Abstract
The ratcheting response of 316 stainless steel samples at the vicinity of notch roots under single- and multi-step loading conditions is evaluated. Multi-step tests were conducted to examine local ratcheting at different low–high–high and high–low–low loading sequences. The stress levels over loading steps and their sequences highly influenced ratcheting magnitude and rate. The change of stress level from low to high promoted ratcheting over proceeding cycles while ratcheting strains dropped in magnitude for opposing sequence where stress level dropped from high to low. Local ratcheting strain values at the vicinity of notch root were found noticeably larger than nominal ratcheting values measured at farer distances from notch edge through use of strain gauges. Ratcheting values in both mediums of local and nominal were promoted as notch diameter increased. To assess progressive ratcheting response and stress relaxation concurrently, the Ahmadzadeh-Varvani (A-V) kinematic hardening rule was coupled with Neuber’s rule enabling to calculate local stress at notch root of steel samples. Local stress/strain values were progressed at notch root over applied asymmetric stress cycles resulting in ratcheting buildup through A-V model. The relaxation of stress values at a given peak-valley strain event was governed through the Neuber’s rule. Experimental ratcheting data were found agreeable with those predicted through the coupled framework.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- \(\bar{b}\) :
-
Internal variable of A-V model
- d :
-
Circular notch diameter
- \({\text{d}}\bar{\varepsilon }\) :
-
Total strain increment tensor
- \({\text{d}}\bar{\varepsilon }_{\text{e}}\) :
-
Elastic strain increment tensor
- \({\text{d}}\bar{\varepsilon }_{\text{p}}\) :
-
Plastic strain increment tensor
- \({\text{d}}\bar{\sigma }\) :
-
Stress increment tensor
- \({\text{d}}\bar{s}\) :
-
Deviatoric stress increment tensor
- dp :
-
Increment of equivalent plastic strain
- e :
-
Nominal strain
- \(E\) :
-
Elastic modulus
- \(k, m\) :
-
Material constants
- \(K_{t}\) :
-
Stress concentration factor
- \(k^{\prime}\) :
-
Cyclic strength coefficient
- \(\bar{n}\) :
-
Unit normal vector to yield surface
- \(n^{\prime}\) :
-
Cyclic strain hardening exponent
- p :
-
Accumulated plastic strain
- R :
-
Stress ratio
- S :
-
Nominal stress
- X :
-
Distance from notch root
- α :
-
Axial backstress component
- \(\bar{\alpha }\) :
-
Backstress tensor
- \(\sigma_{\text{L}} , \varepsilon_{\text{L}}\) :
-
Local stress and strain components
- \(\sigma_{y}\) :
-
Yield strength
- \(\sigma_{\text{ult}}\) :
-
Ultimate strength
- \(\gamma_{1} , \gamma_{2} , C, \delta\) :
-
Coefficients of A-V model
References
A. Varvani-Farahani, A. Nayebi, Fatigue Fract. Eng. Mater. Struct. 41 (2018) 503–538.
D. Yu, G. Chen, W. Yu, D. Li, X. Chen, Int. J. Plast. 28 (2012) 88–101.
W. Wang, X. Zheng, J. Yu, W. Lin, C. Wang, J. Xu, Mater. High Temp. 32 (2017) 172–178.
X. Zheng, J. Wang, J. Gao, L. Ma, J. Yu, J. Xu, Mater. High Temp. 35 (2018) 482–489.
G. Kang, Q. Kan, J. Zhang, Y. Sun, Int. J. Plast. 22 (2006) 858–894.
S.G. Hong, S.B. Lee, Int. J. Fatigue 26 (2004) 899–910.
V.A. Strizhalo, A.I. Zinchenko, Strength Mater. 7 (1975) 420–424.
G.S. Pisarenko, V.A. Strizhalo, V.I. Skripchenko, Strength Mater. 19 (1987) 300–306.
G.S. Pisarenko, V.A. Strizhalo, V.I. Skripchenko, Strength Mater. 19 (1987) 307–312.
W. Hu, C.H. Wang, S. Barter, Analysis of cyclic mean stress relaxation and strain ratchetting behaviour of aluminium 7050, DSTO-RR-0153, Aeronautical and Maritime Research Laboratory, Melbourne, Australia, 1999.
C.H. Wang, L.R.F. Rose, Mech. Mater. 30 (1998) 229–241.
S.M. Rahman, T. Hassan, in: ASME 2005 Pressure Vessels and Piping Conference, American Society of Mechanical Engineers, Denver, Colorado, USA, 2005, pp. 421–427.
M. Firat, Mater. Des. 32 (2011) 3876–3882.
M.E. Barkey, Calculation of notch strains under multiaxial nominal loading, University of Illinois at Urbana-Champaign, Illinois, USA, 1993.
C.H. Lee, V.N. Van Do, K.H. Chang, Int. J. Plast. 62 (2014) 17–33.
K. Kolasangiani, K. Farhangdoost, M. Shariati, A. Varvani-Farahani, Int. J. Mech. Sci. 144 (2018) 24–32.
A. Shekarian, A. Varvani-Farahani, Fatigue Fract. Eng. Mater. Struct. 42 (2019) 1402–1413.
G.R. Ahmadzadeh, A. Varvani‐Farahani, Fatigue Fract. Eng. Mater. Struct. 36 (2013) 1232–1245.
H. Neuber, J. Appl. Mech. 28 (1961) 544–550.
C. Liu, S. Shi, Y. Cai, X. Chen, Int. J. Press. Vessels Piping 169 (2019) 160–169.
X. Chen, R. Jiao, K.S. Kim, Int. J. Plast. 21 (2005) 161–184.
A. Varvani‐Farahani, Fatigue Fract. Eng. Mater. Struct. 40 (2017) 882–893.
S.M. Hamidinejad, A. Varvani-Farahani, Mater. Des. 85 (2015) 367–376.
G.R. Ahmadzadeh, A. Varvani-Farahani, Mech. Mater. 101 (2016) 40–49.
G.R. Ahmadzadeh, S.M. Hamidinejad, A. Varvani-Farahani, J. Pressure Vessel Technol. 173 (2015) 031001.
G.R. Ahmadzadeh, A. Varvani-Farahani, Mater. Des. 51 (2013) 231–241.
P.J. Armstrong, C.O. Fredrick, A mathematical representation of the multiaxial Bauschinger effect, CEGB, Report RD/B/N731 Berkeley Nuclear Laboratories, Berkeley, Gloucestershire, UK, 1966.
M. Rezaiee-Pajand, S. Sinaie, Int. J. Solids Struct. 46 (2009) 3009–3017.
W. Ramberg, W.R. Osgood, Description of stress-strain curves by three parameters, NACA Technical Note 902, NASA Scientific and Technical Information Facilities, Washington, USA, 1943.
Acknowledgements
Authors wish to acknowledge the financial support by the Natural Sciences and Engineering Research Council (NSERC) of Canada.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Shekarian, A., Varvani-Farahani, A. Ratcheting behavior of notched stainless steel samples subjected to asymmetric loading cycles. J. Iron Steel Res. Int. 28, 86–97 (2021). https://doi.org/10.1007/s42243-020-00465-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s42243-020-00465-2