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

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5. Results and Discussion

5.1. EICM and TAM Verification for the Hybrid Joint

5.1.1. Linear-Elastic Model for HDPE Figure 2 shows the normalized bolt load distribution F f / F i and contact pressure contours for EICM and TAM over three iterations. Initial load ratios vary between 0.73 and 1.11, converging to near-uniform values (0.98–1.00) by the third iteration. Final TAM parameters are α = -0.1341, β = -0.1240, γ = 0.0446, δ = 0.0537. Contact pressure peaks at bolt locations, with initial fluctuations at R 0 = 134 mm ranging from 11 to 15 MPa. By the third iteration, pressure becomes uniform at ∼ 14 MPa , indicating improved sealing. These results demonstrate that TAM achieves conver gence and contact stress uniformity comparable to EICM, making it an e ffi cient method for optimizing HDPE–steel flange assembly.

Fig. 2: Scatter of bolt forces and contact pressure contours for (a) EICM and (b) TAM Ezzeldin et al. (2025).

5.1.2. TN Model for HDPE Here the results of the TAM procedure at 23 ◦ C are presented. Converged parameters ( α = -0.2201, β = -0.2552, γ = 0.0843, δ = 0.1025), were obtained with less than 0.002 absolute di ff erence between iterations. These di ff er from Ezzeldin et al. (2025) due to the use of a viscoelastic TN model instead of a linear elastic constitutive behavior. Figure 3 shows the normalized bolt loads after tightening, and their corresponding initial bolt preloads. Final loads align closely with the target 20 kN, within 4% deviation, confirming TAM’s e ff ectiveness in capturing HDPE’s viscoelastic behavior using the TN model.

Fig. 3: Scatter of bolt loads and initial bolt preloads following the bolting of the flange connection, using the TN Model.