Cyclic Behavior of Beams Based on the Chaboche Unified Viscoplastic Model

Document Type : Research Paper

Authors

1 Department of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran

2 Department of Mechanical Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran

3 Amirkabir University of Technology, Tehran, Iran

Abstract

In this paper, ratcheting behavior of beams subjected to mechanical cyclic loads at elevated temperature, using the rate dependent Chaboche unified viscoplastic model with combined kinematic and isotropic hardening theory of plasticity, is investigated. A precise and general numerical scheme, using the incremental method of solution, is developed to obtain the cyclic inelastic creep and plastic strains. Applying the numerical method to the governing equations obtained based on the mentioned unified model, cyclic behavior of the beam due to the combined plastic and creep strains are obtained. Effect of loading rate, creep time, and mean load on ratcheting response and stress amplitude of the beam due to the combination of axial and bending moments at elevated temperatures are obtained. It is shown that increasing the loading rate, results into decrease in ratcheting rate and increase in stress amplitude. Also, the ratcheting strain increases with increasing the creep time while the stress amplitude decreases. The results obtained using the applied method in this paper is verified with the experimental data given in the literature search.

Keywords

Main Subjects

References

[1] Chaboche, J. L., ”Time Independent Constitutive Theories for Cyclic Plasticity”, International Journal of Plasticity, Vol. 32, No. 2, pp. 149-188, (1986).

[2] Chaboche, J. L., and Rousselier, G., ”On the Plastic and Viscoplastic Constitutive Equations Part 1: Rules Developed with Internal Variable Concept”, Journal of Pressure Vessel Technolgy, Vol. 105, No. 2, pp. 153-158, (1983).
[3] Chaboche, J. L., and Rousselier, G., ”On the Plastic and Viscoplastic Constitutive Equations Part 2: Application of Internal Variable Concepts to the 316 Stainless Steel”, Journal of Pressure Vessel Technolgy, Vol. 105, No. 2, pp. 159-164, (1983).

[4] Tong, J. , Zhan, Z. L., and Vermeulen, B., ”Modelling of Cyclic Plasticity an Viscoplasticity of a Nickel-Based Alloy using Chaboche Constitutive Equations”, International Journal of Fatigue, Vol. 26, No. 8, pp. 829-837, (2004).

[5] Zhan, Z., ”A Study of Creep-Fatigue Interaction in a New Nickel-Based Superalloy”, PhD Theis, University of Portsmouth, UK, (2004).

[6] Mahnken, Z., and Stein, E., ”Parameter Identification for Viscoplastic Model Based on Analytical Derivatives of a Least-Squares Functional and Stability Investigations”, International Journal of Plasticity, Vol. 12, No. 4, pp. 451-479, (1996).

[7] Schwertel, J., and Schinke, B., ”Automated Evaluation of Material Parameters of Viscoplastic Constitutive Equations”, Transactions of ASME, Journal of Engineering Materials Technolgy, Vol. 118, No. 3, pp. 273-280, (1996).
[8] Fossum, A. F., ”Parameter Estimation for an Internal Variable Model using Nonlinear Optimization and Analytical/Numerical Response Sensitivities”, Transactions of ASME, Journal of Engineering Matererials Technolgy, Vol. 119, No. 4, pp. 337-345, (1997).
[9] Fossum, A. F, ”Rate Data and Material Parameter Estimation”, Transactions of ASME, Journal Engineering Materials and Technology, Vol. 120, No. 1, pp. 7-12, (1998).
[10] Gong, Y. P., Hyde, C. J., Sun, W., and Hyde, T. H., ”Determination of Material Properties in the Chaboche Unified Viscoplasticity Model”, Journal of Materials Design and Applications, Vol. 224, No. 1, pp. 19–29, (2010).
[11] Frederick, C.O., and Armstrong, C.O., ”A Mathematical Representation of the Multiaxial Bauschinger Effect”, Materials at High Temperatures, Vol. 24, No. 1, pp. 1–26, (2007).
[12] Walker, K. P., ”Research and Development Program for Non-Linear Structural Modeling with Advanced Time-Temperature Dependent Constitutive Relationships”, Technical Report 19820008207, NASA, United Technologies Research Center; East Hartford, CT, United States, Nov. 25, (1981).
[13] Moreno, V., and Jordan, E. H., ”Prediction of Material Thermomechanical Response with a Unified Viscoplastic Constitutive Model”, International Journal of Plasticity, Vol. 2, No. 3, pp. 223–245, (1986).
[14] Murakami, S., and Ohno, N., ”A Constitutive Equation of Creep Based on the Concept of a Creep-Hardening Surface”, International Journal of Solids and Structures, Vol. 18, No. 7, pp. 597 – 609, (1982).

[15] Ohno, N., ”Recent Topics in Constitutive Modeling of Cyclic Plasticity and Viscoplasticity’, ASME Journal of Apllied Mechanics Reviews, Vol. 43, No. 11, pp. 283–295, (1990).

[16] Lee, K. D., and Krempl, E., ”An Orthotropic Theory of Viscoplasticity Based on Overstress for Thermomechanical Deformations”, International Journal of Solids and Structures, Vol. 27, No. 11, pp. 1445–1459, (1991).

[17] Shojaei, A., Eslami, M. R., and Mahbadi, H., ”Cyclic Loading of Beams Based on the Chaboche Model”, International Journal of Mechanics and Materials in Design, Vol. 6, No. 3, pp. 217-228, (2010).
[18] Chaboche, J. L., ”On Some Modifications of Kinematic Hardening to Improve the Description of Ratcheting Effects”, International Journal of Plasticity, Vol. 7, No. 7, pp. 661-678, (1991).
 [19] Chaboche, J. L., ”A Review of Some Plasticity and Viscoplasticity Constitutive Theories”, International Journal of Plasticity, Vol. 105, pp. 1642-1693, (2008).
[20] Mahbadi, H., and Eslami, M.R., ”Load and Deformation Controlled Cyclic Loading of Beams Based on the Isotropic Hardening Model”, Transactions of Iranian Society of Mechanical Engineering, Vol. 3, No. 1, pp. 28-46, (2002).

[21] Mahbadi, H., and Eslami, M. R., ”Load and Deformation Controlled Cyclic Loading of Thick Vessels Based on the Isotropic Hardening Model”, Transactions of Iranian Society of Mechanical Engineering, Vol. 4, No. 1, pp. 5-25, (2003).
[22] Mahbadi, H., Gowhari, A. R, and Eslami, M. R., ”Elastic-Plastic-Creep Cyclic Loading of Beams using the Prager Kinematic Hardening Model”, IMechE Journal of Strain Analysis, Vol. 39, No. 2, pp. 127-136, (2004). 

[23] Eslami, M. R., and Mahbadi, H., ”Cyclic Loading of Thermal Stresses”, Journal of Thermal Stresses, Vol. 24, No. 1, pp. 577-603, (2001). 

[24] Mahbadi, H., and Eslami, M. R., ”Numerical Simulation of Cyclic Loading of Thermal Stresses”, Encyclopedia of Thermal Stresses, Springer Netherlands, pp. 3434–3443. (2014).
Iranian Journal of Mechanical Engineering Transactions of the ISME
Volume 18, Issue 2 - Serial Number 29
September 2017
Pages 63-81

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