Numerical prediction of failure in single point incremental forming using a phenomenological ductile fracture criterion

Besides the high simplicity and flexibility, excessive thinning of the sheet metal is one of the limitations of single point incremental forming (SPIF). To overcome this drawback, a finite element (FE) simulation can be implemented for determination of an appropriate deformation strategy. Since the formability in SPIF is often limited by fracture failure, the prediction of ductile fracture using a FE simulation is of the significant importance. In this paper, by implementing the phenomenological modified Mohr-Coulomb (MMC3) model through an appropriate user subroutine within the commercial FE code Abaqus/Explicit, the ductile fracture in SPIF is investigated. Based on the designed tensile tests, the MMC3 criterion is calibrated for AA6061-T6 aluminum alloy sheet using an inverse approach. The stress and strain states of the localized deformation field in SPIF are comprehensively analyzed. With the aid of stress triaxiality and normalized Lode angle parameter, it is shown that the loading path in SPIF is highly nonlinear. Accordingly, a nonlinear damage accumulation rule is utilized to predict the onset of fracture. The comparison of predicted fracture depths of SPIF parts with experimental ones demonstrates an average discrepancy of 10% for utilizing the MMC3 criterion. A good agreement of the fracture location can also be found between experiments and FE simulations. Numerically computed fracture strains show that the fracture forming limit diagram (FFLD) under a proportional loading, like a tensile test, differs in shape and value from the one obtained under a non-proportional loading like SPIF in which the FFLD is higher.