Numerical Implementation of A Nonlocal Damage Model For A Stress Regime-Dependent Creep Constitutive Model
محورهای موضوعی : Mechanics of Solids
behzad dastgerdi
1
(Master of Science In Mechanical Engineering , College of Engineering, University of Tehran
Verified email at ut.ac.ir)
Mostafa baghani
2
(Tehran University)
کلید واژه: Creep constitutive model, Stress regime-dependent creep behavior, Finite element, Continuum damage mechanics, Nonlocal damage, 1CrMoV Alloy.,
چکیده مقاله :
Several components of aeronautical motors and power plant stations are subjected to high temperatures, leading to creep deformation. It’s common practice to predict crack development in such components by using Continuum Damage Mechanics (CDM). Nevertheless, mesh dependency is a well-known issue in the classical CDM approach. The mesh sensitivity problem can be solved by using a nonlocal continuum approach. In the present study, in order to improve the numerical efficiency, a stress regime dependent creep model has been extended to a nonlocal model using a nonlocal theory from the literature. The nonlocal creep model was applied to a commercial finite element code, such as ABAQUS, with the help of user-defined routines (CREEP+USDFLD) to predict the load point displacement (LPD) and creep crack growth (CCG) for a compact tension (CT) specimen made of high creep strength 1CrMoV steel. A comparison between the results of the new nonlocal model and experimental data was made for verification. The mesh dependency of the new nonlocal model was investigated. The results indicate that the proposed nonlocal creep model demonstrates good mesh objectivity that was not feasible when considering the traditional local creep model.
Several components of aeronautical motors and power plant stations are subjected to high temperatures, leading to creep deformation. It’s common practice to predict crack development in such components by using Continuum Damage Mechanics (CDM). Nevertheless, mesh dependency is a well-known issue in the classical CDM approach. The mesh sensitivity problem can be solved by using a nonlocal continuum approach. In the present study, in order to improve the numerical efficiency, a stress regime dependent creep model has been extended to a nonlocal model using a nonlocal theory from the literature. The nonlocal creep model was applied to a commercial finite element code, such as ABAQUS, with the help of user-defined routines (CREEP+USDFLD) to predict the load point displacement (LPD) and creep crack growth (CCG) for a compact tension (CT) specimen made of high creep strength 1CrMoV steel. A comparison between the results of the new nonlocal model and experimental data was made for verification. The mesh dependency of the new nonlocal model was investigated. The results indicate that the proposed nonlocal creep model demonstrates good mesh objectivity that was not feasible when considering the traditional local creep model.
[1] V.B. Pandey, I.V. Singh, B.K. Mishra, A new creep-fatigue interaction damage model and CDM-XFEM framework for creep-fatigue crack growth simulations, Theoretical and Applied Fracture Mechanics, Volume 124, 2023, 103740, ISSN 0167-844,
[2] Hosseini E, Holdsworth SR and Mazza E, Stress regime-dependent creep constitutive model considerations in finite element continuum damage mechanics. International Journal of Damage Mechanics, 2013; 22(8): 1186–1205.
[3] Holdsworth SR, Abe F, Kern TU and Viswanathan R (eds), Constitutive equations for creep curves and predicting service life. Creep-resistant Steels. Cambridge, England: Woodhead Publishing and CRC Press, 2008; pp. 403–420.
[4] Norton FH, The Creep of Steel at High Temperature. New York: McGraw-Hill, 1929.
[5] Kachanov, L. M., Time of rupture process under varying strain gradients (in Russian), Izvestia Akademii Nauk, USSR, 1958; No. 8, pp: 26-31.
[6] Rabotnov YN, Creep Problems in Structural Members. Amsterdam: North-Holland, 1969.
[7] Murakami S, Kawai M and Rong H Finite element analysis of creep crack growth by a local approach. International Journal of Mechanical Sciences, 1988; 30(7): 491–502.
[8] Murakami S and Liu Y, Mesh-dependence in local approach to creep fracture. International Journal of Damage Mechanics, 1995; 4(3): 230–250.
[9] Murakami S, Liu Y and Mizuno M, Computational methods for creep fracture analysis by damage mechanics. Computer Methods in Applied Mechanics and Engineering, 2000; 183(1): 15–33.
[10] Hyde CJ, Hyde TH, Sun W, et al., Damage mechanics-based predictions of creep crack growth in 316 stainless steel Engineering Fracture Mechanics, 2010; 77(12): 2385–2402.
[11] Hyde TH, Ali BS and Sun W, Analysis and design of a small, two-bar creep test specimen. Journal of Engineering Materials and Technology, 2013; 135(4): 041006
[12] Hyde TH, Ali BS and Sun W, On the determination of material creep constants using miniature creep test specimens. Journal of Engineering Materials and Technology, 2014; 136(2): 021006.
[13] Hyde TH, Li R, Sun W, et al., A simplified method for predicting the creep crack growth in P91 welds at 650 C. Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials Design and Applications, 2010; 224(4): 208–219.
[14] Hyde TH, Saber M and Sun W, Testing and modelling of creep crack growth in compact tension specimens from a P91 weld at 650_C. Engineering Fracture Mechanics, 2010; 77(15): 2946–2957.
[15] Hyde TH, Saber M and Sun W, Creep crack growth data and prediction for a P91 weld at 650_C. International Journal of Pressure Vessels and Piping, 2010; 87(12): 721–729.
[16] Bartsch H, A new creep equation for ferritic and martensitic steels. Steel Research, 1995; 66: 384–388.
[17] Holdsworth SR and Mazza E, Exploring the applicability of the LICON methodology for a 1%CrMoV steel. Materials at High Temperatures, 2008; 25: 267–276.
[18] Y. Xiao, A multi-mechanism damage coupling model, Int. J. Fatigue 26 (11) (2004) 1241–1250.
[19] R.P. Skelton, D. Gandy, Creep–fatigue damage accumulation and interaction diagram based on metallographic interpretation of mechanisms, Mater. High Temp. 25 (1) (2008) 27–54.
[20] L. Zhao, L. Xu, K. Nikbin, Predicting failure modes in creep and creep-fatigue crack growth using a random grain/grain boundary idealized microstructure meshing system, Mater. Sci. Eng. A 704 (2017) 274–286.
[21] L. Xu, J. Rong, L. Zhao, H. Jing, Y. Han, Creep-fatigue crack growth behavior of G115 steel at 650◦ C, Mater. Sci. Eng. A 726 (2018) 179–186.
[22] Z. Tang, H. Jing, L. Xu, L. Zhao, Y. Han, B. Xiao, Y. Zhang, H. Li, Investigating crack propagation behavior and damage evolution in G115 steel under combined steady and cyclic loads, Theor. Appl. Fract. Mech. 100 (2019) 93–104.
[23] Z.C. Fan, X.D. Chen, L. Chen, J.L. Jiang, A CDM-based study of fatigue–creep interaction behavior, Int. J. Press. Vessel. Pip. 86 (9) (2009) 628–632.
[24] A. Huang, W. Yao, F. Chen, Analysis of fatigue life of PMMA at Different frequencies based on a new damage mechanics model, Math. Probl. Eng. (2014) 352676.
[25] N. Liu, H. Dai, L. Xu, Z. Tang, C. Li, J. Zhang, J. Lin, Modeling and effect analysis on crack growth behavior of Hastelloy X under high temperature creep-fatigue interaction, Int. J. Mech. Sci. 195 (2021), 106219.
[26] Kamaludin, S., Thamburaja, P. Efficient Neighbour Search Algorithm for Nonlocal-Based Simulations—Application to Failure Mechanics. J Fail. Anal. and Preven. 23, 540–547 (2023).
[27] Bazant, Z.P., Belytschko, T.B. and Chang, T. P., Continuum theory for strain-softening, Journal of the Engineering Mechanics Division, ASCE, 1984; vol. 110, No.12: 1666-1692.
[28] Bazant, Z.P. and Pijaudier-Cabot, G., Nonlocal continuum damage, localization instability and convergence, Journal of Applied Mechanics, 1988; Vol. 55, No 2: 287- 293.
[29] Bazant, Z. P. F.ASCE., Nonlocal damage theory based on micromechanics of crack interactions, Journal of Engineering Mechanics, March, 1994; Vol. 120, No. 3: 593-617.
[30] Abu Al-Rub, R. K. and Voyiadjis, G. Z., A direct finite element implementation of the gradient-dependent theory, International Journal for Numerical Methods in Engineering, 2005; 63: 603-629.
[31] Dorgan, R. J. and Voyiadjis, G. Z., A Mixed Finite Element Implementation of a Gradient-enhanced Coupled Damage–Plasticity Model, International Journal of Damage Mechanics, 2006; Vol. 15: 201-235.
[32] Andrade FXC, César De Sá JMA, Andrade Pires FM, A ductile damage nonlocal model of integral-type at finite strains: Formulation and numerical issues. International Journal of Damage Mechanics, 2011; 20: 515–557.
[33] Brunet M, Morestin F, Walter H, Damage identification for anisotropic sheet-metals using a non-local damage model. International Journal of Damage Mechanics, 2016; 13: 35–57.
[34] Jirásek M, Non-local damage mechanics with application to concrete. Revue Française de Génie Civil, 2004; 8: 683–707.
[35] Belytschko T, Gracie R, Ventura G, A review of extended/generalized finite element methods for material modeling. Modelling and Simulation in Materials Science and Engineering, 2009; 17: 43001.
[36] Li X, Chen J, An extended cohesive damage model for simulating arbitrary damage propagation in engineering materials. Computer Methods in Applied Mechanics and Engineering, 2017; 315: 744–759.
[37] Li, Xiaole & Gao, Weicheng & Liu, Wei., A mesh objective continuum damage model for quasi-brittle crack modelling and finite element implementation. International Journal of Damage Mechanics, 2019; vol 28.
[38] Seupel, A., Hütter, G., Kuna, M., An efficient FE-implementation of implicit gradient enhanced damage models to simulate ductile failure, Engineering Fracture Mechanics, 2018.
[39] Alban de Vaucorbeil, Vinh Phu Nguyen, Tushar Kanti Mandal, Mesh objective simulations of large strain ductile fracture: A new nonlocal Johnson-Cook damage formulation for the Total Lagrangian Material Point Method, Computer Methods in Applied Mechanics and Engineering, 2022; Volume 389.
[40] Chow, C. L., Mao, J., & Shen, J., Nonlocal Damage Gradient Model for Fracture Characterization of Aluminum Alloy. International Journal of Damage Mechanics, 2011; 20(7), 1073–1093.
[41] V.B. Pandey, M. Kumar, I.V. Singh, B.K. Mishra, S. Ahmad, A.V. Rao, V. Kumar, Mixed-mode creep crack growth simulations using continuum damage mechanics and virtual node XFEM, in: Structural Integrity Assessment, Springer, Singapore, 2020, pp. 275–284.
[42] V.B. Pandey, S.S. Samant, I.V. Singh, B.K. Mishra, An improved methodology based on continuum damage mechanics and stress triaxiality to capture the constraint effect during fatigue crack propagation, Int. J. Fatigue 140 (2020), 105823.
[43] V.B. Pandey, I.V. Singh, B.K. Mishra, Complete Creep Life Prediction Using Continuum Damage Mechanics and XFEM, in: Recent Advances in Computational Mechanics and Simulations, Springer, Singapore, 2020, pp. 169-176.
[44] V.B. Pandey, I.V. Singh, B.K. Mishra, S. Ahmad, A.V. Rao, V. Kumar, Creep crack simulations using continuum damage mechanics and extended finite element method, Int. J. Damage Mech 28 (1) (2019) 3–34.
[45] V.B. Pandey, I.V. Singh, B.K. Mishra, S. Ahmad, A.V. Rao, V. Kumar, A new framework based on continuum damage mechanics and XFEM for high cycle fatigue crack growth simulations, Eng. Fract. Mech. 206 (2019) 172–200.
[46] V.B. Pandey, I.V. Singh, B.K. Mishra, A Strain-based continuum damage model for low cycle fatigue under different strain ratios, Eng. Fract. Mech. 242 (2021), 107479.
[47] S.S. Samant, V.B. Pandey, I.V. Singh, R.N. Singh, Effect of double austenitization treatment on fatigue crack growth and high cycle fatigue behavior of modified 9Cr–1Mo steel, Mater. Sci. Eng. A Vol. 788,139495 (2020).
[48] Ashby MF, A first report on deformation–mechanism maps. Acta Metallurgica, 1972; 20: 887–897.
[49] Maruyama K, In: Abe F, Kern TU and Viswanathan R (eds), Fundamental aspects of creep deformation and deformation mechanism map. Creep–Resistant Steels. Cambridge, England: Woodhead Publishing and CRC Press, 2008; pp. 265–278.
[50] Holdsworth SR and Mazza E, Exploring the applicability of the LICON methodology for a 1%CrMoV steel. Materials at High Temperatures, 2008; 25: 267–276