Propagation of uncertainty from constituents to structural assessments in composite strength modelling
Résumé
In-service safety and reliable lifetime assessments are key challenges for high performance load bearing applications and require great care to be taken during their design. The design of composite material structures can be assisted by computational models. Many complex computational models have been developed for predicting the failure and lifetime analysis of structures. Critical structures such as high pressure composite cylinders require very accurate computational models, to understand the stochastic nature of the predicted structural response. The following issues limit the use of composite strength models for making reliable structural predictions:
-The complex interaction between the fibres and matrix which governs the failure mechanism has not been accurately incorporated in composite strength models.
-Lack of reliable constituent properties which are used as input for the models.
There are several studies aimed at improving the state-of-the-art models. However, accurate constituent properties to be used as input for these models are rarely available. Authors usually do not comment on the uncertainty of the constituent properties reported, which is of major importance for stochastic simulations. Since fibres are the principal load bearing constituents of unidirectional composites, Islam et al. have quantified the uncertainty in the parameters of the fibre strength Weibull distribution arising during to the characterisation process, using a Monte-Carlo approach to capture the stochastic nature of the fibre strength behaviour. Strength of T700 carbon fibres, popularly used in composite pressure vessels, is used as reference. In this study, the influence of uncertainty in input fibre strength on model predictions has been evaluated. A composite strength model developed at Mines ParisTech was used. This model considers physical processes such as fibre failure and its interactions with the surrounding
matrix. It was first developed in 2005 and has been improved over the years to simulate different loading conditions during service of composite structures such as pressure vessels. The strength and lifetime of a composite structure (coupon) is simulated under two different practical loading conditions (monotonically increasing and sustained loading) to elucidate the sensitivity of different structural responses to the input fibre strength distribution. The calculated uncertainties in the shape (m) and scale (sigma_0) parameters of the fibre strength Weibull distribution were used as input for the models. The results are listed as follows:
1) Monotonic loading:
-The failure stress is seen to be significantly dependent on the scale parameter. The observed variation in the predicted failure stress is about 10% from the mean case, for an uncertainty of 10% in scale parameter.
-The sensitivity of the model predictions to the shape parameter was insignificant.
2) Sustained loading:
-The time to failure of the composite specimen was also found to be strongly affected by uncertainties in the scale parameter. The calculated uncertainty of 10% in the input scale parameter resulted in a variation in the predicted lifetime of about 15-30%.
-The calculated uncertainty of 25% in the shape parameter resulted in a variation of about 16% in the predicted lifetime of the specimen.
The structural behaviour predicted by the model is found to be highly sensitive to the uncertainties in the input fibre strength distribution which arise during characterisation. The understanding of the constituent properties and their characterisation process needs to be improved, in order to improve the reliability of computational model predictions, so that the predictions can be used with confidence in industrial applications.