The Effect of Cellular Structure on the Yield Surface of 2D Metal Foams

Metal foams are a new class of materials with interesting structural properties; however no comprehensive understanding of their inelastic behavior has been established yet. Since the experimental studies of these materials have their own limitations، there is a growing research interest towards the mesostructural modeling of these materials. Accordingly many researchers have been trying to generate realistic and representative numerical models of the foams and prepare computational labs in which different aspects of foams mechanical behavior can be thoroughly investigated. The following three kinds of mesostructures have been commonly employed: (1) models based on a unit cell or a building block، (2) random Voronoi diagrams، and (3) CAD structures provided by the X-ray micro-computed tomography. In the current study، the physically representative circle set Voronoi diagrams are employed to define the geometry of 2D metallic foams. It is assumed that the minimum and maximum radii of the circular generators are 0. 5 and 1. 5 mm، respectively. The first sample is generated using linear distribution of cell size while، compared to the first sample، the second and third specimens have less and more small cells. An extra specimen (the forth sample) is also created with the same structure of the first one unless its edges are straight. In the next step، the FE models of the specimens are created using second order Timoshenko beam elements. Finally، the effects of microstructural features (e. g. strut curvature and cell size distribution) on the initial yield surface، elastic properties، and failure modes of the foams are numerically investigated under various biaxial loading conditions. Displacement-controlled loading is used. A newly energy-based approach developed for the identification of initial yield points has been incorporated. The results show that: (a) the size of the initial yield surface is significantly influenced by the curvature of the cell struts، (b) in the principal stresses space، the initial yield surface is bigger in the tension-tension region، (c) for a constant relative density، the presence of more big cells in a sample increases the size of the yield envelope، and (d) the macroscopic yield properties of the specimens can be interpreted according the microscopic failure mechanisms of the plastic yielding، elasto-plastic buckling، and plastic hinging of the struts. Furthermore، it is found that the previously proposed energy-based method for the identification of yield initiation under multiaxial loading conditions has serious shortcomings and needs revision.