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With the rapid development of modern industry and science and technology, the requirements for fluid sealing have been increasing. As a result, research on this type of static seal, namely bolt-flange gasket connections, which are widely used in pipelines of industrial equipment in sectors such as petrochemicals, aerospace, power generation, and nuclear energy, has become particularly important. In complex and large-scale piping systems, there are often tens of thousands of sealing points at bolted flange connections, in accordance with the design methods widely used internationally today. Although it can meet the requirements for general sealing, its seal is not always tight under some more stringent operating conditions such as high temperature and high pressure. The combined effect of medium pressure and temperature can easily lead to a failure in the sealing of bolted flange gasket connection systems. Once such a failure occurs, leakage takes place; in mild cases this affects production and results in economic losses, while in severe cases it leads to the waste of large amounts of raw materials and energy, unpredictable environmental pollution, and even serious safety accidents. Therefore, modern requirements for the sealing of containers and pipes are becoming increasingly stringent. An overview of seals: Based on the relative motion between the sealing surfaces, seals can generally be divided into two main categories: static seals and dynamic seals. In a static seal, the sealing surfaces remain relatively stationary, such as in pipe flanges, threaded connections, and the seals between pressure vessels and their covers. In dynamic seals, the sealing surfaces are in relative motion, such as in rotary seals and reciprocating seals. Based on working pressure, static seals can be divided into medium and low-pressure seals as well as high-pressure seals. For medium and low-pressure static seals, gasket seals using softer materials and wider gaskets are commonly used, while for high-pressure static seals, metal gaskets with harder materials and a very narrow contact width are employed. Based on their working principle, static seals can be further divided into flange gasket seals, self-sealing types, face-to-face sealing, O-ring seals, packing seals, rubber ring seals, threaded gasket seals, threaded connections seals, socket-type connections seals, and sealant seals. The purpose of sealing is to prevent fluids or solid particles from leaking between adjacent mating surfaces, as well as to stop external contaminants such as dust and moisture from entering the components inside mechanical equipment. Sealing elements are essential components for preventing leaks; therefore, strict requirements are placed on them. The basic requirements for seals are as follows: 1. They must exhibit good sealing performance within certain pressure and temperature ranges. 2. It has low wear; it can compensate for wear to a certain extent after it occurs, resulting in a long service life. 3. Low frictional resistance with a stable coefficient of friction. 4. It can adapt to the working medium. 5. Simple structure, easy to install and disassemble, and low cost. 6. Interchangeability should be ensured to achieve standardization and serialization. This article mainly discusses the sealing using flange gaskets. This sealing method involves filling the gap between the sealing surfaces of two connected components (flanges) with gaskets of various types, and then tightening the threads or bolts. The tightening force causes the gaskets to undergo elastic and plastic deformation, thereby filling in any irregularities on the sealing surfaces and achieving a sealed connection. Gaskets and their basic properties General structure of gaskets The general structure of gaskets is shown in Figure 2.1. In the figure, 2 represents the seal element itself, which is the key component in preventing leaks. Common materials used for this purpose are non-metallic materials such as flexible graphite, polytetrafluoroethylene, and fiber-reinforced rubber-based composite sheets. Furthermore, the material of the seal element body can also be a flexible or rigid metal, which is commonly used in applications with high temperatures and pressures. Non-metallic materials are often reinforced with a metal material 5 (reinforcement layer). It also facilitates the manufacturing and processing of sealing elements for brittle materials such as graphite. The reinforcing material can be metal sheets or wire meshes; metal sheets are often stamped to enhance the reinforcing effect and increase elasticity, and they are bonded together through rolling or adhesives. The sealing element may also be provided with a surface layer 4 or 6 to enhance the sealing effect and prevent adhesion to the flange sealing surface. The surface layer material can be PTFE (PolyTetraFluoroEthylene, polytetrafluoroethylene) or metal materials with low yield strength such as gold, brass, soft steel, nickel, Monel, etc.; surface coatings such as lead, tin, PTFE, gold, silver, etc., can also be used. Seals can also be covered with PTFE or metal sleeves; this serves to protect the core material from chemical corrosion by the fluid being sealed, while still preserving the elasticity of the core material, as in gaskets with various types of covering structures. The width of the seal varies depending on the type of gasket. Metal gaskets are generally narrow in width, while flat gaskets have a greater width; they are commonly used in flange connections with lower loads, such as those made of PVC (Polyvinyl Chloride), cast iron, enamel, or glass-lined materials. Most gaskets use flat-faced flanges with a smaller width. The main functions of the inner reinforcement ring 1 are as follows: to prevent the seal element itself from bending inward due to insufficient rigidity; to fill the gap between the seal and the flange surface of the container or pipeline, thereby avoiding interference with fluid flow caused by this gap, as well as erosion of the gasket by the fluid. Since the inner ring is in contact with the fluid, its material must be capable of resisting corrosion by the medium being sealed. The outer reinforcement ring 3 or the outer ring material are both solid metals, and their main functions are: to assist in aligning the sealing element during installation; to prevent the sealing element from being compressed excessively and thus damaged; to reinforce the gasket body; and to prevent the gasket from being blown away as well as to reduce flange rotation. The outer reinforcement ring, since it does not come into contact with the sealing medium and therefore does not require resistance to media corrosion, is often made of carbon steel. The external reinforcing ring can also be integrated with the sealing element, such as wave-tooth composite gaskets or metal toothed gaskets. Types of gaskets: There are a wide variety of sealing gaskets used for flange connections. Based on the material of their sealing components and their structural characteristics, they can be roughly classified into non-metallic soft gaskets, metal composite gaskets (or metal-non-metal composite gaskets), and metal gaskets. Each category can be further divided into several types, as shown in Figure 2.2. The basic properties and parameters of gaskets can generally be described from two aspects: first, the mechanical properties, including compression and rebound properties, as well as stress relaxation properties; second, the sealing performance, which is related to the leakage rate and serves as an important indicator for assessing the overall performance of a gasket. 1. Compression and rebound performance: The compression and rebound performance of gaskets reflects the relationship between the axial load applied to the gasket and its deformation. The compression performance of a gasket refers to the change in its thickness after compression; it is a physical quantity that indicates the stiffness of the gasket. The rebound property of a gasket refers to the amount by which the thickness of the gasket returns to its original value after the compressive load is removed. It can effectively compensate for the separation between the gasket and the sealing surface that may occur under operating conditions due to medium pressure or other factors, thereby maintaining the effectiveness of the gasket’s sealing function. Gaskets made of different materials and with different structural designs have distinct compression and rebound curves. The compression and resilience of gaskets can be evaluated based on their numerical values, as well as by examining the compression and resilience curves of different shapes. The most important factor is to observe the slope of the rebound curve after unloading; the lower the slope, the greater the elastic compensation capacity of the gasket, and thus the less stress loss it experiences. This makes it easier for the gasket to adapt to alternating loads. When evaluating the compressibility and resilience of gaskets, not only are an appropriate compression rate and a maximum resilience rate required, but also an optimal shape for the compression and resilience curves is necessary. Figures 2.3 and 2.4 show the compression and rebound performance curves of the flexible graphite composite gasket. Figure 2.3 shows the compression and rebound characteristic curves under different gasket stresses at a constant temperature of 500°C. Figure 2.4 shows the compression and rebound characteristic curves at different test temperatures, with a gasket pre-tightening pressure of 70 MPa. By observing Figures 2.3 and 2.4, it can be seen that as the stress on the gasket increases, both its elastic and plastic deformations increase; as the temperature rises, the deformation of the gasket increases while its resilience decreases. Neither the compression curve nor the rebound curve is linear, and they do not overlap, indicating that the behavior of the gasket is nonlinear and non-conservative. As can be seen from Figure 2.4, as the temperature increases, the rebound capacity of the gasket decreases. When the temperature rises to a certain level, the amount of rebound of the gasket may no longer be sufficient to compensate for the separation of the flange sealing surfaces caused by external factors, which leads to leakage in the gasket seal and ultimately results in the failure of that seal. Therefore, the gasket compression stress and temperature are the main factors affecting the compression and rebound properties of the gasket. The compression and rebound curves of gaskets can be expressed using the following formula: 2. Stress relaxation property: When a bolt pre-tightening load is applied to a bolted flange gasket sealing system, the compressive stress acting on the gasket causes it to thin out. After operating for a certain period of time, the thickness of the gasket continues to decrease, and the stress on it also gradually diminishes. This phenomenon of stress reduction is known as stress relaxation. The variation of gasket stress over time is the stress relaxation behavior. In fact, the stress relaxation of gaskets is the combined effect of stress relaxation and creep. Stress relaxation is the change in the gasket stress under constant strain, expressed as a percentage of the change in gasket stress under the initial load; creep is the change in strain under constant stress, usually expressed as a percentage of the change in gasket thickness under the initial load. In a prestressed indeterminate system such as that with bolted flange gaskets for sealing connections, the gasket stress is generated as a result of the elongation of the bolts; therefore, gasket creep does not occur under constant stress. Any change in the gasket thickness leads to a change in the bolt elongation, which in turn alters the gasket stress. This interaction between the gasket and the bolts is known as the \"creep relaxation\" of the gasket. The extent of bolt elongation is influenced by the stiffness of the bolt itself, which in turn affects the degree of stress relaxation in the gasket. The creep relaxation property of gaskets is a very important mechanical property that affects the sealing performance of flange joints; it can lead to a decrease in the stress within the gasket, ultimately causing the joint to leak. Figure 2.5 shows the creep curves of flexible graphite composite gaskets at different stress levels and temperatures. As can be seen from Figure 2.5 above, temperature, time, and preload pressure are the main factors affecting the creep relaxation behavior of gaskets. As can be seen from the graph, the higher the temperature level, the greater the creep amount. At the beginning of the test, the creep deformation is significant, and after about 15 minutes, the creep curve becomes flatter. It can be seen that the longer the gasket is exposed to stress, the greater its creep displacement becomes, and the greater the preload stress, the greater the creep displacement as well. The magnitude of the gasket’s creep displacement is also related to the initial deformation under the preload. By processing the various data mentioned above, the relationship between strain and time can be expressed using equation 2-3. 3. Sealing performance: The sealing performance of a gasket refers to the fact that, under certain actual operating conditions, the leakage rate resulting from the gasket’s sealing function is lower than a specified standard leakage rate; or it refers to the extreme operating conditions – such as temperature and pressure – that the gasket’s sealing mechanism can withstand at a given standard leakage rate. The leakage rate refers to the amount of medium that leaks per unit time under standard test conditions. The sealing performance of a gasket is a comprehensive indicator of its quality, while the leakage rate is the most straightforward indicator of a gasket’s quality. The gasket leakage rate is generally determined using standard gasket samples under room temperature or high-temperature conditions. Figure 2.6 shows the relationship curve between the leakage rate and both the medium pressure and the gasket compression stress for flexible graphite composite gaskets at a test temperature of 300°C. Figure 2.7 shows the relationship between leakage rate and medium pressure at different temperatures when the pre-tension stress is 50 MPa. By observing Figures 2.6 and 2.7, it can be seen that the leakage rate has an approximately linear relationship with the medium pressure. Relevant studies indicate that the leakage rate has an approximately negative exponential relationship with the compression stress of the gasket – in other words, as the compression stress increases, the leakage rate decreases accordingly. The leakage rate also has an exponential relationship with temperature; as the temperature rises, the leakage rate increases correspondingly. The leakage rate can be expressed as a function related to the medium pressure, the stress acting on the gasket, and temperature; this relationship can be represented by equation (2-4). Conclusion: Static sealing devices are widely used in industry, agriculture, national defense, and people’s daily lives. This type of static seal connection using bolt flange gaskets is the most commonly used form of connection in petrochemical equipment, vessels, and pipelines. In operational conditions, failure of this sealing structure is generally rarely due to strength failures; rather, it is mainly caused by leakage in the bolt flange gasket system, with the gasket being the key element affecting such leakage. Therefore, the study of the sealing performance of gaskets has always been a focus in the research on flange connections.