Analysis of the Stress on a Half Infinite Cracks with Width
|School||Dalian Maritime University|
|Course||Operational Research and Cybernetics|
|Keywords||comformal mapping fracture dynamics complex variable method singular integral equation|
The fracture dynamics is always the hot point of the research of The fracture mechanics,and the study on the crack is especially so.The classical Griffth crack did much convenience on static analytic,but the tip of the crack had one second step singularity.which is one problem the the mechanics workers who want to delete.In seventies,academician Chen proposed a new model which is called the true crack model in the study of the brittle steel.The key is the width is introduced in the crack.The solution of the problem became a difficulty because of the width.In the later twenty years,nothing about this problem had settled.Mr Yang did the related work in his doctoral dissertation,who given the analytical solution about the Griffth crack with width,which is the first closed form solution as far.This paper did something to extend the model to others and did some investigation.This thesis investigated the stress of the propagating semi-infinite crack with width by two ways.The one is using the complex variable method,and the other is the integral equation method.The study mainly include the work as follows.The first part is the production and the progress of the fracture mechanics and the fracture dynamics.Also its features nowadays.Also the theory base of the true crack in the fracture mechanics is introduced.The second part is focused on the common methods in fracture dynamics.The superiority-inferiority is given.Also the reason of using the complex variable method is interpretated.This sector is belongs to the major division of the thesis.Mainly discussed the two ways in this paper.The first is turning the complex ragion into the simple region in a new flat by using the comformal mapping,then the analytical solution and the discrete solution are obtained.The other is turning the original equation into a new singular integral equation by using the Sherman transformation,then gives the regularization theorem of the singular integral equation.Finally,using the Fredholm theories and methods for solving it.This part is to draw the image of the stress,also find its superiority-inferiority to the traditional stress intensity factor.