An Empirical Approach To Estimate The Uncertainty Of Ballistic Limit Equations
- Paper number
IAC-07-A6.4.08
- Author
Dr. Alessandro Francesconi, University of Padova, Italy
- Coauthor
Dr. Daniele Pavarin, CISAS G. Colombo Center of Studies and Activities for Space, University of Padova, Italy
- Coauthor
Dr. Cinzia Giacomuzzo, University of Padova, Italy
- Coauthor
Mr. Alberto Bettella, University of Padova, Italy
- Coauthor
Prof. Francesco Angrilli, University of Padova, Italy
- Year
2007
- Abstract
The probability of failure of space structures exposed to the impact with micrometeoroid and orbital debris (M/OD) is usually computed by dedicated risk assessment tools, which estimate the number of impact events that can produce a specified level of damage on selected spacecraft components. Such tools employ models of the M/OD environment and require the knowledge of the spacecraft geometry, attitude and orbit. Moreover, the response of structural constituents to hypervelocity impacts (HVI) should be known quantitatively through the specification of special relations named Ballistic Limit Equations (BLE). In the usual practice, BLE are obtained from a series of HVI experiments which provide a penetration-no-penetration information for the structure under test, with no statistic approach. In other words, BLE are derived by simply drawing lines of demarcation between fail and no-fail operating regions, without any possibility of following the damage evolution between different working conditions. As a consequence, it is not possible to specify the uncertainty bounds associated to the BLEs and no confidence intervals can be provided together with the risk predictions, whose reliability is dramatically affected by the inaccuracy of the equations. This paper presents a possible procedure to statistically derive the BLEs, starting from experiments in which the evolution of a damage parameter related to the failure is investigated. For a given structural configuration, such a parameter is measured in different experimental conditions and hence the critical value that it assumes when failure just occurs is known together with its measurement uncertainty. On the other hand, the same measures are used to develop an empirical model (Damage Predictor Equation, DPE) to describe the variation of the damage parameter, even across failure conditions. The comparison of the DPE with the critical value of the parameter above determined finally allows the evaluation of the BLE together with its confidence bounds. Two test cases are reported to show the application of the outlined procedure to situations of practical interest: BLEs are derived for both single wall composite plates and dual wall metallic Whipple Shields. In both cases, failure equations are evaluated and their uncertainty margins are specified.
- Abstract document