Geometry of an inflated membrane in elliptic bulge tests: Evaluation of an ellipsoidal shape approximation by stereoscopic digital image correlation measurements

Abstract

Elliptic bulge tests are conducted on liver capsule, a fibrous connective membrane, associated with a field measurement method to assess the global geometry of the samples during the tests. The experimental set up is derived from a previous experimental campaign of bulge tests under microscope. Here, a stereoscopic Digital Image Correlation (DIC) system is used to measure global parameters on the test and investigate some assumptions made on the testing conditions which could not been assessed with microscopic measurements. In particular, the assumption of an ellipsoidal shape of the inflated membrane is tested by comparing the actual sample shape measured by stereoscopic DIC with an idealized ellipsoidal shape. Results indicate that a rather constant gap exists between the idealized and actual position. The approximation in the calculation of a macroscopic strain through analytical modeling of the test is estimated here. The study of the liver capsule case shows that important differences can be observed in strain calculation depending on the method and assumptions taken. Therefore, analytical modeling of mechanical tests through ellipsoidal approximation needs to be carefully evaluated in every application. Here the field measurement allows assessing the validity of these modeling assumptions. Moreover, it gives precious details about the boundary conditions of the bulge test and revealed the heterogeneous clamping, highlighted by strain concentrations.

Tracking Microstructure Evolution in Complex Biaxial Strain Paths: A Bulge Test Methodology for the Scanning Electron Microscope

“…The bulge test is a method that can be used to measure biaxial stress-strain curves [46], parts of yield surfaces [47][48][49][50] and forming limit curves (FLC) [51], or characterize damage mechanisms [52] of sheet metal (as well as the mechanical response of thin films [53,54] or biological tissues [55,56]). Circular dies are typically used to investigate equi-biaxial strain paths, however elliptical dies can be employed to observe proportional strain paths with a strain ratio different from 1 [57][58][59][60][61][62].…”

Direct stress computations in arbitrarily shaped thin shells and elliptic bulge tests

“…The bulging of planar elliptical membranes was studied by Verron et al [38] using a dynamic finite-element analysis (FEA) and explicit finite difference method (FDM), assuming hyperelastic and viscoelastic material models, respectively. Jayyosi et al [39] analysed the accuracy in fitting an ellipsoid to the inflated shape of an initially planar elliptical membrane of 1, 2 and 4 aspect ratios; they found small shape deviation, which can lead to pronounced errors in the stress or strain determination. Tonge et al [40,41] approximated the deformed cross sections along the planes of symmetry through ellipses.…”