Identical probability distribution of first-ply failure strains and design allowables computation based on multi-sample data of composite laminates

Abstract

Design allowables are of great importance in designing composite structures. The design allowables of conventional metallic materials are easy to obtain. The design allowables of composite materials are generally calculated from the experimental data by using statistical methods. If the test data from different laminates are used as different samples, a great number of tests should be made to get reasonable allowables, or the size of each sample will be very small. A small sample size will result in overly conservative design allowables which may impose an unreasonable weight penalty on the design. Previous studies show that the first-ply failure (FPF) strains of composite laminates are almost the same for those laminates containing the same “weakest” ply. This paper analyzes the identity of the probability distribution of the FPF strains. The FPF strains of Pi 4 symmetric composite laminates containing 90 ° plies are theoretically and experimentally studied. A nonparametric test is made to verify the hypothesis that the experimental data of these laminates are drawn from an identical population. The theoretical discussion and nonparametric test show that the FPF strains of these laminates usually have the same distribution, and the experimental data can be regarded as the observations from a single sample. Statistical methods for computing design allowables based on multi-sample data are discussed for the following two cases: (1) the multi-sample data can be used as a single sample or (2) these data cannot be regarded as being from a single sample.