【作者】 朱莉；

【导师】 李庆芬；

【作者基本信息】 哈尔滨工程大学 ， 机械设计及理论， 2012， 博士

【摘要】 三维复合型断裂问题由于其复杂性，许多问题迄今仍然没有得到一致的结论，有待进一步研究。本文参考以往的研究成果，运用改进的AFM（all fracture modes）试样对三维复合型脆性断裂这一复杂的问题进行深入的数值计算、实验研究和理论探讨，其理论意义和工程应用价值是十分明显的。本文介绍了Richard提出的CTS（compact tension shear）、AFM试样及其加载装置的特点，在其基础上设计出了改进的AFM试样及其加载装置，并论述了采用该试样及其夹具进行三维断裂实验的原理。通过限定单边缺口拉伸（single edge notched tension，简称SENT）试样边界条件将三维断裂问题转化为平面应变问题，利用虚拟裂纹闭合（virtual crack closure，简称VCC）法和等效积分区域（equivalent domain integral，简称EDI）法对SENT试样进行了数值分析，计算了平面应变状态下裂纹前缘的无量纲应力强度因子。并与二维解析解进行比较，发现VCC法计算精确且简便，适合对三维复合型断裂问题进行数值分析。采用VCC法对三种不同厚度比的AFM试样进行了I型、II型、III型加载模式下的断裂行为数值计算。研究了试样厚度比对试样裂纹前缘无量纲应力强度因子分布的影响。研究表明，II型加载导致裂纹前缘诱发产生局部的III型载荷；III型加载导致裂纹前缘诱发产生II型载荷。且III型加载诱发裂纹前缘产生的II型应力为强耦合效应。为了尽可能减小此种耦合效应，本文选择出了合适的试样厚度。对选定厚度的AFM试样模型，采用VCC法计算了I+II复合型、I+III复合型、II+III复合型、I+II+III复合型加载下裂纹前缘的无量纲应力强度因子，并且根据Richard准则计算得到了I型、II型、III型、I+II复合型、I+III复合型、II+III复合型、I+II+III复合型加载下裂纹前缘的无量纲等效应力强度因子，预测了各种类型载荷下的裂纹启裂点。选择透光率高的有机玻璃作为试样材料，运用改进的AFM试样及其夹具，进行了I型、II型、III型、I+II复合型、I+III复合型、II+III复合型、I+II+III复合型加载下的三维断裂试验，观测了各种加载模式下裂纹启裂、不稳定扩展直至断裂破坏的全过程。结果表明，采用VCC法和Richard准则进行数值计算所得启裂点的预测结果，与实验观察到的现象是一致的，验证了数值计算结果的正确。将不同复合比载荷下实验测得的启裂角和临界载荷与经典的断裂准则——最大周向应力准则（或MTS准则）、最小应变能密度因子准则（S准则）、最大应变能释放率准则（G准则），以及现有的Pook准则和Richard准则进行了分析比较，发现了Richard准则结果与断裂实验结果吻合得最好，说明了Richard准则能很好地表征三维脆性断裂行为。本文采用改进的AFM试样，进行了各种复合型加载下三维脆性断裂行为的数值分析及实验研究，得到了很好的三维断裂结果，丰富了三维脆性断裂的研究。更多还原

【Abstract】 Due to the complexity of three dimensional (3D) mixed mode fracture problem, thecorresponding issue is not yet well understood and needs further investigation. Based onprevious relative studies, the3D mixed mode brittle fracture was investigated on modified allfracture modes (AFM) specimen by numerical calculation, experimental study, and theoreticaldiscussion. The corresponding theoretical meaning and engineering application value isdistinct.The compact tension shear (CTS) specimen and the AFM specimen in combination withtheir special loading devices were introduced. Based on their advantages, the modified AFMspecimen and its special loading device were proposed, and the corresponding principle of3Dfracture experiment was discussed.By suppressing corresponding boundary conditions (BCs), the plane strain conditionswere enforced on3D-model of the single edge notched tension (SENT) specimen.Non-dimensional stress intensity factors (SIFs) were calculated by virtual crack closure (VCC)method and equivalent domain integral (EDI) method respectively along the crack front. Bycomparing the numerical results with the corresponding2D reference analytical value, theVCC method was found to be so numerically accurate and handy that it can be fitful fornumerically analyzing3D mixed mode fracture problem.The fracture behavior was computationally investigated by the VCC method on AFMspecimens with three thickness ratios, under mode I, mode II, and mode III loading conditionsrespectively. The influence of thickness ratio was investigated on the distribution ofnon-dimensional SIFs along the crack front. It was obtained that although the specimen isglobally subjected to the mode II loading, the mode III fracture behavior is induced locallyalong the crack front, and vice versa. In particular, it is strong coupling effect that mode IIstresses are induced by mode III loading along the crack front. In order to reduce this couplingeffect as far as possible, the specimen with appropriate thickness was proposed in this paper.For the AFM model with the given thickness, the non-dimensional SIFs along the crackfront were calculated by the VCC method, under mixed mode I+II, mixed mode I+III, mixedmode II+III, and mixed mode I+II+III loading conditions. Based on the previous non-dimensional SIFs data, a series of non-dimensional equivalent SIFs and initial breakpointsalong the crack front were calculated by employing the Richard criterion, for pure mode I, puremode II, pure mode III, mixed mode I+II, mixed mode I+III, mixed mode II+III, and mixedmode I+II+III.Based on the proposed AFM specimen made of transparent material–PMMA and therelated loading device, a series of3D experimental investigations were performed under modeI, mode II, mode III, mixed mode I+II, mixed mode I+III, mixed mode II+III, and mixed modeI+II+III loading conditions. Correspondingly, the complete process was observed from crackinitial break, unstable propagate to final fracture. It was shown that the initial breakpointassessments by the VCC method and the Richard criterion were in agreement withcorresponding experimental findings, and the validity of the computational results wasdemonstrated.Critical loads and initiation angles, which were gained by different mixed mode loadingexperiment, were compared with three classical criterion––the maximum tangential stresscriterion (or MTS criterion), the strain energy density criterion (S criterion), and themaximum energy release rate criterion (G criterion), and recently developed3D fracturecriteria––Pook criterion and Richard criterion. It was found that the prediction by Richardcriterion agrees well with the results by fracture experiment. Therefore, Richard criterion isapplicable for predicting3D brittle fracture behavior.In this paper, with the proposed AFM specimen,3D numerical calculations andexperimental investigation were achieved for mode I, mode II, mode III, mixed mode I+II,mixed mode I+III, mixed mode II+III, and mixed mode I+II+III loading conditions. Thepromising3D fracture results can make contribution to3D brittle fracture investigation.更多还原