Macromodeling of Crack Damage in Steel Beams Subjected to Nonstationary Low Cycle Fatigue
Publication: Journal of Structural Engineering
Volume 142, Issue 10
Abstract
This study proposes a model of crack initiation and propagation in steel beams subjected to ultralow cycle fatigue. The model can be included in the general framework of lumped damage mechanics. A state variable called damage is introduced for each plastic hinge and can be related to the extension of the crack in the real structural component. The damage evolution law is based on the Manson–Coffin law, the Palmgren–Miner rule and two new concepts: the instantaneous plastic amplitude and a crack-driving variable. The model also describes crack closure effects using the unilateral damage assumption. It was validated by the numerical simulation of tests of steel beam-column connections subjected to cyclic loadings with constant and variable amplitudes, as reported in the literature. Advantages and limitations of the model are discussed for wider applications on the damage simulation of steel frame systems subjected to mechanical overloads, typically earthquake loading.
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Acknowledgments
The authors gratefully acknowledge the experimental data provided by Prof. Gang Shi, Tsinghua University, which were invaluable in the development of this research project. They also wish to acknowledge the comments and remarks of Prof Oren Lavan, Israel Institute of Technology. The first author Y. Bai was supported by a research fellowship from the Japan Society for the Promotion of Science (JSPS) (No. P14059). The work presented in this paper was supported by Grant-in-Aid for JSPS Fellows (26 04059) and NSFC (51508459). The third author of this paper acknowledges the financial support of the JSPS (Invitation Fellowship Long-term FY2014) during the period August 2014 to January 2015.
References
Amiri, H. R., Aghakouchak, A. A., Shahbeyk, S., and Engelhardt, M. D. (2013). “Finite element simulation of ultra low cycle fatigue cracking in steel structures.” J. Constr. Steel Res., 89(Oct), 175–184.
Amorim, D. L. N. D. F., Proença, S. P. B., and Flórez-López, J. (2013). “A model of fracture in reinforced concrete arches based on lumped damage mechanics.” Int. J. Solids Struct., 50(24), 4070–4079.
Amorim, D. L. N. D. F., Proença, S. P. B., and Flórez-López, J. (2014). “Simplified modeling of cracking in concrete: Application in tunnel linings.” Eng. Struct., 70(Jul), 23–35.
Araújo, F., and Proença, S. P. B. (2008). “Application of a lumped dissipation model to reinforced concrete structures with the consideration of residual strains and cycles of hysteresis.” J. Mech. Mater. Struct., 3(5), 1011–1031.
Ballio, G., Calado, L., and Castiglioni, C. A. (1997). “Low cycle fatigue behavior of structural steel members and connections.” Fatigue Fract. Eng. Mater. Struct., 20(8), 1129–1146.
Ballio, G., and Castiglioni, C. A. (1995). “A unified approach for the design of steel structures under low and/or high cycle fatigue.” J. Constr. Steel Res., 34(1), 75–101.
Castiglioni, C. A., Mouzakis, H. P., and Carydis, P. G. (2007). “Constant and variable amplitude cyclic behavior of welded steel beam-to-column connections.” J. Earthquake Eng., 11(6), 876–902.
Chai, Y. H., and Romstad, K. M. (1997). “Correlation between strain-based low-cycle fatigue and energy based linear damage models.” Earthquake Spectra, 13(2), 191–209.
Chen, W. F., and El-Metwally, S. E. D. E. (2011). Understanding structural engineering, from theory to practice, CRC Press, Boca Raton, FL.
Cipollina, A., López-Inojosa, A., and Flórez-López, J. (1995). “A simplified damage mechanics approach to nonlinear analysis of frames.” Comput. Struct., 54(6): 1113–1126.
Erberik, A., and Sucuoglu, H. (2004). “Seismic energy dissipation in deteriorating systems through low-cycle fatigue.” Earthquake Eng. Struct. Dyn., 33(1), 49–67.
Hashin, Z. (1980). “A reinterpretation of the Palmgren-Miner rule for fatigue life prediction.” J. Appl. Mech., 47(2), 324–328.
Iyama, J., and Ricles, J. (2009). “Prediction of fatigue life of welded beam-to-column connections under earthquake loading.” J. Struct. Eng., 135(12), 1472–1480.
Jones, S., Fry, G., and Engelhardt, M. (2002). “Experimental evaluation of cyclically loaded reduced beam section moment connections.” J. Struct. Eng., 441–451.
Kaewkulchai, G., and Williamson, E. B. (2004). “Beam element formulation and solution procedure for dynamic progressive collapse analysis.” Comput. Struct., 82(7–8), 639–651.
Kanvinde, A., and Deierlein, G. (2006). “The void growth model and the stress modified critical strain model to predict ductile fracture in structural steels.” J. Struct. Eng., 1907–1918.
Krawinkler, H., and Zohrei, M. (1983). “Cumulative damage in steel structures subjected to earthquake ground motions.” Comput. Struct., 16(1–4), 531–541.
Kuwamura, H. (1998). “Fracture of steel during an earthquake—State-of-the-art in Japan.” Eng. Struct., 20(4–6), 310–322.
Ladeveze, P., and Lemaitre, J. (1984). “Damage effective stress in quasi unilateral conditions.” 16th Int. Congress of Theoretical and Applied Mechanics, North-Holland, Amsterdam, Netherlands.
Lemaitre, J. (1992). A course on damage mechanics, Springer, Berlin.
Lemaitre, J., and Chaboche, J. L. (1985). Mécanique des materiaux solides, Dunod Bordas, Paris.
Liu, Y.-B., and Liu, J.-B. (2004). “A damage beam element model for non-linear analysis of reinforced concrete member.” Earthquake Eng. Eng. Vibr., 2004(2), 95–100 (in Chinese).
Mahin, S. A. (1998). “Lessons from damage to steel buildings during the Northridge earthquake.” Eng. Struct., 20(4–6), 261–270.
Marante, M. E., and Flórez-López, J. (2003). “Three dimensional analysis of reinforced concrete frames based on lumped damage mechanics.” Int. J. Solids and Struct., 40(19), 5109–5123.
Marante, M. E., Picón, R., Guerrero, N., and Flórez-López, J. (2012). “Local buckling in tridimensional frames: Experimentation and simplified analysis.” Latin-Am. J. Solids Struct., 9(6), 691–712.
McCabe, S. L., and Hall, W. J. (1989). “Assessment of seismic structural damage.” J. Struct. Eng., 2166–2183.
Miller, D. K. (1998). “Lessons learned from the Northridge earthquake.” Eng. Struct., 20(4–6), 249–260.
Nakashima, M., Inoue, K., and Tada, M. (1998). “Classification of damage to steel buildings observed in the 1995 Hyogoken-Nanbu earthquake.” Eng. Struct., 20(4–6), 271–281.
Olesen, J. F. (2001). “Fictitious crack propagation in fiber-reinforced concrete beams.” J. Eng. Mech., 272–280.
Park, Y., Iwai, S., Kameda, H., and Nonaka, T. (1996). “Very low cycle failure process of steel angle members.” J. Struct. Eng., 133–141.
Ribeiro, F. L. A., Barbosa, A. R., Scott, M. H., Neves, L. C. (2014). “Deterioration modeling of steel moment resisting frames using finite-length plastic hinge force-based beam-column elements.” J. Struct. Eng., 04014112.
Santoro, M. G., and Kunnath, S. K. (2013). “Damage-based RC beam element for nonlinear structural analysis.” Eng. Struct., 49, 733–742.
Simo, J. C., Kennedy, A., and Govindjee, S. (1988). “Non-smooth multisurface plasticity and viscoelastic loading/unloading conditions and numerical algorithms.” Int. J. Numer. Methods Eng., 26(10), 2161–2185.
Stoakes, C., and Fahnestock, L. (2011). “Cyclic flexural testing of concentrically braced frame beam-column connections.” J. Struct. Eng., 739–747.
Suita, K., Koetaka, Y., Takatsuka, K., and Umeda, T. (2013). “Loading test of beam-to-column connection of frame specimen for shaking table test: Quantification of collapse margin of steel high-rise buildings (Part 3).” Summaries of Technical Papers of Annual Meeting (Structure III), Hokkaido, Sapporo, Japan, 971–972.
Toellner, B. W., Watkins, C. E., Abbas, E. K., and Eatherton, M. R. (2015). “Experimental investigation on the seismic behavior of steel moment connections with decking attachments.” J. Constr. Steel Res., 105, 174–185.
Toi, Y., and Hasegawa, K. H. (2011). “Element-size independent, elasto-plastic damage analysis of framed structures using the adaptively shifted integration technique.” Comput. Struct., 89(23–24), 2162–2168.
Xue, L. (2008). “A unified expression for low cycle fatigue and extremely low cycle fatigue and its implication for monotonic loading.” Int. J. Fatigue, 30(10–11), 1691–1698.
Zhou, H., Wang, Y., Shi, Y., Xiong, J., and Yang, L. (2013). “Extremely low cycle fatigue prediction of steel beam-to-column connection by using a micro-mechanics based fracture model.” Int. J. Fatigue, 48, 90–100.
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© 2016 American Society of Civil Engineers.
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Received: Apr 15, 2015
Accepted: Feb 8, 2016
Published online: Apr 29, 2016
Discussion open until: Sep 29, 2016
Published in print: Oct 1, 2016
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