<p>Most predictive impact models are a combination of physics principles and empirically derived constants fit through trial data to represent a specific experimental condition. These models do not sufficiently account for the uncertainty associated with repeated impact loading. The uncertainty in multiple impact events comes from variability in the impact location, affected area after impact, inertia induced fracture, material response to heating, and many other factors. Because of the meaningful uncertainty in multiple impact modeling, it is useful to apply Bayesian updating to formally combine the predictive capacity of an impact model with limited available test data to improve the model’s accuracy for a specific application and better quatify the uncertainty in the estimates. In this report,&nbsp;existing experimental data for impacts of 0.223 caliber ammunition against AR500 steel panels with 2-inch ballistic rubber is used to create a prior distribution for Bayesian updating. The existing data from the U.S. Army Aberdeen Test Center was gathered by shooting a steel plate while cycling through sixteen independent locations until plate failure – as defined by perforation&nbsp;through the steel panel. The total number of shots delivered to the plate was recorded as the number of shots to failure. The prior distribution for Bayesian calibration is formed based on data for the number of impacts at the failure location. Because sixteen independent plate locations were fired on, however, there is useful data from locations where failure was not reached that cannot be incorporated using traditional, frequenist techniques. After creating&nbsp;the prior distribution of plate failure for a range of total impacts based on the number of shots at the failure location, the test data from the locations where failure was not reached is incorporated using Bayes’ Theorem to create a posterior density which represents an updated model for plate failure for the range of total impacts. The posterior density of plate failure strength – measured in number of shots at the failure location – can then be used as one parameter in a model to determine the safe allowable total number of impacts on the target of interest. This future model must also consider parameters such as the distribution of shots across the plate and the area affected by each impact while making assumptions about the practical variability in impact velocity and obliquity. A model of this type will inform decision makers to develop safe inspection criteria and utilize a safe amount of impacts in training for current and future ammunition.</p>

Application of Bayesian Calibration to Improve Multiple Ballistic Impact Modeling

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

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