THE BROWNIAN BASED APPROACH APPLIED TO A LIMITED SAMPLE SIZE FOR BALLISTIC RESISTANCE EVALUATION: TWO EXPERIMENTAL DATABASES

The field of penetration mechanics covers studies related to materials behavior under impact loading. Usually, the assessment of the ballistic resistance makes use of the V₅₀, the bullet impact velocity with 50 percent probability of perforation of the tested target. However, the estimation of the entire curve of the perforation probability is frequently solicited. Recently, a stochastic model based on the Brownian motion concept has been proposed for that goal. The bullet motion within the target was represented as a stochastic differential equation using the bullet deceleration and a diffusion coefficient. In this paper, the maximum likelihood inference is developed for the estimation of the model parameters. This inference is applied to the complete database (581 observations) and a sample of 20 observations. In both cases, the perforation probability curve is consistent with the confidence intervals on the experimental estimations. The obtained results show that the likelihood inference extends the application of this approach to experimental samples with limited size. In addition, the proposed inference technic is applied to a second experimental database of ballistic impacts to validate the applicability of the proposed modelling methodology using the likelihood inference to various impact cases.