Advances in Materials Science and Engineering

Volume 2017, Article ID 1284560, 8 pages

https://doi.org/10.1155/2017/1284560

## The Magnetic Memory Effect of Ferromagnetic Materials in the Process of Stress-Magnetism Coupling

School of Mechanical Engineering, Liaoning Shihua University, Liaoning Province 113001, China

Correspondence should be addressed to Guoqing Wang; nc.ude.upnl@gniqouggnaw

Received 24 April 2017; Accepted 16 July 2017; Published 14 August 2017

Academic Editor: Michele Zappalorto

Copyright © 2017 Guoqing Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Ferromagnetic materials can produce the magnetic memory effect under stress. This provides a practical method to measure stress concentration. The relation between stress and magnetic characteristic is analyzed through energy balance theory. Force-magnetism coupling process of Fe-C crystal system is simulated by CASTEP software which is based on first principle. Electron band structure, electron density of states, and atomic magnetic moment in the process of force-magnetism coupling process are calculated. Experimental investigation of the magnetic memory effect of ferromagnetic material under different stresses has been undertaken in X52 pipeline. The results show that the magnetic characteristic of ferromagnetic material weakens under stress, and the magnetic memory signals intensity linearly decreases with the increasing stress. When material yields, the variation character of magnetic memory signals suddenly changes and the inflection points of the stress-*B* curves emerge. Experimental investigation is in agreement with the theoretical analysis.

#### 1. Introduction

The ferromagnetic materials widely used in engineering structure have good mechanical properties and exhibit good ductility and toughness under external stress. It can effectively resist stress and deformation and ensure the safe operation of the equipment. However, the defect or discontinuity and other factors often existent in the metal will produce the stress concentration which induces the local large deformation or plastic deformation [1]. The plastic deformation is the early stage of materials damage under stress and always becomes the source of materials failure. So, it can prevent and reduce the damage accidents through detecting the stress concentration and plastic deformation which is induced by stress concentration in engineering field.

The magnetic memory effect is the change of ferromagnetic materials’ magnetization characteristics under the stress in the weak magnetic field of the earth, and when the stress is removed, the change is irreversible [2]. It is a noncontact nondestructive testing method for stress concentration and plastic deformation [3–5]. However, the current research on the mechanism of magnetic memory effect of stress is far from conclusive [6–9]. The magnetic memory mechanism and signal characteristics are explained from different perspectives by a lot of researches, but there is no definite conclusion on them [10–14]. So the study on the mechanism of stress-magnetism coupling of ferromagnetic material and the characteristics of magnetic memory effect has aroused more and more concerns in many countries [15–17].

The present paper explores the magnetic memory effect of ferromagnetic materials under stress. Firstly, the characteristics of the magnetic memory signals on the surface of the ferromagnetic materials are analyzed from the point of view of the energy balance of the ferromagnetic body. Then the process of stress-magnetism coupling is simulated by CASTEP software based on the first principle. The influences of stress on the electron band structure, the electron density of states, and the atomic magnetic moment are analyzed. The quantitative relationship between the stress and the magnetic memory signals is obtained. In the last part, the ferromagnetic pipeline pressure experiments are carried out to verify the theoretical analysis of the magnetic memory effect of ferromagnetic materials under stress.

#### 2. Mechanism Analysis

The basic characteristics of ferromagnetic materials is the magnetic domain structure, and magnetic domain is the basis of all magnetic properties [18]. The essence of magnetic domain is an ordered arrangement of atomic magnetic moment in a small region, and its formation and existence are determined by interaction of various energies. The various energies are subject to the law of thermodynamics that the total free energy reaches minimum upon system equilibrium. Here, the magnetic memory signal characteristics which occur in the process of force and magnetic coupling are analyzed through the energy balance theory.

The magnetic domain will rotate when the external magnetic field is applied. Assume that the angle between the easy magnetization direction of magnetic domain and the direction of the magnetic field is . When the magnetic moment is in the direction of easy magnetization, the energy of the external magnetic field of ferromagnetic magnet is

In the formula, is the vacuum permeability, is the saturation magnetization, and is the external magnetic field strength.

When subjected to external magnetic field, the magnetic moment will rotate a small angle, the energy of the external magnetic field of iron magnet isand is less than . The greater is, the smaller the external magnetic energy is. If there are no other obstacles, the magnetic moment will continue to rotate until . But the stress which exists in a ferromagnetic material will produce stress energy which can be expressed in the following formula:

In the formula, is the magnetostrictive coefficient.

The existence of stress can produce the stress anisotropy, which is the same as the magnetic anisotropy, which hinders the rotation of the magnetic moment. At this time, the influence of the magnetization of the material should be considered, so the total free energy in the unit volume is the sum of the stress energy and the external magnetic field energy ; that is,

Formula (4) derivation can get relation between and :

Under weak magnetic field, the magnetic moment rotation angle is very small, so in formula (5) , , and , so formula (5) can be simplified as

In addition, the magnetization in the direction of the magnetic field can be expressed as

The initial magnetic susceptibility of the material is calculated by (6) and (7):

Formula (8) is the same direction, uniform stress region of the initial magnetic susceptibility. In fact, the ferromagnetic material is a multicrystal, and the stress direction is different in different grains. has a variety of values; therefore, it is needed to find out the average value of in different directions. Assume that the direction of stress is uniform in the domain, and the value in formula (8) is averaged, and the actual crystal magnetic susceptibility is expressed as

Formula (9) shows that the stress leads to the change of magnetic susceptibility and further leads to the change of the magnetization intensity in the local region. Under the action of the external magnetic field , the relationship between the magnetic susceptibility and the magnetic flux density is as follows:

Formula (10) shows that, in the areas of stress concentration, the significantly greater force will reduce the local magnetic flux density, and this leads to magnetic distortion in the local region, that is, the formation of magnetic memory signal.

Here, it should be noted that the stress in formula (10) is equal to external stress when ferromagnetic materials are in the elastic deformation stage. While ferromagnetic materials start to yield, a lot of dislocations and plastic deformation that can reduce the actual stress within materials appear. At present, the stress in formula (10) should be replaced by equivalent stress . The relation between and is

In the formula, is a coefficient which is less than 1 and relates to the number of dislocations and the degree of plastic deformation.

According to the analysis above, the magnetic memory signals characteristic will change when ferromagnetic materials are in the state of plastic deformation.

#### 3. Simulation of the Process of Stress-Magnetism Coupling

Based on the theoretical analysis of the magnetic memory signals characteristics of ferromagnetic material under stress, the first principle method is used to simulate the magnetic memory effect in the process of force magnetic coupling. A model of the *α*-Fe supercellular crystal with body centered cubic lattice structure was built by CASTEP module based on the first principle. The lattice constant in the ground state is set to 2.8664 Å and, respectively, extended four units in the , , and three crystallographic directions. The 4 × 4 × 4 supercell is established. In the actual steel, the carbon element is contained in the model, and the structure of the crystal model is formed by the replacement of the original cell structure. The crystal calculation model is shown as Figure 1.