Forming-limit prediction of perforated aluminium sheets with square holes

Abstract

The forming-limit strains of perforated aluminium alloy (AA5052-O) sheets with square holes were theoretically and experimentally estimated for two types of hole arrangements: square and triangular patterns. The theoretical forminglimit curves were obtained by finite-element analyses on a unit module of the perforated sheets using two different approaches: the phenomenological theory and crystal plasticity theory. Hill's quadratic anisotropic and von Mises yield functions were used for the phenomenological analysis, and the one-element-per-grain model was adopted for the crystal plasticity analysis. To determine the forming limits, two different types of plastic instability criteria were applied. The experimental forming-limit strains were also obtained through a Nakazima stretching test. The theoretical predictability of the forming-limit curves was assessed by comparing the theoretical and experimental results. The comparison demonstrated that (1) the plastic instability criterion based on the external force power predicted qualitatively the same forming-limit curves as the criterion based on the equivalent plastic strain of the ligament for both hole arrangement patterns and (2) although the shapes of the predicted forming-limit curves were in reasonable agreement with the experimental results, the level of the predicted limit strains was considerably higher than that of the experimental limit strains. Thus, it was found that neither of the plastic instability criteria previously proposed for perforated sheets is appropriate to characterise the formability of perforated aluminium sheets with square holes.

Numerical investigation of necking in perforated sheets using the periodic homogenization approach

“…The rolling direction of the metal sheet is assumed to coincide with the major strain direction. Set 1 typically corresponds to plastic anisotropy of aluminum alloys (Chiba et al, 2015). By contrast, set 2 corresponds to an isotropic dense matrix.…”

“…It has been found from this study that perforated sheets with square holes have the best formability limit. Iseki's formability criterion (Iseki et al, 1989) has been subsequently used by Chiba et al (2015) to predict the FLDs of perforated aluminum sheets with square holes. In this analysis, both phenomenological material models (based on Hill'48 and von Mises yield functions) and a crystal plasticity model have been used to describe the mechanical behavior of the dense matrix.…”

“…In this analysis, both phenomenological material models (based on Hill'48 and von Mises yield functions) and a crystal plasticity model have been used to describe the mechanical behavior of the dense matrix. In the above-cited contributions (Chiba et al, 2015;Iseki et al, 1989;Tvergaard, 1981;Tvergaard, 2015), finite element analyses have been combined with the different necking criteria to predict the onset of necking. In the present investigation, we have coupled the periodic homogenization approach with some diffuse and localized necking criteria to predict the forming limits of perforated sheets.…”

Forming-limit strains of perforated steel sheets under biaxial stress state

“…Needless to say, the forming limit of perforated sheets is also influenced by these factors. [7][8][9] However, only a limited number of studies have investigated differences in formability depending on the material type, open area, hole shape, and hole arrangement.…”

“…In our previous study, 9 the apparent limit strains of aluminum square hole perforated sheets were measured using the Nakazima test, and the formability prediction performance of an FEM-based method was evaluated by comparing predicted and experimental results. In the computational prediction, the onset of diffuse necking was used as a forming-limit criterion for the perforated sheets subjected to biaxial deformation, 12 which corresponds to predictions on the safe side in terms of material failure.…”