Evaluation of Stress and Strain Measurement Accuracy in Hydraulic Bulge Test with the Aid of Finite-element Analysis

Abstract

Numerical simulations of the hydraulic bulge test are carried out by the implicit static finite-element method. The sheet specimen is characterized as a rate-independent elastoplastic material with a powerlaw hardening rule. The stress and strain relationship of the specimen is evaluated from the internal pressure and nodal coordinates obtained in the finite-element simulation of the hydraulic bulge test. Varying the gauge lengths of the spherometer and extensometer and the ratio of the initial thickness to the diameter of the specimen, their influences on the estimated stress and strain are investigated. By comparing the estimated stress-strain relationship with that of exact input data, the stress and strain measurement accuracy is assessed. Furthermore, the stress state at the apex is examined for orthotropic specimens and is found to deviate by 1-5% from the equi-biaxial stress state.

Material parameter identification within an integrated methodology considering anisotropy, hardening and rupture

“…As shown by Aretz and Keller (2011) and Yoshida (2013), an equibiaxial stress state cannot be achieved due to the material anisotropy, in particular when r b value is different from unity. The analysis of Aretz and Keller (2011) was based on a virtual material with r b = 0.5 and a real one with r b = 0.36.…”

“…The analysis of Aretz and Keller (2011) was based on a virtual material with r b = 0.5 and a real one with r b = 0.36. Yoshida (2013) investigated numerically the validity of the equibiaxial stress state assumption for the bulge test in case of material anisotropy and concluded that the stress state at the apex can deviate by only 1-5% from the equibiaxial stress state.…”

“…In this study, it should be emphasized that from an experimental point of view, size of the area used in order to calculate the radius of curvature at the apex was small compared to the gauge diameter of the bulge test (185 mm), as proposed in Yoshida (2013). Moreover, when considering the optimized parameter set, a maximum relative gap of 3% between the stress components in the rolling and transverse directions were recorded, as shown in Fig.…”

A Review of Characterization and Modelling Approaches for Sheet Metal Forming of Lightweight Metallic Materials

“…Lightweight sheet metals experience complex stress states including various biaxial deformation states, such as EBT and PS. Hydraulic bulging [ 262 , 263 , 264 ], pneumatic bulging [ 265 ] and bulging with viscous material as medium [ 266 ] experiments are advanced characterization methods to obtain stress–strain curves and the biaxial strain ratio in a large strain range under biaxial deformation [ 267 ]. An example of a bulge test set-up with a circular die and DIC measurement system is presented in Figure 18 .…”

On the identification of material hardening for anisotropic sheets via bulge tests

“…The conventional manual measurements for these parameters are cumbersome and usually require the interruption of the tests. 14,15 With the introduction of a spherometer combined with an extensometer, 4,16 the measurement was simplified to some extent. Recently the DIC (Digital Image Correlation) technique has been adopted in bulge tests as it provides direct monitoring of the strain distribution of the deformed sheet metal.…”