The seven principles of pressure vessel design

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(1) Elastic failure criterion: According to the theory of elastic strength, the limit state of load-bearing capacity of a container is reached when the equivalent stress in areas away from the edges of the container reaches the yield value. It specifies that the yield limit is the stress at which the container fails. After considering the safety factor, the actual stress in the container remains within the elastic range. The design formulas in GB150 for components such as pressure vessels with internal pressure and convex end caps are all established based on the principle of elastic failure. (2) Plastic failure criterion: This criterion holds that when a certain point on the container reaches yield strength, it does not result in the failure of the container. The ultimate load-carrying capacity of the container is reached only when it yields as a whole. It specifies that the full yield pressure is the highest pressure at which the container fails. After considering the safety factor, the strength check condition for the bending stress becomes 1.5’. For brittle materials, although they are also subjected to bending stress, when the surface stress reaches σs, further increase in external load prevents significant plastic deformation at the wall surface, leading to cracking. Therefore, merely considering the introduction of plastic failure criteria in pressure vessel design, material selection should also aim to exclude brittle materials with poor plasticity, or appropriate restrictive measures should be taken. JB4732 \"Steel Pressure Vessels – Code for Analytical Design\" provides a design method based on plastic failure criteria. GB150 formulates the design or stress calculation formulas for elements such as plates, the necks of cylinders (or nozzles) connected by integral flanges (including any type of flange designed as an integral flange), all based on the principle of plastic failure. (3) Elasto-plastic failure criterion The elasto-plastic failure criterion is applicable to the process of repeated loading. According to the concept of stress classification, the limit state of the container’s load-bearing capacity is reached when a certain amount of local plastic deformation occurs in the areas near the container’s edges. It takes into account that excessive plastic deformation caused by edge stress will accelerate fatigue failure or lead to brittle fracture. Due to this failure criterion, local plastic deformation in the structure is permitted; and because the stress distribution is uneven throughout the structure, the local plastic regions are surrounded by large elastic regions, which is why it is called an elastoplastic failure criterion. The elastoplastic failure criterion is also not applicable to brittle materials. JB4732 \"Code for Analysis and Design of Steel Pressure Vessels\" provides a design method based on elasto-plastic failure criteria. The design formulas and charts in GB150 for connections such as those between internal pressure conical heads and cylinders, and between flangeless spherical heads and cylinders, are all established based on the principle of elastoplastic failure. (4) Fatigue failure criterion: This criterion states that under alternating loads, the container reaches its ultimate load-carrying capacity when the maximum alternating stress (at a fixed number of cycles) or the number of cycles (at a fixed maximum alternating stress) attains the values specified by the fatigue design curve. When design specifications require consideration of the fatigue of containers, in addition to performing strength calculations on the containers, fatigue design is also necessary, that is, calculating the service life of the containers. “The container design specifications based on analytical design include fatigue design methods. Since fatigue design involves elastoplastic failure criteria, when incorporating fatigue design into the analysis and design framework, the standard JB/T4732-1995 \"Steel Pressure Vessels – Standards for Analysis and Design\" should be adopted. This standard is more stringent than the GB150 standard for regular design in terms of material selection, design, structure, manufacturing, and inspection. Stress cycle counts exceeding 105 are considered high-cycle fatigue, while those ranging from 102 to 105 are considered low-cycle fatigue. JB/T4732—1995 stipulates that for steel materials with a room-temperature tensile strength of δb≤550MPa, fatigue analysis can be omitted if the number of fatigue cycles is less than 1000. (5) The fracture failure criterion is a calculation criterion based on the concepts of fracture mechanics, which uses the stress or crack size that leads to low-stress brittle fracture of the container as the critical condition. Such critical states and the corresponding fracture failure criteria include the critical stress intensity factor and the K-criterion, the critical crack opening displacement and the COD-criterion, and the critical J-integral and the J-integral criterion. Fracture failure criteria are generally applied to the assessment of in-service pressure vessels with excessive defects, in order to determine whether such vessels can continue to be used (under conditional supervised use) or should be scrapped. (6) Creep failure criterion: This is a design criterion for containers operating at high temperatures. Under the long-term effects of high temperature and certain stress, plastic deformation in the container will continue to accumulate. When its creep rate (or equivalent creep stress) reaches a certain value, it represents the ultimate load-carrying capacity of the container. Creeep issues need to be considered when the temperature of carbon steel exceeds 300–350°C, low-alloy steel exceeds 400°C, low-alloy chromium-molybdenum steel exceeds 450°C, and austenitic stainless steel exceeds 550°C. (7) Corrosion failure criterion: The corrosion failure of chemical pressure vessels refers to the damage that occurs when the vessel walls in contact with the medium are eroded by corrosive substances. This can be divided into two main categories: uniform corrosion and local corrosion. Controlling corrosion failure essentially means selecting the appropriate materials and suitable anti-corrosion measures based on the properties of the medium. Under normal circumstances, the limiting condition for uniform corrosion failure is actually the same as that of elastic failure criteria, that is, a corrosion margin is added to the shell thickness calculated based on the maximum principal stress ； Regarding localized corrosion, it is related not only to the material used for the container but also to the medium, as well as the temperature, pressure, and stress levels under which it is used; therefore, to date, there are no unified constraints for localized corrosion failure.