An isotropic multi-surface model of porous material plasticity is derived and employed to investigate the effects of the third stress invariant in ductile failure. The constitutive relation accounts for both homogeneous and inhomogeneous yielding of a material containing a random distribution of voids. Individual voids are modeled as spheroidal but the aggregate has no net texture. Ensemble averaging is invoked to operate a scale transition from the inherently anisotropic meso-scale process of single-void growth and coalescence to some macroscopic volume that contains many voids. Correspondingly, expressions for effective yield and associated evolution equations are derived from first principles, under the constraint of persistent isotropy. It is found that the well-known vertex on the hydrostatic axis either disappears for sufficiently flat voids or develops into a lower-order singularity for elongated ones. When failure is viewed as the onset of an instability, it invariably occurs after the transition to inhomogeneous yielding with the delay between the two depending strongly upon the Lode parameter. The strain to failure is found to be weakly dependent on the Lode parameter for shear-dominated loadings, but strongly dependent on it near states of so-called generalized tension or compression. Experimentally determined fracture loci for near plane stress states are discussed in light of the new findings. © 2021 Elsevier Ltd