Conservation Law And Its Application In Calculation Of Stress Intensity Factor Of Cracked T-shaped Structural Beam

T-shaped structural parts are widely used in various engineering structures,such as buildings,bridges,ships,aircrafts and vehicles.Its safety has long been a key issue of people’s concern.Cracks are one of the common defect forms of engineering structural parts.Under the action of external load,these cracks will reduce the actual strength of structural members.As the basic parameter of fracture analysis,the crack stress intensity factor is the driving force,resistance and fracture resistance of cracked structures.The basis of fracture analysis methods such as fracture criteria and structural integrity assessment.It can be seen from the theoretical and practical engineering applications that it is very necessary to find a simple and effective method to solve the stress intensity factor.The cracked T-beam is a typical three-dimensional crack structure.In the past,the calculation of its fracture parameters had to rely on numerical solutions,which caused many inconveniences in engineering applications.Therefore,as an important issue in related industries and structural engineering fields,this paper will build a simple calculation method for solving the complex three-dimensional crack stress intensity factor of T-shaped structural beams based on the J₂conservation integral.Taking the analysis and calculation of stress intensity factors of various types of cracks under bending load as an example,the specific implementation process and application of this method are given.First,it introduces the basic definitions and concepts of conservation laws in plane and space problems,and finds a theoretical breakthrough point for constructing methods to solve stress intensity factors.One of the important links is to select a suitable integration path,to show the contribution of the stress intensity factor of the crack tip to the conservation integral,and to provide a theoretical basis for the subsequent solution of the stress intensity factor of a T-shaped structural beam with multiple types of cracks.Then,based on the J₂conservation integral,the stress intensity factor expressions of the T-shaped structural beam edge cracks,the web center（eccentric）cracks,and the corner cracks（T-shaped cracks）are respectively given.The cracked T-shaped structural beam is a kind of complex three-dimensional problem.It is difficult to give an analytical solution to its stress intensity factor using traditional methods.However,it can use the special closed surface path of the J₂integral and use the energy of the transverse expansion of the crack surface The concept of release rate and the contribution of stress and displacement in the near field of the crack tip in the K control zone,the stress and displacement given by the elementary mechanics of the crack section and the far field section,etc.,to the J₂conservation integral,construct a method for solving the stress intensity factor.Since the stress and displacement calculation methods in elementary mechanics are used,the errors in elementary mechanics will inevitably be introduced into the method in this paper.Therefore,the paper also gives a comparison between the solution in this paper and the finite element solution,which shows that the solutions given by the two are in good agreement,indicating that the error of the solution in this paper caused by elementary mechanics is acceptable in engineering.