Investigation of Notch Root Strain Behaviors Under Combined Loadings

Abstract

Notches are the stress raiser regions. Along the notch section, not only the stress distribution becomes non-uniform, but also the stress level reaches the maximum value. These geometrical disorders can be undesirable such as casting cavity but sometimes these disorders are created deliberately for assembly process such as keyway holes or shaft steps. Because of the necessity of these notches. This is important to understand material behavior along this region.

In this study, three different strain paths were generated by the cyclic tensile and torsional loadings and strains of the notch root of a shaft which contains circumferential notch, were investigated through the finite element method (FEM). MSC. Marc commercial program have been used in this study as finite element software. The results have been obtained for kinematic hardening rules and compared with the experimental results obtained from literature studies. Also in this study, a subroutine file was used to calculate the Chaboche kinematic hardening rule parameters according to Swift equation.

Keywords

• Cyclic Plasticity,Kinematic Hardening,Finite Element Method

References

1. [1]. H. Neuber, ‘’Theory of stress concentration for shear strained prismatic bodies with arbitrary stress – strain law,’’ Journal of Applied Mechanics, vol 28, pp. 544-550, Dec. 1961.
2. [2]. H. J. Crews, ‘’Elastoplastic stress – strain behaviour at notch roots in sheet speciments under constant – amplitude loading,’’ Langley Research center, NASA Technical Report, D-5253, 1969.
3. [3]. Barkey, M., E., ‘’Calculation of notch strains under multiaxial nominal loading,’’Ph.D. thesis, University of Illinois, College of Engineering at Urbana-Champaign, Oct. 1993.
4. [4]. M. Hoffmann,’’Ein naeherungsverfahren zur ermittlung mehrachsig elastisch-plastischer kerbbeanspruchungen’’, M.Eng thesis, Darmstadt Technical University, Germany, 1985.
5. [5]. V.B. Koettgen, M. Schoen, and T. Seeger,’’Application of multiaxial load notch strain approximitation procedure to autofrettage of pressurized components,’’American Society for Testing and Materials, pp. 375-396, 1993.
6. [6]. A.A. Moftakhar,’’Calculation of time – independent and time – dependent strains and stresses in notches,’’ M.Eng. thesis, Univercity of Waterloo,1994.
7. [7]. M.Firat,’’Cyclic plasticity modeling and finite element analysis of a circumferentially notched round bar under combined axial and torsion loadings’’, Material and Design, vol. 34, pp 842-852, Feb. 2012.
8. [8]. M. Firat, “A numerical analysis of combined bending – torsion fatigue of SAE notched shaft,” Finite Elemenst in Analysis and Design, vol. 54, pp. 16-27, 2012.

9. [9]. G. E. Dieter, Mechanical Metalurgy, SI metric ed., United Kingdom, 1988.
10. [10]. M. Firat, U. Kocabicak,’’Analytical durability modeling and evaluation – complementary techniques for physical testing of automotive components,’’ Engineering Failure Analysis, vol. 11, pp. 655–674, 2004.
11. [11]. M. Firat, U. Kocabicak,’’A simple approach for multiaxial fatigue damage prediction based on FEM post-processing,’’ Materials and Design, vol. 25, pp. 73–82, 2003.
12. [12]. M.Firat,’’U-channel forming analysis with an emphasis on springback deformation,’’ Material and Design, vol. 28, pp 147-154, Feb. 2007.
13. [13]. Y. K. Lin, K. M. Hsu and P.K. Lee, ‘’The application of flow stress flow stress model to sheet metal forming simulation,’’ Iron & Steel Research & Development Department, China Steel Technical Report, No 23, pp.31-35, 2010.
14. [14]. Y. Jiang and H. Sehitoglu,’’ Modeling of cyclic ratchetting plasticity, part I: development of constitutive relations,’’ Journal of Applied Mechanics, vol. 63, pp. 720-725, Sept 1996.
15. [15]. Y. Jiang and H. Sehitoglu,’’ Modeling of cyclic ratchetting plasticity, part II: comparison of model simulations with experiments,’’ Journal of Applied Mechanics, vol. 63, pp. 726-733, Sept 1996.
16. [16]. N. Ohno and J. D.Wang,“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.
17. [17]. J. Lemaitre and J. L. Chaboche, “Mechanics of Solid Materials”, Cambridge University Press, New York, 1990.