Development of yield criteria for describing the behavior of porous metals with tension-compression asymmetry

A significant difference between the behaviors in tension versus compression is obtained at the polycrystal level if either twinning or non-Schmid effects are included in the description of the plastic deformation at the single crystal level. Examples of materials that exhibit tension-compression asymmetry include hexagonal close packed (HCP) polycrystals and intermetallics (e.g., molybdenum compounds). Despite recent progress in modeling the yield behavior of such materials, the description of damage by void growth remains a challenge.;This dissertation is devoted to the development of macroscopic plastic potentials for porous metallic aggregates in which the void-free, or matrix, material displays tension-compression asymmetry. Using a homogenization approach, new analytical plastic potentials for a random distribution of voids are obtained. Both spherical and cylindrical void geometries are considered for void-matrix aggregates containing an isotropic matrix, while spherical voids are considered for the case of an anisotropic matrix material. The matrix plastic behavior in all cases is described by a yield criterion that captures strength differential effects and can account for the anisotropy that may be exhibited in the void-free material.;For the case when the matrix material is isotropic, the developed analytical potentials for the void-matrix aggregate are sensitive to the second and third invariants of the stress deviator and display tension-compression asymmetry. Furthermore, if the matrix material has the same yield strength in tension and compression, the developed criteria reduce to the classical Gurson criteria for either spherical or cylindrical voids. It has also been demonstrated that the developed isotropic criterion for porous aggregates containing spherical voids captures the exact solution of a hollow sphere loaded in hydrostatic tension or compression. Finite element cell calculations with the matrix material obeying an isotropic yield criterion and displaying tension-compression asymmetry were performed and the comparison between finite element calculations and theoretical predictions demonstrate the versatility of the proposed formulations.;A new anisotropic potential for the porous aggregate was also developed for the case when the matrix material is anisotropic and displays tension-compression asymmetry. If the matrix is isotropic, the proposed analytical anisotropic criterion reduces to the isotropic criterion developed in this dissertation for a void-matrix aggregate containing spherical voids. Comparison between finite element calculations and theoretical predictions show the predictive capabilities of the developed anisotropic formulation. The yield criteria developed in this dissertation are the only criteria available to capture the influence of damage by void growth in HCP metals and other materials that exhibit tension-compression asymmetry.