【作者】 张楠；

【导师】 师俊平；

【作者基本信息】 西安理工大学 ， 工程力学， 2019， 硕士

【摘要】 分形几何学作为研究复杂不规则构形的重要工具,为解决非线性问题提供了重要的理论基础。在断裂领域内,由于诸多材料的断面被实验证实具有分形特征,基于分形理论的分形断裂力学研究成为新兴的重要学科。然而,深入研究分形断裂力学时,发现在测度问题上存在诸多不合理和困惑。泛形理论的提出从根本上解决了分形应用上的困难,在断裂问题的表征上也是合理的。本文以泛形理论为基础,研究含裂纹构件的断裂问题,主要内容如下:首先,考虑裂纹扩展路径的泛形特征,将泛形复杂度和度量码尺这两个关键泛形参数引入到I型裂纹扩展的断裂参量表达式理论推导中,并通过数值算例分析复杂度对应力强度因子和裂纹扩展力的影响。其次,试验研究了不同裂纹形式下铸铁材料的单轴拉伸破坏行为,结果表明,裂纹是导致构件失效的重要原因,并且裂纹越长,构件的拉伸性能越差。另外,通过激光共聚焦显微镜测量了拉伸试件的断面形貌,利用计盒法计算了断面轮廓线复杂度和统计自相似区间,并用试验数据验证了泛形断裂应力和泛形断裂能表达式的准确性。最后,考虑断面的泛形特征是由于材料内部不均匀造成的,通过Weibull统计分布描述材料的非均匀性,结合扩展有限元法对含裂纹试件的裂纹扩展过程进行了数值模拟,并对模拟路径计算了复杂度,模拟结果与试验结果吻合较好,表明了该模型的合理性。另外,对不同Weibull均质度分布下的非均匀模型裂纹的扩展过程进行了模拟,结果表明:材料越均匀,其裂纹路径复杂度越小,验证了材料的非均匀特征会导致构件产生泛形裂纹这一基本思想。更多还原

【Abstract】 Fractal geometry,as an important tool to investigate complex irregular configurations,provides an important theoretical basis for solving non-linear problems.In the field of fracture,the fractal fracture mechanics based on fractal theory has become a new important subject because the fracture surfaces of many materials have fractal characteristics confirmed by experiments.However,when studying the fractal fracture mechanics deeply,it is found that there are unreason and many confusions in the measurement problems.The ubiquitiform theory is a fundamental way to solve the difficulties in fractal application and is reasonable in the characterization of fracture problems.Based on the ubiquitiform theory,in this paper the fracture of cracked members is investigated.The main contents are as following:Firstly,consider the ubiquitiformal characteristics of the crack propagation path and introduce the ubiquitiform complexity and the scale invariance which are two key parameters of ubiquitiform theory to the theoretical derivation of the fracture parameters for mode I crack propagation.Besides,the influence of the complexity on the stress intensity factor and the crack propagation force are analyzed by numerical examples.Secondly,the uniaxial tensile failure behaviors of cast iron with different crack were studied experimentally.The results suggest that crack is an important cause of component failure,and the longer the crack is,the worse the tensile performances of components is.In addition,the cross-section morphology of tensile specimens was measured by laser confocal microscopy.The box counting method was utilized to calculate the complexity of cross-section contour and the statistical self-similarity scale.The accuracy of the expressions of ubiquitiformal fracture stress and ubiquitiformal fracture energy were verified by experimental data.Finally,the ubiquitiformal characteristics of the fracture sections are caused by the inhomogeneity of the materials.Based on Weibull statistical distribution and the extended finite element method,we described the inhomogeneity of the material and numerically simulated the crack propagation process of the specimens with cracks.The complexity of the simulation path was calculated.The simulation results are in good agreement with the experimental results,which indicates the rationality of the model.In addition,the simulation results of crack growth in inhomogeneity models under different Weibull homogeneity distributions show that the more homogeneous the material is,the less complex the crack path is.It verifies the basic idea that the inhomogeneous characteristics of the material will lead to the ubiquitiform crack in the components.更多还原