Analysis of the influence of the stress-strain state of oil and gas equipment metal on the parameters of electromagnetic-acoustic conversion

. In the oil and gas industry, to assess the technical condition of equipment, diagnostic methods and tools are used aimed at identifying defects that are unacceptable, according to regulatory documents. In places where mechanical stress is concentrated, microdefects in the metal structure arise, which, under the influence of static and dynamic loads, develop into macrodefects that cause equipment destruction. To identify areas of concentration of mechanical stress and localize metal microdamages, it is proposed to use a non-contact, high-performance electromagnetic-acoustic diagnostic method. But existing electromagnetic-acoustic diagnostic tools lack sensitivity and information content. The article provides an analysis of the influence of the stress-strain state of the metal on the parameters of electromagnetic-acoustic transformation in order to identify additional informative parameters and methods for their processing to solve the problem of identifying the stress-strain state and damage to the metal structure of oil and gas equipment.


Introduction
During the operation of oil and gas production equipment, under the influence of variable and static thermomechanical, mechanical and vibration loads, irreversible degradation changes occur in the structure of the material, causing a deterioration in their structural properties, which can cause emergency situations.To prevent equipment destruction, it is necessary to identify defects at the earliest stages of origin and development, i.e. it is necessary to monitor and identify changes at the level of the metal structure.
Diagnostic tools based on the use of electromagnetic-acoustic (EMA) conversion are promising for solving this problem.The fundamentals of the theory of the electromagneticacoustic method and the prospects for its application for non-destructive testing of materials and products were outlined back in the 60s -70s of the 20th century in the works of Professor Yu.M. Shkarleta [1].But existing electromagnetic-acoustic diagnostic tools are insufficiently sensitive and informative compared to traditional ultrasonic tools with contact piezoelectric transducers.This is explained by the low efficiency of double mutual conversion of electromagnetic and acoustic waves, while only the parameters of acoustic waves are used as informative parameters and the informative parameters of the electromagnetic component are not used [2][3][4][5].Analysis of the influence on the parameters of the electromagnetic-acoustic signal of changes in the parameters of both electromagnetic and acoustic waves when interacting with inhomogeneities in the metal structure caused by mechanical stresses and defects in the metal structure allows us to form a new set of informative diagnostic parameters.The results of research by domestic and foreign scientists confirm the existence of such relationships and the possibility of using them to improve the electromagnetic-acoustic control method [6][7][8].

Materials and methods
The initial system of equations for the analysis of processes occurring during electromagnetic-acoustic transformation in metals and the surrounding space are Maxwell's equations and the basic equations of the theory of elasticity.An acoustic wave in a metal is generated by an alternating electromagnetic field.The solution to the problems of the theory of electromagnetic and acoustic waves in relation to the problems of diagnostics of oil and gas equipment is to determine changes in space and time in the parameters of wave processes characterizing the stress-strain state (SSS) and damage to the metal structure.This task consists of two stages.At the first stage, the initial system of equations describing the wave field in the medium is used.At the second stage, applying a number of simplifications and setting initial and boundary conditions determined by the specific formulation of the problem, the desired wave equation is obtained [9].G.A. Budenkov and O.V. Nedzvetskaya derived integral wave equations that describe the propagation of acoustic waves generated during electromagnetic-acoustic transformation in media with inhomogeneities in elasticity and density.Local inhomogeneities of the medium, caused by the stress-strain state and damage to the metal structure, are considered as secondary sources of radiation of acoustic waves with parameters depending on the parameters of these inhomogeneities [9].
Defects, dislocations, grain boundaries, microcracks, discontinuities and residual mechanical stresses lead to the appearance of structural nonclassical elastic nonlinearity in solids [10].The magnitude of this nonlinearity can significantly exceed the magnitude of classical nonlinearity associated with anharmonicity of intermolecular forces.Structural nonlinearity is local, its properties are determined by the level of defectiveness of the material at a given point.This makes it possible not only to judge the presence of defects in the material under study, but also to obtain information about their spatial distribution.To study the elastic properties of materials with a non-ideal structure, various methods of nonlinear acoustics are used, such as the acoustoelastic effect, spectral methods and methods of nonlinear resonant ultrasonic spectroscopy [11].
Acoustic field harmonics in a magnetic field are converted into electromagnetic field harmonics, which generate an electrical signal in an electromagnetic-acoustic converter containing a spectrum of harmonic components with certain parameters.As the stress-strain state changes and damage accumulates at the level of the metal structure, an interconnected change in its mechanical, electrical, magnetic and acoustic properties occurs.Already at the stage of converting the electromagnetic field into an acoustic field, in addition to acoustic waves, secondary temporal and spatial harmonics of the electromagnetic field are generated, the parameters of which carry additional information about the electrical and magnetic properties of the metal.All changes in the acoustic, magnetic and electrical properties of the metal, caused by mechanical stresses and damage to the structure, are reflected in the parameters of the harmonics of the secondary electromagnetic field, which are converted into the parameters of the harmonic components of the output signal of the electromagnetic-acoustic transducer.
To increase the efficiency of electromagnetic-acoustic conversion in modern diagnostic devices, high-voltage voltage pulses are supplied to the excitation winding of the converter, which initiate the generation of a wide range of acoustic field harmonics in the volume of the test object.Reflected from the opposite side of the test object, the harmonics of the acoustic field, after interacting with any inhomogeneities in the structure of the material, return to the measuring winding of the transducer, carrying extensive information about the properties of the material.

Results
The electromagnetic field of the electromagnetic-acoustic transducer excites eddy currents in the electrically conducting test object, which in turn, in the presence of an external static magnetic field, excite acoustic waves in the test object.Acoustic waves, after interacting with local structural inhomogeneities, micro-and macrodefects of the metal, are reflected from the opposite surface of the test object and carry information about the structure and defects of the metal.Having reached the electromagnetic-acoustic transducer, the acoustic waves are converted into an electromagnetic field and generate an electrical signal in its measuring winding, the parameters of which reflect the parameters of the acoustic wave, which carries information about the stress-strain state and damage to the metal structure.From the point of view of non-destructive testing and equipment diagnostics, the case of greatest interest is when the source of acoustic wave radiation is located at a certain depth under the surface of an elastic half-space and is concentrated in a certain volume.The combination of such sources can simulate micro-destructions inside the test object.The interaction of an acoustic wave generated by an electromagnetic-acoustic transducer and two oppositely directed forces acting in the region of microcrack initiation leads to the excitation of a response acoustic wave, i.e. an acoustic signal can be formed in the damaged zone of the metal structure even before the crack begins to open.In this case, all the laws governing the excitation of acoustic waves by a pair of forces are valid for acoustic signal sources of this type.The amplitude of the acoustic wave displacement is proportional to the intensity of two oppositely directed forces acting in the area of microcrack initiation, and characterizes the degree of damage to the metal structure or the volume of the crack formed.
Let us consider a source of the type of vertical harmonic force in an elastic half-space, characterized by elastic constants  and , which in the theory of elasticity are called the first and second Lamé coefficients, respectively, and a constant density , these constants determine the values of the longitudinal and transverse velocities of sound in an elastic medium [9] ,… (1) In [9], an approximate solution of the wave equation was obtained in the form of integrals for displacements in longitudinal (Ul) and transverse (Ut) waves: Where F0 is the volumetric density of external force (N/m 3 ); V -small volume in which the external force is concentrated (m 3 ); kl and kt -longitudinal and transverse wave numbers (m -1 );  -observation angle (rad); z -longitudinal cylindrical coordinate (m); h is the distance to the small volume from the origin (m); k is the integration variable; and -transformation parameters; The values of the elastic constants ,  and  change when the stress-strain state of the metal changes, and this change is reflected in the solution of the wave equation for displacements in longitudinal and transverse waves, which makes it possible to estimate the degree of stress-strain state of the metal of electromagnetic-acoustic equipment.The obtained result describes the behavior of acoustic waves in a half-space when certain properties of this half-space change, caused by mechanical stresses, allows us to obtain a solution for a source such as a pair of forces without a moment, simulating an acoustic signal from a microcrack or an area with damaged metal structure.As shown in [1], in fact, the solution to the wave equation for the secondary electromagnetic field consists of a set of solutions for the spatial and temporal harmonic components of this field, which are the result of both the double conversion of electromagnetic and acoustic waves into each other, and the interaction of each of these waves with inhomogeneities in the metal structure of equipment.Spatial and temporal harmonics of the secondary electromagnetic field are caused by the nonlinearity of the electrical, magnetic and acoustic properties of the metal of the equipment, which reflect the stress-strain state and the degree of damage to the metal structure.Thus, the set of parameters of the harmonic components of the secondary electromagnetic field forms an image of the technical condition of the metal of the equipment.Moreover, the parameters of different harmonic components of the secondary electromagnetic field change differently with changes in mechanical stresses and the development of damage in the metal structure; this circumstance allows for separate monitoring of the stress-strain state of the metal and damage to its structure.

Discussion
To study individual stages of electromagnetic-acoustic transformation and identify informative diagnostic parameters, numerical modeling was carried out using the basic software package Comsol Multiphysics version 6 (perpetual academic license No. 9602348) with expansion modules AC/DC -for the electromagnetic part of the problem and Structural Mechanics (module MEMS) -for modeling elastic vibrations in solids (purchased with funds from the Russian Science Foundation grant No. 22-29-00327).The simulation results demonstrate the existence of a relationship between the harmonic parameters of the signal of the electromagnetic-acoustic transducer and the change in the stress-strain state of the object of study in the acoustic field.
Tensile testing of standard flat samples of steels St3sp, 09G2S and 12Х18Н10Т using a Walter + Bai LF TTM-600 computerized testing machine in accordance with GOST 1497-84 showed that with increasing load applied to the test metal sample, as the stress-strain changes state, origin and development of microdefects in the structure, the shape and time parameters of the dynamic signal of the electromagnetic-acoustic transducer change, which indicates a change in the spectral composition of the signal and makes it possible to apply the method of spectral analysis of the signal to identify damage and identify areas of increased concentration of mechanical stress.Spectral analysis of the signal from the electromagnetic-acoustic transducer under uniaxial tension showed that the harmonic parameters for all three steel grades under study monotonically increase with increasing tensile force, reach an extremum and begin to decrease until the sample is completely destroyed.Moreover, each point of the tension diagram corresponds to its own original set of harmonics with certain parameters.Therefore, recognizing the stress-strain state and microdamage of a metal from the totality of these harmonics seems to be a real technical problem.The results obtained are consistent with the research results presented in [9][10][11].
During cyclic load tests, the harmonic parameters of the electromagnetic-acoustic signal changed in waves; there was no clear relationship between the number of load cycles and the change in harmonic parameters.Therefore, to recognize the damage to the metal structure depending on the number of loading cycles, it is necessary to develop a new research methodology with a theoretical justification, it is possible to use additional measuring instruments and conduct research in a new format to identify the parameters of electromagnetic-acoustic transformation that are uniquely related to the number of loading cycles.Promising in this direction is the use of the parameters of a multiply reflected signal of an electromagnetic-acoustic transducer.
When the metal of a physical model of shell-type equipment in the form of a cylindrical vessel was subjected to complex loading using a hydraulic installation, the harmonic parameters of the signal of the electromagnetic-acoustic transducer increased almost linearly with increasing load and correlated with the calculation results and the readings of the resistive strain gauge installation.But such dependencies were observed only in the proportional section of metal loading.The technical characteristics of the hydraulic installation did not allow reaching the nonlinear sections of the loading diagram.Continued research is required for the complex nature of metal loading using a hydraulic installation with the necessary technical characteristics.Measuring the values of electrical conductivity and relative magnetic permeability during testing of samples provides additional information about the condition of the material.

Conclusion
Technological equipment for oil and gas production is classified as hazardous production facilities.Accidents that occur due to the destruction of oil and gas equipment can cause significant environmental and economic damage and lead to casualties.One of the promising areas for increasing the safety of oil and gas equipment operation is the use of diagnostic tools based on the use of electromagnetic-acoustic conversion.The origins of defects in the metal structure are zones of concentration of mechanical stress, so a dual task arises -identifying zones with an unacceptably high concentration of mechanical stress to prevent the occurrence and development of defects in the metal structure, and identifying defects in the metal structure that have already arisen against the background of the stressstrain state of the metal.This problem can be solved by using an electromagnetic-spectral metric method for identifying damage and identifying mechanical stress concentrators, based on a spectral analysis of the temporal and spatial higher harmonic components of the secondary electromagnetic field.
zeroth kind of the first order.