Abstract
In this work, three numerical necking criteria based on finite element (FE) simulations are proposed for the prediction of forming limit diagrams (FLDs) for sheet metals. An elastic–plastic constitutive model coupled with the Lemaitre continuum damage theory has been implemented into the ABAQUS/Explicit software to simulate simple sheet stretching tests as well as Erichsen deep drawing tests with various sheet specimen geometries. Three numerical criteria have been investigated in order to establish an appropriate necking criterion for the prediction of formability limits. The first numerical criterion is based on the analysis of the thickness strain evolution in the central part of the specimens. The second numerical criterion is based on the analysis of the second time derivative of the thickness strain. As to the third numerical criterion, it relies on a damage threshold associated with the occurrence of necking. The FLDs thus predicted by numerical simulation of simple sheet stretching with various specimen geometries and Erichsen deep drawing tests are compared with the experimental results.
Highlights
The formability of sheet metals is usually characterized by forming limit diagrams (FLDs) obtained by the Nakazima or Marciniak deep drawing tests
We investigate the occurrence of necking in a St14 steel material using the elastic–plastic–damage model described above in conjunction with numerical necking criteria
An elastic–plastic model has been coupled with the Lemaitre ductile damage
Summary
The formability of sheet metals is usually characterized by forming limit diagrams (FLDs) obtained by the Nakazima or Marciniak deep drawing tests. Situ et al [9,10,11] applied the same strategy to the Nakazima deep drawing test in order to predict FLDs for sheet metals involving the whole range of strain paths They have shown that the analysis based on major strain rate (i.e., first time derivative of major strain) predicts the onset of fracture, while the maximum of major strain acceleration (i.e., second time derivative of major strain) corresponds to the occurrence of localized necking. The FE model based on the Erichsen deep drawing test (see, e.g., [29]) is used to predict the FLDs of the steel material To determine these forming limit curves for the studied material, three numerical criteria are presented in this work to detect the occurrence of necking in the sheet specimens. All points of the predicted FLDs, which are obtained using the FE simulations combined with the numerical necking criteria, are compared with the experimental results taken from [30]
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