Stress Intensity Factor Of Transverse Crack In Double Groove Circular Thin-walled Tube

The special-shaped thin-walled tube structure is widely used in petrochemical equipment,aerospace,building bridges,marine ships,automobile manufacturing and pipeline laying.According to the different cross-section shapes,it can be divided into square tube,rectangular tube,circular tube,elliptical tube,flat elliptical tube,semicircle tube,diamond tube,multi prism tube,double groove circular thin-walled tube,etc.Due to the influence of processing technology,service conditions?corrosion,load?and other factors,cracks and crack like defects often appear,and their fracture propagation becomes one of the main failure modes of special-shaped thin-walled tube structure.The main content of fracture mechanics is crack behavior and propagation law.Stress intensity factor K is a measure of stress concentration in singular stress field at crack tip,a typical fracture parameter in fracture theory,and an important basis for establishing fracture toughness and fracture criterion of K type fracture.Therefore,it is of great theoretical and practical significance to establish a simple and accurate method to solve the stress intensity factor of special-shaped thin-walled tube structure.In this paper,the conservation law is taken as the theoretical core,and the double groove circular thin-walled tube is taken as the research object,studied the calculation of stress intensity factors of different crack configurations on the cross section of the tube under pure bending load.First of all,a calculation method for stress intensity factor of special-shaped thin-walled tube structure is established by studying the characteristics and application rules of conservation lawJ₂-integral in space and plane fracture problems,as well as the deformation theory of beam in material mechanics.The key of this method is to select the appropriate integration path,to show the contribution of stress intensity factor to the conservation lawJ₂-integral,and to transform theJ₂-integral equation into the equation for solving the stress intensity factor.Then,by using the conservation law,the calculation method of the stress intensity factor at the crack tip of the double groove circular thin-walled tube with single and double cracks at the bottom of the groove,symmetrical arc cracks on the side wall,and corner cracks at the top of the groove is established.For the complex multi crack configuration,when there are many different singular stress fields at the crack tip on the cross section of the tube,the supplementary equation of the relationship between the stress intensity factors of the complex multi crack is obtained based on the deformation assumption of the plane section in the mechanics of materials.TheJ₂-integral equation and the supplementary equation are solved simultaneously,and the expression of the stress intensity factor is finally obtained.Finally,the comparison between the numerical solution and the finite element solution is made,and the relative error is calculated to verify the effectiveness of the theoretical calculation method.In addition,this method can also be used to solve the stress intensity factors of other special-shaped thin-walled tube structures with complex cracks.The calculation process is simple and the calculation efficiency is high.