Forming limit diagram prediction of tailor welded blank by modified M–K model

• Bending strain effect on the FLD level has been investigated in this study.
• A new FLD criterion has been presented by adding the bending strain to the M–K model.
• This modified M–K (MM–K) model was used to predict FLD of tailor welded blanks.
• MM–K model was used as a post-processing criterion in Abaqus software using Abaqus scripting.
• Python programming language was used for scripting in Abaqus.
• Results of MM–K model were verified by experimental tests on IF tailor welded blanks.

The Marciniak and Kuczynski (M–K) model for necking prediction in sheet metal forming was based on the in-plane forming. Bending which was resulted from out-of-plane forming was not considered in the M–K model. Whereas most of the sheet metal forming processes and also standard test of hemispherical punch for forming limit diagram are out-of-plane forming, it is important to consider bending effect in the M–K model. Therefore, in this study bending strain is added to stretching strain of M–K model and a new model is presented for forming limit diagram (FLD) prediction. This modified M–K (MM–K) model is written in the python programming language and it is used as a post-processing criterion for FLD prediction in the commercial software Abaqus. The MM–K model was used to predict FLD and weld line movement in the tailor welded blank forming. It was found that the predicted results by MM–K model are in a good agreement with experimental data.