Quantitative Study Of Micro-Magnetic Nondestructive Testing For Stress And Defect In Ferromagnetic Materials

Steel and other metal alloys are widely used in various industries of the national economy.The structure failure often causes great economic losses,and threatens people's life seriously.The micro-magnetic nondestructive testing is a nondestructive testing technology that can realize the early diagnosis for the ferromagnetic material and then prevents malignant accidents fundamentally.In this work,the micro-magnetic nondestructive testing for ferromagnetic materials is studied theoretically.(1)The magneto-mechanical coupling mechanism of ferromagnetic materials involved in micro-magnetic nondestructive testing is investigated.Based on the thermodynamics principle and considering the influence of stresses on the rotation mechanism of microscopic magnetic domain,the ideal magnetization constitutive relation of ferromagnetic material is established,and the magneto-mechanical constitutive relation of ferromagnetic material under the weak magnetic field is established by the approach principle.The stress magnetization behavior of the medium carbon steel under the weak magnetic field is analyzed.Comparing with other constitutive relations,the prediction results of the proposed constitutive relation are in good agreement with the experimental data.The effects of initial magnetization state,the cyclic loading and the demagnetization effect on magneto-mechanical behavior are given.Quantitative studies show that the magnetization is always close to the ideal magnetization with the increasing stress for different initial magnetization conditions.The theoretical studies also show that the first cyclic loading of the ferromagnetic material eliminates a large amount of irreversible magnetization.The magneto-mechanical process causes a stress loop phenomenon in the cyclic loading process.The demagnetization effect increases the difficulty of magnetization of the material and weakens the magneto-mechanical phenomenon of the material.(2)Based on the theories of elastic mechanics and magnetism,and combining the magneto-mechanical coupling constitutive relation,a forward model of micro-magnetic nondestructive testing under a weak magnetic field is established for ferromagnetic material.The forward model can accurately describe the basic characteristics of the surface micro-magnetic signals accurately for various of ferromagnetic materials.For example,the forward model can describes the influences of the magnitude of the load,the size of the defect,the value of the magnetic field on the micro-magnetic signals.Quantitative studies show that the micro-magnetic signal intensity increases with the increase loading.The peak-to-valley difference values of the horizontal and normal components of the micro-magnetic signal increase with the increase of defect size and load magnitude.The lift-off value does not affect the shape of the micro-magnetic signal,but the degree of non-linear change of the micro-magnetic signal decreases with the increasing lift-off value.In addition,the surface micro-magnetic signal for rectangular stress concentration zone is analyzed theoretically,and the possibility of testing stress concentration early damage is confirmed.(3)The quantitative analysis of defects in micro-magnetic non-destructive testing is researched.In order to achieve the quantitative analysis of defects,this inversion problem is described in detail,the objective function for this inversion problem is given,and an inversion algorithm based on conjugate gradient reconstruction is established.In the iterative process,the exact line search algorithm is used to make the search range of the line estimation updated to the change estimation value and its gradient,so that the inversion algorithm can solve the inverse problem with constraints.Combined with the experimental signal,the validity of the micro-magnetic nondestructive testing is proved by quantitative analysis of the size and position of a hole shape defect problem.Using the micro-signal forward results as the prediction signal,the effective of inversion algorithm is proved for the surface rectangular crack,the surface stress concentration,and the "convex" type irregular surface defects problems.In addition,the influences of signal selection,sampling rate,lift-off value and noise on the accuracy of defect inversion are discussed by using the results of the micro-magnetic signal forward modeling with noise as the prediction signal.(4)A theoretical model to study the influence of loading speed on micro-magnetic non-destructive testing is established.Based on the ideal magnetization relation,and considering the loss caused by loading,a correction of proximity principle is proposed,and a dynamic magneto-mechanical constitutive relation of the ferromagnetic material is established under the weak magnetic field.The constitutive relationship can accurately describe the experiment of the magneto-mechanical area change rule with the increases loading speed.The theoretical analysis shows that the residual magnetization of the material caused by the dynamic history effect is higher than that of the static loading case,and the residual magnetization increases with the increasing dynamic loading speed.On this basis,the dynamic effect in micro-magnetic nondestructive testing is studied.The model can quantitatively describe the variation law of the micro-magnetic signal intensity with the loading speed.Theoretical studies show that the micro-magnetic signal is closely related to the dynamic loading speed,and the influence of loading speed on the testing accuracy is discussed.It is also pointed out that the testing error caused by the loading speed hardly changes with the defect size.One can further understand the magneto-mechanical coupling mechanism for the micro-magnetic nondestructive testing through this research.This research can further improve the theoretical framework of forward problem and inverse problem for micro-magnetic nondestructive testing.This work can provide a effective research idea to solve other non-destructive testing problem.This work provides a theoretical basis for the application of micro-magnetic non-destructive testing in the practical engineering,and establishes a reliable theoretical basis for the health monitoring of ferromagnetic structure.