Improvements of the Crack Extension Algorithm Based on the Maximum Energy Release Rate Criterion

doi:10.3901/JME.2016.10.091

Abstract

Abstract: For a mixed-mode crack propagation analysis according to the maximum energy release rate(MERR) criterion, test and iterative calculation in multiple virtual crack extension directions significantly increases computation time, especially, when using smaller trying angle increments to insure accuracy of the analysis. To overcome the inconvenience, algorithms based on the finite difference method(FDM) and the maximum tangential stress(MTS) criterion are proposed for crack kinking angle prediction, so as to reduce computation time or to improve accuracy. Relevant formulation and algorithms are derived and verified for effectiveness via fatigue crack propagation analysis of a thin plate with holes. Automatic crack extension analysis by mixed language programming with FORTRAN and ANSYS parameter design language (APDL) in the ANSYS software is realized. Comparative analysis revealed that kinking angle prediction errors from FDM are smaller than those by MTS. The kinking angle errors resulted from MTS follow the same rule with the second derivatives of the kinking angle curve, while those from FDM follow the same fluctuation with the first derivatives of the kinking angle curve. It is found that K_II tends to be zero both for the MERR criterion and for the MTS criterion, which is consistent with the the local symmetry criterion(LS), while the MERR criterion seems more akin to the LS criterion in view of the K_II value predicted.

Key words: crack kinking direction, finite difference method, maximum energy release rate, maximum tangential stress

CLC Number:

O346

ZHU Youli, HOU Shuai, WANG Yanli, SUN Hanxiao. Improvements of the Crack Extension Algorithm Based on the Maximum Energy Release Rate Criterion[J]. Journal of Mechanical Engineering, 2016, 52(10): 91-96.

References

[1] ERDOGAN F,SIH G C. On the crack extension in plates under plane loading and transverse shear[J]. J. Basic Engineering,1963,85(2)：519-527.
[2] SIH G C. Strain energy density factor applied to mixed-mode crack problems[J]. International Journal of Fracture,1974,10(1)：305-321.
[3] NEMAT N S,HORII H. Compression-induced nonplanar crack with application to splitting, exfoliation and rockburst[J]. Journal of Geophysical Research,1982,87(8)：6805-6821.
[4] HUSSAIN M A,PU S L,UNDERWOOD J H. Strain energy release rate for a crack under combined mode I and mode II[J]. Fracture Analysis,1974(9)：2-28.
[5] GOLDSTEIN R V,SALGANIK R L. Brittle fracture of solids with arbitrary cracks[J]. International Journal of Fracture,1974,10(10)：507-523.
[6] SUTTON M A,DENG X,MA F,et al. Development and application of a crack tip opening displacement-based mixed mode fracture criterion[J]. Int. J. Struct. Solids,2000,37(2)：3591-3618.
[7] LEN T K. On the method of virtual crack extension[J]. Int. J. Numer. Meth. Eng.,1975(9)：187-207.
[8] BROEK D. Elementary engineering fracture mechanics[M]. Dordrecht：Martinus Nijho Publishers,1986.
[9] KANNINEN M,POPELAR C. Advanced fracture mechanics[M]. Oxford：Oxford University Press,1985.
[10] ANSYS Inc. ANSYS Release 11.0 Documentation[EB/OL]. [2006-12-01]. http：//www.ansys. com/.
[11] NISHIOKA T,MAYUKO M,WON Y J,et al. Simulation of fatigue fracture path prediction in materials containing holes or inclusions using moving finite element method[C]//Transactions of the Japan Society of Mechanical Engineer.A,Tokyo,Japan,2008,74(6)：805-811．
[12] MATTHEW J P. Variable amplitude fatigue analysis using surrogate models and exact XFEM reanalysis[D]. Tallahassee：University of Florida,2011.
[13] COTTERELL B,RICE J R. Slightly curved or kinked cracks[J]. International Journal of Fracture,1980,16(2)：155-169.
[14] JOSHUA H M. Fatigue crack growth analysis with finite element methods and a monte carlo simulation[D]. Charlattesville：Virginia Polytechnic Institute and State University,2014.
[15] NISHIOKA T. Recent advances in numerical simulation technologies for various dynamic fracture phenomena[J]. Computer Modeling in Engineering & Sciences,2005,10(3)：209-215.
[16] DOQUET V,POMMIER S. Fatigue crack growth under non proportional mixed-mode loading in ferritic-pearlitic steel[J]. Fatigue Frac. Eng Mater. Struct.,2004(27)：1051-1060.