On the yield criterion of two-scale porous materials by using Eshelby-type velocity field and Steigmann–Ogden surface model

Abstract

In this work, we investigate the yield strength of porous metallic materials in the presence of both microvoids and nanovoids. A two-level hierarchical model composed of both microscopic and macroscopic representative volume elements (RVEs) are proposed for this purpose. The lower level RVE is made up of an incompressible, perfectly elastoplastic, von Mises matrix and multiple dilute nanovoids. By using a micromechanics-based homogenization method, a microscopic yield criterion is first established in terms of the overall equivalent stress, uniaxial yield strength of the microscopic matrix, Gurtin–Murdoch and Steigmann–Ogden nanovoids surface constants, as well as the microscopic porosity. The lower level RVE is then treated as a material point in the upper level RVE matrix. The macroscopic dissipation rate is evaluated from the conventional deviatoric strain rate used in Gurson’s classical criterion, an Eshelby-type exterior velocity field and the compressibility rate of the macroscopic matrix. Closed-form solutions are eventually determined for such a velocity field and the macroscopic yield function, by simultaneously satisfying the arbitrary macroscopic strain rate boundary conditions and enforcing the principle of minimum dissipation rate. Compared to similar criteria available in the literature, two distinct features can be identified. First, the full version Steigmann–Ogden surface model is considered on nanovoids surface. Second, both the hydrostatic and deviatoric deformation of the microvoid are considered in the velocity field. Extensive parametric studies are conducted to investigate the effects of nanovoids surface bulk modulus, surface shear modulus, surface flexural rigidity, nanovoids radius, and both levels of porosities on the macroscopic yield loci. The results obtained in this article are helpful to the better design and manufacturing of nanoporous metallic materials.