Introduction. Destruction under cyclic loading is one of the most common types of damage to materials. The performance of these materials is largely determined by their resistance to crack growth. The problem is that cyclic loads can cause fatigue failure even at stresses below the ultimate strength of the material. Although the growth of a fatigue crack occurs gradually, the fracture itself can occur suddenly, leading to catastrophic consequences. There are extensive statistics [1] on railway and plane crashes, bridge collapses, and man-made accidents caused by the development of such defects. According to ASM International [2], up to 90% of mechanical failures in mechanical engineering are due to fatigue. In the oil and gas industry, billions of dollars are lost annually due to fatigue cracks in pipelines and drilling rigs. To address this issue, non-destructive defect control methods are introduced. These methods can account for up to 30% of maintenance costs in the aerospace industry. To ensure safe and long-term operation of machine parts and devices, it is essential to achieve their high-strength state with increased crack resistance.

Known methods of achieving a high-strength state [1, 2] involve combining a specific alloy composition with heat treatment methods, minimizing the presence of non-metal inclusions, creating a heterogeneous microstructure, and using surface hardening techniques. Previously, researchers have proposed a technology of heat treatment in a magnetic field (HTMF) [3], which allows for the creation of a high-strength state in steels under certain conditions. A feature of the proposed technology is an increase in strength characteristics without reducing viscosity. At the same time, widely used grades of alloy steels are subjected to almost traditional heat treatment modes, but with the application of permanent magnetic field energy.

Existing methods for increasing crack resistance [1, 2] operate by the following mechanisms: increasing the area of plastic deformation at the crack tip; branching the crack trajectory (increasing its path); creating compressive stresses to slow down crack growth; local hardening along the crack path; reducing the number and size of stress concentrators; creating microstructural barriers. However, there is still not enough information about how cracks behave in steels that have been treated with permanent magnetic fields. Therefore, the aim of this research is to investigate how the resistance to cracks and the rate of crack growth change after HTMF.

Materials and Methods. The features of crack development over time were studied using an installation that creates cyclic oscillations with stabilized amplitude. The design of this installation was described in [4]. The method of electric potentials [5, 6] made it possible to record the moment of origin and the stages of development of fatigue cracks. The data obtained in this way was transferred into real values using a calibration diagram that had known data on crack length and prismatic sample size.

The research results are presented in the form of dependencies with dl/dN – lg∆K axes [2, 7], characterizing the development of fatigue failure. The value of dl/dN ratio determines the exponential rate of crack propagation over a certain number of load cycles. Parameter ∆K demonstrates the range of variation of the stress intensity coefficient (SIC) under cyclic loads and is calculated as the difference between the highest and lowest SIC values:

 (1)

 values were calculated in terms of the maximum stresses (σ), that occur during cyclic bending of a prismatic sample with a crack of length l, according to the formula:

 (2)

Studies were conducted on prismatic samples of 18Kh2N4VA, 30KhGSA steels, which were heat-treated (18Kh2N4VA — air hardening for martensite; 30KhGSA — isothermal quenching at 38°C for lower bainite) for high-strength condition. A magnetic field with strength of 1.6 MA/m was in the magnetic gap of the FL – 1 electromagnet.

An Emma – 4 transmission electron microscope and a ZEISS CrossBeam 340 scanning electron microscope (SEM) were used to study the fine structure

Results. Figure 1 illustrates the dependence of the fatigue crack length on the number of test cycles after various treatments for the studied steels.

Diagrams of the development of fatigue cracks over time are presented in Figure 2. Their appearance illustrates the three stages of crack development. At each of these stages, the crack has a certain propagation velocity: 1st stage — slow growth; 2nd stage — stable growth, and 3rd stage — accelerated or unstable growth [1]. Each of the stages is characterized by its own features of the fracture surface relief [2], which are well detected on the sample fracture after the cyclic bending test.

It can be seen (Fig. 2) that the crack propagation rate significantly decreases after HTMF compared to the treatment without a field, while the range of SIC ∆K values remains commensurate. The fracture of the sample occurs with a longer cyclic crack length and a larger  value, as shown in Table 1. The numerator contains data for processing without a field, and the denominator contains data for processing in a field with a voltage of 1.6 MA/m. Confidence intervals are indicated with a confidence probability of P = 0.95 and the number of measurements n = 5.

Figure 3 a illustrates the mechanism of viscous fracture by nucleation, growth, and coalescence of pores, which is typical for steels a18Kh2N4VA and 30KhGSA. Figure 3 b shows the result of how a crack forms from the pores under the influence of normal stresses.

Figure 4 demonstrates the fragments of cracks under heat treatment conditions in a magnetic field and without a field. An analysis of such data was conducted to identify the dependence of the change in the crack trajectory on the type of heat treatment.

Discussion. The data in Figure 1 indicate that in the case of heat treatment in a magnetic field, the kinetics of crack propagation is more suppressed compared to treatment without a field, and the last stage of destruction occurs with a larger number of test cycles. Kinetic diagrams of fatigue crack development (Fig. 2) also demonstrate a significant decrease in the crack development rate under magnetic field treatment conditions while maintaining the SIC ∆K range. There are suggestions [8, 9] that in cyclic tests it is more expedient to characterize the viscosity by the initial (threshold) value of SIC, corresponding to the beginning of the separation of the main crack by a tear-off mechanism (with a given degree of constraint on plastic deformation), rather than by the maximum value of SIC corresponding to the limiting state. As can be seen from Table 1, the value  increases after the HTMF. It is reasonable to anticipate an increase in the durability and operability of mechanical engineering products after heat treatment in a magnetic field [10, 11], which is also indicated by the results of previous studies on the effect of HTMF on mechanical properties [12, 13].

Monograph [3] summarizes the data that during processing to a high-strength state (the structure of upper martensite or lower bainite [14, 15]), the influence of a magnetic field manifests itself in significant fragmentation of the structure, increased dispersion of individual crystals of the ferromagnetic α-phase and their ensembles (packages), an increase in the specific surface area of the sub-boundaries that impede movement dislocations during loading. Local overstress at the tip of the dislocation cluster can relax through the formation of a crack nucleus, the development of which depends on the nature of the steel structure. Depending on the loading conditions and the initial state of the martensite [16, 17], the growth of a microscopic crack can occur by various mechanisms that determine the appearance of the fracture surface. It should be noted that for the 30KhGSA and 18Kh2N4VA steels under consideration, viscous fracture occurs when pores appear, grow, and combine (Fig. 3 a). Alternating loads lead to fatigue failure by forming a large number of excess vacancies (for example, as a result of inter-dislocation interactions and sliding with the formation of jogs [2, 18]), which can combine to form a pore. Normal stresses acting on the surface of the pore nuclei contribute to the vacancies sink, which leads to the transformation of the pores into a crack (Fig. 3 b).

The formed crack progress depends on the presence of obstacles in its path, which is determined by the features of the existing structure of the material. In this regard, the parameters of the crack propagation trajectory in thin foils were studied using electron microscopy, since they are very dependent on the structure [1]. The results of the fine structure analysis allow us to conclude that the use of HTMF technology does not affect the mechanism of changing the crack trajectory, i.e. the trajectory changes randomly (Fig. 4) when encountering various structural elements (carbides, phase boundaries, etc.) and does not depend on the method of heat treatment.

The autocorrelation functions analysis (AFA) [19, 20] linking the deviation of the crack line from its average position and the 1st derivative of its propagation trajectory (Fig. 5), which characterizes the angular parameters of the change in the trajectory of crack propagation in the foil, allows us to evaluate the effectiveness of the structural barriers caused by HTMF on the path of crack development. AFA allowed us to estimate the effect of HTMF on the statistical parameters of cracks:   — standard deviation of the crack line;   — standard spread of the tangent of the trajectory angle (tortuosity index);  — ranges of interdependence of the linear spread functions and slope tangents, respectively (they characterize an increase in crack length as a result of a single factor). The statistical parameters of cracks  for 30KhGSA steel are shown in Table 2. It shows the standard deviations of the experimental data.

According to the data in Table 2, it can be noted that HTMF affects all the listed statistical characteristics of cracks. Standard tangent spread of the slope angles of the fracture line sections after HTMF increases by 0.12, which corresponds to an increase in the average slope modulus of the crack trajectory by ~6° (from 29 to 35°). At the same time, correlation interval decreases by 0.5 µm.

Conclusion. The main result of this work is the identification of changes in the kinetics of fatigue crack development and the identification of mechanisms that contribute to increased crack resistance after HTMF. Based on the data obtained, it can be concluded that the technology of heat treatment in a magnetic field contributes to the formation of a structure that ensures an increase in the curvature of cracks. There is an increase in the steepness of the bending trajectory due to a greater number of effective barriers (an increase in the dispersion of martensite) in its path. In this respect, the nature of the HTMF's structure organization has much in common with the process of high-temperature thermomechanical treatment. This leads to the development of a new practical method for creating a high-strength state that can be applied to a wide range of steel grades without requiring significant changes to their heat treatment process. In turn, increasing the crack resistance of steels makes it possible to ensure greater safety of various devices and man-made systems, as well as reduce their cost and maintenance costs.