Using the Multi-Parameter Fracture Mechanics for more Accurate Description of Stress/Displacement Crack Tip Fields

Abstract:

Most of fracture analyses often require an accurate knowledge of the stress/displacement field over the investigated body. However, this can be sometimes problematic when only one (singular) term of the Williams expansion is considered. Therefore, also other terms should be taken into account. Such an approach, referred to as multi-parameter fracture mechanics is used and investigated in this paper. Its importance for short/long cracks and the influence of different boundary conditions are studied. It has been found out that higher-order terms of the Williams expansion can contribute to more precise description of the stress distribution near the crack tip especially for long cracks. Unfortunately, the dependences obtained from the analyses presented are not unambiguous and it cannot be strictly derived how many of the higher-order terms are sufficient.

• Periodical: Key Engineering Materials (Volume 586)
• Pages: 237-240
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.586.237
• Online since: September 2013
• Authors: Lucie Šestáková
• Keywords: Higher-Order Terms Coefficients, Over-Deterministic Method, Stress/Displacement Crack-Tip Field, Williams Series Expansion

References

[1] S.G. Larson, A.J. Carlsson, Influence of non-singular stress terms and specimen geometry on small-scale yielding at crack-tips in elastic-plastic materials, J. Mech. Phys. Solids 21 (1973) 263-277.

DOI: 10.1016/0022-5096(73)90024-0

[2] J.R. Rice, Limitations to the small scale yielding approximation for crack tip plasticity, J. Mech. Phys. Solids 22 (1974) 17-26.

DOI: 10.1016/0022-5096(74)90010-6

[3] Z.Z. Du, J.W. Hancock, The effect of non-singular stresses on crack tip constraint, J. Mech. Phys. Solids 39 (1991) 555-567.

DOI: 10.1016/0022-5096(91)90041-l

[4] A.V. Dyskin, Crack growth criteria incorporating non-singular stresses: size effect in apparent fracture toughness, Int. J. Fract. 83 (1997) 191-206.

[5] M.R. Ayatollahi, J. Akbardoost, Size effects on fracture toughness of quasi-brittle materials – A new approach, Eng. Fract. Mech. 92 (2012) 89-100.

DOI: 10.1016/j.engfracmech.2012.06.005

[6] M.L. Williams, On the stress distribution at the base of a stationary crack, J. of Appl. Mech. 24 (1957) 109-114.

[7] M.R. Ayatollahi, M. Nejati, An over-deterministic method for calculation of coefficients of crack tip asymptotic field from finite element analysis, Fatigue Fract. Engng. Mater. Struct. 34 (2011) 159-176.

DOI: 10.1111/j.1460-2695.2010.01504.x

[8] 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, Eng. Fract. Mech. 68 (2001) 1609-1630.

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

[9] R.K.L. Su, S.L. Fok, Determination of coefficients of the crack tip asymptotic field by fractal hybrid finite elements, Eng. Fract. Mech. 74 (2007) 1649-1664.

DOI: 10.1016/j.engfracmech.2006.09.009

[10] P. Tong, T.H.H. Pian, S.J. Lasry, A hybrid element approach to crack problems in plane elasticity, Int. J. Num. Meth. Eng. 7 (1997) 297-308.

DOI: 10.1002/nme.1620070307

[11] Wolfram Mathematica Documentation Center, Wolfram Research, Inc., Champaign, (2007).

[12] L. Šestáková, Mixed-mode higher-order terms coefficients estimated using the over-deterministic method, in: Náprstek et al (Eds. ), Proceedings of 18th International Conference Engineering Mechanics, Prague, 2012, pp.1301-1307.

[13] 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 Eng. Mat. 488-489 (2012) 399-402.

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

[14] 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, Key Eng. Mat. 525-526 (2013) 529-532.

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

[15] L. Šestáková, V. Veselý, Convergence study on application of the over-deterministic method for de-termination of near-tip fields in a cracked plate loaded in mixed-mode, accepted to Appl. Mech. Mat. (2013).

DOI: 10.4028/www.scientific.net/amm.249-250.76

[16] L. Šestáková, 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, accepted to Appl. Mech. Mat. (2013).

DOI: 10.4028/www.scientific.net/amm.245.120

[17] L. Šestáková, V. Veselý, J. Sobek, P. Frantík, Z. Knésl, Accuracy of approximation of stress field in cracked bodies for failure zone extent estimation, submitted to VIII International Conference on Fracture Mechanics of Concrete and Concrete Structures (FraMCoS-8).