Bulge and Dome Testing

Local necking during uniaxial tensile testing limits the characterization of the stress-strain response to true strain values below uniform elongation. Extrapolating the true stress – true strain curve beyond uniform elongation requires selecting a hardening law on which to base the extrapolation. However, the chosen hardening law dramatically affects the extrapolated the true stress – true strain curve. Figure 1^L-20 shows an example of this extrapolation using a bake hardenable steel. Deviation from the real performance leads to inaccurate thinning and fracture predictions, inaccurate springback predictions, and inaccurate predictions of press force and press energy requirements.

Figure 1: The selected hardening law leads to vastly different stress-strain responses extrapolated beyond uniform elongation.^L-20

Bulge testing is one method to generate stress-strain data at higher strains, minimizing the need for extensive extrapolation. Another benefit is that the deformation occurs in two directions (biaxial), which is similar to the metal motion seen in most forming operations and in contrast to uniaxial tensile testing.

In biaxial bulge testing^{K-17, V-7}, a circular sample is clamped around its periphery and pressurized from one side using a viscous incompressible medium, forcing the metal to bulge and expand into a cavity as the pressure increases. Figure 2 shows a typical testing configuration.^F-12 Flow stress is calculated from the dome height of the bulging blank and the pressure in the viscous medium. A non-contact system equipped with Digital Image Correlation (DIC) measures strain. The ISO 16808 Test Standard details the requirements.^I-12

Figure 2: Bulge testing configuration.^F-12

For various reasons, flow stress data at the lowest strains are not as accurate as what is generated at higher strains. This leads to practitioners combining curves, using tensile data at low strains through uniform elongation, and bulge data after that. These blended curves result in a thorough true stress – true strain characterization over a wide range of strains, making it applicable to a variety of formed parts. Figure 3 shows a blended curve for the same alloy highlighted in Figure 1.

Figure 3: Flow curves for a bake hardenable steel generated by combining tensile testing with bulge testing.^L-20

Biaxial bulge testing provides two critical inputs for advanced material characterizations required for simulation: biaxial anisotropy and biaxial yield stress.