Analysis of the extended stress-based forming limit curve considering the effects of strain path and through-thickness normal stress

Abstract

In this study, an approach based on the modified Marciniak-Kuczynski (M-K) method for computation of an extended stress-based forming limit curve (FLC) is presented. The extended stress-based FLC is built based on equivalent plastic stress versus mean stress. This curve has some advantages in comparison with the conventional FLC. This new criterion is much more strain path independent than the conventional FLC. The effect of strain path on the predicted extended stress-based FLC is reexamined. For this purpose, two types of pre-straining on the sheet metal have been loaded. Moreover, the plane stress state assumption is not adopted in the current study. The influence of a through-thickness compressive normal stress is also investigated theoretically. The verifications of the theoretical FLCs are performed by using some available published experimental data.

Theoretical and numerical investigation of the impact of out-of-plane compressive stress on sheet metal formability

“…Additionally, a non-zero principal stress 33 ( = − ) acts in the out-of-plane direction (i.e., in the 3-direction), where is assumed to be a non-negative constant pressure. The validity of this assumption (constant pressure) has been proven in the case of hydroforming processes (see, e.g., [17,18] ). This pressure is also assumed to be uniformly distributed within the plane and the thickness of the sheet.…”

“…(19) in the form of Eq. (18) . In this case, the following expressions for the components ̃ 11 , ̃ 22 , ̃ 12 and ̃ can be derived:…”

Path independent limiting criteria in sheet metal forming

“…Wang et al [18] discussed in details about several DIC procedures to generate FLD. The FLD is affected by many factors, such as strain rate (the forming speed), strain hardening property, normal and planar anisotropy of the sheet metals [19], thickness of sheets, through thickness stress [20,21] and lubrication condition.…”

Numerical and experimental study of formability in deep drawing of two-layer metallic sheets

“…However, it is well known that the strain-based forming limit diagram, introduced by Keeler and Backofen [19] and Goodwin [20], does not estimate the formability limit (the onset of necking) when the sheet metal is subjected to non-linear strain paths. Therefore, an extended strain-based FLD has been represented and this curve is much less sensitive to strain path changes than the conventional forming limit diagram [21,22] Since finite element software such as ABAQUS can calculate the strains incrementally in each element, and therefore, the strain ratio and the equivalent strain in each element can be derived at every increment of deformation. Ultimately, the equivalent strains and corresponding strain ratios for the entire strain path of each element can be extracted from the output file of the FE software, and the deformation process can be analyzed by comparing the equivalent strains vs. strain ratios for the final strain increment with the extended FLD.…”