Analysis On The Crack Tip Plastic Zone And Opening Displacement Of Finite-width Plate Based On Dugdale Model In An Elastic-perfectly Plastic Material

In elastic-plastic fracture mechanics,D.S.Dugdale proposed the famous Dugdale model during analytical analysis of the crack tip plastic zone of an elastic-perfectly plastic metal sheet with a central crack based on the physical nature of non-singularity in the boundary stress field of the plastic zone at the virtual crack tip.The Dugdale model gains the crack tip plastic zone by means of superposition and solution of stress intensity factors at the virtual crack tip,and it has become one of the most famous achievements in fracture mechanics due to its accurate predication of the crack tip plastic zone size in comparison with experimental results.However,the past research shows that the classical Dugdale model is largely applicable to the analytical analysis of infinite-width cracked plates,which confines its applicability and value in the engineering field.In view of the fact that the Dugdale model is difficult to extend to the analysis of finite-width cracked plates,this dissertation firstly gives the analytical solution of stress intensity factors of finite-width cracked plates based on the crack line field analysis method,and then obtains the analytical plastic zone size.The results are in perfect agreement with the experimental results.The crack tip opening displacement is obtained accordingly.The analytical results of the Dugdale model for finite-width cracked plates are also compared with that of the finite element modelling.Furthermore,the plastic zone size of a center-cracked bottom plate of a steel box girder is obtained,which will provide theoretical basis and support for solving practical engineering problems.The main content and achievements of this dissertation are as follows:(1)Based on the crack line field analysis method,the key problem of the modified Dugdale model,i.e.the stress intensity factor at the virtual crack tip of finite-width ModeI cracked plate with uniform tractions on the virtual crack face,is solved.The results agree well with the finite element analysis.When the width of the plate tends to be infinite,the solution is consistent with that of the corresponding infinite-width cracked plate.The solution of this key problem provides basis for the analytical analysis of the Dugdale model of finite width cracked plates.(2)A modified Dugdale model is established for a mode-I center-cracked finitewidth plate with uniform tension at inifinty perpendicular to the cracking direction.Based on the stress intensity factor of the center-cracked finite-width plate obtained above,and,based on the physical nature of non-singularity of the stress field at the virtual crack tip,the relationship between the plastic zone size,the loading ratio,the crack length and the plate width is established.Furthermore,the correction coefficient of the finite-width cracked plate relative to the infinite-width plate,the plastic zone size formula,as well as the relationship between the plastic zone size and the load ratio,are obtained,so the classical Dugdale mode is successfully extended to the analysis of finite-width cracked plates.(3)The difference between the theoretical values and the experimental results for the plastic zone of the classical Dugdale model is analyzed.The results show that the plastic zone size obtained in this disserattaion is in better agreement with the experiment results by Dugdale himself.Thanks to the new solution in this dissertation,the difference between the theoretical values of the plastic zone size for infinite-width cracked plate and that of the experimental results by Dugdale for finite-width cracked plate is eliminated and the underlying reasons are given.The accuracy of the analytical solution in this disseratation are verified.(4)Using Karnofsky's law and Paris displacement formula,based on elastic strain energy and stress intensity factor(corresponding to crack propagation force),the crack tip opening displacement of finite-width cracked plate under uniform tension at infinity is analyzed.The analytical expression of crack tip opening displacement of finite width crack plate expressed in integral form is given and it can be readily used to solve specific crack problems numericall,which will provide theoretical basis for elastic-plastic analysis as well as the establishment of elastic-plastic fracture criterion of finite-width cracked plates in practical engineering problems.(5)The Dugdale model of finte-width cracked plates is used for analytical analysis of a box girder bottom plate.Two situations are taken into account: with and without longitudinal ribs in the bottom plate.Finite element analysis is also conducted.The results show that the Dugdale model of finite-width cracked plates can be effectively used in the analysis of the plastic zone size and the crack tip opening displacement of steel box girder with central crack in the bottom plate.The analytical method by using the modified Dugdale model for enginenring structures is given,which will provide theoretical support for the structural analysis of bridges with cracks.The Dugdale model of finite-width cracked plates in this disserattion expands the application of the classical Dugdale model.It breaks through the limitation that the Dugdale model is difficult to be used in the analysis of finite-width cracked plates in engineering structures.The modified Dugdale model can be directly used in the analysis of practical engineering structures with high accuracy,such as the analysis of the plastic zone size and the crack tip opening displacement of steel box girder bridges which are loaded as the modified Dugdale model.