A statistical approach for failure analysis involving uncertainty in determining ply orientation

Abstract This article presents the uncertainty of the part performance due to the estimated ply orientations of a carbon fiber laminate inspected using ultrasound inspection. Recent developments to quantify the orientation using ultrasound inspection is accurate to within for each lamina. The research presented in the current work statistically analyzes the impact this uncertainty in measurement has on the resulting expected failure envelope using two different analytical methods: (1) Monte‐Carlo (MC) simulation approach extending classical laminate theory and (2) Closed form approach of Mean Value First Order Second Moment method based on derivatives of failure envelope as a function of lamina orientation. The results are validated against a commercial finite element‐based MC simulation approach. The Tsai‐Wu failure criteria is implemented to determine the first ply failure stresses by applying a variety of planer loads to form the failure envelope for a given layup sequence of a carbon fiber reinforced polymer laminate. In this article, using stochastic simulations, the failure envelope is no longer deterministic but is stochastic in nature and converts the reporting from a deterministic factor of safety concept to a probability of failure for a given loading state. The analysis is visualized and quantified using the cumulative‐density‐function (CDF), which demonstrates the similarity between the stochastic results and the classical deterministic approach. To demonstrate a possible end use of the presented statistical analysis, a study of a woven composite laminate is presented where the ply orientation is estimated using ultrasound and the resulting CDF of failure is presented. Highlights Statistical analysis (Monte‐Carlo, mean value, first order, second moment) on the ply orientation variability via ultrasound inspection. Statistical analysis of classical laminate theory and FE based Tsai‐Wu failure model is developed and compared. Tsai‐Wu failure envelope is quantified and visualized using cumulative density function.