Development of Simplified Mechanical Model for Welding Deformation in Multi-Pass Welding

This paper proposes a simplified mechanical model to estimate transverse shrinkage and angular distortion in multi-pass butt welding. The simplified mechanical model is first derived for an I-groove joint by representing the heated weld region with one-dimensional bar elements and by enforcing force equilibrium to obtain closed-form expressions for pass-by-pass deformation increments and cumulative deformation. For non-I-groove joints, the same simplified mechanical model is applied by updating the layer partition and geometric parameters for each pass based on the pass-wise high-temperature region; the inherent shrinkage of each pass is evaluated from the heat input and an equivalent heated-layer thickness. The simplified mechanical model is validated for V-groove multi-pass joints by comparison with thermo-elastic-plastic finite element (FE) analyses and available experimental data, and for X-groove multi-pass joints by comparison with thermo-elastic-plastic FE analyses. In addition, a parametric study on the V-groove angle (40°–70°) for SUS316L demonstrates that the model captures the increasing trend of final transverse shrinkage with groove angle without a pronounced degradation in prediction accuracy. The results show that the simplified mechanical model reproduces both deformation histories and final values with good accuracy while using only a small set of input parameters and negligible computational cost, making it useful for early-stage welding procedure planning and quick parameter studies.