PLASTIC POTENTIAL AND YIELD FUNCTION OF POROUS MATERIALS WITH ALIGNEDAND RANDOMLY ORIENTED SPHEROIDAL VOIDS

Based on an energy approach, the plastic potential and yield function of a porous material containing either aligned or randomly oriented sp heroidal voids are developed at a given porosity and pore shape. The t heory is applicable to both elastically compressible and incompressibl e matrix and, it is proved that, in the incompressible case, the theor y with spherical and aligned spheroidal voids also coincides with Pont e Castaneda's bounds of the Hashin-Shtrikman and Willis types, respect ively. Comparison is also made between the present theory and those of Gurson and Tvergaard, with a result giving strong overall support of this new development. For the influence of pore shape, the yield funct ion and therefore the stress-strain curve of the isotropic porous mate rial are found to be stiffest when the voids are spherical, and those associated with other pore shapes all fall below these values, the wea kest one being caused by the disc-shaped voids. The transversely isotr opic nature of the yield function and stress-strain curves of a porous material containing aligned pores are also demonstrated as a function of porosity and pore shape, and it is further substantiated with a co mparison with an exact, local analysis when the void shape becomes cyl indrical.