Efficient Risk Assessment Using Probability of Fracture Nomographs

The traditional risk-based design processes involve designing the structure based on risk estimates obtained during several iterations of an optimization routine. This approach is computationally expensive for large-scale aircraft structural systems because of the iterative nature of the risk assessment methods. Therefore, this research introduces the concept of risk-based design plots that can be used for both structural sizing and risk assessment of stiffened plates when maximum allowable crack length information is available. These plots are obtained using normalized probability density functions of load and material properties and are applicable for any arbitrary load and strength magnitudes that follow similar scatter. Risk-based design plots serve as a tool for failure probability assessment given geometry and applied load, or they can determine geometric constraints to be used in sizing, given allowable failure probability. This approach would transform a reliability-based optimization problem into a deterministic optimization problem with geometric constraints that implicitly incorporates risk into the design. Moreover, these plots provide a unique graphical tool to visualize the sensitivity of risk to geometric changes and loading conditions. In situations where crack length is defined as a probability distribution, the presented approach can only be applied for various percentiles of crack lengths. To demonstrate the methodology outlined in this research, a cracked flat and stiffened plate configurations of Aluminum 2024-T3 are investigated using both a Stress Intensity Factor and Cohesive Zone Model approach. This research also presents a material property calibration process for the probabilistic cohesive zone model for Aluminum 2024-T3. In order to demonstrate the robustness of the calibration process, it was also applied to a composite (IM7/977-3) double cantilever beam peel test to capture the scatter in experimental measurements of delamination strength.