Finite Element Analysis of a New Specimen for Conducting Fracture Tests under Mixed Mode I/III Loading

Document Type : Original Research Paper


Mechanical Engineering Department, Faculty of Engineering, University of Mohaghegh Ardabili, Ardabil, Iran.


In this paper, a new disc-shaped specimen containing a tilted crack was proposed so as to conduct fracture tests under mixed mode I/III loading. This specimen was able to produce complete mode mixities, ranging from pure mode I to pure mode III. Many finite element analyses were performed to obtain crack parameters (i.e. stress intensity factors at the crack tip) and geometry factors. It was shown that the mode III was added to the mode I loading as the crack angle changed. Moreover, the crack length as well as position of the lower supports was varied to study loading type at the crack tip. Finally, applicability of the proposed specimen in experimental point of view was considered by performing fracture experiments on the asphalt concrete. The results showed that fracture strength of the asphalt concrete decreases as the proportion of mode III at the crack tip enhances.


[1] S. Pirmohammad, M.R. Ayatollahi, Fracture resistance of asphalt concrete under different loading modes and temperature conditions, Constr. Build. Mater. 53 (2014) 235-242.
[2] M.R.M. Aliha, H. Behbahani, H. Fazaeli, M.H. Rezaifar, Study of characteristic specification on mixed mode fracture toughness of asphalt mixtures, Constr. Build. Mater. 54 (2014) 623-635.
[3] I. Artamendi, H. Al-Khalid, A comparision between beam and semi-circular bending fracture tests for asphalt, J. Road. Mater. Pavement. Des. 6 (2006) 163-180.
[4] J.R. Yates, R.A. Mohammed, Crack propagation under mixed mode (I+III) loading, Fatigue. Fract. Eng. M. 19 (1996) 1285-1290.
[5] V.E. Lazarus, J.B. Leblond, S.E. Mouchrif, Crack front rotation and segmentation in mixed mode I + III or I + II + III. Part II: Comparison with experiments, J. Mech. Phis. Solids. 41 (2001) 1421-1443.
[6] T. Fett, G. Gerteisen, S. Hahnenberger, G. Martin, D. Munz, Fracture tests for ceramics under mode-I, mode-II and mixed-mode loading, J. Eur. Ceram. Soc. 15 (1995) 307-312.
[7] G.S. Xeidakis, I.S. Samaras, D.A. Zacharopoulos, G.E. Papakalitakis, Crack growth in a mixed-mode loading on marble beams under three point bending, Int. J. Fracture. 79 (1996) 197-208.
[8] K.P. Chong, M.D. Kuruppu, J.S. Kuszmual, Fracture toughness determination of layered materials, Eng. Fract. Mech. 28 (1987) 43-54.
[9] M.R. Ayatollahi, M.R.M. Aliha, M.M. Hasani, Mixed mode brittle fracture in PMMA - an experimental study using SCB specimens, Mater. Sci. Eng. 417 (2006) 348-356.
[10] S.H. Chang, C.L. Lee, S. Jeon, Measurement of rock fracture toughness under modes I and II and mixed-mode conditions by using disc-type specimen, Eng. Geol. 66 (2002) 79-97.
[11] M.R.M. Aliha, M.R. Ayatollahi, R. Ashtari, Mode I and mode II fracture toughness testing for a coarse grain marble, Appl. Mech. Mater. 5-6 (2006) 181-188.
[12] G.C. Sih, Strain-energy-density factor applied to mixed mode crack problems, Int. J. Fracture. 10 (1974) 305-321.
[13] M.A. Hussain, S.L. Pu, J. Underwood, Strain energy release rate for a crack under combined mode I and mode II, Fracture analysis ASTM STP 560. Philadelphia: American Society for Testing and Materials, (1974) 2-28.
[14] M.R. Ayatollahi, H. Abbasi, Prediction of fracture using a strain based mechanism of crack growth, Build. Res. J. 49 (2001) 167-180.
[15] M. Ameri, A. Mansourian, M. Heidary Khavas, M.R.M. Aliha, M.R. Ayatollahi, Cracked asphalt pavement under traffic loading - A 3D finite element analysis, Eng. Fract. Mech. 78 (2011) 1817-1826.
[16] M.R. Ayatollahi, S. Pirmohammad, K. Sedighiani, Three-dimensional finite element modeling of a transverse top-down crack in asphalt concrete, Comput. Concrete. 13 (2014) 569-585.
[17] L.P. Pook, The fatigue crack direction and threshold behaviour of mild steel under mixed mode I and III loading, Int. J. Fatigue. 7 (1985) 21-30.
[18] H.F. Li, C.F. Qian, Experimental study of I + III mixed mode fatigue crack transformation propagation, Fatigue. Fract. Eng. M. 34 (2011) 53-59.
[19] X. Feng, A.M. Kumar, J.P. Hirth, Mixed mode I/III fracture toughness of 2034 aluminum alloys, Acta. Metall. Mater. 41 (1993) 2755-2764.
[20] Z. Wei, X. Deng, M.A. Sutton, J. Yan, C.S. Cheng, P. Zavattieri, Modeling of mixed-mode crack growth in ductile thin sheets under combined in-plane and out-of-plane loading. Eng. Fract. Mech. 78 (2011) 3082-3101.
[21] S.V. Kamat, M. Srinivas, R.P. Rama, Mixed mode I/III fracture toughness of Armco iron, Acta. Mater. 46 (1998) 4985-4992.
[22] M.R.M. Aliha, A. Bahmani, Sh. Akhondi, Numerical analysis of a new mixed mode I/III fracture test specimen, Eng. Fract. Mech. 134 (2015) 95-110.
[23] D. Tim, B. Birgisson, D. Newcomb, Development of mechanistic-empirical pavement design in Minnesota, J. Tran. Res. Rec. 1629 (1998) 181-188.
[24] M.R.M. Aliha, A. Bahmani, Sh. Akhondi, A novel test specimen for investigating the mixed mode I+ III fracture toughness of hot mix asphalt compositesExperimental and theoretical study, Int. J. Solids. Struct. 90 (2016) 167-177.
[25] M. Ameri, A. Mansourian, S. Pirmohammad, M.R.M. Aliha, M.R. Ayatollahi, Mixed mode fracture resistance of asphalt concrete mixtures, Eng. Fract. Mech. 93 (2012) 153-167.