Finite Element Modeling of Crack Initiation Angle Under Mixed Mode (I/II) Fracture

Document Type: Research Paper


1 Department of Applied Mechanics, Maulana Azad National Institute of Technology Bhopal

2 Advanced Materials Processes Research Institute (CSIR)


Present study deals with the prediction of crack initiation angle for mixed mode (I/II) fracture using finite element techniques and J-Integral based approach. The FE code ANSYS is used to estimate the stress intensity factor numerically. The estimated values of SIF were incorporated into six different crack initiation angle criteria to predict the crack initiation angle. Single edge crack specimens of Araldite-Hardener were used for the present analysis. Load was applied up to critical limit of the specimens containing crack at different angles of inclination. The crack initiation angle obtained using stress intensity factor and J-integral based approach were found close to each other and also found to be in good agreement with the available experimental results in literature. It is also investigated that as crack inclination angle increases material was found to behave in a brittle manner.


[1] Abdalla J.E., Gerstle W.H., 1988, A finite element for arbitrarily precise determination of stress intensity factors, Bureau Of Engineering Report CE-84(88), College of Engineering, University of New Mexico, Albuquerque.

[2] Ayhan A.O., 2004, Mixed mode stress intensity factors for deflected and inclined surface cracks in finite-thickness plates, Engineering Fracture Mechanics 71: 1059-1079.

[3] Barsoum R.S., 1976, On the use of isoparametric finite elements in linear fracture mechanics, International Journal for Numerical Methods in Engineering 10: 25-37.

[4] Barsoum R.S., 1977, Triangular quarter-point elements as elastic and perfectly plastic crack tip elements, International Journal for Numerical Methods in Engineering 11: 85-98.

[5] Cherepanov G.P., 1974, Mechanics of Brittle Fracture, Nauka, Moscow, (in Russian).

[6] Erdogan F., Shi G.C., 1963, On the crack extension in plates under plane loading and transverse shear, Journal of Basic Engineering 85: 519-527.

[7] Griffith A.A., 1921, The phenomena of rupture and flow in solids, Philosophical Transactions of the Royal Society of London, Series A221, pp. 199.

[8] Henshell R.D., Shaw K.G., 1975, Crack tip finite element are unnecessary, International Journal for Numerical Methods in Engineering 9: 495-507.

[9] Josh J., Ptaik S, 1989, On stress intensity factor computation by finite element method under mixed mode loading conditions, Engineering Fracture Mechanics 34(1): 169-177.

[10] Knesl Z., 1988, Stress intensity factor computing under mixed mode loading conditions by the use of energy release rate (in Czech). Strojirenstvi 37: 163-166

[11] Kong X.M., Schluter N., Dahl W., 1995, Effect of triaxial stress on mixed mode-facture, Engineering Fracture Mechanics 52(2) :379-388.

[12] Owen D.R.J., Fawkes A. J., 1983, Engineering Fracture Mechanics-Numerical Methods and Applications, Pineridge Press, Swansea, UK.

[13] Pu S.L., Hussain M.A., Lorenson W.E., 1978, The collapse cubic isoparamteric elements as singular elements for crack problems, International Journal for Numerical Methods in Engineering 12: 1727-1742.

[14] Peter M., Haefele, Lee James D., 1995, Combination of finite element analyses and analytical crack tip solution for mixed mode fracture, Engineering Fracture Mechanics 50(5/6): 849-868.

[15] Petit C., Vergne A., Zhang X., 1996, A comparative numerical review of cracked materials, Engineering Fracture Mechanics 54 (3): 423-439.

[16] Rousseau C.E., Tippur H.V., 2000, compositionally graded materials with cracks normal to the elastic gradient, Acta Materialia 48: 4021- 4033.

[17] Sih G.C., 1974, Strain energy density factor applied to mixed mode crack problems, International Journal of Fracture 10 (3): 305-321.

[18] Sih G.C., 1973, Some basic problems in fracture mechanics and new concepts, Engineering Fracture Mechanics 5: 365-377.

[19] Shafique M.A., Marwan K., 2000, Analyses of mixed mode crack initiation angles under various loading conditions, Engineering Fracture Mechanics 67: 397-419.

[20] Shafique M.A., Marwan K., 2004, A new criterion for mixed mode fracture initiation based on crack tip plastic core region, International Journal of Plasticity 20: 55-84.

[21] Theocaris P.S., Andrianopoulos N.P. 1982, The T-criterion applied to ductile fracture, International Journal of Fracture 20: 125-130.

[22] Theocaris P.S., Andrianopoulos N.P., 1982, The Mises elastic-plastic boundary as the core region in fracture criteria, Engineering Fracture Mechanics 16: 425-432.

[23] Theocaris P.S., Kardomateas G.A., Andrianopoulos N.P., 1982, Experimental study of the T-criterion in ductile fracture, Engineering Fracture Mechanics 17: 439-447.

[24] Tilbrook M.T., Reimanis I.E., Rozenburg K., Hoffman M., 2005, Effect of plastic yielding on crack propagation near ductile/brittle interfaces, Acta Materialia 53: 3935-3949.

[25] Ukadgaonker V.G., Awasare P.J., 1995, A new criterion for fracture initiation, Engineering Fracture Mechanics 51 (2): 265-274.

[26] Zwing P.D., Swedlow J.L., Williams J.G., 1976, Further results on the angled crack problem, International Journal of Fracture 12(1):85-93.