Investigation of the effect of forming parameters in incremental sheet forming using a micromechanics based damage model

The incremental sheet forming (ISF) process is considered as a feasible solution for forming a variety of small batch and even customised sheet components. The quality of an ISF product is affected by various process parameters, e.g. sheet material, step-down, feed rate, tool diameter and lubricant. To produce an ISF part of sufficient quality and accuracy without defects, optimal parameters of the ISF process should be selected. In the present work, experiments and FE analyses were conducted to evaluate the influence of the main ISF process parameters including the step-down, feed rate and tool diameter on the formability and fracture of two types of pure Ti (grade 1 and 2). The Gurson–Tvergaard-Needleman (GTN) damage constitutive model with consideration of stress triaxiality was developed to predict ductile fracture in the ISF process due to void nucleation, growth and coalescence. It was found that the ISF parameters have varying degrees of effect on the formability and fracture occurrence of the two types of pure Ti, and grade 2 pure Ti sheet is more sensitive than grade 1 Ti sheet to the forming parameters due to low ductility

The cohesive band model: A cohesive surface formulation with stress triaxiality

In the cohesive surface model cohesive tractions are transmitted across a two-dimensional surface, which is embedded in a three-dimensional continuum. The relevant kinematic quantities are the local crack opening displacement and the crack sliding displacement, but there is no kinematic quantity that represents the stretching of the fracture plane. As a consequence, in-plane stresses are absent, and fracture phenomena as splitting cracks in concrete and masonry, or crazing in polymers, which are governed by stress triaxiality, cannot be represented properly. In this paper we extend the cohesive surface model to include in-plane kinematic quantities. Since the full strain tensor is now available, a three-dimensional stress state can be computed in a straightforward manner. The cohesive band model is regarded as a subgrid scale fracture model, which has a small, yet finite thickness at the subgrid scale, but can be considered as having a zero thickness in the discretisation method that is used at the macroscopic scale. The standard cohesive surface formulation is obtained when the cohesive band width goes to zero. In principle, any discretisation method that can capture a discontinuity can be used, but partition-of-unity based finite element methods and isogeometric finite element analysis seem to have an advantage since they can naturally incorporate the continuum mechanics. When using interface finite elements, traction oscillations that can occur prior to the opening of a cohesive crack, persist for the cohesive band model. Example calculations show that Poisson contraction influences the results, since there is a coupling between the crack opening and the in-plane normal strain in the cohesive band. This coupling holds promise for capturing a variety of fracture phenomena, such as delamination buckling and splitting cracks, that are difficult, if not impossible, to describe within a conventional cohesive surface model. © 2013 Springer Science+Business Media Dordrecht