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Elastic failure design criterion: This is a measure to prevent yield deformation of the container’s structural components, by limiting the maximum design stress on these components to below the material’s yield point, thus ensuring that they remain in an elastic state and do not experience elastic failure. This is the most traditional design method, and it is also the principle that container design should follow first and foremost today. Plastic failure design criterion: Elastic failure at a certain location of the vessel, such as the inner wall of a thick-walled cylinder, does not mean that the vessel loses its load-carrying capacity. The state in which the entire container reaches overall yield, or in which a local area along the entire wall thickness reaches full yield, is referred to as the plastic failure state. If the material satisfies the ideal plasticity assumption, the deformation will continue to increase indefinitely without the need for an increase in load; this load is known as the ultimate load. Limiting the ultimate load as a basis for design to prevent overall plastic deformation is known as ultimate design. "The \"limit design\" criterion is the plastic failure design criterion. Solving for the ultimate load of a structure using plastic mechanics methods is the basis of this design criterion. Design criteria for failure by explosion: Non-ideal plastic materials retain the ability to strengthen after yielding; therefore, containers (especially those with thick walls) continue to exhibit an increased load-bearing capacity after overall yielding, until they reach the load at which they explode – which is then the maximum load. If container rupture is taken as the failure mode, and the burst pressure is used as the basis for design along with appropriate limits to prevent rupture, this constitutes the design criterion for container burst failure. Elasto-plastic failure design criteria: If a certain local area of a container experiences yield in some of its materials, while the rest of the area remains in an elastic state, and the elastic portion can restrain the plastic flow deformation in the plastic zone, then the structure being in this elasto-plastic state does not necessarily imply failure. The structure is considered to have lost its \"stability\" and experienced elastoplastic failure only when the stress in the plastic zone within a certain elasto-plastic region of the container exceeds the allowable value determined by the \"stability principle\". The stability principle, as a design criterion for elastoplastic failure, is also known as the stability criterion. The fatigue failure design criterion is such that, in order to prevent fatigue failure of the container, the stress amplitude of the maximum alternating stress at the stress concentration areas of the container must be kept within the allowable stress amplitude determined by the low-cycle fatigue design curve; this ensures that no fatigue failure occurs within the specified number of cycles. This is the fatigue failure design criterion. It was developed in the United States in the 1960s. Design criteria for fracture failure: Cracks are difficult to avoid in practice, including those that arise during manufacturing (welding cracks) and those that form or propagate during use (fatigue cracks, stress corrosion cracks). To prevent low-stress brittle fracture caused by such defects, fracture mechanics can be employed to limit the size of these defects or to establish required toughness requirements for the material; this is what constitutes brittle fracture prevention design. The crack resistance design does not mean that newly manufactured containers are allowed to have cracks; rather, it is an estimate of the safety of the containers after several years of use. Newly manufactured containers are designed with the assumption that detectable cracks may form within them; fracture mechanics is used to establish requirements that must be met regarding the toughness of the material – specifically fracture toughness – in order to prevent low-stress brittle fracture of the container. If cracks are detected in a container in service, fracture mechanics can be used to assess its safety, that is, for the evaluation of defects in pressure vessels. This is a method based on the fracture failure design criterion (also known as the crack resistance failure design criterion). The design criterion for creep failure states that by limiting the creep deformation of the high-temperature vessel shell (or the corresponding stress calculated using creep equations) to a specified allowable range, it is possible to ensure that the high-temperature vessel does not experience creep failure during its designated service life. This is the design criterion for creep failure. Design criterion for buckling failure: The buckling of pressure vessels under external loads must be checked for stability in accordance with stability theory; this is the design criterion for buckling failure. The verification of the longitudinal stability of large vertical equipment (such as tower equipment) under wind and seismic loads also falls into this category. The stiffness failure design criterion involves analyzing the deformation of the structure in order to keep the linear and angular displacements at specific points within acceptable limits, thereby ensuring that the structure has sufficient stiffness. For example, in large tray towers where the trays have a large diameter and are thin, it is necessary to limit the deflection of these tray plates, so as to prevent uneven liquid layer thicknesses from leading to uneven gas distribution across the trays and reducing the efficiency of the trays. Similarly, when designing flanges, in addition to ensuring strength, a stiffness verification method should also be employed to limit the lateral deformation of the flanges. Leakage failure design criteria: Reasonable design methods in the sealing design of flanges and shaft seals should ensure that the leakage rate of the medium does not exceed the allowable level. Since the leakage rate of the medium is highly complex and closely related to the structural design, the performance of the sealing materials, and the load applied by the fasteners, it is very difficult to establish design criteria for leakage failure. It has not yet been adopted in most **design specifications. However, the EU’s pressure equipment directives have established design criteria and methods for leakage failure based on extensive research and testing.