Çevrimsel Malzeme Deformasyonlarının Modellenmesi Bölüm I Plastisite Bünye Modelleri

Year 2004, Volume: 6 Issue: 1, 1 - 11, 02.05.2004

Mehmet Fırat

Abstract

Makina parçaları ve yapı
elemanların tasarımında; temel mühendislik faaliyetleri, statik ve dinamik
yüklemeler altında oluşan gerilme ve gerinimlerin hesaplanması, ve belli bir
güvenlik kriterine göre malzeme seçiminden geometrik ölçümlendirmeye kadar olan
bir dizi tasarım kararının alınması olarak ifade edilebilir. Gerek bilgisayar
ortamında değişik sayısal yöntemler kullanılarak yapılan değerlendirmeler ve
gerekse protiplendirme esnasında uygulanan değişik doğrulama testleri, yapısal
deformasyonların gerinim ve gerilme değerleriyle ilişkilendirme gereksinimi
mevcuttur. Bu amaçla yapılacak tüm mühendislik faaliyetleri değişen oranlarda
malzeme bünye modellerinin kullanılması ihtiyacını ortaya çıkarmaktadır. Bu
sebeple tasarım araçlarını kullanan mühendisler açısından malzeme modelleme
bilgisi giderek artan bir önem ifade etmektedir. Bu makalede, tipik mühendislik
metallerinin çok-eksenli çevrimsel dinamik yüklemeler altında
deformasyonlarının benzetimine yönelik literatürde önerilen bünye modelleri
incelenecektir. 

Keywords

Çok Eksenli Çevrimsel Yükleme, Kinematik Peklesme, Plastik Bünye Denklemi

References

• 1. Lemaitre, J., Chaboche, J.L., "Mechanics of Solid Materials", Cambridge University Press, New York, 1990.
• 2. Drucker, D.C., "Introduction to Mechanics of Deformable Solids", McGraw-Hill Company, New York, 1967.
• 3. Mendelson, A., "Plasticity: Theory and Application", The Macmillan Company, New York, 1968.
• 4. Malvern, LE., "Introduction to the Mechanics of a Continuous Medium", Prentice-Hall Inc., New Jersey, 1969.
• 5. Lubliner, J., "Plasticity Theory", Macmillan Publishing Company, New York, 1990.
• 6. Khan, Huang, S., "Continuum Theory of Plasticity", ", John Wiley & Sons Inc., New York, 1995.
• 7. Drucker, D.C., Palgen, L., "On the Stress-Strain Relations Suitable for Cyclic and Other Loadings", Journal of Applied Mechanics, Vol. 48, pp. 479-485,1981.
• 8. Suresh, S., "Fatigue of Materials", Cambridge University Press, New York, 1998.
• 9. Chaboche, J.L., "Constitutive Equations for Cyclic Plasticity and Cyclic Viscoplasticity", International Journal of Plasticity, Vol. 5, pp. 247-302, 1989.
• 10. Auricchio, F., Taylor, R.L., "Two Material Models for Cyclic Plasticity: Nonlinear Kinematic Hardening and Generalized Plasticity", International Journal of Plasticity, Vol. 11, No.1, pp.65-83, 1995.
• 11. Hashiguchi, K., "Mechanical Requirements and Structures of Cyclic Plasticity Models", International Journal of Plasticity, Vol. 9, pp.721-748, 1993.
• 12. .Chaboche, J.L., Rousselier, G., "On the Plastic and Viscoplastic Constitutive Equations, Part I: Rules Developed with Internal Variable Concept", Journal of Pressure Vessel Technology, Vol. 105, pp. 153-158, 1983.
• 13. Wataübe, O., Atluri, S.N, "A New Endochronic Approach to Computational Elasto-plasticity: An Example of Cyclically Loaded Cracked Plate", J. Appl. Mech., Vol.52, pp. 857-864, 1985.
• 14. Watanabe,O., Atluri, S.N, "Constitutive Modeling of Cyclic Plasticity and Creep Using an Internal Time Concept", International Journal of Plasticity, Vol. 2, No.2, pp.107-134, 1986.
• 15. Valanis, K.C., "A Theory of Viscoplasticity without a Yield Surface. Parti. General Theory", Archives of Mechanics, Vol.23, No.4, pp. 517- 533, Warsaw, 1971.
• 16. Valanis, K.C., "A Theory of Viscoplasticity without a Yield Surface. Part.II. Application to Mechanical Behavior of Metals", Archives of Mechanics, Vo1.23, No.4, pp. 535-551, Warsaw, 1971.
• 17. Valanis, K.C., "Fundamental Consequences of a New Intrinsic Time Measure Plasticity as a Limit of the Endochronic Theory", Archives of Mechanics, Vol.32, No.2, pp. 171-191, Warsaw, 1980.
• 18. Pan. W., Chenr, C.H., "Endochronic Description for Viscoplastic Behavior of Metals under Multiaxial Loadings", International Journal of Solids and Structures, Vol. 34, No.I 7, pp.2131- 2160, 1997.
• 19. Pan. W., Chiang, W., and Wang, C., "Endochronic Analysis for Rate-dependent Elasto-plastic Deformation",, International Journal of Solids and Structures, Vol. 36, pp.3215-3237, 1999.
• 20. Prager, W., "A New Method ot Analyzıng Stresses and Strains in Work-Hardening Plastic Solids", Journal of Applied mechanics, Vol.23, pp. 493-496, 1956.
• 21. Ziegler, H., "A Modification of Prager's Hardening Rule", Quarterly of Applied Mathematics, Vo1.17, pp. 55-65.
• 22. Besseling, J.F., "A Theory of Elastic, Plastic, and Creep Deformation of an Initially Isotropic Material Showing Anisotropic Strain-Hardening, Creep Recovery, and Secondary Creep", Journal of Applied Mechanics, Vol. 17, pp. 529- 536,1958.
• 23. Lamda, H.S., Sidebottom, O.M., "Cyclic Plasticity for Nonproportional Paths: Part I-Cyclic Hardening, Erasure of Memory, and Subsequent Strain Hardening Experiments", Journal of Engineering Materials and Technology, Vol. 100, pp. 96-104,1978.
• 24. Lamda, H.S., Sidebottom, O.M., "Cyclic Plasticity for Nonproportional Paths: Part II-Comparisons with Predictions of Three Incremental Plasticity Models", Journal of Engineering Materials and Technology, Vol. 100, pp. 104-111,1978.
• 25. McDowell, D.L., Socie, D.F, and Lamda, S.H., "Multiaxial Nonproportional Cyclic Deformation", Low-cycle Fatigue and Life Prediction, ASTM STP 770, C. Amzallag, B.N. Leis, and P. Rabbe, Eds, American Society for Testing and Materials, Philadelphia, pp. 500-518, 1980.
• 26. Chaboche, J.L., Nouailhas, D., "Constitutive Modeling of Ratcheting Effects, Part I: Experimental Facts and Properties of the Classical Models ", Journal of Engineering Materials and Technology, Vol. 111, pp. 384- 392,1989.
• 27. Chaboche, J.L., Nouailhas, D., "Constitutive Modeling of Ratcheting Effects, Part II: Possibilities of Some Additional Kinematic Rules", Journal of Engineering Materials and Technology, Vol. 111, pp. 409-416,1989.
• 28. Moosbrugger, J.C., McDowell, D.L., "On a Class of Kinematic Hardening Rules for Nonproportional Cyclic Plasticity", Journal of Engineering Materials and Technology, Vol. 111, pp. 87-98,1989.
• 29. Jiang, Y., "Cyclic Plasticity with an Emphasis on Ratcheting", Doktora Tezi, University of Illinois at Urbana-Champaign, 1993.
• 30. Langlais, T., "Computational Methods for Multiaxial Fatigue Analysis", Doktora Tezi, University of Minnesota, 1999.
• 31. Mroz, Z., "An Attempt to Describe the Behavior of Metals under Cyclic Loads Using a More General Workhardening Model", Acta Mechanica, Vol.7, No. 2-3, pp. 199-212, 1969.
• 32. Garud, Y.S., "Multiaxial Fatigue of Metals", Doktora Tezi, Stanford University, 1981.
• 33. Chu, C., "A Three-Dimensional Model of Anisotropic Hardening in Metals and Its Application to the Sheet Metal Forming", Journal of Mechanics and Physics of Solids, Vol. 32, No. 3, pp. 197-212, 1984.
• 34. Hong, N., Shaobo, L., "Biaxial Stress Fatigue Life Prediction by Local Strain Method", International Journal of Fatigue, Vol. 19, No.6, pp.517-522, 1997.
• 35. Shang, D., Wang, D., Yao, W., " A Simple Approach to the Description of Multiaixial Cyclic Stress — Strain Relationship", International Journal of Fatigue, Vol.22, pp. 251- 256, 2000.
• 36. Hassan, T., Kyriakides, S., "Ratcheting in Cyclic Plasticity, Part I: Uniaxial Behavior", International Journal of Plasticity, Vol. 8, pp.91- 116, 1992.
• 37. Hassan, T., Kyriakides, S., "Ratcheting in Cyclic Plasticity, Part II: Multiaxial Behavior", International Journal of Plasticity, Vol. 8, pp.11- 146, 1992. \
• 38. Tipton, S.M, Bannantine J.A., "Inelastic Stress-Strain Predictions for Multiaxial Fatigue Evaluations", Advances in Multiaxial Fatigue, ASTM STP 1191, D.L. McDowell and R.Ellis, Eds., American Society for Testing and Materials, Philadelphia, Dp. 273-297, 1993.
• 39. Jiang, Y., Kurath, P., "A Theoretical Evaluation of Plasticity Hardening Algorithms for Nonproportional Loading", Acta Mechanica, Vol.118, pp. 213-234, 1996.
• 40. Jiang, Y., Kurath, P., "Characteristics of the Armstrong-Frederick Type Plasticity Models", International Journal of Plasticity, Vol.12, No.3, pp. 387-415, 1996.
• 41. McDowell, D.L., "Stress State Dependence of Cyclic Ratcheting Behavior of two Railway Steels", International Journal of Plasticity, Vol. 11, No.4, pp.397-421, 1995.
• 42. Bari, S, "Constitutive Modeling for Cyclic Plasticity and Ratcheting", Doktora Tezi, North Carolina State University, 2000.
• 43. Jiang, Y., Sehitoglu, H., "Cyclic Ratcheting of 1070 Steel Under Multiaxial Stress States", International Journal of Plasticity, \ton°, No.5, pp. 579-608, 1994.
• 44. Dafalias, Y.F., Popov, E.P., "A Model of Nonlinearly Hardening Materials for Complex Loading", Acta Mechanica, Vo1.21, No. 2-3, pp. 173-192, 1975.
• 45. Krieg, R.D., "A Practical Two Surface Plasticity Theory", Journal of Applied Mechanics, 641- 646, 1975.
• 46. Tseng, N.T., Lee, G.C., "Simple Plasticity Model of the Two-Surface Type", Journal of Engineering Mechanics, Vol.109, No.3, pp. 795- R10.1983.
• 47. McDowell, D.L., "A Two Surface Model for Transient Nonproportional Cyclic Plasticity, Pan I: Development of Appropriate Equations", Journal of Applied Mechanics, Yol. 52, pp. 298- 302, 1985.
• 48. McDowell, D.L., "A Two Surface Model for Transient Nonproportional Cyclic Plasticity, Part II: Comparison of Theory with Experiments", Journal of Applied Mechanics, Vol. 52, pp. 303- 308, 1985.
• 49. Bari, S, Hassan, T., "Kinematic Hardening Rules in Uncoupled Modeling for Multiaxial Ratcheting Simulation", International Journal of Plasticity, Vol. 15, pp. 182-198, 1999.
• 50. Bari, S, Hassan, T., "Anatomy of Coupled Constitutive Models for Ratcheting Simulation", International kurna! of Plasticity, Vol. 16, pp. 381-409, 2000.
• 51. Bower, A.F., "Cyclic Hardening Properties of Hard-Drawn Copper and Rail Steel", Journal of Mechanics and Physics of Solids, Vol.37, No.4, pp.455-470, 1989.
• 52. Chaboche, J.L., Rousselier, G., "On the Plastic and Viscoplastic Constitutive Equations, Pan I: Rules Developed with Internal Variable Concept", Journal of Pressure Vessel Technology, Vol. 105, pp. 153-158, 1983.
• 53. Chaboche, IL., Rousselier, G., "On the Plastic and Viscoplastic Constitutive Equations, Part II: Application of Internal Variable Concepts to the 316 Stainless Steels", Journal of Pressure Vessel Technology, Vol. 105, pp. 159-164, 1983.
• 54. Chaboche, J.L., "Time-Independent Constitutive Theories for Cyclic Plasticity", International Journal of Plasticity, Vol. 2, No.2, pp. 149-188, 1986.
• 55. Ohno, N., Wang, J.D., " Two Equivalent Forms of Nonlinear Kinematic Hardening: Application to Non- Isothermal Plasticity" International Journal of Plasticity, Vol. 7, pp. 637-650, 1991.
• 56. Ohno, N., Wang, J.D., "Kinematic Hardening Rules with Critical State of Dynamic Recovery, Part I: Formulation and Basic Features for Ratcheting Behavior", International Journal of Plasticity, Vol. 9, pp. 375-390-650, 1993.
• 57. Ohno, N., Wang, J.D., "Kinematic Hardening Rules with Critical State of Dynamic Recovery, Part II: Applications to Experiments of Ratcheting Behavior", International Journal of Plasticity, Vol. 9, pp. 391-403, 1993.
• 58. Chaboche, J.L., "On Some Modifications of Kinematic Hardening to Improve the Description of Ratcheting Effects", International Journal of Plasticity, Vol. 7, pp. 641-678, 1991.
• 59. Jiang, Y., Sehitoglu, H., "Multiaxial Cyclic Ratcheting Under Multiple Step Loading", International Journal of Plasticity, Vol.10, No.8, pp. 849-870, 1994.
• 60. Jiang, Y., Sehitoglu, H., "Comments on Mroz Multiple Surface Type Plasticity Models", International Journal of Solids and Structures, Vol.33, No.7, pp.1053-1068, 1996.
• 61. Jiang, Y., Sehitoglu, H., "Modeling of Cyclic Ratcheting Plasticity, Part I: Development of Constitutive Relations", Journal of Applied Mechanics, Vol.63, pp.720-725, 1996.
• 62. Jiang, Y., Sehitoglu, H., "Modeling of Cyclic Ratcheting Plasticity, Part II: Comparison of Model Simulations With Experiments", Journal of Applied Mechanics, Vo1.63, pp.726-733, 1996.
• 63. Ristinmaa, M., "Cyclic Plasticity Model Using One Yield Surface Only", International Journal of Plasticity, Vol. 11, No.2, pp. 163-181, 1995.
• 64. Xia, Z., Ellyin, F., "A Constitutive Model with Capability to Simulate Complex Multiaxial Ratcheting Behavior of Materials", International Journal of Plasticity, Vol. 13, No.1-2, pp.127- 142, 1997.
• 65. Chaboche, J.L., Jung, O., "Application of a Kinematic Hardening Viscoplasticity Model with Thresholds to the Residual Stress Relaxation", International Journal of Plasticity, Vol. 13, No.10, pp. 785-807, 1998.
• 66. Basuroychowdhury, I.N., Voyiadjis, G.Z., "A Multiaxial Cyclic Plasticity Model for Nonproportional Loading Cases", International Journal of Plasticity, Vol. 14, No.9, pp.854-870, 1998.
• 67. Wang, H., Barkey, M.E. "A Strain Space Nonlinear Kinematic Hardening/ Softening Plasticity Model" International Journal of Plasticity, Vol. 15, pp. 755-777, 1999.