Analysis Of T-stress Influencing Factors And New Fracture Criterion Correction Based On Williams Element With Generalized Degrees Of Freedom

Seeking physical parameters to control materials' cracks and establishing critical conditions for crack propagation are important tasks in fracture mechanics research.However,both the energy method and the stress parameter method are related to the stress-strain,response of the crack tip when establishing the crack propagation criterion.Traditional linear elastic fracture mechanics thinks that the stress field at the crack tip is dominated by the singular terms,represented by the stress intensity factor.But subsequent studies show that the theoretical analysis is more consistent with the experimental results when considering T-stress.T-stress affects the crack tip stress field,and then affects the crack propagation direction and the crack tip stress intensity factors at the cracking time.Therefore,it is necessary to consider T-stress in addition to stress intensity factor.However,if T-stress and stress intensity factors are solved at the same time,the calculation will become more complicated,so that,T-stress is usually ignored to simplify the calculation,and only solve stress intensity factors.That is why fracture criterion often ignores T-stress.As a traditional parameter in the fracture analysis,stress intensity factor has been matured in its research and application.However,as the high-order term in the stress field of the crack tip,T-stress is difficult to solve,and there is no corresponding systematic research.To solve the above problem,the following researches have been conducted on T-stress in this paper:Firstly,the definition of T-stress is studied.Based on the knowledge of elastic mechanics,the stress field at the crack tip in some simple cases was deduced using the complex stress function of Muskhelishvili.The analytical expression of the T-stress of the bidirectional-directional tension/pressure infinite plate is given,the process of solving the T-stress is perfected,and the physical significance of the T-stress is clarified.From the analytic formula of T-stress,we can see that T-stress is only generated by the ?x term of the stress field of the pure I crack tip,indicating that the T-stress is the stress component generated by the symmetrical load,which is consistent with the definition of the crack surface parallel to it.Secondly,combining the generalized parameter finite element method with the improved Williams series,Williams element with generalized degrees of freedom calculation format for simultaneous solving of T-stress and stress intensity factors is established.Through the generalized parameters,the T-stress and stress intensity factor values can be directly determined,avoiding repeated solution and errors may occur during post-processing.The example shows that the Williams element with generalized degrees of freedom has high accuracy,and in the actual operation,this paper uses the strong modeling ability of ABAQUS software to establish the general area model,and calculates with the original singular area program,making the method of this thesis.It is more comparable,reduces program running time,and improves computational efficiency.Thirdly,according to the analytical method of the T-stress analysis of the center crack infinite slab derived in Chapter 2,using the two methods of the Williams element and ABAQUS,the factors that influence the calculation of the T-stress are first compared theoretically with the stress intensity factor,and then the numerical method is analyzed.Examples show that in most cases,the load and crack size affect the magnitude of T-stress.When the crack is in infinite plate conditions,the T-stress is not affected by the plate size effect,which proves that T-stress is a stress.T-stress is used as a high-order term in the stress field at the crack tip,and there is no higher requirement for the crack tip mesh.When using ABAQUS to calculate the fracture parameters and extracting the results,there is an annoyance in the results of artificial selection.This paper proposes the setting of the number of software lanes N,it should be less than 10,and wrong solutions should be removed.Finally,the generalized parameters in the Williams series are introduced into the crack propagation criterion,and the unified parameters of the generalized parameter crack propagation criterion considering the T-stress are established using the Williams element.The stress stress on the crack tip and the crack propagation path are analyzed.The results show that:considering T-stress can better reflect the real stress field and meet the precision requirements.T-stress has a significant impact on the crack propagation angle and the stress intensity factor at the moment of fracture.When T-stress is different,the crack angle and stress intensity factors at the moment of rupture may be different.Compared with the use of the stress intensity factor to describe the fracture of the material,the theoretical prediction based on the fracture criterion of T-stress is obviously more consistent with the actual experimental results.