Analysis of the magnetoplasticity of steel by constructing the absorption spectrum of mechanical energy at magnetic resonance

The tensile test of nonalloy structural steel St3 and low-alloy steel 40X in an external constant magnetic field with an induction of 1.2T was performed. Deformation energy absorption is a manifestation of the magnetoplastic effect. The similarity of the action of a magnetic field in tensile testing of samples and in the study of classical magnetic resonance is described. A new method for analyzing the magnetoplasticity of bulk samples by analogy with the construction of the energy absorption spectrum at magnetic resonance has been applied. The energy absorption spectrum is plotted in the coordinates of the metal flow stress–dislocation density. The characteristics of the spectrum line are determined: its depth as the value of the absolute decrease in the metal flow stress, as well as its width according to the FWHM (full width at half maximum) value.


Introduction
The magnetoplasticity phenomenon has been studied for more than thirty-five years.The magnetoplastic effect is determined by a combination of processes occurring at different levels of the structure of a substance.These are resonant and relaxation processes in the dislocation-stopper system.The object of the action of a magnetic field (MF) in a metal is a dislocation-a microscopic distortion of the crystal lattice, due to the movement of which the mechanism of sliding deformation is realized.The effect of the impact of the MF is manifested in its advancement and overcoming obstacles, i.e., conditions are created for the detachment of the dislocation from local defects, and its movement is due to long-range fields of internal stresses in the crystal.An explanation of the particular interaction of defects in the crystal structure from the point of view of magnetic resonance was made by the group of Alshits et al. (2003Alshits et al. ( , 2017) ) which is still the generally accepted idea of the mechanism of magnetoplasticity.Experiments on magnetoplasticity can be attributed to the class of phenomena of changes in the course of various processes in materials and their properties (Alshits et al. 2003) (the rate of chemical reactions, the electrical conductivity and B Maksym Kraiev mkraev79@gmail.com 1 Yuzhnoye State Design Office, Dnipro 49008, Ukraine photoconductivity of semiconductors, the viscosity of amorphous alloys, etc.) under the influence of a magnetic field.Similar to the conclusions of Golovin (2004), the experimental methodology with sample deformation is also close to classical radio spectroscopy, except that the response of the system under study to achieving resonance was not a sharp absorption of microwave energy but the absorption of mechanical energy from an applied external load.This means that it is part of a large family of reaction yield detected magnetic resonance (RYDMR) methods, resonance, detected by the magnitude of any response to the action of the magnetic field.The description of magnetoplasticity as a volumetric resonant phenomenon is a topical issue and opens up a new method for studying the structure and properties of metals.

Methods
The magnetoplastic effect was created by tensile testing of cylindrical steel samples with a diameter of 5 mm (in accordance with ISO 6892-1) in a constant MF with induction B = 1.2T.The MF lines are perpendicular to the tension axis of the samples.To compare the indicators, a tensile test of samples without an MF was performed.
The studies were carried out on steel of two grades: nonalloy structural steel St3 (analogues of S235, Fe360, St37, A284Gr.D) with a content of C = 0.14-0.22%and Mn = 0.40-0.65%;low-alloy steel 40X (analogues 41Cr4, 530, 5140) with a content of C = 0.36-0.44%,Mn = 0.50-0.80%and alloyed Cr = 0.80-1.10%.Common steels are selected but have differences among themselves.St3 steel has a ferrite-pearlitic structure, and 40X steel has a pearlite structure.Steel St3 refers to metals of normal strength (yield strength not less than 235 MPa) and was used in the experiments in the state after rolling, and 40X is of increased strength (yield strength not less than 315 MPa) and was used in the experiments in the normalized state.
Strain rate during tensile tests ~0.03 s −1 .The density of dislocations in the metal was determined by X-ray analysis on an X-ray diffractometer in Co K α radiation.
The interpretation of the results of the study was carried out using the concepts of materials science, spin micromechanics and magnetic resonance about the deformation of crystalline bodies by dislocation slip and the role of the MF effect on their dynamics.

Results and discussion
If the magnetoplastic effect is related to resonance phenomena, then its mechanism should be similar to magnetic radio spectroscopy, for example, cyclotron, paramagnetic, or nuclear magnetic resonance.For the implementation of resonance, a constant magnetic field and an alternating electromagnetic field applied in a direction perpendicular to the magnetic induction vector are used.The role of a constant magnetic field is to orient along or across the field of the magnetic moment of the particles of the body under study to create discrete levels of particle energy (Landau or Zeeman levels).The energy absorption mechanism is associated with quantum transitions in these subsystems between discrete energy levels.An alternating electromagnetic field is the main source of energy absorbed selectively by various subsystems of matter.
The experiments on tension and compression of metals presented in Pokoev and Osinskaya (2018), Zhang et al. 2022, Smirnov 2019, Hu et al. 2022) with the additional use of an external constant magnetic field showed a decrease in the flow stress of metals, i.e., increase in the absorption of mechanical energy during deformation.The similarity of installations for magnetic resonance and metal deformation is noteworthy (Fig. 1).As in the case of magnetic resonance, the direction of action of a constant MF is perpendicular to the axis of elongation or compression of the samples (the principal strain axis).The energy source is an external mechanical force that deforms the sample metal.
Compliance with the magnetic resonance condition, which consists of the perpendicular intersection of the fields, ensures the observation of the resonance effect.In the case of deformation, this is the observance of a right angle between the magnetic induction vector and the principal strain axis.The MF effectively affects the dislocation mobility when the magnetic induction vector is perpendicular to the line of the edge dislocation and does not change the dislocation ranges when it is parallel (Morgunov 2004).Both facts prove in practice the unity of the nature of the phenomena of magnetoplasticity and magnetic resonance.
Let us consider the most common type of conservative (normal) dislocation motion along the glide plane.Observance of the magnetic induction vector perpendicular to the dislocation slip plane creates ideal conditions for magnetic resonance.Otherwise, one can also speak about the perpendicularity of the magnetic induction vector and the dislocation Burgers vector.In a polycrystalline body, individual grains are misoriented in volume.The slip planes in different grains are also misoriented.Therefore, magnetic resonance cannot manifest itself simultaneously in the whole body, completely covering its volume.This may be one of the factors explaining the instability of the resonance manifestation in the experiments of various researchers.This casts doubt on the possibility of achieving large effects when using a stationary MF.Based on these considerations, it is of research interest to use a constant MF that changes its position in space in the process of plastic deformation of the metal, for example, the rotation of permanent magnets in the plane of the lines of magnetic induction across the principal strain axis.
According to the resonance condition, a process of periodic (discrete) absorption of external energy with a frequency coinciding with the frequencies of electromagnetic processes in metal subsystems is necessary.Can metal deformation be represented as a discrete process?In the theory of plasticity, where bodies of macroscopic volume are considered, the deformation of a metal is a continuous quantity.However, the mechanism of deformations is at the atomic level, is described by the theory of deformable solids, and is a set of nucleation and movement of defects in the crystal structure.The most common mechanism of deformation is slip, in which the main role is played by the movement of dislocations.A quantum of external mechanical energy is spent on the formation and movement of each defect.The dislocation density in metals can reach 10 7 -10 12 cm −2 .From the experience of magnetic resonance phenomena in ferromagnets, it can be assumed that the resonance frequency is in the region of ultrahigh frequencies (~10 9 -10 11 s −1 ), similar to electron paramagnetic resonance or nuclear magnetic resonance (Weil and Bolton 2007;Chizhik et al. 2014).In confirmation of the wave nature of the process of dislocation movement, namely the existence of its frequency characteristics, Golovin (2004) noted that the dislocation makes millions of unsuccessful attempts to attack the barrier before it is overcome.This happens in a short amount of time.Thus, taking the quantization of energy at the crystalline level, the process of energy absorption during metal deformation can be represented as an ultrahigh frequency wave.
Magnetic resonance in studies of magnetoplasticity manifests itself in a decrease in the flow stress of a metal during plastic deformation.The recorded information is the hardening curves in the stress σ-true (logarithmic) strain ε coordinates, as shown in Fig. 2. The studied process of deformational magnetic resonance is continuous, relatively slowly changing over time.Its description can be made using the principles of the continuous method of slow passage through resonance.The main physical quantity describing the observed phenomenon is the resonant frequency of the process.The resonance frequency is defined as the number of energy quanta absorbed by dislocations and expended on their movement.The flow stress on the density of dislocations of a polycrystalline metal, in accordance with the well-known formulas of Hall-Petch and Taylor, is in a direct power dependence.
The experiments carried out revealed the main effect of the magnetic field at the initial stage of deformation.Quantitatively, the change in the yield strength of the metal exceeds the change in tensile strength.This is explained by the essence of the phenomenon of magnetoplasticity and the influence of a magnetic field at the dislocation mobility stage.As dislocations are blocked in their multiple interactions with dislocations and other barriers, as the free path length decreases, magnetoplasticity gradually disappears.Low-alloy steel shows a greater magnetoplastic effect due to the presence of a larger number of magnetic field targets described earlier.
The analysis of magnetic resonance is carried out on the basis of the analysis of the spectra of absorption or emission of energy.In this case, the absorption process is considered-the volumetric absorption of the deformation energy by a metal sample.The spectra were constructed for the cases of tensile testing of samples at the stage of plastic deformation, i.e., at stresses exceeding the yield strength of steel (Fig. 3).To plot the spectrum along the frequency axis, we chose the values of the dislocation density in metals in the (110) slip plane.
The form of the spectra is similar to the resonance absorption phenomenon.The contour of the absorption line is reduced in shape to a symmetrical parabolic curve and has a pronounced minimum.The contour shape of the absorption line is close to the Gauss curve or even to the Voigt curve used to describe the lines of the spectra.Determination coefficient in Fig. 3b is not good enough.This can be corrected by increasing the number of experiments, which will be appropriate in a special study.
The indicator characterizing the intensity of energy absorption is the value of the absolute decrease in the flow stress of the metal σ max with the cross-sectional area of the sample valid for a given moment of testing under uniform plastic deformation.In spectroscopy, this indicator is called the spectral line depth.
The spectral peak width is estimated from the full width at half maximum (FWHM) value.The values of the characteristics of the contours of the spectral lines are given in Table 1.The FWHM value is the central part of the absorption spectrum.In experiments with steels St3 and 40X, the intensity of energy absorption does not reach zero values, so the spectrum line is not saturated.
Based on the described magnetic resonance, it is possible to create a new method for studying the plasticity and strength of metals.The method will allow us to carry out a qualitative and quantitative analysis of the dynamic development of the defective structure of the metal during deformation, namely: • Evaluation of the dynamic potential of defects in the crystal structure and changes in the increase in their density in the process of deformation.• Determination of the number of crystal structure defects that are potentially capable of movement under mechanical load.• Possibilities of changing the boundaries of the primary linear stage of hardening, changing the strength and plasticity of the metal.The practical value of the method lies in the extended analysis of metal properties for laboratory and industrial purposes.It is worth noting the relative simplicity of the equipment and the similarity to other magnetic resonance methods, which will help create a practical method for data analysis.
when maintaining a right angle between the magnetic induction vector and the axis of the main tensile strain.This is similar to the perpendicular intersection of the constant magnetic and alternating electromagnetic fields in magnetic resonance facilities.The resonant nature of the microscopic processes of the magnetoplastic effect, the scheme of tensile tests, and their results made it possible to suggest considering the resonant effect in the macroscopic volume of the sample.The processing of the tensile curves made it possible to construct the absorption spectra of mechanical energy during plastic deformation of the samples.The absorption of mechanical energy is characterized by an absolute decrease in the metal flow stress.To plot the spectrum, the frequency is represented by the values of the dislocation density in the metal in the slip plane (110).The obtained absorption line contours are close to the Gauss or Voigt curve, which made it possible to use the characteristics of the magnetic resonance spectral line contours for their analysis.This opens up the possibility of creating a new method for analyzing the plasticity and strength of metals.

Fig. 1
Fig. 1 Installation schemes for magnetic resonance (a) and deformation in a magnetic field (b)

Fig. 3
Fig. 3 Absorption spectra of mechanical energy in a magnetic field: a steel St3; b steel 40X

Table 1
Depth and width of spectral lines