Non-linear buckling analysis of GFRP plates

Abstract

Fiber Reinforced Polymer (FRP) has increased rapidly in popularity in the past few decades. The material's advantageous properties, such as a high strength-to-weight ratio and low required maintenance, gave rise to its popularity in multiple major engineering branches. Buckling behaviour develops due to the notably low stiffness-to-strength ratio and the usual high slenderness of FRP plates. The occurrence of initial imperfections increases the tendency of the material to buckle. The load-carrying capacity of structures with post-buckling behaviour can be determined with progressive failure analysis, which requires a damage model that characterises the onset and evolution of damage. In Abaqus, the Hashin damage model is implemented by default, which considers the four failure modes of the material. Numerical analysis of strain-softening materials with local damage leads to deformation localisation in a single element: a finer mesh will decrease the amount of energy dissipated. To prevent this localisation into arbitrarily small regions, the stress is related to the deformation of a finite volume. The damage evolution is described with a stress-displacement response instead of a stress-strain response. The energy needed to open a unit area of the crack, the fracture energy, is defined as a material parameter and depends on the mesh size of the model. The assessment of fracture energy properties in composite materials is challenging due to specimen geometry and fibre lay-up, and accurate data of GFRP fracture energy is largely unknown. When no actual post-failure behaviour is acquired, the lower bound fracture energy can be determined from the material properties. Numerical analysis of uni-directional coupon experiments is performed to determine the input values and response of the lower bound fracture energy. The lower bound fracture energy implementation results in an abrupt drop in stress when the material strength is reached. Increasing the lower bound fracture energy by a minimum of 2% prevented numerical inconsistencies. Progressive failure analysis of multi-directional coupon experiments validated an increase of 10% for the lower bound values. The use of lower bound fracture energy for non-linear buckling analysis is verified with progressive failure analysis of the buckling experiments. The lower bound fracture energy, increased by 10%, approximates the ultimate strength of six tests with an average difference of 7.7%. To analyse the non-linear buckling behaviour of a GFRP plate, a buckling curve is created by varying the plate thickness. The influence of geometric imperfections on a plate's buckling strength is studied by applying different initial imperfections. Two types of boundary conditions are used to analyse if they result in a different buckling curve. A difference in the buckling strength reduction factor of 0.1 is found. Initial imperfections reduce the buckling strength of the material, which is most apparent for plate slenderness around 1.0. An initial imperfection of B/125 resulted in a 40% strength reduction compared to the elastic buckling strength. The average difference in reduction factor between an initial imperfection of B/1000 and B/125 was 16%, with a maximum difference of 26%.