Averting Microstructural Inhomogeneities: A Probabilistic Framework for Elastic Modulus Prediction in Metal Matrix Nanocomposites

Abstract

In this article, a comprehensive study of the elastic modulus of metal matrix nanocomposites (MMNCs) that accounts systematically the influence of the presence of pores and aggregates of nanoparticles. A very effective micromechanical modelling technique was developed. The empirical correlations described the controlling effects of the microstructural features on the stiffness reduction in terms of numbers. The results of the study show that the porosity as well as the clustering of particles, both reduce the effective elastic modulus significantly, primarily due to the increased stress concentration zones and reduction in load transfer paths. The model is checked using the models and data sets used in the experiments. It has been shown to have high prediction accuracy for a broad spectrum of MMNC formulations. In order to cope with the inherent material variability a complementary probabilistic assessment was conducted. Monte Carlo simulations, empirical cumulative distribution functions (ECDFs) and reliability assessments were used to statistically distribute the effective modulus values. The analysis estimates the probabilities of reaching design goals and systematically correlates the dispersion of the modulus with failure probabilities. In this study, a deterministic model and a probabilistic risk analysis are performed together, aiming to present a reliable and performance-oriented framework for the design of MMNCs which was applied to an advanced structural system. The presented combined deterministic and probabilistic framework is realistic and risk-informed and serves as a basis for the structural design of the high performance MMNCs, thus moving the material reliability towards critical applications.