Statistical Strength Measurements of Steel as Applied to Computational Statistically Compensated Fracture and Fragmentation Calculations

The fracture and fragmentation of materials subjected to high strain rate loading is a relevant topic for explosively driven metals, high velocity impacts and other high stress-rate and strain-rate loading events. Metals possess a microstructure whose details create variations in material properties such as strength. The same material microstructure also produces complex damage mechanisms which may lead to macroscopic failure. Ultimately these variations influence the formation of fragments at the macroscopic level. The spatial scale of the microstructure is on the order of micrometers and is not readily accessible to current computational tools and resources for system level calculations. Rather than explicitly model the microstructure, one can attempt to simulate the effects of material non-homogeneity through the use of a statistical description of mechanical properties, of strength, failure or other relevant state descriptions of the model's dependent variables. For the current analysis, a statistical variation was applied to the yield stress. This variation was based upon multiple Rockwell hardness tests which measure strength on the order of 1 mm. This is a length scale which is consistent with the calculation spatial discretization. Fully coupled Euler-Lagrange calculations were performed of a fluid filled steel cylinder impacted by an aluminum spherical projectile. A Weibull distribution of yield stress was applied to the steel cylinder to simulate the heterogeneous nature of the steel. Calculation results were compared to test data to assess the validity of this technical approach as a predictive capability for fracture and fragmentation.