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The J-Integral Method Compared to the API 579-1/ASME FFS-1 Standard to Calculate Stress Intensity Factor (SIF): Leak-Before-Break (LBB) Application with Uncertainty Quantification

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Abstract

Leak-before-break (LBB), as a part of the fitness-for-service (FFS) assessment, is a critical requirement to ensure pressure vessel structural integrity LBB generally means a leak will be detected before an in-service catastrophic failure occurs. Despite some established procedures in API 579-1/ASME FFS-1 or BS 7910 standards, performing a robust LBB assessment is not a regular and straightforward practice in the oil, gas, and petrochemical industries. A mix of different sources has been commonly used in case studies, which could lead to non-consistent results. This paper presents, firstly, a three-dimensional finite element analysis (FEA) within an LBB assessment framework for a cylindrical pressure vessel. The stress intensity factor (SIF) of a defective vessel with a through-thickness crack is numerically calculated using the J-integral method and based on linear elastic fracture mechanics (LEFM) approach. The accuracy of the numerical solutions is then compared with the analytical results proposed by the API 579-1/ASME FFS-1 standard. The maximum (limiting) through-thickness flaw size, which will not grow to an intolerable size during the vessel service life, is calculated analytically and numerically. Afterward, errors in measuring the exact length of the crack during inspections, the internal pressure fluctuations due to the vessel's operational conditions, and uncertainties in characterizing the mechanical properties of the base material, including its minimum yield strength and toughness, are quantified. A reliability analysis is finally evaluated to assess the probability of failure considering these uncertainties.

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Data Availability

The authors declare that the data supporting the findings of this study are available in this paper. The data sets generated for the reliability analysis can be provided upon request.

Abbreviations

\({A}_{0}-{A}_{6}\) :

Parameters tabulated in Annex-9B of API 579-1/ASME FFS-1

\(B\) :

Matrix containing the spatial derivatives of the basis functions

\({C}_{ijkl}\) :

Fourth-order elasticity tensor

\(2c\) :

Crack length

E:

Young’s modulus

\(F\) :

Force vector

\({f}_{i}\) :

Body force

\({G}_{p}\) :

Influence coefficient

\(H\) :

Eshelby’s energy–momentum tensor

\(I\) :

Identity matrix

\(J\) :

J-integral

\(K\) :

Assembled stiffness matrix

\({K}_{\mathrm{I}}\) :

Stress intensity factor

\({K}_{\mathrm{IC}}\) :

Fracture toughness

\({K}_{\mathrm{I}}^{P}\) :

Stress intensity factor attributed to internal pressure

\({K}_{\mathrm{mat}}\) :

Material fracture toughness

\({K}_{r}\) :

Toughness ratio parameter

\({L}_{r}\) :

Collapse ratio parameter

\({M}_{t}\) :

Surface correction factor

\(N\) :

Vector of basis functions

\(n\) :

Outward normal unit vector

\(p\) :

Internal pressure

\({P}_{\mathrm{b}}\) :

Bending stress

\({P}_{\mathrm{f}}\) :

Probability of failure

\({P}_{\mathrm{m}}\) :

Membrane stress

\(q\) :

Unit vector in the virtual crack extension direction

\({R}_{i}\) :

Cylinder inner radius

\(t\) :

Cylinder wall thickness

\(t\) :

Surface traction on the crack surfaces

\({\overline{t} }_{i}\) :

Given traction on the natural boundary

\(T\) :

Assessment temperature

\({T}_{\mathrm{ref}}\) :

Reference temperature, Table 9.2 of API 579-1/ASME FFS-1

\(U\) :

Nodal displacement vector

\(u\) :

Vector of displacement field

\({\overline{u} }_{i}\) :

Given displacement on the essential boundary

\(W\) :

Strain energy function

\(\beta\) :

Reliability index

\(\Gamma\) :

Integration line surrounding the crack tip in the counterclockwise direction

\({\delta }_{ij}\) :

Kronecker symbol

\({\varepsilon }_{ij}\) :

Strain tensor

\(\nu\) :

Poisson’s ratio

\({\upsigma }_{\mathrm{f}}\) :

Flow stress

\({\sigma }_{\mathrm{ref}}\) :

Reference stress

\({\sigma }_{y}\) :

Yield strength of the material

\({\sigma }_{ij}\) :

Cauchy stress tensor

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Acknowledgements

This work has been supported by the Center for International Scientific Studies and Collaborations (CISSC), Ministry of Science, Research and Technology of Iran. Khader M. Hamdia thanks the support provided by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—Projektnummer 492535144.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Arak University of Technology, Arak, 38181-41167, Iran

    Hamid Ghasemi

  2. Center for International Scientific Studies and Collaborations (CISSC), Ministry of Science, Research and Technology of Iran, Tehran, 1314983655, Iran

    Hamid Ghasemi

  3. Institute of Continuum Mechanics, Leibniz Universität Hannover, An der Universität 1, 30823, Garbsen, Germany

    Khader M. Hamdia

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Ghasemi, H., Hamdia, K.M. The J-Integral Method Compared to the API 579-1/ASME FFS-1 Standard to Calculate Stress Intensity Factor (SIF): Leak-Before-Break (LBB) Application with Uncertainty Quantification. Arab J Sci Eng 49, 4643–4654 (2024). https://doi.org/10.1007/s13369-023-08138-4

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