Numerical Analysis of the Influence of In-Plane Constraints on the Crack Tip Opening Displacement for SEN(B) Specimens Under Predominantly Plane Strain Conditions
More details
Hide details
Kielce University of Technology, Faculty of Mechatronics and Mechanical Engineering, Department of Manufacturing Engineering and Metrology, Al. 1000-lecia PP 7, 25-314 Kielce, Poland
Online publication date: 2016-12-08
Publication date: 2016-12-01
International Journal of Applied Mechanics and Engineering 2016;21(4):849-866
This paper presents a numerical analysis of the relationship between in-plane constraints and the crack tip opening displacement (CTOD) for single-edge notched bend (SEN(B)) specimens under predominantly plane strain conditions. It provides details of the numerical model and discusses the influence of external load and in-plane constraints on the CTOD. The work also reviews methods for determining the CTOD. The new formula proposed in this paper can be used to estimate the value of the coefficient dn as a function of the relative crack length, the strain hardening exponent and the yield strength - dn(n, σ0/E, a/W), with these parameters affecting the level of in-plane constraints. Some of the numerical results were approximated using simple mathematical formulae.
Hutchinson J.W. (1968): Singular behaviour at the end of a tensile crack in a hardening material. – Journal of the Mechanics and Physics of Solids, vol.16, No.1, pp.13-31.
Rice J.R. and Rosengren G.F. (1968): Plane strain deformation near a crack tip in a power-law hardening material. – Journal of the Mechanics and Physics of Solids, vol.16, No.1, pp.1-12.
Graba M. (2009): Numerical analysis of the mechanical fields near the crack tip in the elastic-plastic materials. 3D problems. – PhD dissertation, Kielce University of Technology - Faculty of Mechatronics and Machine Building, 387 pages, Kielce 2009 (in Polish).
Neimitz A., Dzioba I., Graba M. and Okrajni J. (2008): The Assessment of the Strength and Safety of the Operation High Temperature Components Containing Crack. – Kielce University of Technology Publishing House, Kielce.
Neimitz A., Dzioba I., Molasy R. and Graba M. (2004): The influence of the constraints on fracture toughness. – Proceeding of the XX Symposium of Fatigue and Fracture Mechanics, Bydgoszcz-Pieczyska, 27-30.04.2004, pp.265-272 (in Polish).
Neimitz A., Graba M. and Gałkiewicz J. (2007): An alternative formulation of the Ritchie-Knott-Rice local fracture criterion. – Engineering Fracture Mechanics, vol.74, pp.1308-1322.
O’Dowd N.P. and Shih C.F. (1991): Family of crack-tip fields characterized by a triaxiality parameter – I. Structure of fields. – J. Mech. Phys. Solids, vol.39, No.8, pp. 989-1015.
O’Dowd N.P. and Shih C.F. (1992): Family of crack-tip fields characterized by a triaxiality parameter – II. Fracture applications. – J. Mech. Phys. Solids, vol.40, No.5, pp.939-963.
Gałkiewicz J. and Graba M. (2006): Algorithm for determination of σ˜ij(n,θ)$\tilde {\rm \sigma} _{ij} (n,{\rm \theta} )$, ε˜ij(n,θ)$\tilde {\rm \varepsilon} _{ij} (n,{\rm \theta} )$, u˜i(n,θ)$\tilde u_i (n,{\rm \theta} )$, dn (n) and In (n) functions in Hutchinson-Rice-Rosengren solution and its 3D generalization. – Journal of Theoretical and Applied Mechanics, vol.44, No.1, pp.19-30.
Wells A.A. (1961): Unstable crack propagation in metals: cleavage and fast fracture. – Proceedings of the Crack Propagation Symposium, tom 1, Paper 84, Cranfield, UK.
Shih C.F. (1981): Relationship between the J-integral and the crack opening displacement for stationary and extending cracks. - Journal of the Mechanics and Physics of Solids, vol.29, pp.305-329.
Omidvar B., Wnuk M.P. and Choroszynski M. (1997): Relationship between the CTOD and the J integral for stationary and growing cracks. – Closed form solutions, International Journal of Fracture 87: pp.331–343.
Gordon J.R., Neale B.K. and Wang Y-Y. (1995): A comparison of J and CTOD as elastic-plastic fracture characterizing parameters, constraint effects in fracture theory and application. – Second Volume, ASTM STP 1244, M. Kirk and A. Bakker, ASTM Philadelphia, pp.425-444.
SINTAP: Structural Integrity Assessment Procedures for European Industry. – Final Procedure, Brite-Euram Project No BE95-1426. – Rotherham: British Steel, 1999.
DRAFT NOTE - J.T. Martin - OGBM/3, R.W.J. Koers - OGBM/3, CTOD versus J-Integral as a fracture parameter, 25042001 – SINTAP, April 8, 1998.
Kumar V., German M.D. and Shih C.F. (1981): An engineering approach for elastic-plastic fracture analysis – Electric Power Research Institute, Inc. Palo Alto, CA (1981), EPRI Report NP-1931.
Graba M. and Gałkiewicz J. (2007): Influence of the crack tip model on results of the finite element method. – Journal of Theoretical and Applied Mechanics, Warsaw, vol.45, No.2, pp.225-237.
Brocks W., Cornec A. and Scheider I. (2003): Computational aspects of nonlinear fracture mechanics. – Bruchmechanik, GKSS-Forschungszentrum, Geesthacht, Germany, Elsevier pp.127-209.
Brocks W. and Scheider I. (2003): Reliable J-values. Numerical aspects of the path-dependence of the J-integral in incremental plasticity. – Bruchmechanik, GKSS-Forschungszentrum, Geesthacht, Germany, Elsevier pp.127-209.
O’Dowd N.P. (1995): Application of two parameter approaches in elastic–plastic fracture mechanics. – Engineering Fracture Mechanics, vol.52, No.3, pp.445-465.
PN-88/H-04336 “Test method for fracture toughness by determining the critical value of J-integral, J Ic”, Polish Committee for Standardization, Metrology and Quality, (1988) (in Polish).
ASTM, 1983, ASTM E 399-83, Standard Test Method for Plane-Strain Fracture Toughness of Metallic Measurement.
ASTM, 2005, ASTM E 1820-05 Standard Test Method for Measurement of Fracture Toughness, American Society for Testing and Materials.
PN-EN 1993 Eurocode 3: Design of steel structures (in Polish).
BS, 1991, BS 7448, Fracture Mechanics Toughness Tests. Method for determination KIC, critical CTOD and critical J values.
ADINA 8.8, ADINA: User Interface Command Reference Manual – Volume I: ADINA Solids & Structures Model Definition, Report ARD 11-2, ADINA R&D, Inc., 2011.
ADINA 8.8, ADINA: Theory and Modeling Guide – Volume I: ADINA Solids & Structures, Report ARD 11-8, ADINA R&D, Inc., 2011.
Sherry A.H., Wilkes M.A., Beardsmore D.W. and Lidbury D.P.G. (2005): Material constraint parameters for the assessment of shallow defects in structural components – Part I: Parameter solutions. – Engineering Fracture Mechanics, vol.72, pp.2373-2395.
Sherry A.H., Hooton D.G., Beardsmore D.W. and Lidbury D.P.G. (2005): Material constraint parameters for the assessment of shallow defects in structural components – Part II: constraint – based assessment of shallow cracks. – Engineering Fracture Mechanics, vol.72, pp.2396-2415.
Graba M. (2016): The hybrid method for determination of elastic-plastic fracture mechanics parameters for SEN(B) specimens. – In press.
Table Curve 3D version 4.0.0, 1993-2002.
Sumpter J.D.G. and Forbes A.T. (1992): Constraint Based Analysis of Shallow Cracks in Mild Steel. – TWI/EWI/IS International Conference on Shallow Crack Fracture Mechanics Test and Application, M.G. Dawes, Ed., Cambridge, UK, paper 7.
Graba M. (2008): The influence of material properties on the Q-stress value near the crack tip for elastic-plastic materials. – Journal of Theoretical and Applied Mechanics, vol.46, No.2, pp.269-290, Warsaw 2008.
Journals System - logo
Scroll to top