Classification and evaluation of residual stress

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1 Residual Stress 1.1 Definition and Classification of Residual Stress During various mechanical processing operations such as casting, pressure processing, welding, cutting, heat treatment, and assembly, components are subjected to various influences from these processes. This results in stresses of different degrees within the component. When these influencing factors disappear, if the effects they had on the component do not vanish completely and some of those effects remain within the component, then such remaining effects are referred to as residual stress. It can be said that residual stress is the stress that exists within an object in a state of equilibrium when no external forces are acting on it. Residual stress is a type of inherent stress. Based on the scale over which it acts, it can be divided into two main categories: macroscopic residual stress and microscopic residual stress. ① Macroscopic residual stress, also known as primary residual stress, is distributed on a macroscopic scale; its magnitude, direction, and properties can be measured using conventional physical or mechanical methods ； ②Micro residual stresses fall within the category of stresses at the microscopic level. Based on the range of their influence, they can be divided into two types: microstructural stresses (also known as type II residual stresses, which are distributed within the grains) and intragranular substructural stresses (also known as type III residual stresses, which act within a single grain). 1.2 The nature of residual stress Residual stress is generally considered to be caused by uneven energy storage, and it results from uneven plastic deformation within the material. Its essence lies in lattice distortion, which is largely induced by dislocations. In mechanical manufacturing, various processing steps often result in residual stresses. Essentially, however, these residual stresses arise from uneven volume changes within the metal’s internal structure, which lead to uneven deformations; the metal then experiences interactions as it tries to reach a state of equilibrium. The reasons for the non-uniform changes can be attributed to non-uniform plastic deformation, non-uniform temperature changes, and non-uniform phase transitions. For example, in the quenching process of metal alloys, large residual stresses are generated within them; mechanical processing disrupts the equilibrium of these residual stresses, resulting in deformation of the parts. When the part has high rigidity and a symmetrical shape, the deformation is minimal. Conversely, the deformation is very noticeable. The actual stress state inside a workpiece is complex, involving the interaction of numerous dislocations, as well as the effects of point defects such as vacancies, and grain boundaries and subgrain boundaries. Therefore, the residual stress within a real workpiece is the result of lattice distortions caused by a multitude of factors. 1.3 Effect of residual stress: Residual stress in mechanical parts and large-scale mechanical components has a significant impact on their fatigue strength, resistance to stress corrosion, dimensional stability, and service life. \"Nitridic cracking\" of low-carbon steel in nitrate solutions, \"chloride cracking\" of austenitic stainless steels in chloride solutions, \"alkaline cracking\" of boiler steel in alkaline solutions, and \"ammonia cracking\" of brass in an ammonia-containing atmosphere are all examples of stress corrosion cracking; all such stress corrosion is primarily caused by residual stresses. Dimensional stability refers to a material’s ability, after heat treatment and processing, to resist permanent deformation under no external forces or under stresses below its elastic limit in an operating environment, as well as its ability to maintain its dimensions unchanged during the processing stage. It is generally believed that the spontaneous changes in metal dimensions during long-term storage are the result of the following factors: ① The instability of the phase and microstructural states of the material ； ②The relaxation of residual internal stresses in parts occurs during various hot and cold working processes as well as during mechanical assembly operations ； ③Paquin et al. believe that the unevenness of properties, namely anisotropic materials, leads to the relaxation of residual stresses induced during heating, which is also an internal cause of dimensional instability. In the instrumentation manufacturing industry, the aviation industry, and the aerospace industry, the dimensional stability of components is increasingly struggling to meet the requirements of modern precision instrument design. In a high-precision gyroscope and compass system, any instability in the dimensions of its components can lead to a shift in its center of mass. Such a shift in the center of mass generates erroneous signals, which in turn introduce errors into the guidance system and affect its precision directly. In the field of aerospace applications, even tiny plastic strains on the order of 10-6 or 10-7 can become significant sources of error. During the machining of thin-walled parts, it is difficult to maintain precision due to deformation, which leads to material waste and product rejection, directly affecting the production efficiency and economic benefits of enterprises. To reduce the weight of their components, aerospace products generally have a shape characterized by high strength and thin walls; additionally, some of them feature semi-circular shapes to meet assembly requirements. For such parts, the consequences of residual deformation caused by residual stresses are extremely severe. Such residual stresses, whether large or small, tensile or compressive, even if they occur only in a very thin surface layer, significantly affect the strength, hardness, fatigue resistance, and corrosion resistance of the parts, thereby further impacting the service life of mechanical products. The issue of residual stress has always attracted attention. During the machining process, uneven plastic deformation caused by external forces and temperature changes is the main cause of residual stresses. During casting, forging, welding, and various cutting processes, workpieces develop residual stresses due to the action of external forces and temperature. The processes of generation, accumulation, and release of residual stresses lead to a redistribution of stress within the parts, which can affect the dimensions and geometric accuracy of those parts as well as the precision of their assembly. It also reduces the parts’ resistance to fatigue, stress corrosion, and creep cracking, ultimately impacting the performance and service life of the machinery and equipment. Therefore, it is of great significance to analyze the mechanisms behind the generation of residual stresses, explore effective methods for testing residual stresses, and improve the residual stress conditions in components. In fact, in various industrial sectors such as machinery, water resources and hydropower, thermal power and nuclear power, aerospace, petrochemicals, metallurgy, railways, and transportation, research on residual stress testing techniques and their applications has always received significant attention. Especially since joining the World Trade Organization, in order to keep up with international standards, residual stress testing has become an essential method for inspection and control in many industries. 2 Methods for eliminating residual stress: Since residual stress can have many adverse effects on the quality of components, professionals in this field have conducted extensive research on how to eliminate it, and have systematically developed methods for removing and controlling residual stress in components. The common methods for eliminating residual stress include the following, and the effectiveness of each method varies. (1) The principle of stress relief using mechanical stretching is to apply a certain amount of permanent tensile plastic deformation to the quenched alloy sheet in the rolling direction, so that the tensile stress combines with the original quenching residual stress, resulting in plastic deformation and thereby reducing and releasing the residual stress. (2) The working principle of the vibration-based residual stress elimination method is to use a portable high-power exciter to induce one or more vibration states in the metal structure, thereby creating elastic deformation similar to that caused by mechanical loading. As a result, the residual stresses in certain parts of the component, combined with the vibration loads, exceed the material’s yield stress and lead to plastic deformation, which in turn results in a reduction and redistribution of internal stresses. (3) The pulsation method can effectively relieve the residual stresses in parts by applying cyclic loads of a certain amplitude and frequency to those parts. (4) Ageing elimination methods generally include the following types. ①Natural aging involves leaving the components outdoors, where residual stresses are relieved over several months or even years, thereby stabilizing the dimensional accuracy of the components. This method is simple and easy to implement, but it has a long production cycle, is difficult to manage, fails to detect defects within the components in a timely manner, and can only reduce residual stress to a small extent. ②Artificial thermal aging: The requirements for the thermal aging process are quite strict, and the rates of heating and cooling have a significant impact on the effectiveness of thermal aging. This method is the most widely used and effective stress-relief technique in current production. But it consumes a lot of energy, is costly, and causes severe pollution ； At the same time, an increase in the aging temperature leads to the precipitation of excessive strengthening phases within the metal, which inevitably results in a significant decrease in strength values and gives rise to a phenomenon of over-aging. Therefore, aging treatment after quenching is usually carried out at lower temperatures (below 200–250°C), which affects the stress-relief effect (only 10–35%). ③Vibration aging is a method in which, under the action of the periodic external force (excitation force) from an exciter, a component is brought into resonance, thereby reducing residual stresses and increasing the relaxation stiffness of the component, so as to stabilize its dimensions. This method has low costs, simple equipment, and a short processing time; it can prevent defects such as warping, oxidation, decarburization, and reduced hardness that occur in metal parts during thermal aging. It has been applied to some extent in production. ④The acoustic aging method, as well as the ultrasonic aging method, were first developed in the former Soviet Union and later adopted in developed countries. Initially, this method was mainly applied in **fields** such as ships, nuclear submarines, and aerospace, where stress reduction is of utmost importance. However, since the ultrasonic method can only address stress issues within a certain depth in the surface layer of components, its application scope is relatively limited, and its cost is quite high. ⑤The thermal shock aging method essentially involves rapidly heating the workpiece, so that the thermal stresses generated during this heating process combine with the residual stresses; these combined stresses exceed the material’s yield limit, leading to plastic deformation and thus allowing the original residual stresses to relax and stabilize quickly. (5) Cryogenic treatment methods can be divided into cryogenic rapid heating method and cold-heat cycling method according to the process. Among these methods, the deep cooling and rapid heating approach involves immersing parts with residual stresses in liquid nitrogen for deep cooling; once the temperature inside and outside is uniform, hot steam is used to spray on them rapidly. The rapid heating and cooling generate heat stresses in opposite directions, thereby canceling out the original residual stress field. (6) Pulse magnetic fields eliminate residual stresses. MPS Corporation has developed a technique for removing residual stresses from metals in a non-thermal manner, known as Pulsed Magnetic Treatment (PMT). With the help of PMT, the structural defects in metals can be improved, thereby eliminating residual stresses in the components. From a microscopic analysis perspective, PMT helps to improve or enhance the dimensional stability of metal parts ； Wear resistance and corrosion resistance also play a role; they have a significant impact on properties such as the magnetic hysteresis characteristics, fatigue, diffusion, and phase changes of metal materials. This technology has seen rapid development in applications for eliminating residual stresses in products such as cold-drawn tubes, welded parts, wires, and springs. (7) Explosion method. It utilizes the energy of the explosive shock wave to cause plastic deformation in the strained area of the component, thereby achieving the purpose of reducing or eliminating residual stresses. This method is commonly used for welded components; explosion treatment can not only completely eliminate the residual tensile stress in the welded area, but it can also create residual compressive stress there as needed. (8) Other methods, such as compression, hammering, shot blasting, rolling, etc. Shot peening is an effective and widely used method for strengthening parts; it also alters the state and distribution of residual stresses on the surface, with the residual compressive stresses generated by shot peening being an important factor in the strengthening mechanism. Among the methods mentioned above, mechanical stretching (compression) can achieve around 90%, constant-temperature aging yields 10–35%, vibration elimination gives 20–70%, and cryogenic treatment results in 25%–83%. Therefore, existing process technologies and methods are not yet capable of fundamentally eliminating residual stresses in the forgings of alloy structural components. 3 Measurement and Evaluation of Residual Stresses In actual production, it is essential to accurately determine the distribution of residual stresses in components, which can generally be obtained through calculation or direct experimentation. To determine the distribution of residual stresses in components, especially in those that are relatively complex, computational methods can sometimes present various difficulties; for example, the calculation process may not be possible due to a lack of information regarding certain mechanical and physical properties of the material. Therefore, it is practically meaningful to adopt experimental testing methods. There are many methods for testing residual stress. Based on whether they cause damage to the component being tested, they can be divided into two main categories: destructive testing (including partial damage detection methods and complete damage detection methods) and non-destructive testing. 3.1 Non-destructive testing methods: Destructive testing methods mainly include drilling, sampling, grooving, core-ring method, delamination, sectioning, and crack detection. The most commonly used methods at present are drilling and the core-ring method; in these methods, part or all of the material surrounding the test point is removed, thereby eliminating the constraints on that point and allowing stress to be released, either in its entirety or partially. In practice, the component to be tested is subjected to mechanical processing methods such as drilling, which causes it to undergo corresponding displacement and strain as a result of the release of some stress; these displacements or strains are then measured. By making appropriate conversions, the original stress in that part of the component can be determined. Therefore, this testing method is also known as the mechanical side test method or stress release method. 3.1.1 Drilling method: In China, this method is also known as the small-hole method or blind-hole method. Through research and improvements by many experts, it has now evolved into a relatively mature technique for measuring residual stresses in components by drilling small holes. The basic idea is to drill a small hole in a component with residual stress; as a result of partial stress release within the area of the hole, corresponding displacements and strains occur. By measuring these displacements or strains and making appropriate conversions, the original stress at that point can be determined. It is widely used in engineering, and its greatest advantage is that it causes minimal damage to the test specimens, without even affecting the normal use of the components. Assume that there is a certain residual stress in an isotropic plate; if a small hole is drilled, the radial stress at the edge of the hole drops to zero, and the stress distribution in the area around the hole changes. This change in stress is known as stress release. The strain is detected by the strain gauge; the closer the strain gauge is to the edge of the hole, the greater the strain it detects, and the higher its sensitivity. Typically, the residual stress on a surface is in a plane stress state; there are three unknowns: the two principal stresses and the principal direction angles. Measurement is carried out using a strain flower composed of three strain-sensitive gauges, with the center of each gauge located at the same radius. The blind hole method is currently the most widely used technique for measuring residual stresses in engineering, and it has been adopted as a standard by the ASTM organization in the United States. In recent years, researchers around the world have continued to conduct extensive research on the blind hole method, conducting in-depth analyses of various process factors and sources of error in practical applications, thereby improving it further. Since the calculation formulas for the blind hole method are derived from a simplified mechanical model of through-holes, they deviate from the actual conditions. To address this issue, finite element numerical analysis is generally used to calculate the stress distribution around blind holes of different sizes and shapes, thereby determining the impact of the hole diameter-to-depth ratio as well as the shape of the hole edges and bottom on stress release. This approach avoids the errors associated with the Kirsch through-hole solution, while also eliminating the need for cumbersome manual experimental calibration. During the drilling process, the drill bit causes the hole walls to undergo elastic deformation, plastic deformation, and cutting. As a result, an additional stress field is generated around the hole walls due to local plastic deformation, which causes the strain gauges attached to that area to experience additional strain. The magnitude of this strain is influenced by factors such as the hole diameter, depth, drilling speed, type of drill bit, sharpness of the cutting edges, size of the strain gauges, and their distance from the center of the blind hole. 3.1.2 Core Ring Method The core ring method is a partial damage detection technique, also known as the partial release method; in China it is referred to as the ring method or slitting method. The method involves using a crown-shaped milling tool to create an annular groove with a core in the middle. The processed ring core should experience the least stress and exhibit the greatest strain release. Special strain gauges are used to measure the strain released at the core area; by applying appropriate formulas, it is possible to determine the magnitude and direction of the residual stress in that area. The ring-core method involves using a crown-shaped milling tool to create an annular groove on the surface of the workpiece to be tested, separating the core part of this ring from the main body of the workpiece; the stresses remaining in the core are then released. This method utilizes the elastic deformation of the material, that is, the stress-release effect, to measure the internal stresses. The strain generated on the surface of the toroidal core is measured using an improved special strain gauge. From the measured results and the calculation formulas, it can be seen that the strain in various directions of the surface is a function of the groove depth Z. 3.1.3 Delamination method: Its working principle is as follows: when a layer of material is removed from a plate that contains residual stresses, the residual stresses within that plate are no longer in equilibrium. When they reach equilibrium again, it causes the plate to bend. The degree of bending of the plate depends on the original distribution of residual stresses in the removed layer and the elastic properties of the remaining material. By removing layers one by one and measuring the curvature after each removal, the original residual stress distribution of the plate can be calculated. This method is often used to determine the residual stresses in specimens with simple geometries, and the testing process is fast. The delamination method is only suitable for flat samples; it can be used to measure internal macroscopic residual stresses, but not surface stresses or stresses in the near-surface layer. 3.2 Non-destructive testing methods: The main non-destructive testing methods include X-ray diffraction, neutron diffraction, synchrotron diffraction, ultrasonic testing, and magnetic testing. Among these, X-ray diffraction further includes conventional X-ray diffraction and hard X-ray diffraction (or synchrotron diffraction). All of these methods utilize certain physical effects arising from the residual stress state in the material to establish a relationship between a specific physical quantity and the residual stress (or strain), and then determine the residual stress by measuring this physical quantity. The principle of X-rays is similar to that of neutron diffraction. Due to their longer wavelength, X-rays have a shorter detection depth and lower precision compared to neutron diffraction. However, X-ray sources are easier to obtain than neutron sources, which is why X-rays are used far more widely in industry than neutron diffraction. Therefore, X-ray diffraction is the most widely used method in engineering, while the other methods are either not yet fully developed theoretically, or the corresponding testing equipment is scarce, which limits their use in engineering applications. 3.2.1 X-ray diffraction method: Although the blind hole method is the most commonly used technique for detecting residual stresses, it more or less causes damage to the component, which is not allowed in many cases; for example, damage is absolutely not permitted in pressure vessels. This has led to the need to explore other testing methods. Among them, the X-ray method is relatively mature; of all the various non-destructive testing methods developed for detecting residual stresses on the surface of polycrystalline materials, X-rays are the most reliable and well-established, and their practicality is recognized by all sectors. The basic principle of X-ray diffraction is to measure strain by detecting changes in the crystal structure. X-rays have limited penetration capability, so they can only measure the average two-dimensional stress in the shallow surface layer of materials and products. The main drawback of this method is the significant limitations regarding size and geometry. The grains that make up a metallic material are composed of countless unit cells with a specific crystal structure. Within the area of the material that is exposed to X-rays, there are sufficient numbers of such grains, and the crystallographic orientations of these grains are sufficiently random such that, for any set of crystal plane indices used in diffraction, there are enough crystal planes with the same indices available for diffraction. When a metal is subjected to force, strain occurs, and the strain of the different crystal planes with varying plane indices within the grains varies as well. By knowing the variation in the interplanar distances of specific plane families within the grain, the magnitude of the strain can be determined using Bragg’s equation; subsequently, the stress value can be calculated based on Hooke’s law. X-ray testing for residual stress generally has the following characteristics: ① Fast speed, simple preparation work ； ②The theory is well-developed, offering high precision and reliable results ； ③Non-destructive testing causes minimal damage to the performance of metal structures; it is a form of non-destructive inspection when used for measuring surface stress. It becomes a destructive inspection method when layer removal is necessary in order to measure internal stress ； ④It can be measured directly without the need to prepare samples ； ⑤It is possible to measure the stress distribution at a specified point ； ⑥Under certain conditions, it is possible to determine the stress in a specified phase within a multiphase material ； ⑦When measuring the elastic strain of a material, it is often the sum of the elastic strain and the plastic strain. Due to the non-destructive nature of X-ray diffraction, this method has been widely studied for the measurement of residual stresses in welded structures. The X-ray method achieves high precision because it obtains information on the deformation of a component by directly measuring the atomic distances in the crystal. However, this method still presents difficulties in testing materials with coarse grains, etc.; it is hard to find diffraction planes for certain materials, and the X-ray testing equipment is also relatively complex. Due to the extremely shallow penetration depth, layer peeling is necessary when measuring internal stresses. For example, studying the formation and distribution of residual stresses in large forgings falls under non-destructive testing. Hard X-ray method, also known as synchrotron diffraction method, has main advantages over traditional X-ray methods: in addition to its much greater penetration depth, it can generate high-energy beams with narrow slits, and the measurement speed is faster than that of the X-ray method. Synchronous diffraction experimental equipment is also extremely scarce, available only in a few laboratories in Europe and the United States; there are no research reports on this topic in China. The scarcity of such devices limits their use in everyday scientific research and testing. 3.2.2 Neutron diffraction method The neutron diffraction method primarily utilizes changes in the lattice constant of a material to determine the stress state of an object. Neutron diffraction generally refers to the Bragg diffraction that occurs when neutrons (thermal neutrons) with a de Broglie wavelength of about 1 angstrom pass through a crystalline material. At present, neutron diffraction is one of the important methods for studying the structure of materials. The basic principles of neutron diffraction are very similar to those of X-ray diffraction. The differences lie in the following: ① X-rays interact with electrons; therefore, their scattering intensity at atoms is proportional to the atomic number. Neutrons, on the other hand, interact with atomic nuclei, and their scattering intensity at different nuclei does not vary monotonically. As a result, neutrons are particularly suitable for determining the positions of light elements in a lattice (since X-rays lack sufficient sensitivity) as well as the positions of elements with similar properties (since X-rays cannot distinguish between such elements easily) ； ②For the same element, neutrons can distinguish between different isotopes, which gives neutron diffraction certain advantages, especially in using the differences between hydrogen and deuterium to label and study organic molecules ； ③Neutrons possess a magnetic moment, and they can interact with atomic magnetic moments to produce magnetic diffraction unique to neutrons. By analyzing this magnetic diffraction, it is possible to determine the magnitude and orientation of the magnetic moments of magnetic atoms in the lattice of magnetic materials; therefore, neutron diffraction is an extremely important technique for studying magnetic structures ； ④Generally speaking, neutrons have a much higher penetration power than X-rays, making them more suitable for structural studies under conditions of high and low temperatures, high pressures, etc., where thick containers are required. The working principle of neutron diffraction is the same as that of other diffraction methods; it also determines stress based on the change in grain spacing caused by elastic deformation within a polycrystalline material, compared to the condition without stress. Its measurement method is also the same as that of the ray method. The greatest advantage of the neutron method is that it enables a much greater penetration depth compared to the X-ray method, along with high spatial resolution; this allows for the complete creation of 3D strain maps of engineering components by moving and rotating the parts being tested. However, its drawback is the need for a special high-intensity neutron source; due to insufficient source intensity, larger samples and longer data collection times are often required, resulting in high testing costs. Neutron diffraction equipment is extremely scarce, available only in a few laboratories in Europe and the United States, and there are no reports of research in this area in China. 3.2.3 Ultrasonic method The ultrasonic method makes use of the phenomenon of acoustic birefringence. Generally, an ultrasonic longitudinal wave in medium 1, when incident at a certain angle of inclination and propagating into medium 2 across the interface between the two media, decomposes into two longitudinal waves and two transverse waves. However, when the incident wave propagates perpendicular to the surface of the isotropic medium, it can be shown that it will generate two waves that are purely of the same type as the incident wave. This principle provides a theoretical basis and experimental foundation for using ultrasound to measure residual stress. An isotropic solid medium exhibits acoustoelasticity under stress (similar to magnetism). That is, under stress, the propagation speed of ultrasonic waves in a solid medium changes due to the different directions and magnitudes of the stress, which in turn leads to anisotropy as a result of the presence of stress. When the stress is in a plane stress state and the ultrasonic waves propagate perpendicular to the stress plane. Ultrasonic waves are broken down into ultrasonic waves in only two directions (reflected waves and refracted waves). The ultrasonic method involves using certain techniques to measure the acoustic birefringence, changes in sound propagation speed, and changes in the ultrasonic spectrum caused by stress; by determining these changes, it is possible to calculate the external forces or residual stresses acting on the object. Ultrasonic testing for residual stress has many advantages: ① It can non-destructively measure the surface and internal stresses of actual components ； ②Stress measurement can be carried out without contacting the actual components, without damaging their surfaces; it is safe to use and causes no environmental harm ； ③Ultrasonic measuring instruments are easy to carry outdoors or to the site for use, and can serve multiple purposes under specific conditions. However, the ultrasonic method is still in the experimental research stage, and there are many problems: ① The measurement results are significantly affected by the material properties, the shape of the workpiece, and its structural organization ； ②There are also many problems when simultaneously measuring actual components with sudden stress changes, complex shapes, and subjected to triaxial stress ； ③The wavelength of sound waves is too long, making it difficult to use interference methods at present; moreover, the sensitivity of such measurements is low. To determine changes in the speed of sound in a medium, high-sensitivity equipment and instruments are necessary, and the measurement process is rather complicated. 3.2.4 Magnetic testing: When residual stresses are present in ferromagnetic materials, their magnetic properties change, and this change in magnetism is utilized to determine the residual stresses within those materials. There are two magnetic methods currently in use: the magnetic noise method and the magnetic strain method. Ferromagnetic materials contain magnetic domains of varying sizes, and each domain has a different magnetization vector. Stress and external magnetic fields can change the size of these domains, thereby altering the dimensions and magnetic properties of the material; this is known as the magnetostrictive effect. Changes in domain size are accompanied by the movement of domain boundaries, while grain boundaries and impurities in the material act as pinning points for these domain boundaries. When a magnetic field or stress is applied to a material, the magnetic domains tend to change. However, due to the presence of pinning sources, the size of the magnetic domains in the affected area changes only when the external force reaches a certain value. The discontinuous movement of domain boundaries generates electromagnetic pulses, known as Barkhausen signals; by analyzing these signals, it is possible to determine the stress distribution. The magnetic noise method relies on the fact that in ferromagnetic materials, under the influence of an external alternating magnetic field, the magnetization domain walls undergo sudden, discontinuous jumps, which releases elastic stress-strain waves. This phenomenon is known as magnetic noise, or Barkhausen magnetic noise (BN). Studies have shown that the magnitude of the BN signal is related to the stress in the material, as well as changes in its microstructure and defects; therefore, some people use the measurement of the amplitude of the pulse voltage signal generated by BN in the detection coil to detect the stress, microstructure, and defects of the material. Obviously, when measuring the magnitude of BN information, it is also necessary to distinguish the effects of various factors in order to determine the stress distribution. In our country, the magnetic method used for measuring residual stress is most commonly the magnetic strain method. The principle is based on the magnetostrictive effect of ferromagnetic materials (such as low-carbon steel), that is, ferromagnetic materials undergo dimensional changes when magnetized ； Conversely, under stress, the magnetization state of ferromagnets (such as magnetic permeability and magnetic flux density) also changes; therefore, by measuring these magnetic changes, it is possible to determine the stress in ferromagnetic materials. Compared with the methods mentioned above, the magnetic method offers advantages such as high measurement speed, large detection depth (reaching several millimeters), and no radiation risk. Additionally, magnetic detectors are easy to carry, allowing for real-time, on-site, and safe measurements of components in use. However, the magnetic method can only be used on ferromagnetic materials, and it is also sensitive to factors such as the material’s structure; all these factors more or less limit the industrial application of the magnetic method.