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High-Speed Forming Limit Curve (FLC)
Full-Field Deformation Analysis and FLC Determination via 3D DIC in Nakajima Testing
The Nakajima test is the most common technique used for determining the forming limit curve (FLC) in sheet materials. The FLC describes the maximum formability of the material, making it possible to reliably assess the failure behavior of a sheet metal and select the ideal material for a desired forming process. Forming limit analysis significantly reduces development times, increases product quality, and serves as a vital material parameter input for finite element method (FEM) simulations.
This case study was conducted in collaboration with our Austrian partner, 4A engineering. The puncture force was applied using their Linovis dynamic testing machine.
Objective
The primary objective of this study was to evaluate and map the forming limit curves for a sheet metal specimen at a static testing speed of 0.001 m/s and a dynamic testing speed of 1 m/s at a room temperature of 23 °C.
Description of the Case Study
The experiment was performed on standardized test specimens made of HC380 steel prepared according to the ISO 12004 standard.
A high-contrast speckle pattern was applied to the samples using matte black and white spray paints before they were tested until fracture. Due to significant out-of-plane motion and the complex nature of the deformation, a 3D DIC configuration was required. The highly dynamic technical setup included:
❖ Testing Machine: 4A engineering’s Linovis dynamic testing machine, capable of reaching testing speeds up to 3.2 m/s, a maximum force of 25 kN, and a maximum stroke of 200 mm.
❖ Optical Setup: A 2D Digital Image Correlation (DIC) system utilizing a Photron Nova S9 high-speed camera paired with a high-fidelity Zeiss 100 mm lens.
❖ Image Acquisition: The camera captured the event at a resolution of 896 x 240 px with an ultra-high frame rate of 40,000 fps.
❖ Testing Speed: This specific configuration allowed the system to precisely record localized strain at a testing speed of 2 m/s.
This setup allowed for high-precision tracking of surface displacements in all three axes (x, y, z), with cameras positioned at different angles to accurately reconstruct the 3D space and provide high accuracy in out-of-plane deformation.
All samples were prepared according to the ISO 12004 standard and had a speckle pattern applied to them using matte black and white spray paints. Then, they were tested until fracture.
A 3D graph may be displayed, showcasing the out-of-plane displacement during the puncture.
Results
Full-field strain was evaluated for all samples as well as the elongation between two points in both horizontal and vertical direction. The gauge length was 2 mm.
The strain, load and displacement data was further processed to obtain the Forming Limit Diagram.
Static test – 0.001 m/s
Dynamic test – 1 m/s
Comparison
The Mercury RT DIC software successfully processed the high-speed imagery, delivering comprehensive insights into the material behavior:
❖ Full-Field Strain Mapping: Provided clear graphical visualizations along with precise quantitative data mapping the material’s structural response to rapid, dynamic loading.
❖ Multi-Point Tracking: Handled virtual extensometers to track elongation between two points at multiple critical locations across the sample surface.
❖ Simulation Material Cards: The computed high-fidelity strain data was imported into Valimat (4A engineering’s proprietary software) to generate fully validated material cards for finite element analysis (FEA).
Nakajima Testing requires 3D DIC
❖ 3D Space Reconstruction: Accurately captures high out-of-plane deformation and complex 3D surface displacements where 2D systems fail.
❖ Full-Field Strain Profiling: Provides continuous surface measurement up to the exact point of fracture, revealing localized deformation behavior.
❖ Static to Dynamic Versatility: Delivers consistent, highly precise deformation analysis across a massive range of testing speeds (from 0.001 m/s to 1 m/s).
❖ FEM Simulation Input: Directly generates high-fidelity material parameters to refine and validate sheet-forming simulations.
For more information about high speed 3D DIC, please Contact us through email info@mercury-dic.com.
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