Modeling of sheet metal fracture for shell finite elements with component level validation

Abstract

Ductile fracture causing premature failure of parts during forming and crash has become an important factor limiting design of car bodies. The increasing usage of advanced high strength steels and other lightweight materials to meet ever-stringent standards on passenger safety and gas emissions makes related advances in experimental and computational mechanics a pressing issue. The industry has been using shell finite elements in design practice due to many practical advantages over solid elements. A constitutive assumption of the plane stress condition in shell elements, violated after the onset of localized necking, is responsible for an inaccurate numerical prediction of mechanical response with mesh-size sensitivity. This thesis proposes a new approach to predict ductile failure with shell elements. It is based on the concept of a Domain of Shell-to-Solid Equivalence (DSSE) in conjunction with the Hosford-Coulomb (HC) fracture initiation model. The latter is a micro-mechanically motivated phenomenological model for solid elements. DSSE is the domain in which shell element solutions are valid and comparable to solid elements. Consequently, it is appropriate to apply the HC model within DSSE. On the other hand, a shell element loses its reliability when exiting DSSE, thus being removed from the rest of a finite element model. A general shape of a localization locus that demarcates DSSE for proportional membrane loading is identified through a Marciniak-Kuczynski type localization analysis. The locus is successfully fitted by a mathematical form of the HC model, and a model parameter is simply determined by the Considére criterion. DSSE is then extended towards non-proportional and combined membrane and bending loading. The DSSE-HC model for shell elements covers three types of ductile failure observed in sheet metals: (1) in-plane shear localization, (2) biaxial fracture not preceded by localized necking, aka surface cracking, and (3) biaxial fracture in consequence of localized necking. Validation is made in two steps. First, the model accuracy is evaluated purely numerically, compared to solid elements. Secondly, a comprehensive experimental validation is performed at both specimen and structural levels. The former covers membrane stretching, stretch bending, pure bending, and in-plane shear. The latter is concerned with triangular cup-drawing.