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A Three-Dimensional Finite Element Analysis of the Stress Intensity Factors for Different Fracture Modes of Homogeneous Bimaterial

Dreidimensionale Finite-Element-Analyse der Belastungsintensitätsfaktoren für verschiedene Bruchmodi von homogenen Bimaterial
Hassan S. Hedia, S. M. Aldousari and N. Fouda
From the journal Materials Testing


The failure of cracked components is governed by the stresses in the vicinity of the crack tip. The singular stress contribution is characterized by stress intensity factors. The stress intensity factors depend on the geometry of the component and on loading condition. This paper addresses the evaluation of stress intensity factors (SIFs) of opening, shearing and tearing modes for compact tension specimens for bonding homogeneous materials. The aim of this work is to find the optimal pre-cracked length, crack notch radius, and crack notch angle in order to eliminate the effect of them on the SIF and then on the fracture toughness. To achieve this goal, a three- dimension finite element analysis (FEA) model using the ANSYS program is constructed for specimens made of homogeneous materials such as stainless steel bonding with epoxy as a filler material. The effects of notch angle, notch tip radius and pre-crack length on the stress intensity factors are studied for different fracture modes. The results for the stress intensity factors KI, KII and KIII are obtained using the linear elastic fracture mechanics (LEFM) approach.


Der Ausfall von Komponenten mit Rissen wird durch Belastungen in der Nähe der Rissspitze bestimmt. Ein einfacher Belastungsbeitrag ist durch Belastungsintensitätsfaktoren gekennzeichnet. Die Belastungsintensitätsfaktoren hängen von der Komponentengeometrie und der Beanspruchungsbedingung ab. Der vorliegende Artikel behandelt die Auswertung von Belastungsintensitätsfaktoren (Stress Intensity Factors, (SIFs) des Öffnungs-, Scher- und Rissbildungsmodus für kompakte Spannungsproben zum Verbinden homogener Materialien. Das Ziel dieser Untersuchung ist die Ermittlung der optimalen Länge vor dem Riss, des Risskerbenradius und des Risskerbenwinkels, um die Auswirkung davon auf den SIF und damit auf den Bruchwiderstand zu beseitigen. Dazu wird ein dreidimensionales Finite-Element-Analyse-Modell mit dem Programm ANSYS für die Proben homogener Materialien wie Edelstahlverbindungen mit Expoxid als Füllmaterial erstellt. Die Auswirkungen von Kerbwinkel, Kerbspitzenradius und der Länge vor dem Riss auf die Belastungsintensitätsfaktoren werden für verschiedene Bruchmodis untersucht. Die Ergebnisse der Belastungsintensitätsfaktoren KI, KII und KIII werden mithilfe des Ansatzes für lineare elastische Bruchmechaniken (Linear Elastic Fracture Mechanics, LEFM) erhalten.

Prof. Dr. Hassan S. Hedia, born 1959, is professor of materials and solid mechanics. He is working at the King Abdulaziz University, KSA. He achieved his BSc in 1981 from the Mechanical Engineering Department at the Cairo University, Egypt and his MSc in 1989 at the Mansoura University, Egypt. His PhD achieved Prof. Helal from the Mechanical Engineering Department at the Leeds University, UK and the Mansoura University, Egypt under channel system. His fields of interest are advanced materials, fracture mechanics, stress analysis and biomechanics.

Dr. S. M. Aldousari, born 1956, is an assistant professor at King Abdulaziz University, KSA. He achieved his BSc in 1980 from the Mechanical Engineering Department at the Collage of Engineering, King Abdulaziz University, KSA and his PhD and MSc in 1993 from the Bradford University, United Kingdom. His field of interest is manufacturing technology.

Dr. N. Fouda, born 1973, is an assistant professor at the Mansoura University, Faculty of Engineer, Mansoura, Egypt. She received her BSc (production Eng,) in 1995 from the Mansoura University, Egypt and her MSc in 2000, her PhD in 2006 from the Mansoura University, Egypt. Her fields of interest are optimum design, stress analysis and mechanics of materials.


1 L.Liu, G. A.Kardomateas, J. W.Holmes: Mixed-mode stress intensity factors for a crack in an anisotropic bi-material strip, International Journal of Solids and Structures41 (2004), pp. 3095310710.1016/j.ijsolstr.2003.11.010 Search in Google Scholar

2 H.Tada, P. C.Paris, G. R.Irwin: The Stress Analysis of Cracks, Handbook, Del Research Corporation (1986)10.1115/1.801535 Search in Google Scholar

3 G. C.Sih: Handbook of Stress Intensity Factors, Institute of Fracture and Solid Mechanics, Lehigh University, Bethlehem, Pennsylvania (1973) Search in Google Scholar

4 D. P.Rooke: Cartwright, Her Majesty's Stationery Office, London (1974) Search in Google Scholar

5 Y.Murakami et al.: Stress Intensity Factors Handbook, Pergamon Press (1986)10.1115/1.2900983 Search in Google Scholar

6 J. C.Lee, L. M.Keer: Study of a Three-Dimensional Crack Terminating at an Interface, Journal of Applied Mechanics53 (1986)10.1115/1.3171757 Search in Google Scholar

7 R. N.Dubey: New insights into crack analysis: General solution vs. LEFM, Engineering Fracture Mechanics60 (1998), No. 1998-5, pp. 50150610.1016/S0013-7944(98)00042-3 Search in Google Scholar

8 S. B.Thomas, M. J.Mhaiskar, R.Sethuraman: Stress intensity factors for circular hole and inclusion using finite element alternating method, theoretical, Applied Fracture Mechanics33 (2000), pp. 7381 Search in Google Scholar

9 W. T.Riddell, R. S.Piascik: A Back Face Strain Compliance Expression for the Compact Tension Specimen, Langley Research Center, Hampton, Virginia, NASA/TM (1998) Search in Google Scholar

10 M. B.Prime: Measuring residual stress and the resulting stress intensity factor in compact tension specimens, Fatigue and Fracture of Engineering Materials and Structures, Vol. 22 (1999), pp. 195204 Search in Google Scholar

11 H. S. M.Hedia, M. A. N.Shabara: Effect of notch tip sharpness and pre-crack on the stress intensity factor – Part I: Finite element analyses of compact tension specimens, Materialprüfung44 (2002), No. 4, pp. 117121 Search in Google Scholar

12 Hedia, H. S. M.; Fattah, A. A., Effect of notch tip sharpness and pre-crack on the stress intensity factor – Part II: Investigation of the shear loading mode, Materialprüfung44 (2002), No. 4, pp. 122125 Search in Google Scholar

13 J. H.Chang, D. J.Wu: Calculation of mixed-mode stress intensity factors for a crack normal to a bimaterial interface using contour integrals, Engineering Fracture Mechanics70 (2003), pp. 1675169510.1016/S0013-7944(02)00202-3 Search in Google Scholar

14 ASTM E 399-83: Standard Method of Test bar Plane Strain Fracture-Toughness of Metallic Materials (1983) Search in Google Scholar

15 ANSYS User's Manual, Version 5.0A (1992) Search in Google Scholar

16 H. S.Hedia, L.Allie, S.Granguli, H.Aglan: The Influence of nanoadhesives on the tensile properties and Mode I – fracture thoughness of bonded joints, Engineering Fracture Mechanics73 (2006), pp. 1826 Search in Google Scholar

Published Online: 2013-05-26
Published in Print: 2010-03-01

© 2010, Carl Hanser Verlag, München