Co-authors​ :

 Carl SCARTH (UNITED KINGDOM), Geir OLAFSSON (UNITED KINGDOM), Janice M. DULIEU-BARTON (UNITED KINGDOM), Andrew T RHEAD (UNITED KINGDOM), Richard BUTLER (UNITED KINGDOM) 

Certification of composite aerospace structures is currently undertaken via a series of tests of increasing size and complexity known as a “test pyramid.” Empirical knockdown factors based on coupon test data are used along alongside relatively few tests at higher length-scales, leading to conservative strain limits and reducing the benefits of structural tailoring. Over-dependence on coupon tests may be overcome through virtual testing. Combined data from both computer models and component-level tests are invaluable to such an approach. To ensure consistency when fusing these different sources of data, it is necessary to quantify the effects of myriad sources of uncertainty due to: i) unknown model inputs (e.g. defects/features, boundary conditions, material property variability), ii) experimental observation errors, and iii) model inaccuracy. Bayesian calibration is a statistical framework which enables predictions to be made, informed by both experimental and numerical data, while formally accounting for all the above sources of uncertainty.

Compression testing has been undertaken on a C-spar containing a central recessed, “joggle” feature, intended to promote nonlinear opening of the spar section under loading leading to significant through-thickness stress. Displacement measurements were taken across the outer surface of the spar via stereo Digital Image Correlation (DIC) using the MatchID image acquisition and processing system. In this study, these measurements are used to calibrate a Finite Element model implemented in Abaqus, incorporating both geometric nonlinearity, and uncertainty in the material properties and conditions of the test. A bespoke data alignment and interpolation routine is implemented to enable point-wise comparisons between model output and the DIC (see Fig. 1 for example alignment). Uncertainty in the model inputs is subsequently quantified and reduced through Bayesian inference. The extent to which differences between the model and DIC are due to model discrepancy or experimental observation error, and the associated uncertainty, are also inferred. Preliminary results showing residuals of a calibrated model compared with DIC data for a fixed load are shown in Fig. 2.

The primary contribution of this work is the incorporation of data-rich DIC taken across multiple load increments spanning a full structural test, alongside full-field output of a nonlinear FE model, within a Bayesian calibration framework. This goal is inherently challenging due to the high-dimensional nature of these quantities. By addressing this challenge, key descriptors can be obtained for confidence levels in the accuracy of structural model, which will be crucial for certification driven by virtual testing.