Influence of Hardening on the Cyclic Plastic Zone Around Crack Tip in Pure Copper CT Specimens

Document Type: Original Article

Authors

Mechanical Engineering Department, Bu-Ali Sina University, Hamedan, Iran.

Abstract

Under cyclic loading, the plastic zone becomes complicated during unloading. The energy-absorbing cyclic plastic zone is a stimulant for crack growth and can be a criterion for determining the damage around the fatigue crack tip. Presenting analytical models for determining the shape and size of the plastic zone often makes restrictive assumptions such as elastic-perfectly plastic response. In this research, the effects of non-linear kinematic hardening behavior of pure copper on the cyclic plastic reaction of the crack tip in different conditions were investigated. Chaboche nonlinear material  model was used to determine the hardening parameters. According to the numerical results, the cyclic plastic zone around the crack tip was constant in the same load range but load ratio had a slight effect on this zone. Moreover, presence of the kinematic hardening in the cyclic loading caused reverse plastic zone to be predicted smaller than analytical model.  According to the results, for materials such as pure copper with kinematic hardening behavior, the cyclic plastic zone increases with increase in the crack length. Therefore, the cyclic plastic zone, as well as other parameters in the fracture mechanics can be a proper criterion for fatigue crack growth studies.

Keywords


[1] P. Paris, F. Erdogan, A critical analysis of crack propagation laws. J. Basic. Eng., 85(4) (1963) 528-533.
[2] S.K. Paul, Numerical models of plastic zones and associated deformations for a stationary crack in a C (T) specimen loaded at different R-ratios, Theo, Appl. Frac. Mech., 84 (2016) 183-191.
[3] S. Mishra, B. Parida, A study of crack-tip plastic zone by elastoplastic finite element analysis. Eng. Frac. Mech., 22(6) (1985) 951-956.
[4] Y. Iino, Fatigue crack propagation work coefficienta material constant giving degree of resistance to fatigue crack growth, Eng. Frac. Mech., 12(2) (1979) 279-299.
[5] R. McClung, Crack closure and plastic zone sizes in fatigue, Fatig. Frac. Eng. Mat. Struct., 14(4) (1991) 455-468.
[6] G.R. Irwin, Plastic zone near a crack and fracture toughness, Proceedings, 7th sagamore conference, IV (1960) 63-78.
[7] D.S. Dugdale, Yielding of steel sheets containing slits, J. Mech. Phys. Sol., 8(2) (1960) 100-104.
[8] C. Jingjie, H. Yi, D. Leilei, L. Yugang, A new method for cyclic crack-tip plastic zone size determination under cyclic tensile load, Eng. Frac. Mech., 126 (2014) 141-154.
[9] B.O. Chikh, A. Imad, M. Benguediab, Influence of the cyclic plastic zone size on the propagation of the fatigue crack in case of 12NC6 steel, Comput. Mat. Sc., 43(4) (2008) 1010-1017.
[10] S. Kwun, M. Fine, Dependence of cyclic plastic work of fatigue crack propagation on K in MA87 A1 P/M alloy, Scripta Metallurgica, 14(1) (1980) 155-158.
[11] J. Rice, Mechanics of crack tip deformation and extension by fatigue, in Fatigue crack propagation, ASTM International, (1967).
[12] R.H. Hertzberg, R.P. Vinci,J.L. Hertzberg, Deformation and fracture mechanics of engineering materials, 5 ed. John Wiley and Sons, (2012).  
[13] R. Seifi, R. Bahrami, Numerical modeling the effects of overloading and underloading in fatigue crack growth, Eng. Fail. Anal., 17(6) (2010) 1475-1482.
[14] Y. Jiang, J. Zhang, Benchmark experiments and characteristic cyclic plasticity deformation. Int. J. Plast., 24(9) (2008) 1481-1515.
[15] S.K. Paul, S. Sivaprasad, S. Dhar, M. Tarafder, S. Tarafder, Simulation of cyclic plastic deformation response in SA333 CMn steel by a kinematic hardening mode, Comput. Mat. Sci., 48(3) (2010) 662-671.
[16] S.K. Paul, S. Tarafder, Cyclic plastic deformation response at fatigue crack tips, Int. J. Press. Ves. Pip., 101 (2013) 81-90.
[17] J.L. Chaboche, Time-independent constitutive theories for cyclic plasticity, Int. J. Plast., 2(2) (1986) 149-188.
[18] C.O. Frederick, P. Armstrong, A mathematical representation of the multiaxial Bauschinger effect. Mater. High. Temp., 24(1) (2007) 1-26.
[19] N. Ohno, J.D. Wang, Kinematic hardening rules with critical state of dynamic recovery, part I: formulation and basic features for ratchetting behavior, Int. J. Plast., 9(3) (1993) 375-390.
[20] W. Prager, Recent developments in the mathematical theory of plasticity, J. Appl. Physic., 20(3) (1949) 235-241.
[21] S. Bari, T. Hassan, Anatomy of coupled constitutive models for ratcheting simulation, Int. J. Plast., 16(3-4) (2000) 381-409.
[22] E606/E606M-12, Standard Test Method for Strain-Controlled Fatigue Testing, ASTM International, West  Conshohocken (PA USA): Book of Standards, (2012).
[23] E. Gdoutos, Solid mechanics and its applicationsfracture mechanics, Springer, The Netherlands, (2005).
[24] ASTM, E647-08, Standard test method for measurement of fatigue crack growth rates, ASTM International: West Conshohocken, PA, (2008).