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A Novel Unified Visco-Plastic Damage Constitutive Model Considering Stress State of TC16 Titanium Alloy during Cold Deformation

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Abstract

To study the stress state of TC16 under different cold forming, to avoid the fracture of TC16 titanium alloy during cold forging. Cold compression, cold tension and cold torsion experiments were carried out on it under different stress states. The fracture strain values and stress–strain relationship under different stress triaxial ratios and normalized Lode's angle at different strain rates were obtained through these experiments. The data obtained from these experiments were constructed using Bai's model. Then, based on the physical evolution mechanism of dislocation density and fracture strain, a new set of coupled ductile damage constitutive equations was proposed using the internal state variable modeling method. To simulate the microscopic damage evolution during cold forming of TC16 alloy. The unknown parameters within the unified constitutive equation are calculated by using an evolutionary algorithm optimization method. The experimental results show that there is a small gap between the values obtained by the proposed damage constitutive equation and the values obtained by the experiment, which shows the superiority of the proposed damage constitutive equation. After importing it into DEFORM-3D software through a subroutine, the distribution and evolution of micro-damage of bars with different notch radii during cold drawing are predicted. The finite element simulation further verifies the validity and accuracy of the prediction of the coupled ductile damage constitutive equation.

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References

  1. Z. Pater, J. Tomczak, and T. Bulzak, Analysis of a Cross Wedge Rolling Process for Producing Drive Shafts, Int. J. Adv. Manuf. Technol., 2018, 94, p 1–9.

    Article  Google Scholar 

  2. J. Lin, Materials and Process Modelling in Metal Forming Applications, 2015.

  3. Y. Lou, J.W. Yoon, and H. Huh, Modeling of shear ductile fracture considering a changeable cut-off value for stress triaxiality, in: AIP Conference Proceedings American Institute of Physics, 2014.

  4. T.S. Cao, Models for Ductile Damage and Fracture Prediction in Cold Bulk Metal Forming Processes: A Review, Int.J. Mater. Form., 2017, 10, p 139–171.

    Article  Google Scholar 

  5. M. Brünig, S. Gerke, and V. Hagenbrock, Stress-State-Dependence of Damage Strain Rate Tensors Caused by Growth and Coalescence of Micro-Defects, Int. J. Plast, 2014, 63, p 49–63.

    Article  Google Scholar 

  6. M. Brünig, D. Brenner, and S. Gerke, Stress State Dependence of Ductile Damage and Fracture Behavior: Experiments and Numerical Simulations, Eng. Fract. Mech., 2015, 141, p 152–169.

    Article  Google Scholar 

  7. L.F. Peng, Z.T. Xu, M.W. Fu, and X.M. Lai, Forming Limit of Sheet Metals in Meso-Scale Plastic Forming by Using Different Failure Criteria, Int. J. Mech. Sci., 2016, 120, p 190–203.

    Article  Google Scholar 

  8. M.G. Cockcroft and D.J. Latham, Ductility and the Workability of Metals, J. Inst. Met., 1968, 96, p 33–39.

    CAS  Google Scholar 

  9. J.R. Rice and D.M. Tracey, on the ductile enlargement of voids in triaxual stress fields, J. Mech. Phsicas Solids, 1969, 17, p 201–217.

    Article  Google Scholar 

  10. P. Brozzo, B. Deluca, and R. Rendina, A new method for the prediction of formability in metal sheets, in: Proceedings of the 7th Biennial conference of IDDRG on sheet metal forming and formability, 1972.

  11. Y. Bai and T. Wierzbicki, A New Model of Metal Plasticity and Fracture with Pressure and Lode Dependence, Int. J. Plast, 2008, 24, p 1071–1096.

    Article  CAS  Google Scholar 

  12. L. Xue and T. Wierzbicki, Ductile Fracture Characterization of Aluminum Alloy 2024–T351 Using Damage Plasticity Theory, Int. J. Appl. Mech., 2009, 01, p 267–304.

    Article  Google Scholar 

  13. Y. Lou and H. Huh, Prediction of Ductile Fracture for Advanced High Strength Steel with a New Criterion: Experiments and Simulation, J. Mater. Process. Tech, 2013, 213, p 1284–1302.

    Article  CAS  Google Scholar 

  14. A.L. Gurson, Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I—Yield Criteria and Flow Rules for Porous Ductile Media, J. Eng. Mater. Technol., 1977, 99, p 2.

    Article  Google Scholar 

  15. V. Tvergaard and A. Needleman, Analysis of the Cup-Cone Fracture in a Round Tensile Bar, Acta Metall., 1984, 32, p 157–169.

    Article  Google Scholar 

  16. P.G. Kossakowski, The Influence of Microstructural Defects on the Stress State of S235JR Steel under Plastic Deformation, Solid State Phenom., 2016, 250, p 69–76.

    Article  Google Scholar 

  17. M.E. Torki, S.M. Keralavarma, and A.A. Benzerga, An Analysis of Lode Effects in Ductile Failure, J. Mech. Phys. Solids, 2021, 153, 104468.

    Article  Google Scholar 

  18. K. Nahshon and J.W. Hutchinson, Modification of the Gurson Model for Shear Failure, Eur. J. Mech., 2008, 27, p 1–17.

    Article  Google Scholar 

  19. K.L. Nielsen and V. Tvergaard, Effect of a Shear Modified Gurson Model on Damage Development in a FSW Tensile Specimen, Int. J. Solids Struct., 2009, 46, p 587–601.

    Article  CAS  Google Scholar 

  20. L.M. Kachanov and D. Krajcinovic, Introduction to Continuum Damage Mechanics, J. Appl. Mech., 1987, 54, p 481.

    Article  Google Scholar 

  21. J. Lemaitre and J.L. Chaboche, Mechanics of solid materials || Damage mechanics, Cambridge University Press, 1990, p 346–450

    Book  Google Scholar 

  22. J.X. Wang and A.N. Jiang, Integration Algorithm for Isotropic Hardening Using Lemaitre's Coupled Elastoplastic Damage Model and Program Implementation, Eng. Mech., 2015, 20–27.

  23. M. Brünig and A. Michalski, A Stress-State-Dependent Continuum Damage Model for Concrete Based on Irreversible Thermodynamics, Int. J. Plast, 2016, 90, p 31–43.

    Article  Google Scholar 

  24. M. Brünig, A Continuum Damage Model Based on Experiments and Numerical Simulations—A Review, Springer International Publishing, 2015.

    Book  Google Scholar 

  25. M. Brünig, M. Schmidt, and S. Gerke, Numerical Analysis of Stress-State-Dependent Damage and Failure Behavior of Ductile Steel Based on Biaxial Experiments, Comput. Mech., 2020 https://doi.org/10.1007/s00466-020-01932-z

    Article  Google Scholar 

  26. T. Wierzbicki, Y. Bao, Y.-W. Lee, and Y. Bai, Calibration and Evaluation of Seven Fracture Models, Int. J. Mech. Sci., 2005, 47, p 719–743.

    Article  Google Scholar 

  27. H. Traphner, T. Clausmeyer, and A.E. Tekkaya, Methods for Measuring Large Shear Strains in in-Plane Torsion Tests, J. Mater. Process. Technol., 2019 https://doi.org/10.1016/j.jmatprotec.2019.116516

    Article  Google Scholar 

  28. M. Dunand and D. Mohr, Optimized Butterfly Specimen for the Fracture Testing of Sheet Materials Under Combined Normal and Shear Loading—ScienceDirect, Eng. Fract. Mech., 2011, 78, p 2919–2934.

    Article  Google Scholar 

  29. L. Morin, J.B. Leblond, D. Mohr, and D. Kondo, Prediction of Shear-Dominated Ductile Fracture in a Butterfly Specimen Using a Model of Plastic Porous Solids Including Void Shape Effects, Eur. J. Mech. A Solids, 2017, 61, p 433–442.

    Article  Google Scholar 

  30. B. Huang, X. Miao, X. Luo, Y. Yang, and Y. Zhang, Microstructure and Texture Evolution Near the Adiabatic Shear Band (ASB) in TC17 TITANIUM Alloy with Starting Equiaxed Microstructure Studied by EBSD, Mater. Charact., 2019, 151, p 151–165.

    Article  CAS  Google Scholar 

  31. Q. Xue, Y.J. Ma, J.F. Lei, R. Yang, and C. Wang, Evolution of Microstructure and Phase Composition of Ti-3Al-5Mo-4.5V Alloy with Varied β Phase Stability, J. Mater. Sci. Technol., 2018, 34, p 103–108.

    Google Scholar 

  32. T.S. Cao, M. Mazière, K. Danas, and J. Besson, A Model for Ductile Damage Prediction at Low Stress Triaxialities Incorporating Void Shape Change and Void Rotation, Int. J. Solids Struct., 2015, 63, p 240–263.

    Article  Google Scholar 

  33. F.Q. Gu and H.L. Liu, A Novel Weight Design in Multi-objective Evolutionary Algorithm, in: 2010 International Conference on Computational Intelligence and Security, CIS 2010, Nanning, Guangxi Zhuang Autonomous Region, China, December 11–14, 2010, 2010.

  34. J. Lin, B.H. Cheong, and X. Yao, Universal Multi-Objective Function for Optimising Superplastic-Damage Constitutive Equations, J. Mater. Process. Technol., 2002, 125–126, p 199–205.

    Article  Google Scholar 

  35. J. Lin and T.A. Dean, Modelling of Microstructure Evolution in Hot Forming Using Unified Constitutive Equations, J. Mater. Process. Technol., 2005, 167, p 354–362.

    Article  CAS  Google Scholar 

  36. L. Yang, B. Wang, G. Liu, H. Zhao, and W. Xiao, Behavior and Modeling of Flow Softening and Ductile Damage Evolution in Hot Forming of TA15 Alloy Sheets, Mater. Des., 2015, 85, p 135–148.

    Article  CAS  Google Scholar 

  37. Y. Huo, J. Lin, Q. Bai, B. Wang, and H. Ji, Prediction of Microstructure and Ductile Damage of a High-Speed Railway Axle Steel during Cross Wedge Rolling, J. Mater. Process. Technol., 2017, 239, p 359–369.

    Article  Google Scholar 

  38. Y. Liu, J. Lin, T.A. Dean, and D.C.J. Farrugia, A Numerical and Experimental Study of Cavitation in a Hot Tensile Axisymmetric Testpiece, J. Strain Anal. Eng. Des., 2005, 40, p 571–586.

    Article  Google Scholar 

  39. Y. Bai and T. Wierzbicki, A Comparative Study of Three Groups of Ductile Fracture Loci in the 3D Space, Eng. Fract. Mech., 2015, 135, p 147–167.

    Article  Google Scholar 

  40. B. Li, J. Lin and X. Yao, A Novel Evolutionary Algorithm for Determining Uniÿed Creep Damage Constitutive Equations, Int. J. Mech. Sci., 2002, 44, p 987–1002.

    Article  Google Scholar 

Download references

Acknowledgments

This project is funded by the National Natural Science Foundation of China (Grant No. 51805314), Key Technologies Research and Development Program (Grant No. 2018YFB1307900) and Shanghai Association for Science and Technology (Grant No. 16030501200).

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Authors and Affiliations

  1. School of Mechanical and Automotive Engineering, Shanghai University of Engineering Science, Shanghai, 201620, China

    Yuanming Huo, Wanbo Yang, Tao He, Jie Bai, Jianye Gao & Cunlong Huo

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  1. Yuanming Huo
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  2. Wanbo Yang
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  3. Tao He
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Huo, Y., Yang, W., He, T. et al. A Novel Unified Visco-Plastic Damage Constitutive Model Considering Stress State of TC16 Titanium Alloy during Cold Deformation. J. of Materi Eng and Perform 32, 4522–4540 (2023). https://doi.org/10.1007/s11665-022-07415-x

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