Parameters
Weld type
Heat input Q1000 J/mm
Preheat temp. T₀25 °C
Yield stress σ_y350 MPa
Plate thickness t12.0 mm
Number of passes1
—
Peak tensile res. stress [MPa]
—
Peak compressive [MPa]
—
Angular distortion Δφ [°]
—
Transverse shrinkage [mm]
—
Long. shortening [mm/m]
—
Peak HAZ temp. [°C]
—
Stress zone half-width b [mm]
—
Pass correction factor
Longitudinal Residual Stress σ_L(y) [MPa]
HAZ Thermal Cycle T(t) [°C]
Masubuchi Model & Distortion Formulas
Masubuchi model longitudinal residual stress distribution:
$$\sigma_L(y) = \sigma_y\left[1-\left(\frac{y}{b}\right)^2\right]\exp\!\left[-\frac{1}{2}\left(\frac{y}{b}\right)^2\right]$$where $b$ is the characteristic half-width (function of fusion width). Angular distortion estimate: $\Delta\phi \approx \dfrac{0.02 Q}{\sigma_y \cdot t^2}$ [rad]
Transverse shrinkage: $\Delta T \approx \dfrac{0.2 A_w}{t}$ ($A_w$: fusion cross-section area)
Rosenthal peak temperature: $T_{max} = T_0 + \dfrac{Q}{2\pi\lambda r_0 \rho c_p}$
CAE Applications: Hand-calculation verification for Abaqus / Sysweld / Simufact Welding thermo-elastic-plastic analyses. Inherent strain method for large-scale welded structure distortion prediction. Pre-screening whether welding distortion exceeds allowable tolerance.