考虑应变梯度效应的三点弯梁模型解析研究——第二部分:局部化带的位移及转角
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摘要
基于梯度塑性理论,分析了应变软化及真实裂纹扩展阶段的局部化带的张拉位移和转角。在弹性阶段,可以由弹性理论来确定二者的关系。真实裂纹出现后,利用平衡条件、几何条件及梯度以来的应变软化本构关系,得到了真实裂纹长度与局部化带长度的关系。当真实裂纹刚出现时,局部化带长度达到最大值。在任何阶段,局部化带到中性轴的距离单调降低,局部化带的张拉位移和转角受梁深、带宽、弹模及下降模量等的影响。弹模及下降模量越大,带宽越小,则局部化带的张拉位移和转角都增加。而且,在前两个阶段,张拉位移都线性增加,但在后两个阶段,转角都非线性增加。
The tensile displacement and angle of rotation of tensile strain localized band are analyzed in strain softening stage and in real crack propagation stage based on gradient-dependent plasticity. In elastic stage, the effect of strain gradient can be neglected due to uniform elastic deformation. The relation between the displacement and the rotation is determined by classical elastic theory. After the real crack is initiated in the tensile side of the three-point bending beam, using the stress equilibrium, assumption of plane cross sections and strain softening constitutive relation dependent on strain gradient, a relation between real crack length and tensile strain localized band length is presented. When the real crack just occurs, the tensile stress in the tensile side of the beam is decreased to zero and the tensile localized band length reaches its maximum. In each stage, the distance between neutral axis and tensile strain localized zone decreases monotonously. Both the tensile displacement and angle of rotation of tensile strain localized band are influenced by depth of beam, thickness of localized band, elastic modulus and softening modulus, etc. The opening displacement and angle of rotation increase with softening modulus, elastic modulus and decreasing thickness of localized band. In addition, the tensile displacement increases linearly in elastic stage and strain softening stage. However, the angle of rotation increased nonlinearly in strain softening stage and in real crack propagation stage.
The tensile displacement and angle of rotation of tensile strain localized band are analyzed in strain softening stage and in real crack propagation stage based on gradient-dependent plasticity. In elastic stage, the effect of strain gradient can be neglected due to uniform elastic deformation. The relation between the displacement and the rotation is determined by classical elastic theory. After the real crack is initiated in the tensile side of the three-point bending beam, using the stress equilibrium, assumption of plane cross sections and strain softening constitutive relation dependent on strain gradient, a relation between real crack length and tensile strain localized band length is presented. When the real crack just occurs, the tensile stress in the tensile side of the beam is decreased to zero and the tensile localized band length reaches its maximum. In each stage, the distance between neutral axis and tensile strain localized zone decreases monotonously. Both the tensile displacement and angle of rotation of tensile strain localized band are influenced by depth of beam, thickness of localized band, elastic modulus and softening modulus, etc. The opening displacement and angle of rotation increase with softening modulus, elastic modulus and decreasing thickness of localized band. In addition, the tensile displacement increases linearly in elastic stage and strain softening stage. However, the angle of rotation increased nonlinearly in strain softening stage and in real crack propagation stage.
引文
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[13]李兴高,高延法.开采对底板岩体渗透性的影响[J].岩石力学与工程学报,2003,22(7):1078-1082.LiXinggao,GaoYanfa.Influence of mining on floor infiltration coefficients[J].ChineseJournal ofRockMechanics andEngineering,2003,22(7):1078-1082.
[14]郝圣旺,李慧剑,黎振兹,等.紧凑四点剪切砼II型断裂实验研究与数值分析[J].工程力学,2003,20(2):138-141.HaoShengwang,LiHuijian,LiZhenzi, et al.A combined experimental and numerical investingation of fracture of compact four-point-shear concrete specimens[J].EngineeringMechanics,2003,20(2):138-141.(inChinese)
[15]沈新普,ZenonMroz.循环载荷下层间界面反平面剪切破坏的解析解:1.卸载行为[J].工程力学,2001,18(3):97-104.ShenXinpu,ZenonMroz.Analytical solution for interface failure under cyclic loading:1. unloading behavior[J].EngineeringMechanics,2001,18(3):97-104.(inChinese)
[2]UlfkjaerJ P,KrenkS,BrinckerR.Analytical model for fictious crack propagation in concrete beams[J].Journal ofEngineeringMechanics,ASCE,1995,121(1):7-15.
[3]SundaraRajaIyengarK T,RavirajS.Analytical study ofFracture in concrete beams using blunt crack model[J].Journal ofEngineeringMechanics,ASCE,2001,127(8):828-834.
[4]余怀忠,尹祥础,夏蒙棼,等.加卸载响应比(LURR)理论的实验研究[J].中国地震,2003,19(1):58-66.YuHuaizhong,YinXiangchu,XiaMengfen, et al.Experimental research on the theory ofLURR (load/unload response ratio)[J].EarthquakeResearch inChina,2003,19(1):58-66.(inChinese)
[5]谭云亮,赵同彬,颜伟.顶板活动地震波突变特征的小波识别[J].岩石力学与工程学报,2003,22(1):1874-1877.TanYunliang,ZhaoTongbin,YanWei.Wavelet identifyication for roof-failure-induced seismic wave feature[J].ChineseJournal ofRockMechanics andEngineering,2003,22(1):1874-1877.
[6]李海波,蒋会军,赵坚,等.动荷载作用下岩体工程安全的几个问题[J].岩石力学与工程学报,2003,22(11):1887-1891.LiHaibo,JiangHuijun,ZhaoJian, et al.Some problems about safety analysis of rock engineering under dynamic load[J].ChineseJournal ofRockMechanics andEngineering,2003,22(11):1887-1891.
[7]朱珍德,徐卫亚,张爱军.脆性岩石损伤断裂机理分析与试验研究[J].岩石力学与工程学报,2003,22(9):1411-1416.ZhuZhende,XuWeiya,ZhangAijun.Mechanism analysis and testing study on damage and fracture of brittle rock[J].ChineseJournal ofRockMechanics andEngineering,2003,22(9):1411-1416.
[8]王明洋,葛涛,戚承志,等.爆炸荷载作用下岩石的变形与破坏研究(I)[J].防灾减灾工程学报,2003,23(2):43-54.WangMingyang,GeTao,QiChengzhi, et al.Study of deformation and failure of rock under explosion load(PartI)[J].Journal ofDisasterPrevention andMitigationEngineering,2003,23(2):43-54.(inChinese)
[9]许传华,任青文.围岩稳定分析的非线性理论研究[J].岩土工程技术,2003,(3):142-146.XuChuanhua,RenQingwen.Nonlinear theories research of stability of surrounding rock[J].GeotechinicalEngineeringTechnique,2003,(3):142-146.(inChinese)
[10]杨强,程勇刚,张浩.基于格构模型的岩石类材料开裂数值模拟[J].工程力学,2003,20(1):117-120,126.YangQiang,ChengYonggang,ZhangHao.Simulation of cracking processes of rock materials by lattice mode[J].EngineeringMechanics,2003,20(1):117-120,126.(inChinese)
[11]来兴平,王双红,蔡美峰.子波变换在围岩非稳态破坏信号分析中的应用[J].金属矿山,2003,(2):15-17.LaiXingping,WangShuanghong,CaiMeifeng.Application of subwave conversion in the analysis of unstable failure signal of surrounding rock[J].MetalMine,2003,(2):15-17.(inChinese)
[12]徐涛,唐春安,张哲,等.单轴压缩条件下脆性岩石变形破坏的理论、试验与数值模拟[J].东北大学学报(自然科学版),2003,24(1):87-90.XuTao,TangChunan,ZhangZhe, et al.Theoretical, experimental and numerical studies on deformation and failure of brittle rock in uniaxial compression[J].Journal ofNortheasternUniversity(NaturalScience),2003,24(1):87-90.(inChinese)
[13]李兴高,高延法.开采对底板岩体渗透性的影响[J].岩石力学与工程学报,2003,22(7):1078-1082.LiXinggao,GaoYanfa.Influence of mining on floor infiltration coefficients[J].ChineseJournal ofRockMechanics andEngineering,2003,22(7):1078-1082.
[14]郝圣旺,李慧剑,黎振兹,等.紧凑四点剪切砼II型断裂实验研究与数值分析[J].工程力学,2003,20(2):138-141.HaoShengwang,LiHuijian,LiZhenzi, et al.A combined experimental and numerical investingation of fracture of compact four-point-shear concrete specimens[J].EngineeringMechanics,2003,20(2):138-141.(inChinese)
[15]沈新普,ZenonMroz.循环载荷下层间界面反平面剪切破坏的解析解:1.卸载行为[J].工程力学,2001,18(3):97-104.ShenXinpu,ZenonMroz.Analytical solution for interface failure under cyclic loading:1. unloading behavior[J].EngineeringMechanics,2001,18(3):97-104.(inChinese)
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