基于光滑边域有限元法的二维裂纹扩展分析
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摘要
为了提高预测裂纹扩展路径的准确性和效率,本文将光滑边域有限元法和虚拟裂纹闭合法相结合,利用常应变三角形单元,获得裂纹尖端处的断裂控制参量应力强度因子,并运用最大拉应力准则求得裂纹在荷载作用下的启裂方向,对裂纹扩展轨迹给出自动跟踪方法;对三个典型二维裂纹扩展模型,预测了裂纹扩展路径,并将结果与参考文献中的结果进行对比,验证方法的有效性与准确性。数值结果表明:该方法具有单元简单、网格尺寸要求低、裂纹尖端处单元不需特殊处理等优点,是分析裂纹扩展问题简洁高效的数值计算方法。
In order to improve the solution accuracy and efficiency of the crack path prediction, the edge-based smoothed finite element method(ES-FEM) and virtual crack closure technique(VCCT) are combined to calculate the stress intensity factor of the crack tip, by using constant strain triangular element. The maximum tensile stress criterion is used to determine the crack propagation direction. The strategy for ES-FEM tracking crack propagation is given. The crack propagation paths are predicted for three typical two-dimensional crack growth models. The results are in good agreement with the results in the references. The numerical method shows many advantages: using simple elements, less requirements for meshing, no particular disposal on crack-tip elements, etc. Therefore it is a simple and efficient numerical method for analyzing crack propagation problems.
In order to improve the solution accuracy and efficiency of the crack path prediction, the edge-based smoothed finite element method(ES-FEM) and virtual crack closure technique(VCCT) are combined to calculate the stress intensity factor of the crack tip, by using constant strain triangular element. The maximum tensile stress criterion is used to determine the crack propagation direction. The strategy for ES-FEM tracking crack propagation is given. The crack propagation paths are predicted for three typical two-dimensional crack growth models. The results are in good agreement with the results in the references. The numerical method shows many advantages: using simple elements, less requirements for meshing, no particular disposal on crack-tip elements, etc. Therefore it is a simple and efficient numerical method for analyzing crack propagation problems.
引文
[1]LIU G R,NGUYEN T T.Smoothed finite element methods[J].Tsinghua science&technology,2010,12(5):497-508.
[2]LIU G R,NGUYEN T T,LAM KY.An edge-based smoothed finite element method(ES-FEM)for static,free and forced vibration analyses of solids[J].Journal of sound&vibration,2009,320(4):1100-1130.
[3]NGUYEN T T,LIU G R,NGUYEN X H.An n-sided polygonal edge-based smoothed finite element method(nES-FEM)for solid mechanics[J].International journal for numerical methods in biomedical engineering,2011,27(9):1446-1472.
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[5]谢伟,贺旭东,吴建国,等.二维光滑边域有限元法在弹性力学中的应用研究[J].西北工业大学学报,2017,35(1):7-12.(XIE Wei,HE Xudong,WU Jianguo,et al.An edge-based smoothed finite element method for 2D mechanics problems[J].Journal of northwestern polytechnical university,2017,35(1):7-12(in Chinese)).
[6]周立明,孟广伟,王晖,等.基于光滑有限元的含裂纹复合材料的虚拟裂纹闭合法[J].湖南大学学报(自然科学版),2014,41(8):36-40.(ZHOU Liming,MENG Guangwei,WANG Hui,et al.Virtual crack closure technique based on smoothed finite element method for composite materials with cracks[J].Journal of Hunan university(natural sciences),2014,41(8):36-40(in Chinese)).
[7]蔡勇,王琥,李光耀,等.基于边光滑三角形壳元和统一计算架构的板料成形仿真并行计算方法[J].机械工程学报,2012,48(6):32-38.(CAI Yong,WANG Hu,LI Guangyao,et al.Parallel simulation of sheet metal forming based on EST element and compute unified device architecture[J].Journal of mechanical engineering,2012,48(6):32-38(in Chinese)).
[8]CHEN H D,WANG Q S,LIU G R,et al.Simulation of thermoelastic crack problems using singular edge-based smoothed finite element method[J].International journal of mechanical sciences,2016(115/116):123-134.
[9]RYBICKI E F,KANNINEN M F.A finite element calculation of stress intensity factors by a modified crack closure integral[J].Engineering fracture mechanics,1977,9(4):931-938.
[10]XIE D,SHERRILL B,BIGGERS J.Progressive crack growth using interface element based on the virtual crack closure technique[J].Finite element in analysis and design,2006,42(11):977-984.
[11]XIE D,JR S B B.Strain energy release rate calculation for a moving delamination front of arbitrary shape based on the virtual crack closure technique.part I:formulation and validation[J].Engineering fracture mechanics,2006,73(6):771-785.
[12]XIE D,JR S B B.Strain energy release rate calculation for a moving delamination front of arbitrary shape based on the virtual crack closure technique.part II:sensitivity study on modeling details[J].Engineering fracture mechanics,2006,73(6):786-801.
[13]RICCIO A,DAMIANO M,RAIMONDO A,et al.A fast numerical procedure for the simulation of inter-laminar damage growth in stiffened composite panels[J].Composite structures,2016,145:203-216.
[14]KRUEGER R.Virtual crack closure technique:history,approach,and applications[J].Applied mechanics reviews,2002,57(1):109-143.
[15]BROEK D.Elementary engineering fracture mechanics[M].Dordrecht:Sijthoff&Noordhoff,1978.
[16]MOES N,DOLBOW J,BELYTSCHKO T.A finite element method for crack growth without remeshing[J].International journal for numerical methods in engineering,1999,46(1):131-150.
[17]VARFOLOMEEV I,BURDACK M,MOROZ S,et al.Fatigue crack growth rates and paths in two planar specimens under mixed mode loading[J].International journal of fatigue,2014,58(1):12-19.
[18]LIU Y J,LI Y X,XIE W.Modeling of multiple crack propagation in2-D elastic solids by the fast multipole boundary element method[J].Engineering fracture mechanics,2017,172:1-16.
[19]INGRAFFEA A R,GRIGORIU M.Probabilistic fracture mechanics:a validation of predictive capability[J].Probabilistic fracture mechanics a validation of predictive capability,1990.
[20]ARREA M.Mixed-mode crack propagation in mortar and concrete:81-13[R].Ithaca:Cornell University,1982.
[21]YANG Z.Fully automatic modelling of mixed-mode crack propagation using scaled boundary finite element method[J].Engineering fracture mechanics,2006,73(12):1711-1731.
[22]LI Jianbo,FU Xiang’an,CHEN Baibin,et al.Modeling crack propagation with the extended scaled boundary finite element method based on the level set method[J].Computers and structures,2016,167:50-68.
[2]LIU G R,NGUYEN T T,LAM KY.An edge-based smoothed finite element method(ES-FEM)for static,free and forced vibration analyses of solids[J].Journal of sound&vibration,2009,320(4):1100-1130.
[3]NGUYEN T T,LIU G R,NGUYEN X H.An n-sided polygonal edge-based smoothed finite element method(nES-FEM)for solid mechanics[J].International journal for numerical methods in biomedical engineering,2011,27(9):1446-1472.
[4]JIANG C,ZHANG Z Q,LIU G R,et al.An edge-based/node-based selective smoothed finite element method using tetrahedrons for cardiovascular tissues[J].Engineering analysis with boundary elements,2015,59:62-77.
[5]谢伟,贺旭东,吴建国,等.二维光滑边域有限元法在弹性力学中的应用研究[J].西北工业大学学报,2017,35(1):7-12.(XIE Wei,HE Xudong,WU Jianguo,et al.An edge-based smoothed finite element method for 2D mechanics problems[J].Journal of northwestern polytechnical university,2017,35(1):7-12(in Chinese)).
[6]周立明,孟广伟,王晖,等.基于光滑有限元的含裂纹复合材料的虚拟裂纹闭合法[J].湖南大学学报(自然科学版),2014,41(8):36-40.(ZHOU Liming,MENG Guangwei,WANG Hui,et al.Virtual crack closure technique based on smoothed finite element method for composite materials with cracks[J].Journal of Hunan university(natural sciences),2014,41(8):36-40(in Chinese)).
[7]蔡勇,王琥,李光耀,等.基于边光滑三角形壳元和统一计算架构的板料成形仿真并行计算方法[J].机械工程学报,2012,48(6):32-38.(CAI Yong,WANG Hu,LI Guangyao,et al.Parallel simulation of sheet metal forming based on EST element and compute unified device architecture[J].Journal of mechanical engineering,2012,48(6):32-38(in Chinese)).
[8]CHEN H D,WANG Q S,LIU G R,et al.Simulation of thermoelastic crack problems using singular edge-based smoothed finite element method[J].International journal of mechanical sciences,2016(115/116):123-134.
[9]RYBICKI E F,KANNINEN M F.A finite element calculation of stress intensity factors by a modified crack closure integral[J].Engineering fracture mechanics,1977,9(4):931-938.
[10]XIE D,SHERRILL B,BIGGERS J.Progressive crack growth using interface element based on the virtual crack closure technique[J].Finite element in analysis and design,2006,42(11):977-984.
[11]XIE D,JR S B B.Strain energy release rate calculation for a moving delamination front of arbitrary shape based on the virtual crack closure technique.part I:formulation and validation[J].Engineering fracture mechanics,2006,73(6):771-785.
[12]XIE D,JR S B B.Strain energy release rate calculation for a moving delamination front of arbitrary shape based on the virtual crack closure technique.part II:sensitivity study on modeling details[J].Engineering fracture mechanics,2006,73(6):786-801.
[13]RICCIO A,DAMIANO M,RAIMONDO A,et al.A fast numerical procedure for the simulation of inter-laminar damage growth in stiffened composite panels[J].Composite structures,2016,145:203-216.
[14]KRUEGER R.Virtual crack closure technique:history,approach,and applications[J].Applied mechanics reviews,2002,57(1):109-143.
[15]BROEK D.Elementary engineering fracture mechanics[M].Dordrecht:Sijthoff&Noordhoff,1978.
[16]MOES N,DOLBOW J,BELYTSCHKO T.A finite element method for crack growth without remeshing[J].International journal for numerical methods in engineering,1999,46(1):131-150.
[17]VARFOLOMEEV I,BURDACK M,MOROZ S,et al.Fatigue crack growth rates and paths in two planar specimens under mixed mode loading[J].International journal of fatigue,2014,58(1):12-19.
[18]LIU Y J,LI Y X,XIE W.Modeling of multiple crack propagation in2-D elastic solids by the fast multipole boundary element method[J].Engineering fracture mechanics,2017,172:1-16.
[19]INGRAFFEA A R,GRIGORIU M.Probabilistic fracture mechanics:a validation of predictive capability[J].Probabilistic fracture mechanics a validation of predictive capability,1990.
[20]ARREA M.Mixed-mode crack propagation in mortar and concrete:81-13[R].Ithaca:Cornell University,1982.
[21]YANG Z.Fully automatic modelling of mixed-mode crack propagation using scaled boundary finite element method[J].Engineering fracture mechanics,2006,73(12):1711-1731.
[22]LI Jianbo,FU Xiang’an,CHEN Baibin,et al.Modeling crack propagation with the extended scaled boundary finite element method based on the level set method[J].Computers and structures,2016,167:50-68.