on the initial void radius R0 , critical value of
average void radius for fracture under monotonic loading Rcritical , constant C and is independent on stress and critical strain states. VGI monotonic can be calibrated by material tests.
In CVGM, cyclic loading and void shrinkage during negative triaxialities are considered. The void growth index for cyclic loading is expressed as VGI cyclic
p final
tensile cycles ( i .e.,T 0)
p initial
exp 1.5T d p
p final
compressive cycles ( i .e.,T 0)
p initial
exp 1.5T d
p
(4)
Ductile fracture occurs when the following inequality is satisfied. critical VGI cyclic VGI cyclic
(5)
critical The critical value of the cyclic void growth index VGI cyclic is defined as a reduction from its monotonic
critical counterpart VGI monotonic ,
critical critical VGI cyclic f D VGI monotonic
where function f D
(6)
reflects the material damage D accumulated during prior inelastic loading cycles.
Kanvinde and Deierlein [9] proposed the following functional form of f D ,
f D exp D D= paccumulated
(7) (8)
where is material parameter that defines the rate at which VGI cyclic degrades with respect to D , paccumulated equals to the equivalent plastic strain at the start of the most recent tensile excursion. The cyclic damage parameter can be determined using cyclic tests of the notched round bar specimens. critical VGI cyclic is back-calculated for each experiment by substituting the triaxialities and plastic strains (obtained by
nonlinear FEM) leading up to the measured failure point into Eqs. (4) and (5). The cyclic damage parameter can then be determined by fitting the exponential function of Eq. (6) to a scatter plot of the measured values of critical critical VGI cyclic / VGI monotonic and paccumulated
[10]
.
Note that a characteristic length l of the material must be defined for CVGM. Only when Inequality (5) is satisfied over the material characteristic length l , the predicted ductile fracture occurs. The characteristic
length l represents the minimum volume of material necessary for void coalescence based on inclusion
spacing and other aspects of the material microstructure. The most commonly used approach for determination of l is derived from the dimple diameter on the fracture surface. The dimple diameter is representative of the
intervoid spacing and can be measured from scanning electron micrographs of the fracture surface of the material
. In Ref. [12], the value of the characteristic length l was determined as the average size of the
[16]
plateaus and valleys based on 10 measurements from the scanning electron micrograph of the fracture surface of Q345 steel.
2.2 Improved Cyclic Void Growth Mode (ICVGM) Ductile fracture can be predicted accurately with CVGM for materials subjecting symmetric ULCF loading. However, there is obvious conflict in CVGM when asymmetric loading consisting of a large inelastic tensile cycle followed by a negligibly small inelastic compressive cycle is considered. On one hand, material damage D is defined as the accumulated equivalent plastic strain equaling to the sum of prior tensile portion and compressive portion. Due to the large amount of equivalent plastic strain from the tensile portion, the value of critical VGI cyclic reduces significantly during every cycle. On the other hand, with only negligibly small inelastic
compressive excursion in every load cycle, the loading excursion is similar with a monotonic loading and the critical value of VGI cyclic would reduce slightly. To solve this conflict, Myers, et al. [12] improved CVGM by redefining
the damage measure D accumulated only during the previous compressive cycles, as shown in Eq. 9.
D cp
p
(9)
compressive cycles ( i .e.,T 0)
3. ULCF fracture prediction for tensile weld details of typical beam-to-column connections 3.1 Brief introduction of tests conducted in reference [15] A total number of 20 specimens for the tensile weld detail of typical beam-to-column connections (as shown in Fig.1) were tested under monotonic tensile or cyclic load by Shi, et al. [15] of Tsinghua University, among which specimens SP-5B and SP-4B were tested under symmetric and asymmetric cyclic loads respectively. In this section, micromechanical approaches, CVGM and ICVGM, were employed for the ULCF fracture prediction of specimens SP-5B and SP-4B. The prediction was compared with corresponding test results to verify the applicability and accuracy of the micromechanical approaches. Specimens SP-5B and SP-4B are both made from Q345 steel. The configuration of the specimens is as shown in Fig. 2. Full penetration groove welds were adopted to connect the beam flange and beam web to the column flange. The welding details are as shown in Fig. 3. A quarter-circle-shaped access hole (R=30mm) was machined for the passing through of the beam flange welds. A backing bar was adopted for specimen SP-5B to improve the quality of the beam flange welds, which is common in practice. Specimen SP-5B was tested under symmetric cyclic axial load, which is determined in accordance with Specification of seismic test methods for Buildings JGJ101-1996 [17]. The loading procedure consisted of two phases, as shown in Fig. 4(a). The test was first conducted under load control with load increment of 200kN for every load levels until the first yield occurred. Then, the specimen was loaded cyclically under displacement control till the fracture of the specimen. The displacement increment was set to be 2Δy, where Δy is the axial displacement at the first yield. For each load level, the load cycled twice.
Specimen SP-4B was tested under asymmetric cyclic axial load, as shown in Fig. 4(b). At the tension side, the loading procedure was just the same as that for specimen SP-5B. While at the compression side, the test was conducted under load control and the maximum compression force was set to be -50kN for all load cycles after the first yield. And again, for each load level, the load cycled twice. Related test results are as shown in Table 1. Both specimens SP-5B and SP-4B fractured under ULCF load at the HAZ of the bottom end of the welds between beam web and column flange (location F in Fig. 2), just above the access hole. The experimental number of cycles to fracture was listed as 16 for specimens SP-5B and 31 for specimens SP-4B in Ref. [15] and can be counted from hysteretic curves obtained by tests. 3.2 Setup of finite element analysis model Finite element model was setup for the local region of specimens SP-5B and SP-4B with general finite element software ABAQUS
[18]
. In consideration of the symmetry of their configuration, only one-half of each
specimen needs to be modeled. Deposit metal of the welds connecting beam web and beam flange with column flange was included in the model, as well as the backing bar for specimen SP-5B, as shown in Fig. 5. 8-node solid element C3D8R implemented in ABAQUS was adopted for the model discretization. For all materials, the elastic modules is set to be E= 2.06 10 5MPa and the Poisson ratio =0.3. Tri-linear model was adopted for the stress-strain relationship and related material properties of the base metal and the deposit metal are as shown in Table 2. The plasticity behavior was modeled by Mises yield criterion and combined hardening criterion was adopted to simulate the plastic circulation flow of all materials. All the nodes on the right end surface of the finite element model were completely fixed. Nodes on the left end surface were coupled to reference point RP-1 at the centroid. All the degrees of freedom of RP-1 were restrained except the translation along the longitudinal direction. Cyclic loading as shown in Fig. 4(a) and (b) were applied on RP-1 along longitudinal direction for specimens SP-5B and SP-4B respectively.
Primary analysis showed that the maximum equivalent plastic strain occurs at location F, as shown in Fig. 5, which locates at the HAZ of the bottom end of the welds between beam web and column flange. This location was consistent with the fracture position of the test specimens. Ultra fine mesh was then adopted at this location to capture the ductile fracture caused by ULCF. The size of the mesh was smaller than 0.3mm, the average value of the characteristic length l of Q345 steel [12]. Hysteretic curves obtained by finite element analysis for specimens SP-5B and SP-4B, as shown in Fig. 6, agreed very well with the test results, which validated the rationality and reliability of the finite element models. The ULCF fracture of the two specimens can then be predicted based on the finite element models. 3.3 ULCF fracture prediction Micromechanical approaches, CVGM and ICVGM, were employed for ULCF fracture prediction of the tensile weld detail of typical beam-to-column connections in this section. Micromechanical fracture parameters in CVGM were calibrated in reference [12] for Q345 steel in HAZ and the deposited metal, as shown in Table 3. (1)ULCF fracture prediction by CVGM Equivalent plastic strain distribution for specimens SP-5B and SP-4B under the peak tension load is shown in Fig. 7. VGI cyclic values were calculated for elements around the stress concentration and it was found that the element with maximum equivalent plastic strain also has the highest VGI cyclic value. According to CVGM, ULCF facture will initiate at the location of this element, which locates at the HAZ of the bottom end of the welds between beam web and column flange, marked again as location F in Fig. 7. The fluctuation of VGI cyclic under cyclic tension and compression loadings was calculated for the critical element at location F by Eq. (4). The values of
critical VGI cyclic at the start of every tensile excursion were calculated
for the critical element at location F by Eq. (5), with the material accumulated damage D being calculated by Eq. (7).
ULCF fracture prediction for specimen SP-5B by CVGM is as shown in Fig. 8(a). The ULCF fracture occurs at the 15th load cycle. ULCF fracture prediction for specimen SP-4B by CVGM is as shown in Fig. 8(b). The ULCF fracture occurs at the 26th load cycle. (2) ULCF fracture prediction by ICVGM In ICVGM, the ULCF fracture was also predicted according to the value of VGI cyclic , which was calculated the same way as that in CVGM. Therefore, the initial facture was predicted to occur at the same location as that in CVGM, which was shown as location F in Fig. 7. The value of VGI cyclic under each tension and compression cycle was calculated by Eq. (4), and the value of
critical VGI cyclic at the start of the most recent tensile excursion was calculated by Eq. (5), with the material
accumulated damage D being calculated by Eq. (9). ULCF fracture predictions for specimens SP-5B and SP-4B by ICVGM are as shown in Fig.9. The ULCF fracture occurs at the 16th load cycle for specimen SP-5B and 33th load cycle for specimen SP-4B. ULCF lifetime predicted by the two micromechanical approaches was compared with corresponding test results in Table 4. ULCF fracture of specimen SP-5B predicted by both CVGM and ICVGM agreed very well with the test results. While, for specimen SP-4B, the prediction by CVGM is too conservative and ICVGM gave more accurate ULCF fracture prediction than CVGM, which proved better applicability of ICVGM for ULCF under asymmetric cyclic load.
4. Prediction of ULCF fracture caused by artificial crack 4.1 Artificial crack at the interface between the backing bar and the column flange In the construction of typical beam-to-column connections, backing bar is a common practice to improve the quality of the groove welds between the beam flange and the column flange. If the backing bar is not to be
removed after welding, the vertical unfused interface between the backing bar and the column flange, as shown in Fig. 10, acts as an open crack, which is known as artificial crack. Under earthquake actions, this artificial crack may extend along the interface between the deposited metal and the column flange and lead to ULCF fracture eventually [19]. ULCF fracture caused by the artificial crack is a typical failure mode observed in 1994 Northridge earthquake. In this section, specimen SP-5B and specimen SP-4B with a hypothetical backing bar were taken as case studies, and the ULCF fracture caused by the artificial crack was studied by ICVGM approach. 4.2 Finite element model with artificial crack detail Finite element models were setup for the local region of specimens SP-5B and SP-4B with artificial crack detail as shown in Fig. 10. The finite element models are almost the same as those in section 3.2, but with artificial crack configurated at the unfused interface between the backing bar and the column flange. Hard surface-to-surface contact was defined between the two surfaces of the artificial crack. Ultra fine mesh was discretized at the tip of the artificial crack to capture the ULCF fracture. The size of the mesh is smaller than the average value of the characteristic length l
of Q345 steel. The width and thickness of the backing bar are
20mm and 5mm respectively. Symmetric and asymmetric cyclic loads as shown in Fig. 4(a) and (b) were applied on specimens SP-5B and SP-4B respectively. 4.3 Prediction of ULCF fracture at the tip of the artificial crack by ICVGM Equivalent plastic strain distribution for specimens SP-5B and SP-4B under the peak tension load is shown in Fig. 11. VGI cyclic values were calculated for elements around the tip of the artificial crack and it was found that the element with maximum equivalent plastic strain also has the highest VGI cyclic value. The element locates just above the tip of the artificial crack in the root of the groove welds, shown as location FC in Fig. 11. According to ICVGM, ULCF facture will initiate at this location.
The fluctuation of VGI cyclic under cyclic tension and compression loadings was calculated for the critical element at location FC by Eq. (4). The values of
critical at the start of every tensile excursion were VGI cyclic
calculated for the critical element at location FC by Eq. (5), with the material accumulated damage D being calculated by Eq. (9). ULCF fracture prediction for specimens SP-5B and SP-4B by ICVGM is as shown in Fig. 12. The ULCF fracture occurs at the 21th and 35th load cycle respectively. Though ULCF lifetimes of specimens SP-5B and SP-4B at location Fc are all a little longer than those at the most dangerous location F, the tip of the artificial crack is still a potential source of ULCF fracture, to which close attention need to be paid in the construction of the connection. It should be noted that finer mesh with element size of l*/2 at the artificial crack tip was adopted for comparison analysis. It was found that there is little effect of the element size on the ULCF fracture prediction. The resulted number of cycles to fracture based on the finer mesh is only one cycle earlier than that based on the coarser mesh for specimen SP-5B. 4.4 Measures to eliminate ULCF fracture caused by the artificial crack Popov et al.
[18]
proposed two measures to eliminate the ULCF fracture caused by the artificial crack. A
direct method is to remove the backing bar using a carbon arc, and then apply fillet welds along the root of the groove welds between the beam flange and the column flange, which is expensive and may damage the main groove welds. The other measure is to place continuous fillet welds along the edge of the backing bar to close the artificial crack. With the fillet welds, the opening tendency of the artificial crack under tension load can be stopped. The efficiency of placing continuous fillet welds to close the artificial crack can be evaluated by comparing the values of VGI cyclic of the element at location FC before and after placing the fillet welds, as shown in Fig.
13. An obvious decrease of VGI cyclic can be observed with the existing of the fillet welds. During the cyclic loading, the VGI cyclic values are always less than the critical value,
critical , which means no ULCF fracture VGI cyclic
will occur in the artificial crack region any more. So, placing a continuous fillet welds along the backing bar is an efficient way to reduce the fracture possibility caused by the artificial crack, and the ductile of the beam-to-column connection can be improved.
5. Conclusion Two micromechanical approaches, cyclic void growth model (CVGM) and improved cyclic void growth model (ICVGM), were employed for the prediction of ultra-low cycle fatigue (ULCF) fracture of the tensile weld detail of typical steel beam-to-column connections. Following conclusions were obtained. (1) ULCF fracture location predicted by CVGM and ICVGM agreed well with corresponding test results. Further analysis showed that there are two potential sources of ULCF fracture in typical steel beam-to-column connections, one at the bottom end of the welds between beam web and column flange, and the other at the tip of the artificial crack between the backing bar and the column flange. (2) ULCF lifetime under symmetric load predicted by both CVGM and ICVGM agreed very well with test results. For asymmetric load, the prediction by CVGM is too conservative and ICVGM gave more accurate ULCF life prediction. (3) Placing a continuous fillet welds along the backing bar is an efficient way to reduce the fracture possibility caused by the artificial crack, and by doing so the ductile of the beam-to-column connection can be improved.
Acknowledgements The authors of this paper would like to express their appreciation for the financial support given by the National Natural Science Foundation of China (No. 51178307).
References: [1] Skiles JL, Campbell III HH. Why steel fractured in the Northridge Earthquake. Welding Journal, 1994, 73(11), 67- 71. [2] Kuwamura, H. Fracture of steel welded joints under severe earthquake motion. Proceedings of the 11th World Conference on Earthquake Engineering, Paper No. 466, 1996. [3] Miner MA. Cumulative damage in fatigue. Journal of Applied Mechanics, 1945, 12:159-164. [4] Manson SS. Fatigue: A complex subject-Some simple approximations. Journal of Experiment Mechanics, 1965, 5(7):193-226. [5] Tateishi K, Hanji T, Minami K. A prediction model for extremely low cycle fatigue strength of structural steel. International Journal of Fatigue, 2007, 29:887-896. [6] Rice JR, Tracey DM. On the ductile enlargement of voids in triaxial stress fields. Journal of the Mechanics and Physics of Solids, 1969, 17(3): 201-217. [7] Kuwamura H and Yamamoto K. Ductile crack as a trigger of brittle fracture in steel. Journal of Structural Engineering, ASCE, 1997, 123(6): 729-735. [8] Kuwamura H. Transition between fatigue and ductile fracture in steel. Journal of Structural Engineering, ASCE, 1997, 123(7): 864-870. [9] Kanvinde AM, Deierlein GG. Cyclic void growth model to assess ductile fracture initiation in structural steels due to ultra-low cycle fatigue. Journal of Engineering Mechanics, ASCE, 2007, 133(6):701-712. [10] Kanvinde AM, Deierlein GG. Validation of cyclic void growth model for fracture initiation in blunt notch and dogbone steel specimens. Journal of Structural Engineering, ASCE, 2008, 134(9):1528-1537. [11] Myers AT, Kanvinde AM, Deierlein GG, Baker JW. Probabilistic formulation of the cyclic void growth
model to predict ultra-low cycle fatigue in structural steel. Journal of Engineering Mechanics, ASCE, 2014, 140(6):1528-1537. [12] Liao FF. Study on micromechanical fracture criteria of structural steels and it applications to ductile fracture prediction of connections. Tongji University, Shanghai, 2012 (in Chinese). [13] Liao FF, Wang W, Chen YY. Extremely low cycle fatigue fracture prediction of steel connections under cyclic loading. Journal of Tongji University (Natural Science), 2014, 42(4):539-546, 617 (in Chinese). [14] GB50017-2014 Code for design of steel structure. China Planning Press, Beijing, 2014 (in Chinese). [15] Shi YJ, Xiong J, Wang YQ. Study on damage behavior of weld of beam-to-column connection in steel frame I: experiment. Journal of Building Structures, 2012, 33(3):48-55 (in Chinese). [16] Kanvinde AM, Deierlein GG. The void growth model and the stress modified critical strain model to predict ductile fracture in structural steels. Journal of Structural Engineering, ASCE, 2006, 132(12), 1907–1918. [17] JGJ 101-1996 Specification of test methods for earthquake resistant building. China Architecture & Building Press, Beijing, 1996 (in Chinese). [18] ABAQUS. Theory Manual Version 6.10. H.K.S, 2012. [19] Popov EP, Yang TS, Chang SP. Desgn of MRF connections before and after 1994 Northridge earthquake. Engineering Structures, 1998, 20:1030-1038.
Fig. 1 Location of tensile weld detail in typical beam-to-column connections
Fig. 2 Configuration of the test specimen for the tensile weld detail
(a) Weld between beam web and column flange
(b) Weld between beam flange and column flange
2000
4
Displacement Controll
1000
2
fy
0
3000
6 Load Controll
2000 1000
0
4
Diaplacement Controll
2
fy
-1000
-2
-1000
0 9 10 11 12 Nmax=-50kN -2
-2000
-4
-2000
-4
-6
-3000
0
1
2
3
4
5
6
7
8
9
0
10 11 12
-3000
0
1
2
3
4
5
6
7
8
Displacement/Δy
6 Load Controll
Load/kN
3000
Displacement/Δy
Load/kN
Fig. 3 Welding details of the specimen
-6
Loading Cycles
Loading Cycles
(a) Symmetric loading for specimen SP-5B
(b) Asymmetric loading for specimen SP-4B
Fig. 4 Cyclic loading procedures for tests on the tensile weld detail
Fig. 5 FE model for specimen SP-5B
1000 750 500 250 0 -250 -500 -750 -1000
1000
Load/kN
Load/kN
750 500 250 0 -250 -500
-3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3
Displacement/mm
(a) For specimen SP-5B
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
Displacement/mm
(b) For specien SP-4B
Fig. 6 Load-displacement curves by finite element analysis
(a) For specimen SP-5B
(b) For specimen SP-4B Fig. 7 Equivalent plastic strain distribution at location F under the peak tension load
(a) For specimen SP-5B
(b) For specimen SP-4B Fig. 8 ULCF fracture prediction by CVGM
(a) For specimen SP-5B
(b) For specimen SP-4B Fig. 9 ULCF fracture prediction by ICVGM
Fig. 10 FE model with artificial crack detail
(a) For specimen SP-5B
(b) For specimen SP-4B with a hypothetical backing bar Fig. 11 Equivalent plastic strain distribution at location Fc under the peak tension load
(a) For specimen SP-5B
(b) For specimen SP-4B with a hypothetical backing bar Fig. 12 Prediction of ULCF fracture caused by artificial crack by ICVGM
(a) For specimen SP-5B
(b) For specimen SP-4B with a hypothetical backing bar Fig. 13 Comparison of
VGI cyclic
values at Fc before and after placing the fillet welds
Table 1 Test results for specimens SP-5B and SP-4B Number of
Specimen No.
Fracture position
total cycles
SP-5B
16
the HAZ of the bottom end of the weld between
SP-4B
31
beam web and column flange
Table 2 Material properties for specimens SP-5B and SP-4B Yield
Ultimate
Yield strain
Ultimate
strength/MPa
strength/MPa
εy
strain εu
12
369.9
638.0
0.02
0. 2
Q345
10
438.0
638.0
0.02
0. 2
E5015
—
391.4
615.8
0.02
0. 2
Material
t/mm
Q345
Table 3 Material parameters of Q345 steel for CVGM
l /mm Material
critical VGI monotonic
Lower
Average
Upper limit
limit value
value
value
HAZ
2.53
0.33
0.072
0.329
0.671
Deposited metal
2.63
0.31
0.062
0.202
0.311
Table 4 Comparison of the predicted UCLF lifetime with corresponding test results Specimen No.
CVGM
ICVGM
Test results
SP-5B
15
16
16
SP-4B
26
33
31
Highlights: (1) ULCF fracture location was predicted by CVGM and ICVGM. the prediction agreed well with corresponding test results. (2) ULCF lifetime for symmetric loading predicted by both CVGM and ICVGM greed very well with corresponding test results. For asymmetric load, the prediction by CVGM is too conservative and ICVGM gave more accurate ULCF life prediction. (3) Artificial crack at the interface between the backing bar and the column flange is also a potential location of ULCF fracture. Placing a continuous fillet welds along the backing bar is an efficient way to reduce the fracture possibility.