blog about Study Optimizes Convex Pressure Vessel Head Design Standards

In high-tech fields such as deep-sea exploration, aerospace, and petrochemical industries, pressure vessels that withstand external pressure play a vital role. The safety of convex heads—key components of these vessels—directly determines the stability of entire systems. A design flaw causing buckling or failure in a deep-sea submersible's head or a rocket fuel tank could lead to catastrophic consequences. Therefore, in-depth research and optimization of convex head design methods carry significant practical importance.

When subjected to external pressure, convex heads primarily face two failure modes: buckling and yielding. Engineering designs typically employ experience-based knockdown factors (KDF) to reduce theoretical buckling pressures for safety. However, with advancements in materials science and manufacturing, this conservative approach may lead to material waste and increased costs. Consequently, accurately predicting buckling behavior and optimizing design methods have become research priorities.

The knockdown factor (KDF) is defined as the ratio of experimental buckling pressure in actual heads to theoretical buckling pressure in ideal heads. Early research focused on determining KDF values through experiments, but results showed significant variability due to difficulties in precisely controlling defects. Recent manufacturing advancements—particularly Lee et al.'s polymer-coated spherical mold method—have enabled production of heads with controlled defects, offering new pathways for accurate KDF prediction.

• Defect Types and Buckling Performance: Researchers have conducted extensive experiments and numerical simulations on various defect types. Yan et al. studied how geometric parameters of through-thickness defects affect buckling, while Abbasi et al. found that bulges minimally impact spherical head buckling. Derveni et al. examined interactions between defects.
• Real Manufacturing Defects: Other studies analyzed hemispherical heads containing actual manufacturing defects, providing engineering guidance. Wagner et al. proposed using notches as equivalent geometric defects to determine lower-bound buckling pressures, introducing single dents via controlled displacement.

• Hemispherical Heads: As the simplest convex heads, their design methods are relatively mature. However, their greater depth limits certain applications.
• Spherical Heads: Despite significant edge bending stresses at crown-transition zones, their shallower depth and simpler manufacturing make them widely used. Lu et al. studied elastic-plastic buckling behavior under external pressure via finite element analysis, while Blachut et al. investigated stability in multi-layer metal spherical heads. Wang et al. analyzed stress states and buckling pressures in water heater bottom heads.
• Ellipsoidal Heads: Their smoother curvature transitions provide more uniform stress distribution. With intermediate depth between hemispherical and spherical heads, they're easier to manufacture via stamping. Zingoni developed theories for evaluating membrane stress distribution; Li proposed simplified analysis methods for axisymmetric ellipsoidal head vessels; Ross studied buckling modes in fiberglass-reinforced plastic ellipsoidal heads.

Despite emerging design methods, fundamental rules in pressure vessel standards remain engineering cornerstones. Global economic powers have established respective standards for convex head design. This analysis focuses on six key standards:

• China: GB/T 150.3, GB/T 4732.3
• United States: ASME VIII-1, ASME VIII-2, ASME Code Case 2286-6
• European Union: EN 13445-3

ASME VIII-1 employs chart-based methods to determine allowable external pressures. These charts—derived from extensive experimental data and theoretical analysis—offer convenience but limited precision. ASME VIII-2 (since 2007) shifted to formula-based methods incorporating ASME Code Case N-284 and 2286-6 principles, calculating allowable circumferential compressive membrane stresses. The 2019 edition introduced standardized equations based on stress-strain curve models, accurately simulating material responses in as-manufactured states for all materials—carbon steel, low-alloy steel, high-alloy, and non-ferrous alloys—replacing previous carbon/low-alloy steel methods.

The EN 13445-3 (2002-2021 editions) uses curves to determine allowable external pressures, adopting lower-bound curves derived from PD5500 standards (successors to British BS5500).

GB/T 150.3 also uses chart methods for external pressure head design, with some charts based on Chinese experimental data and others referencing ASME Section II, Part D. GB/T 4732.3 employs methods similar to ASME Code Case 2286-6, with Appendix C providing additional tangent modulus calculation rules—including equations from ASME Code Case 2286-6 for carbon/low-alloy steels and stress-strain curve models from ASME VIII-2.

This section details comparisons of hemispherical, spherical, and ellipsoidal head design rules across standards, focusing on differences in key parameters (e.g., tangent modulus, design factors) and their impacts.

Tangent modulus (material stress-strain curve slope at specific stress levels) critically influences buckling pressure calculations, with varying computation methods across standards. Design factors (safety margin coefficients) also differ, reflecting varying safety considerations.

Given spherical/ellipsoidal heads' design complexity, some standards use equivalent methods converting them to hemispherical heads for calculation. This section compares these methods' advantages and limitations.

For intuitive standard comparisons, this article calculates buckling pressures for various spherical/ellipsoidal heads using different standards, contrasting results with equivalent hemispherical heads.

Selected engineering cases demonstrate thickness calculations for heads using different standards, clarifying each standard's applicability and trade-offs.

This comprehensive review and comparative analysis of convex head design rules under external pressure provides engineering references and research guidance. Future directions include:

• Developing precise buckling prediction models: Leveraging improved computing and experimental techniques to reduce reliance on empirical KDFs.
• Studying new materials' buckling behavior: Investigating novel materials' performance under external pressure for engineering applications.
• Optimizing design methods: Tailoring approaches to specific applications, balancing safety with cost efficiency.