Meso-scale modeling of spall in a heterogeneous two-phase material

The influence of the heterogeneous second-phase particle structure and applied loading conditions on the ductile spall response of a model two-phase material was investigated. Quantitative metallography, three-dimensional (3D) meso-scale simulations (MSS), and small-scale spall experiments provided the foundation for this study. Nodular ductile iron (NDI) was selected as the model two-phase material for this study because it contains a large and readily identifiable second-phase particle population. Second-phase particles serve as the primary void nucleation sites in NDI and are, therefore, central to its ductile spall response. A mathematical model was developed for the NDI second-phase volume fraction that accounted for the non-uniform particle size and spacing distributions within the framework of a length-scale dependent Gaussian probability distribution function (PDF). This model was based on novel multi-scale sampling measurements. A methodology was also developed for the computer generation of representative particle structures based on their mathematical description, enabling 3D MSS. MSS were used to investigate the effects of second-phase particle volume fraction and particle size, loading conditions, and physical domain size of simulation on the ductile spall response of a model two-phase material. MSS results reinforce existing model predictions, where the spall strength metric (SSM) logarithmically decreases with increasing particle volume fraction. While SSM predictions are nearly independent of applied load conditions at lower loading rates, which is consistent with previous studies, loading dependencies are observed at higher loading rates. There is also a logarithmic decrease in SSM for increasing (initial) void size, as well. A model was developed to account for the effects of loading rate, particle size, matrix sound-speed, and, in the NDI-specific case, the probabilistic particle volume fraction model. Small-scale spall experiments were designed and executed for the purpose of validating closely-coupled 3D MSS. While the spall strength is nearly independent of specimen thickness, the fragment morphology varies widely. Detailed MSS demonstrate that the interactions between the tensile release waves are altered by specimen thickness and that these interactions are primarily responsible for fragment formation. MSS also provided insights on the regional amplification of damage, which enables the development of predictive void evolution models.