| Ferromagnetic materials are widely used in construction,railway,pipelines,sensors,actuators and motors due to their good mechanical and magnetic properties.With the change of the external environment and the degradation of the performance of the ferromagnetic component,the stress of the component no longer meets the allowable stress at the time of design.Accurate measurement of the stress state inside the component is the key to ensure its safe operation.The unique magnetoelastic coupling characteristics of ferromagnetic materials provide a new way for ferromagnetic components to measure stress by magnetic method.However,due to the imperfection of the magnetoelastic coupling theory of ferromagnetic materials,the non-monotonic effect of tensile stress on the magnetic properties of materials has not been reasonably explained.The research on the magnetoelastic effect under multi-axial stress load and cyclic alternating load in engineering is not deep enough.The time-consuming problem of the existing stress inversion algorithm makes the measurement of stress by magnetic method still in the exploratory stage.In this paper,the magnetic properties of ferromagnetic materials under stress and magnetic field loads and the forward and inverse analysis methods of magnetoelastic effect are studied as follows :Firstly,a simplified multi-scale magnetoelastic constitutive model is proposed.Based on the multi-scale method and energy conservation framework,the model transforms the change of magnetization into the change of magnetic domain volume fraction,and constructs the differential equation of magnetic domain volume fraction with stress and magnetic field.Considering the contribution of the second-order stress term to the magnetoelastic energy in the magnetic domain Gibbs free energy formula,the volume fraction of the non-hysteresis magnetic domain related to the stress and magnetic field is obtained.According to the Jiles-Atherton hysteresis theory,the differential expression of the hysteresis volume fraction is obtained,and the macroscopic magnetization and magnetostrictive strain of the material are obtained by homogenization method.Compared with the existing models,the proposed model solves the problem that the tensile stress has a non-monotonic effect on the magnetization of the material,and also solves the problem that the existing models cannot simulate the effect of simultaneous changes of stress and magnetic field on the magnetic properties of the material.Secondly,the dynamic magnetoelastic constitutive model of the effect of load frequency on the magnetic properties of materials is established.The existing experiments show that the magnetic field loading frequency and the stress loading frequency have a significant effect on the magnetic properties of ferromagnetic materials.The hysteresis loss theory can be used to solve the influence of the magnetic field loading frequency,but the effect of the stress loading frequency on the magnetic properties of the material has not yet established an effective theoretical model.On the one hand,based on the proposed simplified multi-scale magnetoelastic effect model,combined with the loss separation theory,a dynamic equal stress magnetoelastic effect model is established and solved by a more stable linear multi-step method,which explains the influence of magnetic field frequency on hysteresis loop under constant stress.On the other hand,based on the discrete energy average model,the rate-dependent equation of the transition time required for magnetic domain deflection is introduced,and a dynamic isomagnetic magnetoelastic effect model is established,which accurately explains the influence of stress loading frequency on the stress-magnetization hysteresis loop.Then,based on the constitutive model of magnetoelastic effect and finite element method,the forward analysis method of magnetoelastic coupling of ferromagnetic components is proposed and verified by experimental research.Most of the existing theoretical and experimental studies analyze the magnetoelastic coupling characteristics of rod-shaped or plate-shaped specimens.However,there are few studies on the components that are often subjected to multi-axial stress in engineering practice.Based on the proposed magneto-elastic effect constitutive model,this paper conducts forward analysis on the surface magnetic field distribution of rail components that produce multi-axial stress under bending stress.A rail bending stress loading test platform is designed and built to study the relationship between the surface normal magnetic field of rail specimens and constant load and cyclic load under geomagnetic field and external magnetic field.The test results are basically consistent with the forward analysis results,which verifies the effectiveness and universality of the proposed theory.It has certain guiding significance for the magnetic nondestructive testing of rail stress.Finally,the existing stress inversion calculation method is improved and optimized.A closed-loop pseudo-inverse method for stress inversion calculation is proposed by analogy with defect magnetic flux leakage inversion calculation.The core of the closed-loop pseudoinverse method lies in the forward model and the iterative optimization algorithm.The existing method uses the finite element model as the forward model to ensure high solution accuracy but at the same time increase the calculation time.Therefore,the Kriging surrogate model is proposed to replace the finite element model,which can greatly reduce the calculation time while ensuring the calculation accuracy.The particle swarm optimization method is used to replace the traditional conjugate gradient method to improve the global convergence and stability of the stress inversion calculation. |
