满足断裂过程区裂纹张开位移条件应力函数的半解析解法
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摘要
基于Duan-Nakagawa模型,采用加权积分法,提出了一种满足断裂过程区裂纹张开位移条件应力函数的半解析解法.该方法结合边界选点法,通过叠加含有相同裂纹长度但断裂过程区长度不同的解析函数,得到满足给定裂纹张开位移的权函数,再进行加权积分得到相应的应力函数和位移函数.以带板对称边裂纹I型问题为例,应用上述方法成功导出了特定的应力函数和位移函数,以及相应的拉应变软化曲线和断裂能.
Based on the Duan-Nakagawa model,with the weighted integral method,a semi-analytical method for stress functions meeting crack opening displacements in fracture process zones was proposed.The weighted function was determined by means of the boundary selected point method and the superposition of analytical functions with the same crack length but different fracture process zone lengths,to meet the given crack opening displacement in the fracture process zone,and then the final stress function and displacement function can be obtained with the weighted integral method. As an example,a special analytical solution for a double edge notched plate under Mode-I loading was derived,and the tensile strain softening curve and the fracture energy were obtained.
Based on the Duan-Nakagawa model,with the weighted integral method,a semi-analytical method for stress functions meeting crack opening displacements in fracture process zones was proposed.The weighted function was determined by means of the boundary selected point method and the superposition of analytical functions with the same crack length but different fracture process zone lengths,to meet the given crack opening displacement in the fracture process zone,and then the final stress function and displacement function can be obtained with the weighted integral method. As an example,a special analytical solution for a double edge notched plate under Mode-I loading was derived,and the tensile strain softening curve and the fracture energy were obtained.
引文
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[15]冯孝杰.大体积混凝土软化曲线的新确定方法[D].硕士学位论文.杭州:浙江工业大学,2012.(FENG Xiaojie.A new method of determining softening curve of mass concrete[D].Master Thesis.Hangzhou:Zhejiang University of Technology,2012.(in Chinese))
[16]SU R K L,CHEN H H N,KWAN A K H.Incremental displacement collocation method for the evaluation of tension softening curve of mortar[J].Engineering Fracture Mechanics,2012,88:49-62.
[17]DUAN S J,NAKAGAWA K.Stress functions with finite stress concentration at the crack tips for a central cracked panel[J].Engineering Fracture Mechanics,1988,29(5):517-526.
[18]ZHU M,CHANG W V.An unsymmetrical fracture process zone model and its application to the problem of a radical crack with an inclusion in longitudinal shear deformation[C]//Proceedings of FRAMCOS-3/Fracture Mechanics of Concrete Structures.Freiburg,Germany,1997:1097-1106.
[19]段树金,前田春和,藤井康寿,等.沿直线有多条裂纹的薄板弯曲问题[J].工程力学,1999,16(3):21-29.(DUAN Shujin,MAEDA H,FUJII K,et al.The problem of bending of a thin plate with a number of cracks along the line[J].Engineering Mechanics,1999,16(3):21-29.(in Chinese))
[20]DUAN S J,NAKAGAWA K.A mathematical approach of fracture macromechanics for strain-softening material[J].Engineering Fracture Mechanics,1989,34(5):1175-1182.
[21]ROELFSTRA P E,WITTMANN F H.Numerical method to link strain softening with failure of concrete[C]//Fracture Toughness and Fracture Energy in Concrete.Amsterdam,Netherlands,1986:163-175.
[2]DUGDALE D S.Yielding of steel sheets containing slits[J].Journal of the Mechanics and Physics of Solids,1960,8(2):100-104.
[3]RUSCH H,HILSDORF H.Deformation characteristics of concrete under axial tension[R].Vorunterschungen 44,Munich,Bericht,1963.
[4]EVANS R H,MARATHE M S.Microcracking and stress-strain curves for concrete in tension[J].Material and Structures,1968,1(1):61-64.
[5]HILLERBORG A,MODEER M,PETERSON P.Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements[J].Cement and Concrete Research,1976,6(6):773-782.
[6]ELICES M,GUINEA G V,GOMEZ J,et al.The cohesive zone model:advantages,limitations and challenges[J].Engineering Fracture Mechanics,2002,69(2):137-163.
[7]卿龙邦,李庆斌,管俊峰,等.基于虚拟裂缝模型的混凝土断裂过程区研究[J].工程力学,2012,29(9):112-116.(QING Longbang,LI Qingbin,GUAN Junfeng,et al.Study of concrete fracture process zone based on fictitious crack model[J].Engineering Mechanics,2012,29(9):112-116.(in Chinese))
[8]BAZANT Z P.Concrete fracture models:testing and practice[J].Engineering Fracture Mechanics,2002,69(2):165-205.
[9]LI Q B,ANSARI F.High-strength concrete in uniaxial tension[J].ACI Materials Journal,2000,97(1):49-57.
[10]丁晓唐,丁鑫,刘海霞,等.混凝土直拉试验和三点弯曲断裂试验确定的软化曲线的比较[J].水电能源科学,2014,32(1):116-118.(DING Xiaotang,DING Xin,LIU Haixia,et al.Comparison study of softening curves of concrete by direct tension test and three-point bending fracture test[J].Water Resources and Power,2014,32(1):116-118.(in Chinese))
[11]ZHAO Z,ZHANG J,ZHOU H,et al.Two methods for determining softening relationship of dam concrete and wet-screened concrete[J].Advances in Structural Engineering,2016,15(15):1125-1138.
[12]RICE J R.A path independent integral and the approximate analysis of strain concentration by notches and cracks[J].Journal of Applied Mechanics,1968,35(2):379-386.
[13]赵志方,李铭,赵志刚.逆推混凝土软化曲线及其断裂能的研究[J].混凝土,2010(7):4-7.(ZHAO Zhifang,LI Ming,ZHAO Zhigang.Research on reversing softening curve and fracture energy of concrete[J].Concrete,2010(7):4-7.(in Chinese))
[14]赵志方,王刚,周厚贵,等.混凝土拉伸软化曲线确定方法的对比研究[J].浙江工业大学学报,2015,43(4):455-459.(ZHAO Zhifang,WANG Gang,ZHOU Hougui,et al.A comparative study of the methods for determining the tensile softening curve of concrete[J].Journal of Zhejiang University of Technology,2015,43(4):455-459.(in Chinese))
[15]冯孝杰.大体积混凝土软化曲线的新确定方法[D].硕士学位论文.杭州:浙江工业大学,2012.(FENG Xiaojie.A new method of determining softening curve of mass concrete[D].Master Thesis.Hangzhou:Zhejiang University of Technology,2012.(in Chinese))
[16]SU R K L,CHEN H H N,KWAN A K H.Incremental displacement collocation method for the evaluation of tension softening curve of mortar[J].Engineering Fracture Mechanics,2012,88:49-62.
[17]DUAN S J,NAKAGAWA K.Stress functions with finite stress concentration at the crack tips for a central cracked panel[J].Engineering Fracture Mechanics,1988,29(5):517-526.
[18]ZHU M,CHANG W V.An unsymmetrical fracture process zone model and its application to the problem of a radical crack with an inclusion in longitudinal shear deformation[C]//Proceedings of FRAMCOS-3/Fracture Mechanics of Concrete Structures.Freiburg,Germany,1997:1097-1106.
[19]段树金,前田春和,藤井康寿,等.沿直线有多条裂纹的薄板弯曲问题[J].工程力学,1999,16(3):21-29.(DUAN Shujin,MAEDA H,FUJII K,et al.The problem of bending of a thin plate with a number of cracks along the line[J].Engineering Mechanics,1999,16(3):21-29.(in Chinese))
[20]DUAN S J,NAKAGAWA K.A mathematical approach of fracture macromechanics for strain-softening material[J].Engineering Fracture Mechanics,1989,34(5):1175-1182.
[21]ROELFSTRA P E,WITTMANN F H.Numerical method to link strain softening with failure of concrete[C]//Fracture Toughness and Fracture Energy in Concrete.Amsterdam,Netherlands,1986:163-175.