Skip to main content
Top
Published in: Acta Mechanica 2/2020

27-11-2019 | Original Paper

Accurate evaluation of stress intensity factors using dual interpolation boundary face method

Authors: Yunqiao Dong, Jianming Zhang, Weicheng Lin

Published in: Acta Mechanica | Issue 2/2020

Login to get access

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Accurate computation of stress intensity factors for two-dimensional cracks by a dual interpolation boundary face method (DiBFM) is presented in this paper. Dual interpolation method combines traditional element polynomial interpolation and moving least-squares approximation. Dual interpolation elements are obtained by adding virtual nodes on the boundary of traditional discontinuous elements, and they unify traditional continuous and discontinuous elements. With the dual interpolation elements, both the continuous and discontinuous fields can be approximated, and the accuracy of interpolation increases by two orders compared with the corresponding discontinuous elements. In addition, a new singular element based on the dual interpolation method for modeling displacement fields around the crack tip is proposed in this paper. The stress intensity factors are extracted from the relative displacements between the crack surfaces. Using the DiBFM combined with the proposed singular element, accurate results of the stress intensity factors can be obtained. Numerical examples have demonstrated the accuracy and efficiency of the proposed method.
Literature
1.
go back to reference Rooke, D.P., Cartwright, D.J.: Compendium of Stress Intensity Factors. Her Majesty’s Stationery Office, London (1976) Rooke, D.P., Cartwright, D.J.: Compendium of Stress Intensity Factors. Her Majesty’s Stationery Office, London (1976)
2.
go back to reference Murakami, Y.: Stress Intensity Factors Handbook. Pergamon Press, Oxford (1987) Murakami, Y.: Stress Intensity Factors Handbook. Pergamon Press, Oxford (1987)
3.
go back to reference Brebbia, C.A., Telles, J.C.F., Wrobel, L.C.: Boundary Element Techniques: Theory and Applications in Engineering. Springer, Berlin (1984)CrossRef Brebbia, C.A., Telles, J.C.F., Wrobel, L.C.: Boundary Element Techniques: Theory and Applications in Engineering. Springer, Berlin (1984)CrossRef
4.
go back to reference Cisilino, A.: Linear and Nonlinear Crack Growth Using Boundary Elements. WIT Press, Southampton (2000)MATH Cisilino, A.: Linear and Nonlinear Crack Growth Using Boundary Elements. WIT Press, Southampton (2000)MATH
5.
go back to reference Cheng, A.H.D., Cheng, D.T.: Heritage and early history of the boundary element method. Eng. Anal. Bound. Elem. 29, 268–302 (2005)CrossRef Cheng, A.H.D., Cheng, D.T.: Heritage and early history of the boundary element method. Eng. Anal. Bound. Elem. 29, 268–302 (2005)CrossRef
6.
go back to reference Sladek, V., Sladek, J., Tanaka, M.: Nonsingular BEM formulations for thin-walled structures and elastostatic crack problems. Acta Mech. 99(1–4), 173–190 (1993)MathSciNetCrossRef Sladek, V., Sladek, J., Tanaka, M.: Nonsingular BEM formulations for thin-walled structures and elastostatic crack problems. Acta Mech. 99(1–4), 173–190 (1993)MathSciNetCrossRef
7.
go back to reference Xie, G.Z., Zhang, D.H., Meng, F.N., et al.: Calculation of stress intensity factor along the 3D crack front by dual BIE with new crack front elements. Acta Mech. 228(9), 3135–3153 (2017)MathSciNetCrossRef Xie, G.Z., Zhang, D.H., Meng, F.N., et al.: Calculation of stress intensity factor along the 3D crack front by dual BIE with new crack front elements. Acta Mech. 228(9), 3135–3153 (2017)MathSciNetCrossRef
8.
go back to reference Xu, Z., Su, C., Guan, Z.W.: Analysis of multi-crack problems by the spline fictitious boundary element method based on Erdogan fundamental solutions. Acta Mech. 229(8), 3257–3278 (2018)MathSciNetCrossRef Xu, Z., Su, C., Guan, Z.W.: Analysis of multi-crack problems by the spline fictitious boundary element method based on Erdogan fundamental solutions. Acta Mech. 229(8), 3257–3278 (2018)MathSciNetCrossRef
9.
go back to reference Guo, Z., Liu, Y.J., Ma, H., et al.: A fast multipole boundary element method for modeling 2-D multiple crack problems with constant elements. Eng. Anal. Bound. Elem. 47, 1–9 (2014)MathSciNetCrossRef Guo, Z., Liu, Y.J., Ma, H., et al.: A fast multipole boundary element method for modeling 2-D multiple crack problems with constant elements. Eng. Anal. Bound. Elem. 47, 1–9 (2014)MathSciNetCrossRef
10.
go back to reference Liu, Y.J., Xu, N.: Modeling of interface cracks in fiber-reinforced composites with the presence of interphases using the boundary element method. Mech. Mater. 32(12), 769–783 (2000)CrossRef Liu, Y.J., Xu, N.: Modeling of interface cracks in fiber-reinforced composites with the presence of interphases using the boundary element method. Mech. Mater. 32(12), 769–783 (2000)CrossRef
11.
go back to reference Pan, E.: A general boundary element analysis of 2-D linear elastic fracture mechanics. Int. J. Fract. 88(1), 41–59 (1997)MathSciNetCrossRef Pan, E.: A general boundary element analysis of 2-D linear elastic fracture mechanics. Int. J. Fract. 88(1), 41–59 (1997)MathSciNetCrossRef
12.
go back to reference Blandford, G.E., Ingraffea, A.R., Liggett, J.A.: Two-dimensional stress intensity factor computations using the boundary element method. Int. J. Numer. Meth. Eng. 17(3), 387–404 (1981)CrossRef Blandford, G.E., Ingraffea, A.R., Liggett, J.A.: Two-dimensional stress intensity factor computations using the boundary element method. Int. J. Numer. Meth. Eng. 17(3), 387–404 (1981)CrossRef
13.
go back to reference Wen, P.H., Fan, T.H.: The discontinuity displacement method applied to three-dimensional co-planar crack problem for any boundary value condition. Eng. Fract. Mech. 48(5), 691–702 (1994)CrossRef Wen, P.H., Fan, T.H.: The discontinuity displacement method applied to three-dimensional co-planar crack problem for any boundary value condition. Eng. Fract. Mech. 48(5), 691–702 (1994)CrossRef
14.
go back to reference Ma, H., Guo, Z., Dhanasekar, M., et al.: Efficient solution of multiple cracks in great number using eigen COD boundary integral equations with iteration procedure. Eng. Anal. Bound. Elem. 37(3), 487–500 (2013)MathSciNetCrossRef Ma, H., Guo, Z., Dhanasekar, M., et al.: Efficient solution of multiple cracks in great number using eigen COD boundary integral equations with iteration procedure. Eng. Anal. Bound. Elem. 37(3), 487–500 (2013)MathSciNetCrossRef
15.
go back to reference Xie, G.Z., Zhang, J.M., Huang, C., et al.: A direct traction boundary integral equation method for three-dimension crack problems in infinite and finite domains. Comput. Mech. 53(4), 575–586 (2014)MathSciNetCrossRef Xie, G.Z., Zhang, J.M., Huang, C., et al.: A direct traction boundary integral equation method for three-dimension crack problems in infinite and finite domains. Comput. Mech. 53(4), 575–586 (2014)MathSciNetCrossRef
16.
go back to reference Hong, H.K., Chen, J.T.: Derivations of integral equations of elasticity. J. Eng. Mech. 114(6), 1028–1044 (1988)CrossRef Hong, H.K., Chen, J.T.: Derivations of integral equations of elasticity. J. Eng. Mech. 114(6), 1028–1044 (1988)CrossRef
17.
go back to reference Chen, J.T., Hong, H.K.: Review of dual boundary element methods with emphasis on hypersingular integrals and divergent series. Appl. Mech. Rev. 52(1), 17–33 (1999)CrossRef Chen, J.T., Hong, H.K.: Review of dual boundary element methods with emphasis on hypersingular integrals and divergent series. Appl. Mech. Rev. 52(1), 17–33 (1999)CrossRef
18.
go back to reference Wang, P.B., Yao, Z.H.: Fast multipole DBEM analysis of fatigue crack growth. Comput. Mech. 38(3), 223–233 (2006)CrossRef Wang, P.B., Yao, Z.H.: Fast multipole DBEM analysis of fatigue crack growth. Comput. Mech. 38(3), 223–233 (2006)CrossRef
19.
go back to reference Zhang, J.M., Qin, X.Y., Han, X., et al.: A boundary face method for potential problems in three dimensions. Int. J. Numer. Meth. Eng. 80(3), 320–337 (2009)MathSciNetCrossRef Zhang, J.M., Qin, X.Y., Han, X., et al.: A boundary face method for potential problems in three dimensions. Int. J. Numer. Meth. Eng. 80(3), 320–337 (2009)MathSciNetCrossRef
20.
go back to reference Zhang, J.M., Huang, C., Lu, C.J., et al.: Automatic thermal analysis of gravity dams with fast boundary face method. Eng. Anal. Bound. Elem. 41, 111–121 (2014)CrossRef Zhang, J.M., Huang, C., Lu, C.J., et al.: Automatic thermal analysis of gravity dams with fast boundary face method. Eng. Anal. Bound. Elem. 41, 111–121 (2014)CrossRef
21.
go back to reference Zhou, F.L., Li, Y., Zhang, J.M., et al.: A time step amplification method in boundary face method for transient heat conduction. Int. J. Heat Mass Transf. 84, 671–679 (2015)CrossRef Zhou, F.L., Li, Y., Zhang, J.M., et al.: A time step amplification method in boundary face method for transient heat conduction. Int. J. Heat Mass Transf. 84, 671–679 (2015)CrossRef
22.
go back to reference Zhang, J.M., Lin, W.C., Dong, Y.Q., et al.: A double-layer interpolation method for implementation of BEM analysis of problems in potential theory. Appl. Math. Model. 51, 250–269 (2017)MathSciNetCrossRef Zhang, J.M., Lin, W.C., Dong, Y.Q., et al.: A double-layer interpolation method for implementation of BEM analysis of problems in potential theory. Appl. Math. Model. 51, 250–269 (2017)MathSciNetCrossRef
23.
go back to reference Zhang, J.M., Lin, W.C., Dong, Y.Q.: A dual interpolation boundary face method for elasticity problems. Eur. J. Mech. A/Solids 73, 500–511 (2019)MathSciNetCrossRef Zhang, J.M., Lin, W.C., Dong, Y.Q.: A dual interpolation boundary face method for elasticity problems. Eur. J. Mech. A/Solids 73, 500–511 (2019)MathSciNetCrossRef
Metadata
Title
Accurate evaluation of stress intensity factors using dual interpolation boundary face method
Authors
Yunqiao Dong
Jianming Zhang
Weicheng Lin
Publication date
27-11-2019
Publisher
Springer Vienna
Published in
Acta Mechanica / Issue 2/2020
Print ISSN: 0001-5970
Electronic ISSN: 1619-6937
DOI
https://doi.org/10.1007/s00707-019-02573-x

Other articles of this Issue 2/2020

Acta Mechanica 2/2020 Go to the issue

Premium Partners