Damage-Plastic Constitutive Model of Thin-Walled Circular Steel Tubes for Space Structures
Publication: Journal of Engineering Mechanics
Volume 146, Issue 12
Abstract
In this paper, we establish a coupled damage-plastic constitutive model in the scheme of small deformation assumption, based on a continuum damage mechanics model proposed by Lemaitre, for the thin-walled circular steel tubes widely used in space structures. First, a new damage evolution law is developed for steel tubes. Then the isotropic damage-plastic constitutive model is created within the thermodynamics framework. In addition, the numerical integration algorithm for the proposed model is formulated based on the well-established operator split methodology and is implemented into ANSYS through the user-defined material subroutines. The uniaxial tension test and the spatial hysteresis experiment for thin-walled circular steel tubes are performed, which serves as calibration conditions for the new proposition. The model parameters are determined by the inverse optimization method and the least squares fitting method. Numerical results obtained from the proposed and Lemaitre model are compared with experimental data obtained by spatial hysteresis, and the predictive ability of both models is discussed in terms of the force-displacement hysteretic curves, the initiation and propagation of fracture, and the evolution of the damage variable. It is illustrated that the established model presents a good agreement with experimental observation. Furthermore, it performs a better prediction compared to Lemaitre’s model. Lemaitre’s model is able to predict the correct location for fracture onset but fails to capture the potential path of fracture propagation and the displacement at the fracture.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code generated or used during the study are proprietary or confidential in nature and may only be provided with restrictions.
Acknowledgments
This study was funded by the Guangxi Natural Science Foundation (2018JJB160052), a research grant from the Talent of Guangxi Plan (T3030097947), the starting research grant for High-Level Talents from Guangxi University (A3030051003), the Science and Technology Major Project of Guangxi Province (AA18118029), and the Luxembourg National Research Fund for Intuitive Modeling and SIMulation Platform (IntuiSIM) (PoC17/12253887).
References
Armero, F., and S. Oller. 2000a. “A general framework for continuum damage models. I: Infinitesimal plastic damage models in stress space.” Int. J. Solids Struct. 37 (48–50): 7409–7436. https://doi.org/10.1016/S0020-7683(00)00205-5.
Armero, F., and S. Oller. 2000b. “A general framework for continuum damage models. II: Integration algorithms, with applications to the numerical simulation of porous metals.” Int. J. Solids Struct. 37 (48–50): 7437–7464. https://doi.org/10.1016/S0020-7683(00)00206-7.
Benallal, A., R. Billardon, and I. Doghri. 1988. “An integration algorithm and the corresponding consistent tangent operator for fully coupled elastoplastic and damage equations.” Commun. Appl. Numer. Methods 4 (6): 731–740. https://doi.org/10.1002/cnm.1630040606.
Benzerga, A. A., J. Besson, and A. Pineau. 2004. “Anisotropic ductile fracture. II: Theory.” Acta Mater. 52 (15): 4639–4650. https://doi.org/10.1016/j.actamat.2004.06.019.
Berto, L., A. Saetta, R. Scotta, and D. Talledo. 2014. “A coupled damage model for RC structures: Proposal for a frost deterioration model and enhancement of mixed tension domain.” Constr. Build. Mater. 65 (Aug): 310–320. https://doi.org/10.1016/j.conbuildmat.2014.04.132.
Berto, L., A. Saetta, and D. Talledo. 2015. “Constitutive model of concrete damaged by freeze–thaw action for evaluation of structural performance of RC elements.” Constr. Build. Mater. 98 (Nov): 559–569. https://doi.org/10.1016/j.conbuildmat.2015.08.035.
Castañeda, P. P., and M. Zaidman. 1994. “Constitutive models for porous materials with evolving microstructure.” J. Mech. Phys. Solids 42 (9): 1459–1497. https://doi.org/10.1016/0022-5096(94)90005-1.
Chen, W. F., and D. Han. 2012. Plasticity for structural engineers. New York: Springer.
Chinese Standard. 2002. Metallic materials—Tensile testing at ambient temperature. GB/Т 228-2002. Beijing: Chinese Standard.
Chow, C. L., and J. Wang. 1987. “An anisotropic theory of continuum damage mechanics for ductile fracture.” Eng. Fract. Mech. 27 (5): 547–558. https://doi.org/10.1016/0013-7944(87)90108-1.
Cyril, B. A. J. B. 2003. “On modelling the growth and the orientation changes of ellipsoidal voids in a rigid plastic matrix.” Model. Simul. Mater. Sci. 11 (3): 365. https://doi.org/10.1088/0965-0393/11/3/309.
Deliktas, B., G. Z. Voyiadjis, and A. N. Palazotto. 2009. “Simulation of perforation and penetration in metal matrix composite materials using coupled viscoplastic damage model.” Composites, Part B 40 (6): 434–442. https://doi.org/10.1016/j.compositesb.2009.04.019.
Desmorat, R., and S. Cantournet. 2008. “Modeling microdefects closure effect with isotropic/anisotropic damage.” Int. J. Damage Mech. 17 (1): 65–96. https://doi.org/10.1177/1056789507069541.
De Souza Neto, E. A. 2002. “A fast, one-equation integration algorithm for the Lemaitre ductile damage model.” Commun. Numer. Methods Eng. 18 (8): 541–554. https://doi.org/10.1002/cnm.511.
De Souza Neto, E. A., and D. Perić. 1996. “A computational framework for a class of fully coupled models for elastoplastic damage at finite strains with reference to the linearization aspects.” Comput. Methods Appl. Mech. Eng. 130 (1–2): 179–193. https://doi.org/10.1016/0045-7825(95)00872-1.
Doghri, I., and R. Billardon. 1995. “Investigation of localization due to damage in elasto-plastic materials.” Mech. Mater. 19 (2–3): 129–149. https://doi.org/10.1016/0167-6636(94)00011-5.
Gologanu, M., J. Leblond, G. Perrin, and J. Devaux. 1997. Recent extensions of Gurson’s model for porous ductile metal. New York: Springer.
Gurson, A. L. 1977. “Continuum theory of ductile rupture by void nucleation and growth. I: Yield criteria and flow rules for porous ductile media.” J. Eng. Mater. Technol. 99 (1): 2–15. https://doi.org/10.1115/1.3443401.
Halm, D., and A. Dragon. 1998. “An anisotropic model of damage and frictional sliding for brittle materials.” Eur. J. Mech. A. Solids 17 (3): 439–460. https://doi.org/10.1016/S0997-7538(98)80054-5.
Hammi, Y., D. J. Bammann, and M. F. Horstemeyer. 2004. “Modeling of anisotropic damage for ductile materials in metal forming processes.” Int. J. Damage Mech. 13 (2): 123–146. https://doi.org/10.1177/1056789504039255.
Hammi, Y., and M. F. Horstemeyer. 2007. “A physically motivated anisotropic tensorial representation of damage with separate functions for void nucleation, growth, and coalescence.” Int. J. Plast. 23 (10): 1641–1678. https://doi.org/10.1016/j.ijplas.2007.03.010.
Johnson, G. R., and W. H. Cook. 1985. “Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures.” Eng. Fract. Mech. 21 (1): 31–48. https://doi.org/10.1016/0013-7944(85)90052-9.
Ju, J. W. 1989. “On energy-based coupled elastoplastic damage theories: Constitutive modeling and computational aspects.” Int. J. Solids Struct. 25 (7): 803–833. https://doi.org/10.1016/0020-7683(89)90015-2.
Kachanov, L. M. 1958. “Time of the rupture process under creep conditions.” Izv. Akad. Nauk, SSSR, Otd. Tekh. Nauk 8 (1): 26–31.
Kailasam, M., N. Aravas, and P. P. Castaneda. 2000. “Porous metals with developing anisotropy: Constitutive models, computational issues and applications to deformation processing.” Comput. Model. Eng. Sci. 1 (2): 105–118.
Kailasam, M., and P. P. Castañeda. 1998. “A general constitutive theory for linear and nonlinear particulate media with microstructure evolution.” J. Mech. Phys. Solids 46 (3): 427–465. https://doi.org/10.1016/S0022-5096(97)00095-1.
Keralavarma, S. M., and A. A. Benzerga. 2008. “An approximate yield criterion for anisotropic porous media.” C. R. Méc. 336 (9): 685–692. https://doi.org/10.1016/j.crme.2008.07.008.
Kumar, S., and T. Usami. 1996. “Damage evaluation in steel box columns by cyclic loading tests.” J. Struct. Eng. 122 (6): 626–634. https://doi.org/10.1061/(ASCE)0733-9445(1996)122:6(626).
Lee, B. J., and M. E. Mear. 1999. “Stress concentration induced by an elastic spheroidal particle in a plastically deforming solid.” J. Mech. Phys. Solids 47 (6): 1301–1336. https://doi.org/10.1016/S0022-5096(98)00104-5.
Lemaitre, J. 1985. “A continuous damage mechanics model for ductile fracture.” J. Eng. Mater. Technol. 107 (1): 83–89. https://doi.org/10.1115/1.3225775.
Lemaitre, J. 1986. “Local approach of fracture.” Eng. Fract. Mech. 25 (5): 523–537. https://doi.org/10.1016/0013-7944(86)90021-4.
Lemaitre, J., R. Desmorat, and M. Sauzay. 2000. “Anisotropic damage law of evolution.” Eur. J. Mech. A. Solids 19 (2): 187–208. https://doi.org/10.1016/S0997-7538(00)00161-3.
Li, G., Z. Shen, and J. Huang. 1999. “Spatial hysteretic model and elasto-plastic stiffness of steel columns.” J. Constr. Steel Res. 50 (3): 283–303.
Liu, Q. Y., A. Kasai, and T. Usami. 1999. “Parameter identification of damage-based hysteretic model for pipe-section steel bridge piers.” J. Struct. Eng. 45 (1): 1005–1016.
Maire, E., C. Bordreuil, L. Babout, and J. Boyer. 2005. “Damage initiation and growth in metals. Comparison between modelling and tomography experiments.” J. Mech. Phys. Solids 53 (11): 2411–2434. https://doi.org/10.1016/j.jmps.2005.06.005.
Malcher, L., and E. N. Mamiya. 2014. “An improved damage evolution law based on continuum damage mechanics and its dependence on both stress triaxiality and the third invariant.” Int. J. Plast. 56 (1): 232–261. https://doi.org/10.1016/j.ijplas.2014.01.002.
Malcher, L., F. A. Pires, and J. C. De Sá. 2012. “An assessment of isotropic constitutive models for ductile fracture under high and low stress triaxiality.” Int. J. Plast. 30 (1): 81–115. https://doi.org/10.1016/j.ijplas.2011.10.005.
McClintock, F. A. 1968. “A criterion for ductile fracture by the growth of holes.” J. Appl. Mech. 35 (2): 363–371. https://doi.org/10.1115/1.3601204.
Monchiet, V., and G. Bonnet. 2013. “A Gurson-type model accounting for void size effects.” Int. J. Solids Struct. 50 (2): 320–327. https://doi.org/10.1016/j.ijsolstr.2012.09.005.
Park, Y., and A. Ang. 1985. “Mechanistic seismic damage model for reinforced concrete.” J. Struct. Eng. 111 (4): 722–739. https://doi.org/10.1061/(ASCE)0733-9445(1985)111:4(722).
Park, Y., A. Ang, and Y. Wen. 1985. “Seismic damage analysis of reinforced concrete buildings.” J. Struct. Eng. 111 (4): 740–757. https://doi.org/10.1061/(ASCE)0733-9445(1985)111:4(740).
Pelà, L., M. Cervera, and P. Roca. 2013. “An orthotropic damage model for the analysis of masonry structures.” Constr. Build. Mater. 41 (1): 957–967. https://doi.org/10.1016/j.conbuildmat.2012.07.014.
Pires, F. A., J. C. de Sá, L. C. Sousa, and R. N. Jorge. 2003. “Numerical modelling of ductile plastic damage in bulk metal forming.” Int. J. Mech. Sci. 45 (2): 273–294. https://doi.org/10.1016/S0020-7403(03)00051-1.
Rice, J. R. 1968. “A path independent integral and the approximate analysis of strain concentration by notches and cracks.” J. Appl. Mech. 35 (2): 379–386. https://doi.org/10.1115/1.3601206.
Rousselier, G. 1987. “Ductile fracture models and their potential in local approach of fracture.” Nucl. Eng. Des. 105 (1): 97–111. https://doi.org/10.1016/0029-5493(87)90234-2.
Rousselier, G. 2001. “Dissipation in porous metal plasticity and ductile fracture.” J. Mech. Phys. Solids 49 (8): 1727–1746. https://doi.org/10.1016/S0022-5096(01)00013-8.
Segurado, J., and J. LLorca. 2004. “A new three-dimensional interface finite element to simulate fracture in composites.” Int. J. Solids Struct. 41 (11–12): 2977–2993. https://doi.org/10.1016/j.ijsolstr.2004.01.007.
Shen, Z., and D. Bao. 1997. “An experiment-based cumulative damage mechanics model of steel under cyclic loading.” Adv. Struct. Eng. 1 (1): 39–46.
Shen, Z., B. Dong, and W. Cao. 1998. “A hysteresis model for plane steel members with damage cumulation effects.” J. Constr. Steel Res. 48 (2): 79–87.
Simo, J. C., and T. Hughes. 2008. Computational inelasticity. New York: Springer.
Singh, A. K., and P. C. Pandey. 1999. “An implicit integration algorithm for plane stress damage coupled elastoplasticity.” Mech. Res. Commun. 26 (6): 693–700. https://doi.org/10.1016/S0093-6413(99)00080-4.
Tang, C. Y., C. L. Chow, W. Shen, and W. H. Tai. 1999. “Development of a damage-based criterion for ductile fracture prediction in sheet metal forming.” J. Mater. Process. Technol. 91 (1–3): 270–277. https://doi.org/10.1016/S0924-0136(98)00442-7.
Teng, X. 2008. “Numerical prediction of slant fracture with continuum damage mechanics.” Eng. Fract. Mech. 75 (8): 2020–2041. https://doi.org/10.1016/j.engfracmech.2007.11.001.
Tvergaard, V. 1981. “Influence of voids on shear band instabilities under plane strain conditions.” Int. J. Fract. 17 (4): 389–407. https://doi.org/10.1007/BF00036191.
Tvergaard, V., and A. Needleman. 1984. “Analysis of the cup-cone fracture in a round tensile bar.” Acta Metall. 32 (1): 157–169. https://doi.org/10.1016/0001-6160(84)90213-X.
Usami, T., and S. Kumar. 1996. “Damage evaluation in steel box columns by pseudodynamic tests.” J. Struct. Eng. 122 (6): 635–642. https://doi.org/10.1061/(ASCE)0733-9445(1996)122:6(635).
Voyiadjis, G. Z. 2012. Advances in damage mechanics: Metals and metal matrix composites. Burlington, NJ: Elsevier.
Voyiadjis, G. Z., and F. H. Abed. 2005. “Microstructural based models for bcc and fcc metals with temperature and strain rate dependency.” Mech. Mater. 37 (2–3): 355–378. https://doi.org/10.1016/j.mechmat.2004.02.003.
Voyiadjis, G. Z., and F. H. Abed. 2006. “A coupled temperature and strain rate dependent yield function for dynamic deformations of bcc metals.” Int. J. Plast. 22 (8): 1398–1431. https://doi.org/10.1016/j.ijplas.2005.10.005.
Voyiadjis, G. Z., and F. H. Abed. 2007. “Transient localizations in metals using microstructure-based yield surfaces.” Model. Simul. Mater. Sci. 15 (1): S83–S95. https://doi.org/10.1088/0965-0393/15/1/S08.
Voyiadjis, G. Z., and R. K. A. Al-Rub. 2003. “Thermodynamic based model for the evolution equation of the backstress in cyclic plasticity.” Int. J. Plast. 19 (12): 2121–2147. https://doi.org/10.1016/S0749-6419(03)00062-7.
Voyiadjis, G. Z., S. H. Hoseini, and G. H. Farrahi. 2012. “Effects of stress invariants and reverse loading on ductile fracture initiation.” Int. J. Solids Struct. 49 (13): 1541–1556. https://doi.org/10.1016/j.ijsolstr.2012.02.030.
Voyiadjis, G. Z., and P. I. Kattan. 1992a. “Finite strain plasticity and damage in constitutive modeling of metals with spin tensors.” Appl. Mech. Rev. 45 (3S): S95. https://doi.org/10.1115/1.3121396.
Voyiadjis, G. Z., and P. I. Kattan. 1992b. “A plasticity-damage theory for large deformation of solids—I. Theoretical formulation.” Int. J. Eng. Sci. 30 (9): 1089–1108. https://doi.org/10.1016/0020-7225(92)90059-P.
Voyiadjis, G. Z., and P. I. Kattan. 2006. Advances in damage mechanics: Metals and metal matrix composites with an introduction to fabric tensors. 2nd ed. Burlington, NJ: Elsevier.
Voyiadjis, G. Z., and P. I. Kattan. 2009. “A comparative study of damage variables in continuum damage mechanics.” Int. J. Damage Mech. 18 (4): 315–340. https://doi.org/10.1177/1056789508097546.
Voyiadjis, G. Z., and T. Park. 1996. “Anisotropic damage for the characterization of the onset of macro-crack initiation in metals.” Int. J. Damage Mech. 5 (1): 68–92. https://doi.org/10.1177/105678959600500104.
Voyiadjis, G. Z., and T. Park. 1999. “The kinematics of damage for finite-strain elasto-plastic solids.” Int. J. Eng. Sci. 37 (7): 803–830. https://doi.org/10.1016/S0020-7225(98)00100-1.
Wen, J., Y. Huang, K. C. Hwang, C. Liu, and M. Li. 2005. “The modified Gurson model accounting for the void size effect.” Int. J. Plast. 21 (2): 381–395. https://doi.org/10.1016/j.ijplas.2004.01.004.
Xue, L. 2007. “Damage accumulation and fracture initiation in uncracked ductile solids subject to triaxial loading.” Int. J. Solids Struct. 44 (16): 5163–5181. https://doi.org/10.1016/j.ijsolstr.2006.12.026.
Xue, L., and T. Wierzbicki. 2008. “Ductile fracture initiation and propagation modeling using damage plasticity theory.” Eng. Fract. Mech. 75 (11): 3276–3293. https://doi.org/10.1016/j.engfracmech.2007.08.012.
Zhai, Y., Z. Deng, N. Li, and R. Xu. 2014. “Study on compressive mechanical capabilities of concrete after high temperature exposure and thermo-damage constitutive model.” Constr. Build. Mater. 68 (1): 777–782. https://doi.org/10.1016/j.conbuildmat.2014.06.052.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 146 • Issue 12 • December 2020
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Jan 29, 2020
Accepted: May 18, 2020
Published online: Sep 21, 2020
Published in print: Dec 1, 2020
Discussion open until: Feb 21, 2021
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.