Abstract
The effect of the width to thickness ratio on the bendability of sheet metal is investigated using the finite element method (FEM) employing the Gurson–Tvergaard–Needleman (GTN) model. Strain path changes in the sheet with change in the width/thickness ratio. It is shown that bendability and fracture strain increase significantly by decrease in the width/thickness ratio. The stress state is almost uniaxial when the stress ratio (α) is close to zero for narrow sheets. Stress ratio is nothing but the major stress to minor stress ratio. This delays the growth and coalescence of micro-voids as the volumetric strain and stress triaxiality (pressure/effective stress) decrease. On the other hand, ductility decreases with increase in α for wider sheets. Fracture bending strain is calculated and, as expected, it increases with decrease in the width/thickness ratio. Furthermore, a brief study is performed to understand the effect of superimposed hydrostatic pressure on fracture strain for various sheet metals with different width/thickness ratios. It is found that the superimposed hydrostatic pressure increases the ductility, and that the effect of the width/thickness ratio in metals on ductility is as significant as the effect of superimposed hydrostatic pressure. Numerical results are found to be in good agreement with experimental observations.
Highlights
Bending is an important property in sheet metals as bending occurs as a part of several forming operations, such as in deep drawing in auto industry [1,2,3,4]
Fracture strains for different meshes are calculated and shown in
It is found that a lower width/thickness ratio improves bendability significantly as the stress triaxiality decreases in the sheet, leading to lower fracture strain
Summary
Bending is an important property in sheet metals as bending occurs as a part of several forming operations, such as in deep drawing in auto industry [1,2,3,4]. The strain state in sheet metals changes with changing the width/thickness of a specimen and the fracture strain increases with decreasing this ratio. To the best of our knowledge, the effect of width/thickness of a specimen on bendability is not considered numerically in detail elsewhere It is explained in [1,2] that bendability of sheet metals is dependent on the width to thickness ratio of sheet metals. The fracture strain in metals is dependent on stress triaxiality [13,14]. It is observed that the fracture strain increases from plain strain state to the uniaxial state when the stress triaxiality decreases. The stress state of a material changes with changing the width to thickness ratio. The maximum achievable α is 0.5 for the plane strain state where the ductility is a minimum
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