Nowadays, product manufacturing can be divided into two groups:​ relatively simple products produced in a large production chain and complex (specialized) components produced in reduced batches. Within the second group, prototyping through incremental sheet forming (ISF) has been subject of several studies. ISF refers to processes where the plastic deformation occurs by repeated contact with a relatively small tool. A crucial aspect in the ISF processes is that the final shape is determined only by the tool movement. The focus of this research is the single point incremental forming (SPIF) process variant, where a clamped sheet metal is deformed by using a relatively small spherical tool.

SPIF has several advantages over traditional forming, such as the high formability attainable by the material. Different hypothesis haven been proposed to explain this behavior, but there is still not a clear and definitive understanding of the relation between the particular stress and strain state induced in the material during SPIF and the material degradation leading to localization or fracture.

In this thesis, a fundamental research is proposed using the finite element (FE) code Lagamine, developed within the University of Liège. Numerical implementation and validation of the Gurson-Tvergaard-Needleman (GTN) damage model into this FE code is performed. An experimental test campaign is developed to characterize plastic and damage behavior and to validate the damage model for the DC01 steel grade. Finally, this damage model is applied to simulate the SPIF process in order to verify if it is capable to predict failure. The thesis discusses the material parameter identification for classical plasticity models, describing the anisotropy and hardening behavior of the sheet metal. The derivation of the equations of the numerical damage model and the efficiency of the implementation is presented in great detail. A methodology for the numerical parameter identification of the damage model is proposed, including microscopic measurements by optical microscopy and strain and displacement field measurements by digital image correlation (DIC). The identified Gurson model is applied to simulate standard SPIF geometries, like the line, cone and pyramid tests. The simulations are performed using the solid-shell element formulation and validated in terms of shape and force prediction. Literature reviews of the Gurson model and the SPIF process are also included.

The experimental results show that the selected material (DC01 steel sheet) exhibits a slight anisotropic behavior and work-hardening stagnation on cyclic tests. The performed microscopic measurements are not representative of the actual damage, but they give a qualitative estimation of the physical mechanism of fracture. The initial porosity of the material was determined using optical microscopy measurements in the base material.

The numerical implementation of the model is developed with all variables integrated in an implicit way, based on the backward Euler scheme. Nucleation, coalescence and shear extensions implementations are validated by results obtained from the literature. The macroscopic campaign allowed to identify the parameters for nucleation, coalescence and shear. An unique set of results matching all experiments was not possible to obtain, so different sets of parameters are retrieved following an approach that includes inverse modeling and sensitivity analysis. A numerical-experimental comparison of strain values in the loading direction shows that the model is able to correctly predict the strain distribution except during localization of the strain. Globally, the obtained set of material parameters is in good agreement with the experimental results.

For SPIF FE simulations, the results of the shape prediction are in good agreement with the experimental results, both for the line and pyramid test. Nevertheless, the force prediction is too high compared to reference values. On the other hand, the GTN model is capable to detect failure in a pyramid and a cone, but the prediction is too premature compared to the experimental failure angle for the same material and geometry.

An accurate prediction of failure for the SPIF process was not possible to achieve. The GTN model extended to shear presents inherent flaws that prevent an accurate prediction of the failure angle for the SPIF process. Hence, an extensive research on the damage mechanisms leading to fracture for SPIF cannot rely (only) on the GTN model. The classical coalescence model of the GTN model is insufficient to correctly predict failure. Hence, it is recommended that further analysis concentrates on the description of this particular stage of damage evolution. During the development of this thesis, a robust implementation of the GTN model into the FE code Lagamine was done, including an extensive experimental database of microscopic and macroscopic measurements for the DC01 steel sheet. Other phenomena can be explored thanks to this model.