Reliability analysis of rectangular plate under in-plane tensile loading using continuum damage mechanics theory

Document Type : Research Article

Authors

1 Aerospace Research Institute (Ministry of Science, Research and Technology), Tehran, Iran.

2 ARI

Abstract

In this paper, the reliability of rectangular plates without holes and containing a central circular hole under static tensile load has been studied. To investigate the initiation and evolution of damages, continuum damage mechanics approach together with finite element has been used. Constitutive equations with scalar damage have been obtained for the plate and implemented in finite element code, ABAQUS.  To analyze the probability of failure the first/second order reliability methods have been used and then, limit state function and random variables according to the continuum damage mechanics model obtained. The force-displacement curves for various sizes of the hole are obtained. With the addition of a central hole in a plate with a diameter of 2 to 10 mm, failure load is reduced by approximately 60 to 80%, which is consistent with the concepts of stress concentration. Finally, the probability of failure of each plate with different hole sizes is approximated and sensitivity analysis on the coefficient of variation is performed. The reliability of the specimen with a diameter of 10 mm has the lowest value, while the plate without a hole has the highest value and among the random variables, the critical damage is the most effective one in reliability.

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References

 [1] L. Kachanov, Time of the rupture process under creep conditions, Izy Akad, Nank SSR Otd Tech Nauk, 8 (1958) 26-31.
[2] Y.N. Robotnov, Creep problems in structural members, North-HoUand Publishing Co., Amsterdam,  (1969) 358.
[3] J.-L. Chaboche, Thermodynamically founded CDM models for creep and other conditions, in:  Creep and Damage in Materials and structures, Springer, 1999, pp. 209-283.
[4] J. Lemaitre, A course on damage mechanics, Springer Science & Business Media, 2012.
[5] J.-L. Chaboche, Continuum damage mechanics: Part I—General concepts,  (1988).
[6] J. Simo, J. Ju, Strain-and stress-based continuum damage models—II. Computational aspects, International journal of solids and structures, 23(7) (1987) 841-869.
[7] J.C. Simo, J. Ju, Strain-and stress-based continuum damage models—I. Formulation, International journal of solids and structures, 23(7) (1987) 821-840.
[8] J. Cordebois, F. Sidoroff, Damage induced elastic anisotropy, in:  Mechanical Behavior of Anisotropic Solids/Comportment Méchanique des Solides Anisotropes, Springer, 1982, pp. 761-774.
[9] N. Bonora, D. Gentile, A. Pirondi, G. Newaz, Ductile damage evolution under triaxial state of stress: theory and experiments, International Journal of Plasticity, 21(5) (2005) 981-1007.
[10] M. Brünig, O. Chyra, D. Albrecht, L. Driemeier, M. Alves, A ductile damage criterion at various stress triaxialities, International journal of plasticity, 24(10) (2008) 1731-1755.
[11] L. Malcher, E. Mamiya, An improved damage evolution law based on continuum damage mechanics and its dependence on both stress triaxiality and the third invariant, International Journal of Plasticity, 56 (2014) 232-261.
[12] V.N. Van Do, The behavior of ductile damage model on steel structure failure, Procedia engineering, 142 (2016) 26-33.
[13] G. Majzoobi, M. Kashfi, N. Bonora, G. Iannitti, A. Ruggiero, E. Khademi, Damage characterization of aluminum 2024 thin sheet for different stress triaxialities, Archives of Civil and Mechanical Engineering, 18 (2018) 702-712.
[14] S. Razanica, R. Larsson, B. Josefson, A ductile fracture model based on continuum thermodynamics and damage, Mechanics of Materials, 139 (2019) 103197.
[15] N. Bonora, G. Testa, A. Ruggiero, G. Iannitti, D. Gentile, Continuum damage mechanics modelling incorporating stress triaxiality effect on ductile damage initiation, Fatigue & Fracture of Engineering Materials & Structures,  (2020).
[16] M. Ganjiani, A damage model for predicting ductile fracture with considering the dependency on stress triaxiality and Lode angle, European Journal of Mechanics-A/Solids,  (2020) 104048.
[17] K. Hayakawa, S. Murakami, Y. Liu, An irreversible thermodynamics theory for elastic-plastic-damage materials, European Journal of Mechanics-A/Solids, 17(1) (1998) 13-32.
[18] J. Lemaitre, R. Desmorat, Engineering damage mechanics: ductile, creep, fatigue and brittle failures, Springer Science & Business Media, 2005.
[19] M. Lemaire, Structural reliability, John Wiley & Sons, 2013.
[20] A. Haldar, S. Mahadevan, Reliability assessment using stochastic finite element analysis, John Wiley & Sons, 2000.
[21] M.A. Farsi, A.R. Sehat, Experimental and Numerical Study on Aluminum Damage Using a Nonlinear Model of Continuum Damage Mechanics, Journal of Applied and Computational Sciences in Mechanics, 27(2) (2016) 41-54, (in Persian).
[22] M.A. Farsi, A.R. Sehat, Comparison of Nonlinear Models for Prediction of Continuum Damage in Aluminum under Different Loading, Joural of Mechanical Engineering, 46(4) (2017) 211-220, (in Persian).
Amirkabir Journal of Mechanical Engineering
Volume 53, Issue 6
September 2021
Pages 3645-3656

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