Modeling ductile fracture in ship structures with shell elements

Abstract

Large thin-walled structures provide the means for cost and energy efficiency in structural design. The design of such structures for crash resistance requires reliable FE simulations. In these simulations large plane stress shell elements are used. Simulations require the knowledge of the true stress–strain response of the material until fracture initiation and beyond. Because of the size effect, local material relation determined with experiments is not applicable to large shell elements. The mesh size dependency arises because of the high stress and strain gradients preceding the ductile fracture of metals. Essentially, plane stress shell elements require the equivalent average plane stress material curve. The fact that the stress state in the material affects the fracture ductility further complicates the analysis. This thesis investigates the damage process of shell elements under multi-axial tension. Emphasis is placed on the combined effects of stress state and element size. A novel numerical approach is presented that provides an equivalent plane stress material curve up to the point of fracture initiation for large shell elements under multi-axial tension loading. The fracture initiation strain is found to scale in combination with stress state and element size. Mesh size dependence is shown to be weaker in plane strain and equi-biaxial tension than in uniaxial tension. Simulations employing this scaling yield very good convergence in panel analysis with different mesh densities. The results also demonstrate that the equivalent plane stress material curve is of a softening type. Softening characterizes consecutive stages of the damage process in large elements: necking, fracture initiation, and propagation. A method is presented to calibrate the damage parameters describing softening for the tearing type of crack propagation under in-plane loading. The damage parameters depend on element size and on the failure mode; that is, how the fracture initiates and under which conditions the crack starts to propagate. The softening model calibrated for stiffened panels is used to simulate a ship collision accident. The simulations showed that softening effectively reduces the mesh dependency. However, it is very complicated to define proper calibration parameters a priori for real structures. Therefore, in crashworthiness analysis where importance is on absorbed energy of the structure, fracture models based on sudden element deletion remain attractive for practical engineering work. The presented fracture modeling approach is applicable to slender shell structures in which fracture initiation and tearing in membrane state dominate the structural response. Approach should be extended for bending dominated problems and other materials such as welds in the future.