Abstract
This paper investigates two critical issues, namely propagation of multi-scale uncertainty, and selection of failure criteria, related to reliability analysis of composites by using multi-scale methods. Due to the multi-scale architecture of composites, uncertainties exist in both microscale and macroscale parameters. It is necessary, therefore, to consider random variables at various length scales to ensure accurate estimates of the reliability of composites. Three types of homogenization methods, namely rule of mixtures, Mori–Tanaka and computational homogenization, are adopted to link these two scales, and to propagate uncertainty from micro to macro scales. By integrating these homogenization methods with the stochastic finite element method and structural reliability methods, the reliability of composites can be investigated with a limit state function based on a chosen failure criterion. This multi-scale reliability analysis procedure has been applied to analyse laminated fibre reinforced composites made of AS4/3501 carbon/epoxy. Firstly, a comparative study has been conducted to evaluate the performance of the assumed homogenization methods for the reliability of composites, and to identify advantages compared with a single scale analysis. The results show that multi-scale analysis can provide more accurate reliability estimates. Secondly, several popularly used failure criteria for composites have been compared using multi-scale reliability analysis.
Highlights
The trend towards the increasing use of composites is being seen in diverse industries including aerospace, automotive, marine and construction
As one of the 19 leading failure criteria used in the worldwide failure exercises, Tsai–Wu failure criterion presented in [25,26] shows good performance [18]
The commonly used Monte Carlo Importance Sampling (MCIS) is combined with the described multi-scale finite element method to estimate the probability of failure, which is served as a benchmark to verify the FORM based reliability calculation
Summary
The trend towards the increasing use of composites is being seen in diverse industries including aerospace, automotive, marine and construction. Multi-scale modelling methods are ideal tools to link micro-scale parameters with macro-scale parameters and to propagate uncertainties from micro-scale to macro-scale [6,7] They have demonstrated their capability to provide sufficiently accurate structural performance simulations due to the fact that it does not require any assumption on the constitutive model at ply level. Different homogenization methods including rule of mixtures, Mori–Tanaka and computational homogenization have been adopted to link micro-scale parameters with macro-scale parameters and propagated uncertainties from micro to macro These methods have been integrated with stochastic finite element method and structural reliability method to conduct reliability analysis for composites. A comparative study of some frequently used failure criteria has been performed from a structural reliability analysis perspective This has been conducted by using computational homogenization method based multi-scale reliability analysis. Failure criteria can be broadly classified into two groups according to whether failure modes are separated or not
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