Based On Catastrophe Theory To Establish Casing Damage Model

In order to accurately describe casing collapse deformation. In this paper, the nature of casing collapse deformation process is studied based on the principle of energy method. Its uses the casing plastic deformation theory to carry out a mechanical model for the casing pipe. Then establish a balance between the casing damage based on the principle of virtual work that is the internal force of the work and the external force of the work are equal and establish the casing damage mechanics model. According to the established casing damage mechanics model, based on the fold catastrophe theory to set up the energy dependence of casing external collapse load, which could provides a new criterion for judging the damage of casing collapse. The paper provides a new method for the study of casing collapse deformation. The main work is as follows:Firstly, the paper carries out the basic overview of the catastrophe theory. And then introduces the research object of catastrophe theory and summarizes the application of catastrophe theory in all aspects. Through the analysis of the Zeeman catastrophema-chine, the basic principle of catastrophe theory, the indication of mutation and the type of mutation were introduced. Comparison of cusp catastrophe model and fold catastrophe model, fold catastrophe model is more suitable for this paper.Secondly, study on casing collapse deformation from the viewpoint of energy more can reveal the nature of the deformation process. Based upon the casing plastic deformation theory, a mechanical model for the casing pipe was built. Establish casing damage mechanics balance relationship based on principle of virtual work under lateral loads, that is work of the internal force is equal to the external work, mechanical model of casing damage can be obtained.Once again, on the basis of the established mechanical model for the casing pipe, Based on the theory of catastrophe to establish casing external collapse energy relationships, finally, based on fore theoretical criteria for casing damage is established. If there is mutation in casing collapse, the amount of energy released is not zero, X along the branch 1 suddenly jumped to branch 2 when reaches a certain point, casing gathering and release energy, the casing collapse deformation; if there is mutation in casing collapse, the amount of energy released is zero, X from the branch 1 through the origin to the branch 2, the failure mode of the casing is asymptotic failure, this process does not occur aggregation gather and release energy.Finally, in order to verify calculation model of energy release, the results of the test data in the literature[39] is cited. When the casing collapse deformation, catastrophe theory is introduced to determine whether casing collapse deformation. Main influencing factors of casing collapse strength are analyzed. The effects of yield strength, geometrical imperfections and residual stress on the casing are analyzed by means of energy release. The thickness ratio and yield strength are the main factors that influence the collapse deformation of casing. The residual stress and the geometric imperfections of the casing have a certain influence on the strength of casing collapse. The higher the diameter thickness ratio and the yield strength, the stronger the collapse resistance of casing. On the contrary, the lower the residual stress and the geometric imperfections, the collapse deformation of casing is more likely to occur.