How to Enhance Efficiency and Accuracy of the Over-Deterministic Method Used for Determination of the Coefficients of the Higher-Order Terms in Williams Expansion

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Abstract:

Using higher-order terms of the Williams expansion is necessary for assessment of fracture behavior of quasi-brittle materials. Multi-parameter fracture mechanics enables more accurate determination of the stress/displacement field even in a larger distance from the crack tip, thus the extended zone with non-elastic behavior typical for this kind of material can be well described. The so-called over-deterministic method (ODM) seems to be a suitable tool for the higher-order terms coefficients calculation, but its utilization exhibits some limitations. Therefore, extensive analyses have been performed in order to summarize recommendations regarding the mesh sensitivity, boundary conditions influence, etc. List of pieces of advice and author’s experiences presented in the end of this work should contribute to more accurate and effective utilization of the ODM.

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120-125

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December 2012

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[1] M.L. Williams, On the stress distribution at the base of a stationary crack, Journal of Applied Mechanics 24 (1957) 109-114.

Google Scholar

[2] Z.J. Chao, X. Zhang, Constraint effect in brittle fracture, in: R.S. Piacik, J.C. Newman, D.E. Dowling (Eds.), Proceedings of 27th National Symposium on Fatigue and Fracture, ASTM STP 1296, Philadelphia, 1997, pp.41-60.

DOI: 10.1520/stp16227s

Google Scholar

[3] F. Berto, P. Lazzarin, On higher order terms in the crack tip stress field, International Journal of Fracture 161 (2010) 221-226.

DOI: 10.1007/s10704-010-9443-3

Google Scholar

[4] B.L. Karihaloo, Size effect in shallow and deep notched quasi-brittle structures, International Journal of Fracture 95 (1999) 379-390.

DOI: 10.1007/978-94-011-4659-3_21

Google Scholar

[5] B.L. Karihaloo, H.M. Abdalla, Q.Z. Xiao, Size effect in concrete beams, Engineering Fracture Mechanics 70 (2003) 979-993.

DOI: 10.1016/s0013-7944(02)00161-3

Google Scholar

[6] B.L. Karihaloo, Q.Z. Xiao, Accurate determination of the coefficients of elastic crack tip asymptotic field by a hybrid crack element with p-adaptivity, Engineering Fracture Mechanics 68 (2001) 1609-1630.

DOI: 10.1016/s0013-7944(01)00063-7

Google Scholar

[7] P. Tong, T.H.H. Pian, S.J. Lasry, A hybrid element approach to crack problems in plane elasticity, International Journal for Numerical Methods in Engineering 7 (1997) 297-308.

DOI: 10.1002/nme.1620070307

Google Scholar

[8] R.K.L. Su, S.L. Fok, Determination of coefficients of the crack tip asymptotic field by fractal hybrid finite elements, Engineering Fracture Mechanics 74 (2007) 1649-1664.

DOI: 10.1016/j.engfracmech.2006.09.009

Google Scholar

[9] Q.Z. Xiao, B.L. Karihaloo, X.Y. Liu, Direct determination of SIF and higher order terms of mixed mode cracks by a hybrid crack element, International Journal of Fracture 125 (2004) 207-225.

DOI: 10.1023/b:frac.0000022229.54422.13

Google Scholar

[10] M.R. Ayatollahi, M. Nejati, An over-deterministic method for calculation of coefficients of crack tip asymptotic field from finite element analysis. Fatigue & Fracture of Engineering Materials & Structures 00 (2010) 1-18.

DOI: 10.1111/j.1460-2695.2010.01504.x

Google Scholar

[11] B.L. Karihaloo, Q.Z. Xiao, Higher order terms of the crack tip asymptotic field for a notched three-point bend beam. International Journal of Fracture 112 (2001) 111-128.

Google Scholar

[12] B.L. Karihaloo, H.M. Abdalla, Q.Z. Xiao, Coefficients of the crack tip asymptotic field for wedge splitting specimens. Engineering Fracture Mechanics 70 (2003) 2407-2420.

DOI: 10.1016/s0013-7944(03)00005-5

Google Scholar

[13] ANSYS Program Documentation, User's manual version 10.0, Swanson Analysis System, Inc., Houston, 2005.

Google Scholar

[14] Wolfram Mathematica Documentation Center, Wolfram Research, Inc., Champaign, 2007.

Google Scholar

[15] R.K.L. Su, S.L. Fok, Determination of coefficients of the crack tip asymptotic field by fractal hybrid finite elements. Engineering Fracture Mechanics 74 (2007) 1649-1664.

DOI: 10.1016/j.engfracmech.2006.09.009

Google Scholar

[16] S.R. Chidgzey, A.J. Deeks, Determination of coefficients of crack tip asymptotic fields using the scaled boundary finite element method. Engineering Fracture Mechanics 72 (2005) 2019-2036.

DOI: 10.1016/j.engfracmech.2004.07.010

Google Scholar

[17] T. Fett, T-stresses in rectangular plates and circular disks. Engineering Fracture Mechanics 60 (1998) 631-652.

DOI: 10.1016/s0013-7944(98)00038-1

Google Scholar

[18] L. Šestáková, Tuning of an over-deterministic method for calculation of higher-order terms coefficients of the Williams expansion for basic cracked specimen configurations, in: L. Náhlík, M. Zouhar, M. Ševčík, S. Seitl, Z. Majer (Eds.), Proceedings of Conference Applied Mechanics, IPM AS CR, Brno, 2011, pp.211-214.

Google Scholar

[19] L. Šestáková, Mixed-mode higher-order terms coefficients estimated using the over-deterministic method, in: J. Náprstek, C. Fischer (Eds.), Proceedings of 18th International Conference Engineering Mechanics, ITAM AS CR, Prague, 2012, pp.1301-1307.

Google Scholar

[20] V. Veselý, J. Sobek, L. Šestáková, S. Seitl, Accurate description of near-crack-tip fields for the estimation of inelastic zone extent in quasi-brittle materials, accepted to Key Engineering Materials (expected in 2013).

DOI: 10.4028/www.scientific.net/kem.525-526.529

Google Scholar

[21] L. Šestáková, V. Veselý, Z. Keršner, Over-deterministic method convergence study on a mixed-mode geometry, under review in Applied Mechanics and Materials (expected in 2013).

Google Scholar

[22] V. Veselý, L. Šestáková, S. Seitl, Influence of boundary conditions on higher order terms of near-crack-tip stress field in a WST specimen, Key Engineering Materials 488-489 (2012) 399-402.

DOI: 10.4028/www.scientific.net/kem.488-489.399

Google Scholar