Experimental and Theoretical Assessment of Mode II Fracture Toughness for Cracked Ductile Specimens with High Strain-Hardening

Document Type : Research Article

Authors

1 IUST

2 Faculty of New Science and Technologies, University of Tehran

Abstract

In this research, the mode II fracture toughness of O-notched diagonally loaded square plate samples with pre-existing cracks which are made of stainless steel 316L with specifications of highly ductile behavior and great strain hardening is investigated theoretically and experimentally. For this purpose, several fracture tests are carried out on the pre-cracked specimens to determine the fracture toughness experimentally. The experimental observations and the load-displacement curves obtained from the fracture tests illustrate that the pre-cracked specimens undergo large plastic deformations at the onset of crack propagation. Afterward, the fictitious material concept is used to estimate the values of fracture toughness achieved experimentally. By using the fictitious material concept, the fracture toughness of pre-cracked specimens fabricated from stainless steel 316L could be estimated without the need for complicated and time-consuming elastic-plastic failure analysis and by performing only linear elastic analysis. For this purpose, the fictitious material concept is simply combined with mean stress, generalized mean stress, maximum tangential stress, generalized maximum tangential stress, strain energy density, and generalized strain energy density criteria. It is shown that the combination of fictitious material concepts with four linear elastic brittle fracture criteria is quite successful in predicting the mode II fracture toughness of ductile pre-cracked specimens. 

Keywords

Main Subjects


[1] R. Hojjati-Talemi, S. Cooreman, D. Van Hoecke, Finite element simulation of dynamic brittle fracture in pipeline steel: A XFEM-based cohesive zone approach, Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 232(5) (2018) 357-370.
[2] O. Zvirko, N. Kret, O. Tsyrulnyk, T. Vengrynyuk, Influence of textures of pipeline steels after operation on their brittle fracture resistance, Materials Science, 54(3) (2018) 400-405.
[3] W. Li, Z. Jin, G. Cusatis, Size effect analysis for the characterization of marcellus shale quasi-brittle fracture properties, Rock Mechanics and Rock Engineering, 52(1) (2019) 1-18.
[4] S. Chandra, R. Sarkar, A. Bhowmick, P. De, P. Chakraborti, S. Ray, Crack tip opening angle (CTOA) and δ5 measurements on SENT and DENT specimens of a thin interstitial-free steel sheet, Engineering Fracture Mechanics, 225 (2020),  https://doi.org/10.1016/j.engfracmech.2019.106861.
[5] P. Kuhn, G. Catalanotti, J. Xavier, P. Camanho, H. Koerber, Fracture toughness and crack resistance curves for fiber compressive failure mode in polymer composites under high rate loading, Composite Structures, 182 (2017) 164-175.
[6] J.R. Rice, A path independent integral and the approximate analysis of strain concentration by notches and cracks, Journal of Applied Mechanics, 35(2) (1968) 379-386.
[7] J. Ding, W. Xu, Determination of mode I interlaminar fracture toughness of composite by a wedge-insert double cantilever beam and the nonlinear J integral, Composites Science and Technology, 206 (2021), https://doi.org/10.1016/j.compscitech.2021.108674.
[8] Y. Wang, G. Wang, S. Tu, F. Xuan, Ductile fracture prediction based on J-integral and unified constraint parameters for cracked pipes, Engineering Fracture Mechanics, 215 (2019) 1-15.
[9] F. Antunes, R. Branco, P. Prates, L. Borrego, Fatigue crack growth modelling based on CTOD for the 7050‐T6 alloy, Fatigue & Fracture of Engineering Materials & Structures, 40(8) (2017) 1309-1320.
[10] K. Samadian, S. Hertelé, W. De Waele, Measurement of CTOD along a surface crack by means of digital image correlation, Engineering Fracture Mechanics, 205 (2019) 470-485.
[11] Y. Zhang, J. Shuai, Z. Lv, K. Xu, Investigation of the effects of material parameters on the relationship between crack tip constraint and CTOD fracture toughness, Theoretical and Applied Fracture Mechanics, 108 (2020), https://doi.org/10.1016/j.tafmec.2020.102615.
[12] J.S. Kim, N.O. Larrosa, A.J. Horn, Y.J. Kim, R.A. Ainsworth, Notch bluntness effects on fracture toughness of a modified S690 steel at 150° C, Engineering Fracture Mechanics, 188 (2018) 250-267.
[13] W. Musraty, B. Medjo, N. Gubeljak, A. Likeb, I. Cvijović-Alagić, A. Sedmak, M. Rakin, Ductile fracture of pipe-ring notched bend specimens–Micromechanical analysis, Engineering Fracture Mechanics, 175 (2017) 247-261.
[14] Ł. Derpeński, Ductile fracture behavior of notched aluminum alloy specimens under complex non-proportional load, Materials, 12(10) (2019), https://doi.org/10.3390/ma12101598.
[15] J. Pan, Y. Wang, Y. Li, Ductile fracture in notched bulk metallic glasses, Acta Materialia, 136 (2017) 126-133.
[16] V.Madrazo, S.Cicero, I.A.Carrascal, On the point method and the line method notch effect predictions in Al7075-T651, Engineering Fracture Mechanics, 79 (2012) 363-379.
[17] W.Q. Wang, A.J. Li, P.N. Li, D.Y. Ju, An engineering approach for notch elastic-plastic fracture analysis, International Journal of Pressure Vessels and Piping, 60(1) (1994) 1-16.
[18] H.Neuber, Theory of stress concentration for shear-strained prismatical bodies with arbitrary nonlinear stress-strain law, Journal of Applied Mechanics, 28(4) (1961) 544-550.
[19] K.Molski, G.Glinka, A method of elastic-plastic stress and strain calculation at a notch root, Materials Science and Engineering, 50(1) (1981) 93-100.
[20] G.Glinka, Energy density approach to calculation of inelastic strain-stress near notches and cracks, Engineering Fracture Mechanics, 22(3) (1985) 485-508.
[21] P.Lazzarin, R.Zambardi, The equivalent strain energy density approach re‐formulated and applied to sharp V‐shaped notches under localized and generalized plasticity, Fatigue & Fracture of Engineering Materials & Structures, 25(10) (2002) 917-928.
[22] A.R.Torabi, Estimation of tensile load-bearing capacity of ductile metallic materials weakened by a V-notch: The equivalent material concept, Materials Science and Engineering: A, 536 (2012) 249-255.
[23] H.R.Majidi, S.M.J.Razavi, A.R.Torabi, Application of EMC‐J criterion to fracture prediction of U‐notched polymeric specimens with nonlinear behaviour, Fatigue & Fracture of Engineering Materials & Structures, 42(1) (2019) 352-362.
[24] A.R.Torabi, M.Alaei, Application of the equivalent material concept to ductile failure prediction of blunt V-notches encountering moderate-scale yielding, International Journal of Damage Mechanics, 25(6) (2016) 853-877.
[25] A.R.Torabi, A.S.Rahimi, M.R.Ayatollahi, Mixed mode І/ІІ fracture prediction of blunt V-notched nanocomposite specimens with nonlinear behavior by means of the Equivalent Material Concept, Composites Part B: Engineering, 154 (2018) 363-373.
[26] A.R.Torabi, R.Habibi, B.M.Hosseini, On the ability of the equivalent material concept in predicting ductile failure of U-notches under moderate-and large-scale yielding conditions, Physical Mesomechanics, 18(4) (2015) 337-347.
[27] H.Salavati, H.Mohammadi, Ductile Failure Prediction of U-Notched Bainitic Functionally Graded Steel Specimens Using the Equivalent Material Concept Combined with the Averaged Strain Energy Density Criterion, Physical Mesomechanics, 22(3) (2019) 255-260.
[28] A.R.Torabi, The equivalent material concept: Application to failure of O-notches, Engineering Solid Mechanics, 1(4) (2013) 129-140.
[29] A.R.Torabi, M.R.Ayatollahi, M.Torabi, A.S.Rahimi, Crack growth onset in thin aluminum sheets under mixed mode I/II loading: A new form of the Equivalent Material Concept, Thin-Walled Structures, 144 (2019), https://doi.org/10.1016/j.tws.2019.106337.
[30] A.R. Torabi, M. Kamyab, Notch ductile failure with significant strain‐hardening: The modified equivalent material concept, Fatigue & Fracture of Engineering Materials & Structures, 42(2) (2019) 439-453.
[31] ASTM E399-20, Standard Test Method for Linear-Elastic Plane-Strain Fracture Toughness of Metallic Materials AI, West Conshohocken, PA, (2020), www.astm.org.
[32] A.R. Torabi, M. Kamyab, The fictitious material concept, Engineering Fracture Mechanics, 209 (2019) 17-31.
[33] M. Aliha, M. Ayatollahi, Geometry effects on fracture behaviour of polymethyl methacrylate, Materials Science and Engineering: A, 527(3) (2010) 526-530.
[34] M. Ayatollahi, M. Aliha, Analysis of a new specimen for mixed mode fracture tests on brittle materials, Engineering Fracture Mechanics, 76(11) (2009) 1563-1573.
[35] M.R. Ayatollahi, M. Aliha, S. Rahmanian, Finite Element Analysis of an Improved Center Crack Specimen, in:  Key Engineering Materials, 347 (2007) 441-446.
[36] ASTM E8 / E8M-08, Standard Test Methods for Tension Testing of Metallic Materials. ASTM International WC, PA, (2008), www.astm.org.
[37] ASTM A240 / A240M-20a. Standard Specification for Chromium and Chromium-Nickel Stainless Steel Plate, Sheet, and Strip for Pressure Vessels and for General Applications. ASTM International WC, PA, 2020, www.astm.org.
[38] A.R. Torabi, M. Kamyab, Mixed mode I/II failure prediction of thin U-notched ductile steel plates with significant strain-hardening and large strain-to-failure: The Fictitious Material Concept, European Journal of Mechanics-A/Solids, 75 (2019) 225-236.
[39] M.L.Williams, On the Stress Distribution at the Base of a Stationary Crack, Journal of Applied Mechanics, 24 (1) (1956) 109-114.
[40] G.C. Sih, Strain-energy-density factor applied to mixed mode crack problems, International Journal of fracture, 10(3) (1974) 305-321.
[41] M.R. Ayatollahi, M.R. Moghaddam, F. Berto, A generalized strain energy density criterion for mixed mode fracture analysis in brittle and quasi-brittle materials, Theoretical and Applied Fracture Mechanics, 79 (2015) 70-76.
[42] F. Erdogan, G. Sih, On the crack extension in plates under plane loading and transverse shear, J. Basic Eng, 85(4) (1963) 519-525.
[43] D.J. Smith, M.R. Ayatollahi, M.J. Pavier, The role of T‐stress in brittle fracture for linear elastic materials under mixed‐mode loading, Fatigue & Fracture of Engineering Materials & Structures, 24(2) (2001) 137-150.
[44] S. Shahbaz, M.R. Ayatollahi, A.R. Torabi, S. Cicero, Fracture Behavior of Two Biopolymers Containing Notches: Effects of Notch Tip Plasticity, Applied Sciences, 10(23) (2020), https://doi.org/10.3390/app10238445.
[45] A.R. Torabi, A. Rahimi, M. Ayatollahi, Fracture study of a ductile polymer-based nanocomposite weakened by blunt V-notches under mode I loading: Application of the Equivalent Material Concept, Theoretical and Applied Fracture Mechanics, 94 (2018) 26-33.
[46] A.R. Torabi, E. Pirhadi, Stress-based criteria for brittle fracture in key-hole notches under mixed mode loading, European Journal of Mechanics-A/Solids, 49 (2015) 1-12.
[47] A. Kotousov, Effect of plate thickness on stress state at sharp notches and the strength paradox of thick plates, International Journal of Solids and Structures, 47(14-15) (2010) 1916-1923.
[48] A. Kotousov, P. Lazzarin, F. Berto, S. Harding, Effect of the thickness on elastic deformation and quasi-brittle fracture of plate components, Engineering Fracture Mechanics, 77(11) (2010) 1665-1681.
[49] L.P. Pook, A. Campagnolo, F. Berto, P. Lazzarin, Coupled fracture mode of a cracked plate under anti-plane loading, Engineering Fracture Mechanics, 134 (2015) 391-403.