基于单元应力外推法的中心裂纹板应力强度因子精度研究
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摘要
利用ABAQUS有限元软件建立有限宽中心裂纹板的裂纹扩展有限元模型,选取裂纹前端不同数目单元,采用三种基于单元应力外推法的最小二乘法拟合应力场和位移场数据对(ri,KIi),得到中心裂纹板裂纹尖端处I型裂纹应力强度因子。通过与理论解对比,结果表明:每种方法都对应一个最佳单元选取数目,方法二对应的最佳单元选取数目最小,方法三对应的最佳单元选取数目居中,方法一对应的最佳单元选取数目最大;裂纹前端单元选取数目小于最佳数目时数值解小于理论解,裂纹前端单元选取数目大于最佳数目时数值解大于理论解;应力强度因子的求解精度与单元选取数目和拟合方法有关。三种方法的比较分析,对采用基于单元应力外推法求解应力强度因子时单元数目和拟合方法的选取具有指导意义。
A finite element model for crack-expanding in the limited-width plate with central cracks in the light of the finite element software of ABAQUS in the paper,upon the basis of which different numbers of elements of the front end of the crack are selected and three element-stress-extrapolation-method-based least square method is adopted to fit the data pair(ri,KIi)of the stress field and the displacement field so as to obtain the I-type cracking intensity factor for the front end of the crack in the plate with central cracks.On the basis of comparing the results with those of the theoretical solution,it is found that each of the methods is relative to a selected number of the optimal element.The selected number of the optimal element relative to Method Two is the least,the selected number of the optimal element relative to Method Three is in the middle,and the selected number of the optimal element relative to Method One is the largest.When the selected number of the front end element ofthe crack is less than the optimal number,the value solution is less than the theoretical solution.When theselected number of the front end element of the crack is greater than the optimal number,the value solution is also greater than the theoretical solution.The accuracy of the stress intensity factor is related to both the selected number of the element at the front end of the crack and the fitting method.Through the comparative analysis of the three methods,it is found that the paper may serve as a useful reference for the choice of the numbers of elements and the fitting methods when the stress intensity factor is obtained by the element-stress-based extrapolation method.
A finite element model for crack-expanding in the limited-width plate with central cracks in the light of the finite element software of ABAQUS in the paper,upon the basis of which different numbers of elements of the front end of the crack are selected and three element-stress-extrapolation-method-based least square method is adopted to fit the data pair(ri,KIi)of the stress field and the displacement field so as to obtain the I-type cracking intensity factor for the front end of the crack in the plate with central cracks.On the basis of comparing the results with those of the theoretical solution,it is found that each of the methods is relative to a selected number of the optimal element.The selected number of the optimal element relative to Method Two is the least,the selected number of the optimal element relative to Method Three is in the middle,and the selected number of the optimal element relative to Method One is the largest.When the selected number of the front end element ofthe crack is less than the optimal number,the value solution is less than the theoretical solution.When theselected number of the front end element of the crack is greater than the optimal number,the value solution is also greater than the theoretical solution.The accuracy of the stress intensity factor is related to both the selected number of the element at the front end of the crack and the fitting method.Through the comparative analysis of the three methods,it is found that the paper may serve as a useful reference for the choice of the numbers of elements and the fitting methods when the stress intensity factor is obtained by the element-stress-based extrapolation method.
引文
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[12]ALBRECHT P,LENWARI A.Stress intensity factor for center-cracked plate with crack surface interference[J].Engineering fracture mechanics,2006,73(08):1035-1045
[13]彭国良,闫辉,杜太焦.I型裂纹虚拟裂纹闭合法的误差分析及修正[J].固体力学学报,2016,37(03):280-283
[2]马文涛,许艳,马海龙.修正的内部基扩充无网格法求解多裂纹应力强度因子[J].工程力学,2015,32(10):18-24
[3]程勒.断裂力学[M].北京:科学出版社,2006:8-12
[4]LIU P F,HOU S J,CHU J K,et al.Finite element analysis of postbuckling and delamination of composite laminates using virtual crack closure technique[J].Composite structures,2011,93(06):1549-1560
[5]ZENG W,LIU G R,JIANG C,et al.An effective fracture analysis method based on the virtual crack closure-Integral technique implemented in cs-Fem[J].Applied mathematical modelling,2016,40(05):3783-3800
[6]QIAO D,CHANG Y Z,JIAN P,et al.Experiment finite element analysis and epri solution for J-integral of commercially pure titanium[J].Rare metal materials and engineering,2014,43(02):257-263
[7]TUAN B M,陈云飞.平板表面裂纹应力强度因子和应力分布规律的确定[J].东南大学学报(自然科学版),2014,44(04):728-734
[8]杨巍,张宁,许良.基于有限元法对裂纹尖端应力强度因子的计算[J].沈阳航空航天大学学报,2014,31(03):19-23
[9]KASTRATOVI C′G,GRBOVI C′A,VIDANOVI C′N.Approximate method for stress intensity factors determination in case of multiple site damage[J].Applied mathematical modelling,2015,39(19):6050-6059
[10]任中俊,陈跃欣.有限大平板中心裂纹应力强度因子分析[J].矿业工程研究,2013,28(04):1-3
[11]KIM S,LEE H-C.A finite element method for computing accurate solutions for poisson equations with corner singularities using the stress intensity factor[J].Computers&mathematics with applications,2016,71(11):2330-2337
[12]ALBRECHT P,LENWARI A.Stress intensity factor for center-cracked plate with crack surface interference[J].Engineering fracture mechanics,2006,73(08):1035-1045
[13]彭国良,闫辉,杜太焦.I型裂纹虚拟裂纹闭合法的误差分析及修正[J].固体力学学报,2016,37(03):280-283