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Elastoplastic Multistep Loading of High-Pressure Flanged Vessel Nozzle with U-Notch
3D B-Rep high-pressure flanged vessel nozzle with an external U-notch stress concentrator solved across 6 nonlinear load steps with J₂ von Mises elastoplasticity and isotropic hardening.
Pressure-vessel nozzles and flanged pipe necks feature geometric transitions where local stresses exceed the initial yield strength during hydrotest or operational overload, redistributing load through contained plastic flow. A linear elastic analysis overpredicts peak stress and cannot quantify permanent strain. Here, a 3D B-Rep flanged nozzle (`notched_nozzle.step`, flange OD 100 mm, neck OD 60 mm, bore ID 30 mm, U-notch r = 5 mm, height 90 mm) made of pressure-vessel steel (E = 200 GPa, σ_y = 280 MPa, H = 2.5 GPa) is loaded in 6 increments to 220 MPa axial pull, capturing stress redistribution at σ_vm = 283.11 MPa and peak plastic strain ε_p = 0.455%.
1. Geometry & FEA Mesh
- •3D B-Rep CAD model (`notched_nozzle.step`, 8 CAD faces, volume 184.57 cm³, flange OD 100 mm, neck OD 60 mm, bore ID 30 mm).
- •6,192 TET4 elements, 1,890 nodes (5,670 DOFs).
- •J₂ elastoplastic steel: E = 200 GPa, ν = 0.30, yield strength σ_y = 280 MPa, tangent hardening modulus H = 2.5 GPa.
2. Loads & Boundary Conditions
- •Bottom flange mounting face fully fixed (`fix surface number 19`).
- •Top nozzle rim (`surface number 26`) loaded by axial tension p = −220 MPa ramped across 6 nonlinear load steps (`nlgeom set on=on steps=6`).
3. Simulation Results & Findings
- ✓Elastic response on steps 1–2 transitions into plastic yielding at the U-notch root on steps 3–6, with 1,336 of 6,192 elements (21.6%) entering plasticity at full load.
- ✓Von Mises stress plateaus along the hardening curve at σ_vm = 283.11 MPa (vs >380 MPa fictitiously predicted by linear elasticity).
- ✓Maximum equivalent plastic strain reaches ε_p = 4.55 × 10⁻³ (0.455%) at the notch root with axial elongation |u|_max = 0.1215 mm.
WebCAE's native J₂ return-mapping elastoplastic solver with step-by-step history enables ASME Sec. VIII Div. 2 / EN 13445 limit-load and plastic-strain qualification of pressure vessels and piping.
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