Study On Mechanism And Criterion For Brittle/Ductile Fracture And Theory Of Crack-tip Deformation

The linear elastic fracture mechanics has been widely used in the analysis of the stress field at the neighborhood of crack-tip while the singularity around the crack-tip is considered. It is indicated by fracture experimental tests that the theory of linear elastic mechanics is still applicable in the analysis of problems of macroscopic fracture. Under condition of small-scale yield, the distribution of stress and strain at the region of crack-tip can be described by theory of the linear elastic fracture mechanics. On the other hand, the studies and application of the elasto-plastic fracture theory are limited due to the sophistication of the elasto-plastic fracture problem. The experimental data for ductile fracture can not be well interpreted at present. In this thesis, a comprehensive study on the crack mechanisms and fracture criterions for both brittle fracture and ductile fracture are made. The main work includes the following parts.1. Based on the investigations on fracture behavior in both macroscopic scale and microscopic scale, the relationship between both scales of fracture is examined. It is indicated that the micro damage patterns of crack-tip in the fracture process have significant effects on the crack evolution and feature behaviour of crack-tip especially on the ductile fracture process. Based on the analysis of the relationship between the cracking types and the loading modes at the region of crack-tip in the brittle fracture and ductile fracture process, the difference between load mode and crack type is clarified, and the crack type and the stress intensity factors and fracture toughness under various loading modes are reclassified and redefined. The ambiguous recognition on the relationship of the azimuth angle of crack initiation point and the crack initiation direction, which are taken as identical in the traditional fracture mechanics, is clarified.2. Two fracture mechanisms for the brittle fracture and the ductile fracture are developed respectively. According to the different fracture mechanisms, the crack-tip is simplified and corresponding crack-tip fracture models are developed.3. For brittle fracture process, based on the simplified crack-tip brittle fracture model, the universal software of FEM, ABAQUS, and the universal tool software of analysis, MATLAB are used to analyze the distributions of stresses at the neighborhood of crack-tip under loading of I-mode and H-mode and the mixed-mode. According to the fracture mechanism and simplified crack-tip model proposed in the thesis, the criterion based on the maximum stress on the radial plane (MSRP) of crack-tip is presented for brittle fracture. The theoretical expression of the MSRP criterion for brittle fracture under mixed-mode loading and the formulae for prediction of the crack initiation angles are given. The curve of predicted crack initiation angles and the envelope curve of stress intensity factors of K_I-K_II under various conditions with different stress compound stress ratios are given. Through the comparison with the brittle fracture experimental data, the rationality of the proposed brittle fracture mechanism and the MSRP criterion are illustrated. By curve-fitting for the envelope curve of K_I-K_II computed, the empirical relation of the fracture criterion for crack-tip under mixed-mode loading is given. .4. Although many theoretical analyses and experimental investigations have been made for the ductile or elasto-plastic fracture problem, it seems that the theories andexperiments which have been achieved cannot be directly used in engineering practice. Therefore, deep understanding on behavior of ductile fracture is required. The theories of elasto-plastic fracture developed cannot well match with the experimental data which display a certain randomness and discreteness. The discreteness between theoretical predictions and experimental observations is usually attributed to the inaccuracies due to non-homogeneity of materials around crack-tip and the random errors generated in the experimental tests and observations of ductile fracture. In order to well interpret the experimental data, an alternating mechanism of ductile fracture is proposed based on examination of elasto-plastic stress distributions of the crack-tip. It is shown by analyzing the fracture process and plastic zone of the crack-tip that the orientation of crack initiation is not the same as initial cracking orientation of the crack. For the condition in which the plastic deformation at the crack-tip has minor influence on the stress distributions of the crack-tip, a simplified model of the crack-tip for ductile fracture is developed. By examining the effect of Poisson's ratio of materials on the stress field of the crack-tip in the high stress zone, it is found that the stresses of three directions in the crack-tip play a significant role in the evolution of the crack. The maximum Mises stress at the crack-tip will control the propagation of the crack when the Poisson's ratio is equal to 0.5. Based on these analyses, the MMSRP criterion of ductile fracture is proposed. The criterion is based on the maximum Mises stress on radial plane at the crack-tip. The theoretical expressions for the proposed criterion and cracking angle of crack are given. The proposed criterion is compared with other conventional criteria of ductile fracture and related experimental data and the rationality and reliability of the proposed criterion are illustrated.5. By examining the experimental data of ductile fracture, it is shown that two types of crack initiation and evolution exist in the ductile fracture process. For these two types of crack development, the main controlling factor will be different. When the plastic deformations or displacements are induced in the crack-tip zone, the deformation analyses of the crack-tip is performed by the universal FEM software, ABAQUS based on the proposed mechanism of ductile fracture. The deformation crack-tip model for ductile fracture of the crack-tip is developed to consider the effect of the deformation of the crack-tip. Through the analyses of the deformation process of the crack-tip under different modes of loading, the transformation interrelation of the coordinates between the configurations before and after deformation is established. The ratio of the action radius of stresses in the neighborhood of the crack-tip respectively before and after deformation is defined as the polar radius deformation multiple which is used to modify the stresses and deformations which take account the deformation effect of the crack-tip according to the stresses and deformations before cracking.6. Based on the proposed deformation crack-tip theory, the strain factor kd is proposed to express the nonlinear effect induced by the micro-distortion and plastic deformation. Furthermore based on the elastic theory of fracture mechanics, the I-mode ductile-brittle fracture and II-mode ductile plastic fracture are analyzed. The experimental data can be well matched by using MATLAB through properly choosing the strain factor. The cracking direction angle predicted by the proposed theory can well agree with the experimental observations. It is shown that the numerical analyses by using the proposed method can reasonably describe the stress distribution of the crack-tip in ductile fracture process and can interpret the ductile fracture behavior of different types. It is concluded that the maximum circumferential tensile stress of the...