Consultant Pressure Equipment Integrity, Wagnerlaan 37,9402 SH, Assen, The Netherlands (NL)
For the design of pressure vessels, a thorough knowledge of the possible failure mechanisms and failure modes is required. This article focuses on the failure modes that are of crucial importance in the design. It is therefore evident that pressure vessels shall be designed and manufactured to avoid the failure modes during manufacture, transport, installation, operating and maintenance under specified and reasonably feasible service conditions. Compliance with the applicable design code or standard is intended to ensure pressure - and structural integrity. 'Failure mode' is the basic manner or mechanism of the failure or deterioration process. It is also known as 'damage mechanism'. The design of a pressure vessel is a complex and highly specialized task that requires a deep understanding of engineering principles, materials science, and safety standards. By adhering to established codes and standards and employing advanced analytical techniques, engineers can design pressure vessels that are safe, reliable, and efficient.
In the world of pressure vessel design, attention to detail and a commitment to safety are paramount. As technology advances and industries evolve, the principles and practices of pressure vessel design will continue to adapt, ensuring that these critical components remain safe and effective in a wide range of applications.
Stress analysis of a pressure vessel is the process of evaluating the structural integrity and appropriate strength of the vessel under internal and external pressures. It involves determining the stresses, strains, and deformations that occur due to pressure, temperature, and external loads.
The critical design parameters for calculating the specification of a pressure vessel are design pressure, maximum allowable working pressure, design temperature, maximum allowable stress, joint efficiency, and corrosion allowance.
The most essential parts of a pressure vessel include the shell, heads, nozzles, supports, and nozzles. Together, each plays a pivotal role in ensuring the vessel's functionality and safety.
II. Overview of Failure modes
Ultimately, the design engineer must account for any potential failure modes [1] in his pressure vessel design efforts. Failure is the condition in which a structure no longer meets its purpose.
Modes of failure that should be considered include:
Limit state: the occurrence of permanent excessive deformation.
Relevant material properties: yield strength, creep rate
Limit state: the loss of coherence of the device under pressure over large areas.
Determining material properties: tensile strength, creep rupture strength.
Limit state: occurrence of fatigue cracks.
Determining material properties: high-elongation fatigue strength.
Limit state: Elastic deformations that render the pressurized device or component unsuitable for its task.
Determining material property: modulus of elasticity.
Limit state: rapidly progressing low-deformation fracture.
Determining material property: Notch toughness, notch sensitivity.
Limit state: Excessive deformation or fracture due to the action of progressive plastic deformation occurring during each load cycle.
Determining material property: yield strength.
Limit state: Progressive change in shape at constant or decreasing load.
Determining material property: elastic modulus, yield strength.
A further distinction must be made between the following load types as shown in Table 1 below.
Table 1: Load types
|
Load types |
|
|
Global classification |
Influence on: |
|
a) by time: - stationary - transient |
the determination of the decisive design load |
|
b) by cause: - mechanically - thermally |
material behaviour and choice, allowable stress |
|
c) by nature: - static - varying |
design, shaping, material behaviour, choice of materials, allowable stress |
Contemporary recognized design codes and standards for (unfired) pressure vessels, including ASME SECTION VIII-Division 1 and 2 (USA), PD 5500 (UK), EN 13445 (EU), AD 2000 (D), CODAP (F), AS1210 (AUS), GB-150 (CHN), GOST 34233.3 (RUS) and IS 2825 (IND), were developed with a conscious effort to avoid various modes of failure as mentioned above. Moreover, the technical issues covered in the design rules for pressure vessels have been, and are still being developed to guard against anticipated failure modes. The technical issues generally are related to the following: elastic stress analyses, shakedown, limit analysis, thermal transients, residual stress, distortion, dynamic and seismic responses, manufacturer tolerances and imperfections and defects. These issues are essentially the input to the design philosophy, which guards against the failure modes. The design codes and standards, which embody these design rules, usually include considerations of design stresses, materials, manufacture, inspection and testing.
Finally, we will pay some attention to "concepts of design ". Some topics, concepts and characteristics which are usually considered , implicitly or explicitly, in pressure vessel design, can be identified as in Table 2. It is helpful to think of each of the topics as giving rise to concepts, which in turn have characterising parameters or criteria. In this context a 'concept' is a convenient way of distilling a complex analysis into a simple framework to capture the essence of the behavioural complexity in a simple manner. This in turn allows the situation to be characterised by a parameter (often a simple number) and/or compared against some design criterion. Note that the complexity increases as one goes down the list of topics in Table 2. The topics identified above have been developed and form the basis of the present design approaches.
Table 2: Pressure Vessel Design Topics
|
Topics |
Concepts |
Characterisations |
|
Elastic Stress Analysis |
Stress Concentration Factor |
Maximum Stress Nominal or Membrane Stress SCF |
|
Plasticity |
First Yield Shakedown Limit Load |
Yield Pressure Shakedown Pressure Limit Pressure |
|
Cracked Bodies |
LEFM PYFM GYFM |
Stress Intensity Factor Toughness |
|
Fatigue |
Crack Initiation Crack Propagation Cumulative Damage |
Number of Cycles to Initiation Number of Cycles for Propagation Cumulative Damage |
|
Time Dependant |
Elastic Analogy Reference Stress Damage |
Steady State Reference Stress/Displacement/Time Damage Parameters |
|
Combination |
Ratcheting Creep/Fatigue Fracture |
Damage Summation Bree Type Diagram |
|
Abbreviations SCF = Stress Concentration Factor LEFM = Linear Elastic Fracture Mechanics PYFM = Post-Yield Fracture Mechanics GYFM = General Yielding Fracture Mechanics |
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Design by Rule versus Design by Analysis
The Design by Rule (DBR) approach which is applied in all design codes and standards yields pressure vessels that can withstand common failure modes and which uses usually simple formulas for the dimensioning of standard geometries. Note that DBR is often referred to as DBF (Design by Formula). On the other hand, it is also possible to use the so-called Design by Analysis (DBA) approach which is essentially based on the idea that if proper stress analysis can be conducted then a better, less conservative, assessment of the design can be made than would otherwise be the case by the usual approach of Design by Rule. Note that some international design codes pay more or less detailed attention to the Design by Analysis methodology. Design by Analysis (DBA) is an engineering approach that relies on complex mathematical models and analysis to evaluate the behaviour and performance of a design under different conditions and is normally applied to pressure vessel components that fall outside the DBR remit. It is a comprehensive and rigorous process that involves numerical Finite Element Analysis (FEA). However, finite element analysis software is readily available and its use is becoming increasingly common in engineering design. However, one should not underestimate the qualifications necessary to correctly evaluate pressure vessels using finite element analysis. The engineer using FEA to evaluate a pressure vessel should be experienced with finite element analysis in general, know how to correctly use the particular FEA software chosen, and be well-versed in the requirements of the applicable design code.
CONCLUSION
Designing pressure vessels in accordance with recognized codes or standards is of paramount importance and ensures adequate prevention of potential failure modes. By adhering to the guidelines within these codes or standards, engineers and manufacturers can confidently design, manufacture and operate pressure vessels that meet the highest standards of quality and safety. Hence, understanding and implementing these requirements is essential to avoid potential risks and ensure the long-term integrity of pressure vessels.
REFERENCES
Walther Stikvoort "Awareness of critical design aspects for pressure vessels "The International Journal of Engineering and Science (IJES), Volume 8, Issue 4 Series II, pp. 58-64, 2019
Walther Stikvoort "Awareness of critical design aspects for pressure vessels "The International Journal of Engineering and Science (IJES), Volume 8, Issue 4 Series II, pp. 58-64, 2019
Walther Stikvoort, Fundamentals Of Pressure Vessel Design, Int. J. in Engi. Sci., 2025, Vol 2, Issue 4, 9-12. https://doi.org/10.5281/zenodo.15226950
10.5281/zenodo.15226950
