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Frontiers of Structural and Civil Engineering

Front. Struct. Civ. Eng.    2014, Vol. 8 Issue (2) : 178-186     https://doi.org/10.1007/s11709-014-0245-y
RESEARCH ARTICLE |
Cyclic stress-strain behavior of structural steel with yield-strength up to 460 N/mm2
Yiyi CHEN1,Wei SUN2,Tak-Ming CHAN3,*()
1. State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China
2. Architecture Design & Research Institute of Tongji University (Group) Co. Ltd., Shanghai 200092, China
3. School of Engineering, University of Warwick, Coventry CV4 7AL, UK
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Abstract

This paper presents a constitutive model based on Ramberg-Osgood equation to describe the hysteresis material behavior of structural carbon steel with nominal yield strength between 235 to 420 N/mm2. The proposed model was calibrated against a series of cyclic material tests with strain amplitude varying from 0.5% to 2.0%. A simple relationship between the modular parameter K and the yield strength fy was proposed. The calibrated Ramberg-Osgood model revealed excellent agreement with the experimental results and captured further the experimental behavior of test specimens with nominal yield strength of 460 N/mm2. The proposed constitutive model was also adopted in conjunction with the combined kinematic/isotropic materials description in ABAQUS to mimic a full scale experimental test under cyclic loading. The numerical results revealed close agreement with the experimental observations.

Keywords constitutive model      finite element analysis      hysteresis curve      Ramberg-Osgood equation     
Corresponding Authors: Tak-Ming CHAN   
Issue Date: 19 May 2014
 Cite this article:   
Yiyi CHEN,Wei SUN,Tak-Ming CHAN. Cyclic stress-strain behavior of structural steel with yield-strength up to 460 N/mm2[J]. Front. Struct. Civ. Eng., 2014, 8(2): 178-186.
 URL:  
http://journal.hep.com.cn/fsce/EN/10.1007/s11709-014-0245-y
http://journal.hep.com.cn/fsce/EN/Y2014/V8/I2/178
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Yiyi CHEN
Wei SUN
Tak-Ming CHAN
1Group2Grade3yield strength fy/MPa4ultimate strength fu/MPa5fy/fu6elongation δ%
1Q235C2804570.6124.8
2Q235B3084780.6424.7
3Q345B3505230.6724.8
4Q345B3585520.6520.7
5Q345B3925390.7324.0
6Q390C4035590.7222.8
7Q420D4125770.7122.5
Tab.1  Mean measured dimensions and key results from direct tensile tests
Fig.1  Cyclic loading protocols. (a) Cyclic ascend; (b) cyclic alternate; (c) cyclic tensile
parametersspecimen designationstrain amplitude
0.0050.0100.0150.020
K/MPa1-11076101610251054
1-21025105310011048
n1-18.4311.6613.7715.50
1-29.6612.6815.7217.59
r21-10.9980.9970.9950.993
1-20.9990.9960.9940.995
Tab.2  Group 1 specimens Ramberg-Osgood parameters
parametersspecimen designationstrain amplitude
0.0050.0100.0150.020
K/MPa2-11003103210541071
2-21118109910581096
n2-19.0610.9412.5213.30
2-27.959.6911.4812.48
r22-10.9970.9980.9970.997
2-20.9950.9980.9970.997
Tab.3  Group 2 specimens Ramberg-Osgood parameters
parametersspecimen designationstrain amplitude
0.0050.010.0150.02
K/MPa3-11146115211591177
3-21179121111651177
n3-19.7511.5713.5414.81
3-29.1311.1713.2414.46
r23-10.9980.9980.9970.997
3-20.9930.9980.9970.997
Tab.4  Group 3 specimens Ramberg-Osgood parameters
parametersspecimen designationstrain amplitude
0.0050.0100.0150.020
K/MPa4-11260126312561263
4-21270126912681282
n4-18.4910.1411.8412.95
4-28.0810.4611.1812.10
r24-10.9980.9980.9970.997
4-20.9980.9980.9970.997
Tab.5  Group 4 specimens Ramberg-Osgood parameters
parametersspecimen designationstrain amplitude
0.0050.0100.0150.020
K/MPa5-11138114311371142
5-21141117711451159
n5-110.9811.1913.2314.42
5-211.2011.3113.8415.11
r25-10.9950.9980.9960.996
5-20.9950.9970.9970.997
Tab.6  Group 5 specimens Ramberg-Osgood parameters
parametersspecimen designationstrain amplitude
0.0050.0100.0150.020
K/MPa6-11320131813091317
6-21315138013071315
n6-18.959.4010.6911.42
6-28.838.8910.4811.12
r26-10.9960.9980.9970.997
6-20.9960.9980.9970.997
Tab.7  Group 6 specimens Ramberg-Osgood parameters
parametersspecimen designationstrain amplitude
0.0050.010.0150.02
K/MPa7-11250125412461255
7-21220124211951209
n7-110.8210.8712.2413.47
7-210.8011.2813.7514.96
r27-10.9950.9980.9960.996
7-20.9960.9980.9970.996
Tab.8  Group 7 specimens Ramberg-Osgood parameters
Fig.2  Hysteresis loops for Group 1 specimens. (a) Cyclic Ascend (1-1); (b) cyclic alternate (1-2)
modular parameter K/MPaspecimen designation
1-12-13-14-15-16-17-1
maximum1076107111771263114313201255
minimum1016100311461256113713091246
mean Kmean1043104011591261114013161251
standard deviation27.4629.3813.433.322.944.834.11
COV0.0260.0280.0160.0030.0030.0040.003
Tab.9  Modular parameters for hysteresis loops
yield stress/MPaKmean/MPaKpredicted/MPaKmean/Kpredicted
280104310331.01
308104010830.96
350115911591.00
358126111731.08
392114012340.92
403131612531.05
412125112690.99
Tab.10  Modular parameter and yield strength relation
Fig.3  Hysteresis loops for Group 1 specimen under cyclic ascend loading protocol
Fig.4  Hysteresis loops for Group 1 specimen under cyclic alternate loading protocol
Fig.5  The effect of loading protocols on hysteresis loops
Fig.6  Hysteresis loops for Group 8 specimen under cyclic ascend loading protocol
Fig.7  Hysteresis loops for Group 9 specimen under cyclic ascend loading protocol
Fig.8  Specimen dimension (in mm)
Fig.9  Loading protocol
Fig.10  Finite element model
Fig.11  Hysteresis loops.
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