Experimental investigations on the cracking and mechanical responses of PMMA samples with two 3D embedded elliptic flaws under uniaxial compression

Abstract

In this paper, the cracking and mechanical responses are studied for the Polymethylmethacrylate (PMMA) sample with two three-dimensional embedded coplanar elliptic flaws subjected to uniaxial compression. The experi- mental results indicate that both the peak stress and crack initiation stress first decrease and then increase with increasing flaw angle, and they increase linearly with increasing flaw spacing. Moreover, five crack modes occur in these tested samples, including the coplanar secondary cracks, wing cracks, petal cracks, anti-wing cracks, and vertical giant cracks. The growth length of wing cracks is approximately equal to the length of the long axis of pre- existing flaw. However, the maximum width is roughly equal to half the length of the long axis of pre-existing elliptic flaw. The final failure modes include the splitting failure induced by wing cracks and vertical giant cracks, and the mixed tensile-shear failure induced by coplanar secondary cracks and wing cracks.

Keywords

Two 3D embedded coplanar elliptic flaws / Mechanical properties / Cracking behaviors / PMMA sample / Uniaxial compression

References

[1] P. Cao, T.Y. Liu, C.Z. Pu, H. Lin, Crack propagation and coalescence of brittle rock- like samples with pre-existing cracks in compression, Eng. Geol. 187 ( 2015) 113-121.

[2] A. Bobet, H.H. Einstein, Fracture coalescence in rock-type materials under uniaxial and biaxial compression, Int. J. Rock Mech. Min. Sci. 35 ( 1998) 863-888.

[3] M. Havaej, J. Coggan, D. Stead, D. Elmo, A combined remote sensing-numerical modelling approach to the stability analysis of Delabole slate Quarry, Cornwall, UK, Rock Mech. Rock Eng. 49 ( 2016) 1227-1245.

[4] M. Sartori, F. Baillifard, M. Jaboyedoff, J.D. Rouiller, Kinematics of the 1991 randa rockslides (Valais, Switzerland), Nat. Hazards. Earth Syst Sci. 3 ( 2003) 423-433.

[5] M.A. Brideau, M. Yan, D. Stead, The role of tectonic damage and brittle rock fracture in the development of large rock slope failures, Geomorphology 103 ( 2009) 30-49.

[6] R.H.C. Wong, K.T. Chau, C.A. Tang, P. Lin, Analysis of crack coalescence in rock-like materials containing three flaws—part I: experimental approach, Int. J. Rock Mech. Min. Sci. 38 ( 2001) 909-924.

[7] C.H. Park, A. Bobet, Crack coalescence in samples with open and closed flaws: a comparison, Int. J. Rock Mech. Min. Sci. 46 ( 2009) 819-829.

[8] S.Q. Yang, X.R. Liu, H.W. Jing, Experimental investigation on fracture coalescence behavior of red sandstone containing two unparallel fissures under uniaxial compression, Int. J. Rock Mech. Min. Sci. 63 ( 2013) 82-92.

[9] S.Q. Yang, W.L. Tian, Y.H. Huang, P.G. Ranjith, Y. Ju, An experimental and numerical study on cracking behavior of brittle sandstone containing two non- coplanar fissures under uniaxial compression, Rock Mech. Rock Eng. 49 ( 2016) 1497-1515.

[10] X.Y. Zhuang, J.W. Chun, H.H. Zhu, A comparative study on unfilled and filled crack propagation for rock-like brittle material, Theor. Appl. Fract. Mech. 72 ( 2014) 110-120.

[11] X.P. Zhou, H. Cheng, Y.F. Feng, An experimental study of crack coalescence behavior in rock-like materials containing multiple flaws under uniaxial compression, Rock Mech. Rock Eng. 47 ( 2014) 1961-1986.

[12] H. Cheng, X.P. Zhou, J. Zhu, Q.H. Qian, The effects of crack openings on crack initiation, propagation and coalescence behavior in rock-like materials under uniaxial compression, Rock Mech. Rock Eng. 49 ( 2016) 3481-3494.

[13] P. Yin, R.H.C. Wong, K.T. Chau, Coalescence of two parallel pre-existing surface cracks in granite, Int. J. Rock Mech. Min. Sci. 68 ( 2014) 66-84.

[14] R.H.C. Wong, C.M. Law, K.T. Chau, W.S. Zhu, Crack propagation from 3-D surface fractures in PMMA and marble samples under uniaxial compression, Int. J. Rock Mech. Min. Sci. 41 ( 2004) 37-42.

[15] R.H.C. Wong, Y.S.H. Guo, L.Y. Li, K.T. Chau, W.S. Zhu, S.C. Li,Anti-wing crack growth from surface flaw in real rock, in:Proceedings of the 16th European Conference of Fracture, 2006, pp. 825-826. Alexandroupolis.

[16] R.H.C. Wong, Y.S.H. Guo, L.Q. Liu, P.X. Liu, S.P. Ma,Nucleation and growth of anti- wing crack from tips of strike-slip flaw, in:Proceedings of the 42nd US Rock Mechanics Symposium (USRMS), 2008, pp. 221-229. San Francisco.

[17] S. Abharian, V. Sarfarazi, M.F. Marji, H. Rasekh, Experimental and numerical evaluation of the effects of interaction between multiple small holes and a single notch on the mechanical behavior of artificial gypsum specimens, Theor. Appl. Fract. Mech. 121 ( 2022), 103462.

[18] J.W. Fu, H.D. Haeri, V. Sarfarzi, K. Asgari, M.F. Marji, The shear behaviors of concrete-gypsum specimens containing double edge cracks under four-point loading conditions, Theor. Appl. Fract. Mech. 119 ( 2022), 103361.

[19] X.P. Zhou, J.Z. Zhang, L.N.Y. Wong, Experimental study on the growth, coalescence and wrapping behavior of 3D cross-embedded flaws under uniaxial compression, Rock Mech. Rock Eng. 51 ( 2018) 1379-1400.

[20] X.P. Zhou, L. Fu, W. Ju, F. Berto, An experimental study of the mechanical and fracturing behavior in PMMA sample containing multiple 3D embedded flaws under uniaxial compression, Theor. Appl. Fract. Mech. 101 ( 2019) 207-216.

[21] A.V. Ayskin, L.N. Germanovich, R.J. Jewell, H. Joer, J.S. Krasinski, K.K. Lee, Study of 3D mechanisms of crack growth and interaction in uniaxial compression, ISRM News J 2 ( 1994) 17-20.

[22] A.V. Dyskin, R.J. Jewell, H. Joer, E. Sahouryeh, K.B. Ustinov, Experiments on 3D crack growth in uniaxial compression, Int. J. Fract. 65 ( 1994) 77-83.

[23] A.V. Dyskin, E. Sahouryeh, R.J. Jewell, H. Joer, K.B. Ustinov, Influence of shape and locations of initial 3D cracks on their growth in uniaxial compression, Eng. Fract. Mech. 70 ( 2003) 2115-2136.

[24] E. Sahouryeh, A.V. Dyskin, L.N. Germanovich, Crack growth under biaxial compression, Eng. Fract. Mech. 69 ( 2002) 2187-2198.

[25] Y.S. Guo, C.J. Lin, W.S. Zhu, S.C. Li, Experimental research on propagation and coalescence process of three-dimensional flaw-sets, Chin. J. Rock Mech. Eng. 27 ( 2008) 3191-3195 (in Chinese).

[26] J.W. Fu, K. Chen, W.S. Zhu, X.Z. Zhang, X.J. Li, Progressive failure of new modelling material with a single internal crack under biaxial compression and the 3-D numerical simulation, Eng. Fract. Mech. 165 ( 2016) 140-152.

[27] P.R. Sheorey, Empirical Rock Failure Criteria, Balkema AA, Rotterdam, 1997, pp. 176-181.