Porosity effect on the constitutive model of porous material under nanoindentation

Porosity is an important factor for porous medium materials and can influence the dominant mechanisms of material properties, such as hardness and elastic modulus, and also the induced stress field. This study aims to investigate the influence between porosity and some important material properties by performing finite element (FE) simulations of nanoindentations with a spherical indenter. To clarify the mechanical effects induced by porosity, the continuum-based constitutive model has to be enriched and therefore the numerical model is modified to implicitly take into account the porous characteristics of materials of interest. In this study, the Gurson's model is employed to incorporate porosity into the constitutive equations. By developing a user-defined material subroutine in ABAQUS, the relationship between porosity and stress tensor can be intrinsically described. Moreover, two dimensional finite element models are established to simulate the mechanism behavior of porous materials in nanoindentation tests. In addition, both loading and unloading steps are performed in finite element analysis to simulate the actual behavior of porous materials in nanoindentation tests. Based on the comparison with dense material, the effects of porosity on the dominant mechanisms of material properties are investigated. By extracting the stress-strain relationship under uniaxial loading, the constitutive response of materials with different porosities is formulated by using a power-law model. With a dense elastic material, the proposed FE model is validated against the Hertz solution. The numerical predictions agree with the analytical solutions. By revisiting the accuracy of Gurson's model, some discussions were made on the advantages and disadvantages of 2-dimensional FE models to simulate the deformation behaviour of porous material under nanoindentation. Some parametric studies on porosity and mechanical strength are performed. Finally, how the porosity influences the material properties is quantitatively illustrated with some conclusions.