Ductile failure of cylindrically porous materials. Part I: plane stress problem and experimental results

The ductile failure of porous metallic materials is studied here using the lower and upper bound methods of Limit Analysis (LA), a problem treated by Gurson with his famous kinematical approach in 1977. The present work is devoted to determining the strength of porous materials with long circular cylindrical cavities in the case of plane stress. The numerical methods developed here use the Hill–Mandel method based on the homogenization theory of heterogeneous media within the Limit Analysis framework. The use of kinematical and static approaches gave an excellent estimation of the yield criterion for all the cases studied. The existence of a corner of the yield surface on the hydrostatic axis is pointed out, a corner not predicted by the preceding authors, except Rousselier and Ponte Castañeda. The numerical results then are compared with yield domain expressions proposed by different authors and with experimental results of uniaxial tensile strength of aluminum ramdomly perforated sheets. The results show that the Richmond and Smelser model was the most accurate in terms of our predictions. In a companion paper (part II) other cases of symmetry are investigated.