ORIGINAL ARTICLE
The two-parameter fracture criterion based on the J-A concept
Yu. G. Matvienko,
Corresponding Author
Yu. G. Matvienko
Mechanical Engineering Research Institute of the Russian Academy of Sciences, Moscow, Russia
Correspondence
Yu.G. Matvienko, Mechanical Engineering Research Institute of the Russian Academy of Sciences, Moscow, Russia.
Email: [email protected]
Search for more papers by this authorYu. G. Matvienko,
Corresponding Author
Yu. G. Matvienko
Mechanical Engineering Research Institute of the Russian Academy of Sciences, Moscow, Russia
Correspondence
Yu.G. Matvienko, Mechanical Engineering Research Institute of the Russian Academy of Sciences, Moscow, Russia.
Email: [email protected]
Search for more papers by this authorFirst published: 09 June 2023
Abstract
The present paper deals with the J-A concept in two-parameter elastic–plastic approaches of fracture mechanics. The cumulative damage rule in a solid is employed to construct the quantitative elastic–plastic J-A fracture criterion. As a result, the constraint corrected elastic–plastic fracture toughness as a function of the crack-tip constraint parameter A, the yield stress, the strain hardening exponent and the failure stress has been proposed. The significant effect of the strain hardening exponent on the normalized constraint corrected fracture toughness is observed. The value of the normalized constraint corrected fracture toughness decreases with the increase of the applied failure stress and the decrease of the crack aspect ratio to a certain values, and then it stabilizes.
Highlights
- The cumulative damage rule in a solid and the J-A concept are employed.
- Quantitative two-parameter J-A fracture criterion is proposed.
- The constraint corrected fracture toughness is described as a function of crack-tip constraint.
- The effect of the constraint parameter A is analyzed for some standard specimens.
Open Research
DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available from the corresponding author upon reasonable request.
REFERENCES
- 1Williams ML. On the stress distribution at the base of a stationary crack. J Appl Mech. 1957; 24(1): 109-114.
- 2Larsson SG, Carlsson AJ. Influence of non-singular stress terms and specimen geometry on small-scale yielding at crack tips in elastic-plastic materials. J Mech Phys Solids. 1973; 21(4): 263-277.
- 3Rice JR. Limitations to the small scale yielding approximation for crack tip plasticity. J Mech Phys Solids. 1974; 22(1): 17-26.
- 4Radaj D. T-stress corrected notch stress intensity factors with application to welded lap joints. Fatigue Fract Eng Mater Struct. 2010; 33(6): 378-389.
- 5Pook LP. The linear elastic analysis of cracked bodies, crack paths and some practical crack path examples. Eng Fract Mech. 2016; 167: 2-19.
- 6Pluvinage G, Capelle J, Hadj Meliani M. A review of fracture toughness transferability with constraint and stress gradient. Fatigue Fract Eng Mater Struct. 2014; 37(11): 1165-1185.
- 7Gupta M, Alderliesten RC, Benedictus R. A review of T-stress and its effects in fracture mechanics. Eng Fract Mech. 2015; 134: 218-241.
- 8Matvienko YG. The effect of crack-tip constraint in some problems of fracture mechanics. Eng Fail Anal. 2020; 110:104413.
- 9O'Dowd NP, Shih CF. Family of crack-tip fields characterized by a triaxiality parameter - I. Structure of fields. J Mech Phys Solids. 1991; 39(8): 989-1015.
- 10Yang S, Chao YJ, Sutton MA. Higher-order asymptotic fields in a power law hardening material. Eng Fract Mech. 1993; 45(1): 1-20.
- 11Nikishkov GP. An algorithm and a computer program for the three-term asymptotic expansion of elastic–plastic crack tip stress and displacement fields. Eng Fract Mech. 1995; 50(1): 65-83.
- 12Nikishkov GP, Bruckner-Foit A, Munz D. Calculation of the second fracture parameter for finite cracked bodies using a three-term elastic-plastic asymptotic expansion. Eng Fract Mech. 1995; 52(4): 685-701.
- 13Hutchinson JW. Singular behaviour at the end of a tensile crack tip in a hardening material. J Mech Phys Solids. 1968; 16(1): 13-31.
- 14Rice JR, Rosengren GF. Singular behaviour at the end of a tensile crack tip in a hardening material. J Mech Phys Solids. 1968; 16(1): 13-31.
- 15Ding P, Wang X. Solutions of the second elastic–plastic fracture mechanics parameter in test specimens. Eng Fract Mech. 2010; 77(17): 3462-3480.
- 16Matvienko YG, Nikishkov GP. Two-parameter J-A concept in connection with crack-tip constraint. Theoret Appl Fract Mech. 2017; 92: 306-317.
- 17Hebel J, Hohe J, Friedmann V, Siegele D. Experimental and numerical analysis of in-plane and out-of-plane crack tip constraint characterization by secondary fracture parameters. Int J Fract. 2007; 146(3): 173-188.
- 18Kim JH, Moon HJ, Earmme YY. Inplane and antiplane T-stresses for an interface crack in anisotropic bimaterial. Mech Mater. 2001; 33(1): 21-32.
- 19Kim Y, Chao YJ, Zhu XK. Effect of specimen size and crack depth on 3D crack-front constraint for SENB specimens. Int J Solids Struct. 2003; 40(23): 6267-6284.
- 20Neimitz A, Galkiewicz J. Fracture toughness of structural components: influence of constraint. Int J Pres Ves pip. 2006; 83(1): 42-54.
- 21Graba M. On the parameters of geometric constraints for cracked plates under tension – three-dimensional problems. Int J Appl Mech Eng. 2017; 22(4): 901-919.
10.1515/ijame-2017-0058 Google Scholar
- 22Leong KH, Yusof F. Three-dimensional crack tip constraint of shallow cracks in tension and bending. Int J Fract. 2021; 231(2): 169-187.
- 23Guo WL. Elastoplastic three dimensional crack border field – I. Singular structure of the field. Eng Fract Mech. 1993; 46(1): 93-104.
- 24Guo WL. Elastoplastic three dimensional crack border field – II. Asymptotic solution for the field. Eng Fract Mech. 1993; 46(1): 105-113.
- 25Guo WL. Elastoplastic three dimensional crack border field – III. Fracture parameters. Eng Fract Mech. 1995; 51(9): 51-71.
10.3901/JME.2015.09.051 Google Scholar
- 26Neimitz A, Lipiec S. Fracture toughness correction due to the in- and out-of-plane constraints. Theoret Appl Fract Mech. 2021; 112:102844.
- 27Zhao J. Three-parameter approach for elastic-plastic stress field of an embedded elliptical crack. Eng Fract Mech. 2009; 76(16): 2429-2444.
- 28Cui P, Guo W. Higher order J-Tz-AT solution for three-dimensional crack border fields in power-law hardening solids. Eng Fract Mech. 2019; 222:106736.
- 29Yang J, Wang GZ, Xuan FZ, Tu ST. Unified characterisation of in-plane and out-of-plane constraint based on crack-tip equivalent plastic strain. Fatigue, Eng, Mater, Struct. 2013; 36(6): 504-514.
- 30Mu MY, Wang GZ, Xuan FZ, Tu ST. Unified correlation of in-plane and out-of plane constraints effects with cleavavage fracture toughness. Theoret Appl Fract Mech. 2015; 80: 121-132.
- 31Wang YH, Wang GZ, Tu ST, Xuan FZ. In-plane and out-of-plane constraint characterization of different constraint parameters for semi-elliptical surface cracks in pipes. Eng Fract Mech. 2020; 235:107161.
- 32Xu JY, Wang GZ, Xuan FZ, Tu ST. Unified constrained parameter based on crack-tip opening displacement. Eng Fract Mech. 2018; 200: 175-188.
- 33Xiao JY, Wang GZ, Tu ST, Xuan FZ. Engineering estimation method of unified constraint parameters for semi-elliptical surface cracks in plates. Eng Fract Mech. 2020; 229:106935.
- 34Zheng Y, Wang GZ, Wang K, Xuan FZ, Tu ST. Correlation of the master curve reference temperature T0 with unified constraint parameter. Eng Fract Mech. 2021; 253:107867.
- 35Zhen Y, Chang Q, Cao Y, Niu R. A novel unified characterization parameter of in-plane and out-of-plane constraints based on critical CTOA. Fatigue Fract Eng Mater Struct. 2021; 44(5): 1305-1317.
- 36Simha CHM. A note on a plastic work-based parameter for correlating constraint and toughness. Eng Fract Mech. 2020; 240:107356.
- 37O'Dowd NP. Applications of two parameter approaches in elastic-plastic fracture mechanics. Eng Fract Mech. 1995; 52(3): 445-465.
- 38Koçak M, Webster S, Janosch JJ, Ainsworth RA, Koerc R. FITNET: fitness-for-service. Fracture-Fatique-Creep-Corrosion, GKSS Research Centre Geesthacht GmbH; 2008.
- 39Neimitz A, Dzioba I. The influence of the out-of-plane and in-plane constraint on fracture toughness of high strength steel in the ductile to brittle transition temperature range. Eng Fract Mech. 2015; 147: 431-448.
- 40Nikishkov GP. Prediction of fracture toughness dependence on constraint parameter A using the weakest link model. Eng Fract Mech. 2016; 152: 193-200.
- 41Liu Z, Wang X, Zhang Z, Jin P, Chen X. Solutions and applications of 3D elastic–plastic constraint parameters for clamped single edge notched tension (SENT) specimens. Eng Fract Mech. 1922; 272:108713.
10.1016/j.engfracmech.2022.108713 Google Scholar
- 42Nikishkov GP, Atluri SN. Calculation of fracture mechanics parameters for an arbitrary three-dimensional crack by the equivalent domain integral method. Int J Numer Methods Eng. 1987; 24(9): 1801-1821.
- 43Nikishkov GP, Matvienko YG. Elastic-plastic constraint parameter A for test specimens with thickness variation. Fatigue Fract Eng Mater Struct. 2016; 39(8): 939-949.
- 44Cherepanov GP. The propagation of cracks in a continuous medium. J Appl Math Mech. 1967; 31(3): 503-512.
- 45Rice JR. A path-independent integral and the approximate analysis of strain concentration by notches and cracks. J Appl Mech. 1968; 135: 379-386.
10.1115/1.3601206 Google Scholar
- 46Matvienko YG. J-estimation formulas for nonlinear crack problem. Int J Fract. 1994; 68(1): R15-R18.
- 47Berto F, Lazzarin P, Matvienko YG. J-integral evaluation for U- and V-blunt notches under Mode I loading and materials obeying a power hardening law. Int J Fract. 2007; 146(1-2): 33-51.
- 48Matvienko YG, Morozov EM. Calculation of the energy J-integral for bodies with notches and cracks. Int J Fract. 2004; 125(3/4): 249-261.
- 49Ding P, Wang X. An estimation method for the determination of the second elastic–plastic fracture mechanics parameters. Eng Fract Mech. 2012; 79: 295-311.
- 50Kumar V., German M.D., Shih C.F. An engineering approach for elastic-plastic fracture analysis. EPRI report NP-1931. Electric Power Research Institute, Palo Alto, CA. 1981.
- 51Anderson TL. Fracture mechanics: fundamentals and applications. Taylor & Francis Group; 2005.
10.1201/9781420058215 Google Scholar
- 52Sumpter JDG. An experimental investigation of the T-stress approach. In: EM Hackett, K-H Schwalbe, RH Dodds, eds. Constraint effects in fracture, ASTM STP 1171; 1993: 492-502.
