在基于最大能量释放率判据(Maximum energy release rate, MERR)的复合型裂纹扩展分析中,因需要对多个虚拟裂纹扩展方向进行试算和迭代运算,这会大大增加计算量,特别是为保证计算精度不得不选取很小的试算转角增量时,该问题会很突出。为此,提出分别基于有限差分法(Finite difference method, FDM)和最大周向应力判据(Maximum tangential stress, MTS)的裂纹转角预测方法,以减小计算量或提高计算精度。推导相关计算公式和算法,利用FORTRAN与ANSYS参数化设计语言(ANSYS parameter design language, APDL)语言混合编程的方法实现了基于ANSYS有限元环境下的裂纹扩展自动分析,并通过对带孔薄板的疲劳裂纹扩展分析,验证了所提出方法的有效性。分析发现,FDM的预测误差小于MTS的预测误差。MTS预测的转角误差曲线与转角曲线的一阶导数有相同的变化规律,而FDM预测转角的误差曲线与转角曲线的二阶导数有相同的变化规律。根据MERR和MTS判据得到的KII值趋近于零,这与局部对称判据(Local symmetry, LS)一致,但MERR和LS判据的计算结果更接近。
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 KII 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 KII value predicted.
[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.
