Three-parameter Research On Three-dimensional Fracture For Macrostructures

The safety and reliability of huge-scale mechanical systems are significant for national economy and national defence. With the extensive application of complex structures (e.g. airplane, pressure vessels, high-speed railway, etc.), the precision and reliability of them must be improved. The structure design based on the two-dimensional (2D) fracture theory and damage tolerance method (e.g. linear elastic K-T theory and elastic-plastic J-Q method etc.) has been difficult to meet the demand of reliability and economy. Therefore, people must develop the three-dimensional theory in order to grasp the mechanical behavior of structures under the complex stress state. Recently, though the three-dimensional (3D) fracture theory has obtained quite great progress (e.g. the 3D fatigue fracture theory and fracture criterion by Guo can be used to solve some key problem in engineering based on 3D out-of-plane constraint factor). However, a lot of research is focused on the through-thickness straight crack when the 3D constraint factor is considered. Many key problems have not been solved about many typical three-dimensional elastic and elastic-plastic cracks at home and abroad, and how to accomplish the object needs a lot of work from the lab to the engineering applications, which is becoming more and more severe drawback of the development and engineering application for fracture mechanics. Because the 3D stress field of linear elastic crack front and elastic-plastic crack front has an important role on predicting the residual life and evaluating the residual strength of 3D structures, various typical three-dimensional cracks have been investigated based on detailed continuum mechanics and finite element method (FEM) in the dissertation. The following main creativities are achieved:1) The analytical solution of elastic stress field near 3D cracks front is hardly available. Based on the 3D elastic FEM, we study four typical 3D cracks (through-thickness straight crack, embedded elliptical crack, semi-elliptical crack and quarter elliptical crack). The 3D singular elements with four mid-side nodes at the quarter points are used around the crack front to simulate the inverse square foot singularity at the crack tip, and then the 3D finite element model for the various 3D crack are completed. Through secondary development of finite element software, the distributions of the three parameters (stress intensity factor K, T-stress and out-of-plane constraint factor T_z) are all obained, and the effect of Poisson's ratio is also consided. By fitting the numerical results with the least squares method, empirical fromulae have been given for the convenience of engineering applications. Finally, the three-parameter K-T-T_z approach is provided, which can accurately describe the stress field around the crack front. The series of achievements provide the firm theory bridge against predicting the residual life of 3D structures effectively.2) By introducing the elastic-plastic Poisson's ratio v_eq(T_z=v_eq), the quasi-analytical solution for the mode I elastic-plastic plane strain crack tip fields is presented. The solution extends the dominating region from the region T_z=0.5 (HRR solution) to whole plastic zone. For a given point (r/(J/σ₀),θ), the value of v_eq at this point can be determined by an iteration procedure, and then various stress and energy parameters can be obtained. Based on the above results, the T_z can be determined by introducing veq (T_z≠veq) for 3D crack, and then the 3D crack tip fields can be described finally.3) Based on the 3D elastic-plastic FEM, we study three typical 3D cracks (embedded elliptical crack, semi-elliptical crack and quarter elliptical crack). Through secondary development of finite element software, the distribution of the three parameters (J-integral, Q-stress and out-of-plane constraint factor T_z) are all obained, By the numerical computation and theoretical analysis, the semi-analytical fromulae of T_z,σ_e andε_e have been given for the convenience of engineering applications. Finally, the three-parameter J-Q_T-T_z approach is provided, which can accurately describe the stress field around the crack front. The series of achievements provide the firm theory foundation against evaluating the residual strength of 3D structures effectively.From the above results, the 3D elastic and elastic-plastic fracture criteria are proposed based on the strain energy density factor theory and 3D constaint theory, and then they are used to the experimental results. The effects of T-stress effect are hardly displayed in the 3D fracture criteria. At the same time, the elastic-plastic fracture criterion has been proved to be effective by use of experimental data. Finally, the prediction of general 3D fatigue crack growth has been given by a series of experiential formulae. The achievements provide the firm theory bridge from the residual strength to the residual life of 3D structures.Furthermore, the mechanical properties of nacre and the multi-cracked prismatic shaft torsion problem are both investigated based on the Back-propagation Neural Network theory. As a fundamental issue for the mechanical properties of nacre, the elastic properties single-crystal of calcite have long been made great efforts to study, while the large scatter of the available data are arise widely. In appendix A, the elastic constants of single-crystal calcite (CaCO₃) have been obtained by extensive first-principles calculations based on the density functional theory. In appendix B, the nanoindentation process of nacre has been simulatied based on 3D elastic-plastic FEM. In appendix C, a new processing method for the multi-cracked prismatic shaft torsion problem is presented based on the Back-propagation Neural Network. We provide an optimizing project of Back-propagation training and fast simulate the experimental results of the torsion rigidity. The examples prove that the project introduced in this paper is accurate and converge quickly.