考虑罗德角参数的钢材薄板延性断裂标定方法
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摘要
在钢结构中钢梁腹板的断裂表现出很强的剪切断裂特征,因此在预测其断裂行为时除了考虑应力三轴度以外,还应考虑与剪切状态有关的罗德角参数的影响。该文提出了一种适用于钢材薄板延性断裂预测的标定方法。共设计了5组试件,分别为平板试件、开孔平板、开槽平板、90°剪切平板和45°剪切平板。利用平板试件和停机平板试件单向拉伸试验,结合有限元反演得到钢材的全过程真实应力-应变曲线。然后将其代入各试件有限元模型进行计算,标定出各试件对应的等效断裂应变、平均应力三轴度和平均罗德角参数。最后利用Matlab优化工具箱对断裂模型进行优化拟合,确定模型中的各项待定参数。
It was observed that shear fracture dominates in the fracture of steel beam webs. For this reason, the lode angle parameter should be taken into account along with the stress triaxiality. A new ductile fracture calibration method applicable to thin steel plates is proposed in this paper. Five groups of specimens were designed in this paper. They are flat plates, holed flat plates, flat grooved plates, 90° shear plates and 45° shear plates. The true stress-ture strain(?-?) curves were obtained through flat plate, halted flat plate specimens and relevant finite element(FE) method iterations. The FE models of other specimens were computed with this σ-εrelationship and compared with related experimental results to obtain the corresponding equivalent fracture strain,average stress triaxiality and average lode angle parameter. With the help of the Matlab Optimization Toolbox, the optimal parameters of the fracture model can be determined.
It was observed that shear fracture dominates in the fracture of steel beam webs. For this reason, the lode angle parameter should be taken into account along with the stress triaxiality. A new ductile fracture calibration method applicable to thin steel plates is proposed in this paper. Five groups of specimens were designed in this paper. They are flat plates, holed flat plates, flat grooved plates, 90° shear plates and 45° shear plates. The true stress-ture strain(?-?) curves were obtained through flat plate, halted flat plate specimens and relevant finite element(FE) method iterations. The FE models of other specimens were computed with this σ-εrelationship and compared with related experimental results to obtain the corresponding equivalent fracture strain,average stress triaxiality and average lode angle parameter. With the help of the Matlab Optimization Toolbox, the optimal parameters of the fracture model can be determined.
引文
[1]许金泉.材料强度学[M].上海:上海交通大学出版社,2009.??y h÷y?y h?yèáyè?y Xu Jinquan.Strength of materials[M].Shanghai:Shanghai Jiao Tong University Press,2009.(in Chinese)
[2]McClintock F A.A criterion for ductile fracture by the growth of holes[J].Journal of applied mechanics,1968,35(2):363-371.
[3]Rice J R,Tracey D M.On the ductile enlargement of voids in triaxial stress fields[J].Journal of the Mechanics and Physics of Solids,1969,17(3):201-217.
[4]Johnson G R,Cook W H.Fracture characteristics of three metals subjected to various strains,strain rates,temperatures and pressures[J].Engineering Fracture Mechanics,1985,21(1):31-48.
[5]Bao Y.Prediction of ductile crack formation in uncracked bodies[D].Boston:Massachusetts Institute of Technology,2003.
[6]Wilkins M L,Streit R D,Reaugh J E.Cumulative-strain-damage model of ductile fracture:simulation and prediction of engineering fracture tests[R].Lawrence Livermore National Lab,California,USA,1980:1-65.
[7]Xue L.Damage accumulation and fracture initiation in uncracked ductile solids subject to triaxial loading[J].International Journal of Solids and Structures,2007,44(16):5163-5181.
[8]Bai Y.Effect of loading history on necking and fracture[D].Boston:Massachusetts Institute of Technology,2007:1-262.
[9]Wierzbicki T,Bao Y,Bai Y.A new experimental technique for constructing a fracture envelope of metals under multi-axial loading[C]//Proceedings of the 2005SEM Annual Conference and Exposition on Experimental and Applied Mechanics,Portland,USA:Society for Experimental Mechanics(SEM),2005,1:1295-1303.
[10]Bai Y,Wierzbicki T.A new model of metal plasticity and fracture with pressure and Lode dependence[J].International Journal of Plasticity,2008,24(6):1071-1096.
[11]王万祯.结构钢开裂准则及断裂试验分析[J].工程力学,2008,25(5):27-31.Wang Wanzhen.Crack criterion and fracture tests of structural steel[J].Engineering Mechanics,2008,25(5):27-31.(in Chinese)
[12]王仲仁,胡卫龙,胡蓝.屈服准则与塑性应力-应变关系理论及应用[M].北京:高等教育出版社,2014.Wang Zhongren,Hu Weilong,Hu Lan.Yield criteria and plastic stress-strain relations theory and application[M].Beijing:Higher Education Press,2014.(in Chinese)
[13]Bai Y,Wierzbicki T.A comparative study of three groups of ductile fracture loci in the 3D space[J].Engineering Fracture Mechanics,2015,135:147-167.
[2]McClintock F A.A criterion for ductile fracture by the growth of holes[J].Journal of applied mechanics,1968,35(2):363-371.
[3]Rice J R,Tracey D M.On the ductile enlargement of voids in triaxial stress fields[J].Journal of the Mechanics and Physics of Solids,1969,17(3):201-217.
[4]Johnson G R,Cook W H.Fracture characteristics of three metals subjected to various strains,strain rates,temperatures and pressures[J].Engineering Fracture Mechanics,1985,21(1):31-48.
[5]Bao Y.Prediction of ductile crack formation in uncracked bodies[D].Boston:Massachusetts Institute of Technology,2003.
[6]Wilkins M L,Streit R D,Reaugh J E.Cumulative-strain-damage model of ductile fracture:simulation and prediction of engineering fracture tests[R].Lawrence Livermore National Lab,California,USA,1980:1-65.
[7]Xue L.Damage accumulation and fracture initiation in uncracked ductile solids subject to triaxial loading[J].International Journal of Solids and Structures,2007,44(16):5163-5181.
[8]Bai Y.Effect of loading history on necking and fracture[D].Boston:Massachusetts Institute of Technology,2007:1-262.
[9]Wierzbicki T,Bao Y,Bai Y.A new experimental technique for constructing a fracture envelope of metals under multi-axial loading[C]//Proceedings of the 2005SEM Annual Conference and Exposition on Experimental and Applied Mechanics,Portland,USA:Society for Experimental Mechanics(SEM),2005,1:1295-1303.
[10]Bai Y,Wierzbicki T.A new model of metal plasticity and fracture with pressure and Lode dependence[J].International Journal of Plasticity,2008,24(6):1071-1096.
[11]王万祯.结构钢开裂准则及断裂试验分析[J].工程力学,2008,25(5):27-31.Wang Wanzhen.Crack criterion and fracture tests of structural steel[J].Engineering Mechanics,2008,25(5):27-31.(in Chinese)
[12]王仲仁,胡卫龙,胡蓝.屈服准则与塑性应力-应变关系理论及应用[M].北京:高等教育出版社,2014.Wang Zhongren,Hu Weilong,Hu Lan.Yield criteria and plastic stress-strain relations theory and application[M].Beijing:Higher Education Press,2014.(in Chinese)
[13]Bai Y,Wierzbicki T.A comparative study of three groups of ductile fracture loci in the 3D space[J].Engineering Fracture Mechanics,2015,135:147-167.