Void nucleation is studied both experimentally and computationally with the aim of identifying a macroscopic criterion for nucleation by particle cracking. Three types of circumferentially notched cylindrical specimens made of a low-alloy steel were used, in order to vary the stress triaxiality in the notch region. The tensile tests were interrupted at various loads below the fracture load. The specimens were sectioned parallel to the loading axis, and the locations of cracked and uncracked titanium-nitride inclusions were identified. No evidence was found of void nucleation by inclusion debonding. Finite-element calculations were carried out for each specimen geometry using conventional isotropic-hardening plasticity theory. The ability of various potential void-nucleation criteria to predict the onset of void nucleation by inclusion cracking is explored.References 8, 21 through 23, 32 through 34, 37, and 38. In steels, most studies found that microvoids first form around ellipsoidal MnS inclusions in the steels through debonding of the steel-sulfide interface. Two reasons have been suggested to explain why these interfaces are so weak. One is that the difference in the coefficient of thermal expansion between these inclusions and the matrix is such that this interface is in tension. [35] The other is that sulfur segregated to this interface weakens it. [36] A significant amount of research has also addressed the issue of how these large voids link up to cause fracture. Most results indicate that small voids form around the carbides very late in the fracture process, and these small voids help link the large voids formed around the sulfides. [3,28,30,36] In most of these steels, the sulfides are arrayed in the material so that the fracture plane contains the long axis of the ellipsoidal inclusions. Relatively little work has been done for materials in which the long axis is perpendicular to the fracture plane, which would presumably make these inclusions less effective as void nuclei. In addition, there has been relatively less work investigating the role that inclusions other than sulfides play in nucleating the initial microvoids (e.g., References 8 and 23). Cox and Low [30] reported results on an 18-Ni maraging steel in which the nucleating inclusions were titanium carbo-nitrides. They found that these inclusions cracked when a critical stress was reached and that these cracked inclusions nucleated microvoid formation.Various void-nucleation criteria have been proposed based on experimental observations or micromechanical analyses. [34,[39][40][41][42][43] In order to formulate a physically based nucleation criterion, careful attention must be paid to the mechanism by which this process occurs. As suggested earlier, the two most common mechanisms would be either debonding of the interface between the inclusion and the matrix, as has been reported for MnS, or cracking of the second-phase inclusions, which has been reported for the titanium carbo-nitrides in maraging steel or Fe-Si inclusions in aluminum alloys...

Deformations of a planar doubly periodic array of square elastic inclusions in an isotropically hardening elastic-viscoplastic matrix are analysed. The arrays considered have multiple inclusions per unit cell, but in each array all inclusions have the same size. Overall plane strain tension with a superposed tensile biaxial stress is imposed. A finite deformation formulation is used with a cohesive surface constitutive relation describing the bonding between the inclusion and the matrix. A characteristic length is introduced from dimensional considerations since the cohesive properties include the work of separation and the cohesive strength. The system analysed is used to study inclusion distribution effects on void nucleation, with the aim of providing background for incorporating the effect of clustering on void nucleation into phenomenological constitutive relations for progressively cavitating plastic solids. For low values of the triaxiality of the imposed stress state, void nucleation occurs after extensive overall plastic straining and regular distributions have a higher value of the void nucleation strain than random distributions. For larger values of stress triaxiality, where void nucleation occurs at relatively small overall plastic strains, the effect of inclusion size dominates the effect of inclusion distribution and smaller inclusions give rise to higher void nucleation strains. The ability of various scalar measures of clustering to characterize the computed dependence of void nucleation on inclusion distribution is explored. Within the context of a phenomenological description of void nucleation, it is found that the effective void nucleation stress is approximately a linear function of the overall hydrostatic tension with a coefficient 0.40-0.44 for regular distributions and 0.25-0.35 for random distributions. The results also suggest a possible dependence of the effective void nucleation stress on a simple scalar measure of clustering.