PSI - Issue 80

Sherif Ezzeldin et al. / Procedia Structural Integrity 80 (2026) 195–202

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S. Ezzeldin / Structural Integrity Procedia 00 (2023) 000–000 Table 1: Two-step loading sequence for TAM parameter identification, adapted from Ezzeldin et al. (2025).

F ′

F b − 1

b − 1 −

Bolt b is tightened to load F b . Bolts b + 1, b + 2, and b − 1 were tightened simultaneously in the first load step to loads F b + 1 , F b + 2 , F b − 1 , re spectively, and after tightening bolt b, their loads become F ′ b + 1 , F ′ b + 2 , F ′ b − 1 , respectively. Bolt b − 2 is not tightened in the first load step.

α =

F b α estimates the loss of load of bolt b − 1 whenbolt b is tightened, with bolt b − 2 not tightened in the first load step. F b β estimates the loss of load of bolt b + 1 when bolt b is tightened, with bolt b + 2 tightened in the first load step. F b δ estimates the loss of load of bolt b + 2 whenbolt b is tightened, with bolt b + 1 tightened in the first load step. β = F ′ b + 1 − F b + 1 δ = F ′ b + 2 − F b + 2

F ′

F b + 2

b + 2 −

Bolt b is tightened to load F b . Bolt b + 2 was tightened in the first load step to load F b + 2 , and after tightening bolt b, its load becomes , F ′ b + 2 . Bolt b + 1 is not tightened in the first load step.

γ =

F b γ estimates the loss of load of bolt b + 2 whenbolt b is tightened, with bolt b + 1 not tightened in the first load step.

3. Constitutive Behavior of HDPE

In previous work, the HDPE stub-end, steel blind flange, backing ring, and bolts were modeled as linear elastic isotropic materials, with E = 1 GPa and ν = 0 . 4 for HDPE and E = 200 GPa and ν = 0 . 3 for steel components Barsoum et al. (2019). This simplification of treating HDPE as a linear elastic isotropic material was su ffi cient to evaluate the applicability of the TAM procedure to hybrid flange connections and compare it to EICM. In contrast, this study employs the elastic-viscoplastic three-network (TN) model calibrated by Shahin et al. Shahin et al. (2020), which is specifically designed for thermoplastic polymers like HDPE Bergstrom and Bischo ff (2010); Bergstrom (2015); Hansen and Kristiansen (2011); Frontini et al. (2013). Building on the Bergstrom hybrid model Bergstro¨m et al. (2002), the TN model improves numerical accuracy and e ffi ciency by incorporating three parallel networks. For full details on the model formulation, see Bergstrom and Bischo ff (2010).

4. Methodology

The TAM methodology in FEA follows the load cases outlined in Table 1. In Run 1, bolts are tightened to reach the target final load F d . Two loading cases are considered: (1) tightening of bolts 1, 2, 3, and 8; and (2) tightening of bolts 1 and 2 in the first step, followed by bolts 5 and 3 in the second step, respectively. The TAM parameters α , β and δ are derived from the first case, while γ is obtained from the second. Using these values, the interaction matrix [ A ] is constructed via Eq. (2) to relate final loads F f to required initial preloads F i . Based on this, updated initial preloads are applied in the next simulation run. After each FEA run, the TAM parameters are checked for convergence, ensuring less than 1% absolute di ff erence between iterations. If not met, the matrix [ A ] is recalculated and the process repeated until convergence. To evaluate temperature e ff ects, simulations begin at 23 ◦ C with linear heating over 8 hours. Four isothermal cases (23, 40, 60 and 80 ◦ C) are considered to assess bolt relaxation without retorqueing, while two additional cases include retorqueing at 23 and 60 ◦ C. An annual temperature profile typical of the Arabian Gulf Weather and Climate (2024) is also applied over one year to simulate real-world conditions. Re-torqueing is triggered if average contact stress drops near or below 2.85 MPa, to maintain joint integrity.