Numerical analysis of fracture toughness in tessellated materials by continuous distributed dislocation technique

Abstract

In this study, a plane-packed tessellated structure that models the natural structure of living organisms is investigated to find an alternative material that is tougher than currently used materials such as ceramic matrix composites. We generalize a method for generating a plane-packed tessellated structure of a regular polygon with n tips, and develop a numerical procedure for analyzing the stress field in the tessellated structure based on the continuous distributed dislocation (CDD) method. The effects of n and the loading direction, which is defined as the azimuthal angle measured from the side of the polygon, on the fracture toughness values are examined using the fractal dimension D. It is revealed that the crack propagation path deflects significantly as the loading angle approaches the value of 2-nπ/2n. The deflected crack shape is also characterized using D. It is discovered that D and the fracture toughness value vary with similar trends with the loading angle. The relationship between the polygon shape and loading angle shows that the fracture toughness increases with D, which characterizes the complexity of the crack path, and the number of vertices in the polygon. Therefore, it can be concluded that controlling D and the plane geometry can effectively improve the fracture toughness of materials.