Metal Sheet Forming Limits With 3D Bending-Strain Mapping

The patent transitions from conventional two-dimensional forming limit curves (maximum principal strain vs. minimum principal strain) to a three-dimensional forming limit boundary surface by adding bending deformation degree as a third dimension. This is achieved by performing bulge forming tests with multiple hemispherical punches of different curvatures to introduce controlled bending deformation, then constructing the 3D boundary surface that simultaneously considers in-plane strains and bending deformation. This dimensional expansion allows accurate prediction of fracture in press forming processes where bending deformation occurs.

The patent changes the parameter set used to define forming limits from conventional two parameters (maximum and minimum principal strains) to three parameters by incorporating bending deformation degree. This parameter expansion allows the forming limit boundary surface to accurately represent the reduced ductility of high-strength steel sheets under combined bending and in-plane deformation conditions. By matching the bending deformation degree in tests to actual press forming conditions, the method provides reliable fracture prediction for high-strength materials.

The patent segments the forming limit characterization into multiple discrete bending deformation levels, each represented by a hemispherical punch of specific curvature. Instead of attempting to model continuous bending variations, the method uses a finite set of representative punches (e.g., three or more with different curvature radii) to cover the range of bending conditions. This segmentation approach makes the testing apparatus manageable while still capturing the essential effect of bending deformation on forming limits.