Top

Journal of Materials Engineering and Performance

Published in:

12-03-2018

An improved Armstrong–Frederick-Type Plasticity Model for Stable Cyclic Stress–Strain Responses Considering Nonproportional Hardening

Authors: Jing Li, Zhong-ping Zhang, Chun-wang Li

Published in: Journal of Materials Engineering and Performance | Issue 4/2018

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

This paper modified an Armstrong–Frederick-type plasticity model for investigating the stable cyclic deformation behavior of metallic materials with different sensitivity to nonproportional loadings. In the modified model, the nonproportionality factor and nonproportional cyclic hardening coefficient coupled with the Jiang–Sehitoglu incremental plasticity model were used to estimate the stable stress–strain responses of the two materials (1045HR steel and 304 stainless steel) under various tension–torsion strain paths. A new equation was proposed to calculate the nonproportionality factor on the basis of the minimum normal strain range. Procedures to determine the minimum normal strain range were presented for general multiaxial loadings. Then, the modified model requires only the cyclic strain hardening exponent and cyclic strength coefficient to determine the material constants. It is convenient for predicting the stable stress–strain responses of materials in engineering application. Comparisons showed that the modified model can reflect the effect of nonproportional cyclic hardening well.

previous article Assessing Constitutive Models for Prediction of High-Temperature Flow Behavior with a Perspective of Alloy Development

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

D.F. Socie and G.B. Marquis, Multiaxial Fatigue, Society of Auto Engineers Inc, Warrendale, 2000CrossRef

D.F. Socie, Multiaxial Fatigue Damage Models, J. Eng. Mater. Technol. (Trans. ASME), 1987, 109, p 293–298CrossRef

N. Shamsaei, A. Fatemi, and D.F. Socie, Multiaxial Cyclic Deformation and Non-proportional Hardening Employing Discriminating Load Paths, Int. J. Plast., 2010, 26, p 1680–1701CrossRef

N. Shamsaei and A. Fatemi, Effect of Microstructure and Hardness on Non-proportional Cyclic Hardening Coefficient and Predictions, Mater. Sci. Eng. A, 2010, 527, p 3015–3024CrossRef

J.L. Chaboche, A Review of Some Plasticity and Viscoplasticity Constitutive Theories, Int. J. Plast., 2008, 24, p 1642–1693CrossRef

S. Bari and T. Hassan, Anatomy of Coupled Constitutive Models for Ratcheting Simulation, Int. J. Plast., 2000, 16, p 381–409CrossRef

P.J. Armstrong, and C.O. Frederick, A Mathematical Representation of the Multiaxial Bauschinger Effect. Report RD/B/N 731, Central Electricity Generating Board, 1966

J.L. Chaboche, On some Modifications of Kinematic Hardening to Improve the Description of Ratcheting Effects, Int. J. Plast., 1991, 7, p 661–678CrossRef

J.L. Chaboche, Modeling of Ratchetting: Evaluation of Various Approaches, Eur. J. Mech. A Solids, 1994, 13, p 501–518

10.

N. Ohno and J.D. Wang, Kinematic Hardening Rules with Critical State of Dynamic Recovery, Part I: Formulation and Basic Features for Ratchetting Behavior, Int. J. Plast., 1993, 9, p 375–390CrossRef

11.

N. Ohno and J.D. Wang, Kinematic Hardening Rules with Critical State of Dynamic Recovery, Part II: Application to Experiments of Ratchetting Behavior, Int. J. Plast., 1993, 9, p 391–403CrossRef

12.

Y. Jiang and H. Sehitoglu, Modeling of Cyclic Ratchetting Plasticity, Part I: Development of Constitutive Relations, J. Appl. Mech. (Trans. ASME), 1996, 63, p 720–725CrossRef

13.

Y. Jiang and H. Sehitoglu, Modeling of Cyclic Ratchetting Plasticity, Part II: Comparison of Model Simulations with Experiments, J. Appl. Mech. (Trans. ASME), 1996, 63, p 726–733CrossRef

14.

Z. Mróz, On the Description of Anisotropic Work Hardening, J. Mech. Phys. Solids, 1967, 15, p 163–175CrossRef

15.

Y.S. Garud, A New Approach to the Evaluation of Fatigue Under Multiaxial Loadings, J. Eng. Mater. Technol. (Trans. ASME), 1981, 103, p 118–125CrossRef

16.

D.L. McDowell, A Two Surface Model for Transient Nonproportional Cyclic Plasticity, Part I: Development of Appropriate Equations, J. Appl. Mech. (Trans. ASME), 1985, 52, p 298–302CrossRef

17.

D.L. McDowell, A Two Surface Model for Transient Nonproportional Cyclic Plasticity, Part II: Comparison of Theory with Experiments, J. Appl. Mech. (Trans. ASME), 1985, 52, p 303–308CrossRef

18.

D.L. McDowell, An Evaluation of Recent Developments in Hardening and Flow Rules for Rate-Independent Non-proportional Cyclic Plasticity, J. Appl. Mech. (Trans. ASME), 1987, 54, p 323–334CrossRef

19.

Y. Jiang and P. Kurath, Characteristics of the Armstrong–Frederick Type Plasticity Models, Int. J. Plasticity, 1996, 12, p 387–415CrossRef

20.

J.L. Chaboche, K. Dang Van, G. Cordier, Modelization of the Strain Memory Effect on the Cyclic Hardening of 316 Stainless Steel. In: Structural Mechanics in Reaktor Technology, in Transaction of 5th International Conference on Structural Mechanics in Reactor Technology, vol L11/3 (Berlin, 1979).

21.

R. Döring, J. Hoffmeyer, T. Seeger, M. Vormwald, A short crack growth model for the prediction of fatigue lives under multiaxial nonproportional loading, in 6th International Conference on Biaxial/Multiaxial Fatigue and Fracture, Lissabon (2001), pp. 571–578

22.

J. Hoffmeyer, R. Döring, T. Seeger, and M. Vormwald, Deformation Behaviour, Short Crack Growth and Fatigue Lives Under Multiaxial Nonproportional Loading, Int. J. Fatigue, 2006, 28, p 508–520CrossRef

23.

R. Döring, J. Hoffmeyer, M. Vormwald, and T. Seeger, A Plasticity Model for Calculating Stress–Strain Sequences Under Multiaxial Nonproportional Cyclic Loading, Comput. Mater. Sci., 2003, 28, p 587–596CrossRef

24.

Y. Jiang and P. Kurath, Nonproportional Cyclic Deformation: Critical Experiments and Analytical Modeling, Int. J. Plast., 1997, 13, p 743–763CrossRef

25.

E. Tanaka, A Nonproportionality Parameter and a Cyclic Viscoplastic Constitutive Model Taking into Account Amplitude Dependence and Memory Effects of Isotropic Hardening, Eur. J. Mech. A Solids, 1994, 13, p 155–173

26.

Y. Jiang and P. Kurath, A Theoretical Evaluation of Plasticity Hardening Algorithms for Nonproportional Loadings, Acta Mech., 1996, 118, p 213–234CrossRef

27.

S.H. Doong, D.F. Socie, and I.M. Robertson, Dislocation Substructures and Nonproportional Hardening, J. Eng. Mater. Technol., 1990, 112, p 456–464CrossRef

28.

E. Tanaka, S. Murakami, and M. Ooka, Effects of Strain Path Shapes on Nonproportional Cyclic Plasticity, J. Mech. Phys. Solids, 1985, 33, p 559–575CrossRef

29.

G.Z. Voyiadjis and W. Huang, A Modeling of Crystal Plasticity with Backstress Evolution, Eur. J. Mech. A Solids, 1996, 15, p 553–573

30.

S. Krishna, T. Hassan, I.B. Naceur, K. Sai, and G. Cailletaud, Macro versus microscale constitutive models in simulating proportional and nonproportional cyclic and ratcheting responses of stainless steel 304, Int. J. Plast., 2009, 25, p 1910–1949CrossRef

31.

M.A. Meggiolaro and J.T.P. Castro, Prediction of Non-proportionality Factors of Multiaxial Histories Using the Moment of Inertia Method, Int. J. Fatigue, 2014, 61, p 151–159CrossRef

32.

J. Li, C.W. Li, Y.J. Qiao et al., Fatigue Life Prediction for Some Metallic Materials Under Constant Amplitude Multiaxial Loading, Int. J. Fatigue, 2014, 68, p 10–23CrossRef

33.

K. Kanazawa, K.J. Miller, and M.W. Brown, Low Cycle Fatigue Under out of Phase Loading Conditions, ASME J. Eng. Mater. Techol., 1977, 99, p 222–228CrossRef

34.

A. Benallal and D. Marquis, Constitutive Equations for Non-proportional Cyclic Elasto-Viscoplasticity, ASME J. Eng. Mater. Tech., 1987, 109, p 326–336CrossRef

35.

X. Chen, Q. Gao, and X.F. Sun, Low Cycle Fatigue Under Nonproportional Loading, Fatigue Fract. Eng. Mater. Struct., 1996, 19, p 839–854CrossRef

36.

J. Mei and P. Dong, A new path-dependent fatigue damage model for nonproportional multiaxial loading, Int. J. Fatigue, 2016, 90, p 210–221CrossRef

37.

T. Itoh, M. Sakane, M. Ohnami, and D.F. Socie, Nonproportional Low Cycle Fatigue Criterion for Type 304 Stainless Steel, J. Eng. Mater. Technol. (Trans. ASME), 1995, 117, p 285–292CrossRef

38.

T. Itoh, X. Chen, T. Nakagawa, and M. Sakane, A Simple Model for Stable Cyclic Stress-Strain Relationship of Type 304 Stainless Steel Under Nonproportional Loading, J. Eng. Mater. Technol. (Trans. ASME), 2000, 122, p 1–9CrossRef

39.

A. Fatemi, Fatigue and Deformation Under Proportional and Nonproportional Biaxial Loading. Ph.D. dissertation, University of Iowa, 1985.

40.

Y.Y. Jiang, W. Ott, C. Baum, M. Vormwald, and H. Nowack, Fatigue Life Predictions by Integrating EVICD Fatigue Damage Model and an Advanced Cyclic Plasticity Theory, Int. J. Plast., 2009, 25, p 780–801CrossRef

41.

M.V. Borodii and S.M. Shukaev, Additional Cyclic Strain Hardening and its Relation to Material Structure, Mechanical Characteristics, and Lifetime, Int. J. Fatigue, 2007, 29, p 1184–1191CrossRef

42.

D.F. Mo, G.Q. He, Z.Y. Zhu et al., Fatigue Fractures and Mechanism of Al-7Si-0.3Mg Cast Alloy Under Nonproportional Loadings, Acta Metall. Sin., 2009, 45, p 861–865 ((in Chinese))

Title: An improved Armstrong–Frederick-Type Plasticity Model for Stable Cyclic Stress–Strain Responses Considering Nonproportional Hardening
Authors: Jing Li
Zhong-ping Zhang
Chun-wang Li
Publication date: 12-03-2018
Publisher: Springer US
Published in: Journal of Materials Engineering and Performance / Issue 4/2018
Print ISSN: 1059-9495
Electronic ISSN: 1544-1024
DOI: https://doi.org/10.1007/s11665-018-3271-4

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Other articles of this Issue 4/2018

Effect of Rolling Temperature on the Microstructure and Tensile Properties of 47Zr-45Ti-5Al-3V Alloy

Hydrogen Embrittlement Susceptibility and Safety Control of Reheated CGHAZ in X80 Welded Pipeline

A Comparative Study of Fracture Toughness at Cryogenic Temperature of Austenitic Stainless Steel Welds

Investigation of the Microstructural Changes and Hardness Variations of Sub-Zero Treated Cr-V Ledeburitic Tool Steel Due to the Tempering Treatment

Effect of Al-Si Coating on Weld Microstructure and Properties of 22MnB5 Steel Joints for Hot Stamping

Microstructural Evolution and the Precipitation Behavior in X90 Linepipe Steel During Isothermal Processing

Premium Partners