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On the fracture toughness of polymeric nanocomposites: Comprehensive stochastic and numerical studies

  • Polymeric nanocomposites (PNCs) are considered for numerous nanotechnology such as: nano-biotechnology, nano-systems, nanoelectronics, and nano-structured materials. Commonly , they are formed by polymer (epoxy) matrix reinforced with a nanosized filler. The addition of rigid nanofillers to the epoxy matrix has offered great improvements in the fracture toughness without sacrificing other important thermo-mechanical properties. The physics of the fracture in PNCs is rather complicated and is influenced by different parameters. The presence of uncertainty in the predicted output is expected as a result of stochastic variance in the factors affecting the fracture mechanism. Consequently, evaluating the improved fracture toughness in PNCs is a challenging problem. Artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS) have been employed to predict the fracture energy of polymer/particle nanocomposites. The ANN and ANFIS models were constructed, trained, and tested based on a collection of 115 experimental datasets gathered from the literature. The performance evaluation indices of the developed ANN and ANFIS showed relatively small error, with high coefficients of determination (R2), and low root mean square error and mean absolute percentage error. In the framework for uncertainty quantification of PNCs, a sensitivity analysis (SA) has been conducted to examine the influence of uncertain input parameters on the fracture toughness of polymer/clay nanocomposites (PNCs). The phase-field approach is employed to predict the macroscopic properties of the composite considering six uncertain input parameters. The efficiency, robustness, and repeatability are compared and evaluated comprehensively for five different SA methods. The Bayesian method is applied to develop a methodology in order to evaluate the performance of different analytical models used in predicting the fracture toughness of polymeric particles nanocomposites. The developed method have considered the model and parameters uncertainties based on different reference data (experimental measurements) gained from the literature. Three analytical models differing in theory and assumptions were examined. The coefficients of variation of the model predictions to the measurements are calculated using the approximated optimal parameter sets. Then, the model selection probability is obtained with respect to the different reference data. Stochastic finite element modeling is implemented to predict the fracture toughness of polymer/particle nanocomposites. For this purpose, 2D finite element model containing an epoxy matrix and rigid nanoparticles surrounded by an interphase zone is generated. The crack propagation is simulated by the cohesive segments method and phantom nodes. Considering the uncertainties in the input parameters, a polynomial chaos expansion (PCE) surrogate model is construed followed by a sensitivity analysis.

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Document Type:Doctoral Thesis
Author: Khader M. Hamdia
DOI (Cite-Link):
URN (Cite-Link):
Series (Serial Number):ISM-Bericht // Institut für Strukturmechanik, Bauhaus-Universität Weimar (2018,4)
Referee:Professor Klaus GürlebeckGND, Prof. Dr. Roberto BrighentiORCiD
Advisor:Professor Timon RabczukORCiDGND
Date of Publication (online):2018/07/12
Date of first Publication:2018/07/12
Date of final exam:2018/04/20
Release Date:2018/07/12
Publishing Institution:Bauhaus-Universität Weimar
Granting Institution:Bauhaus-Universität Weimar, Fakultät Bauingenieurwesen
Institutes:Fakultät Bauingenieurwesen / Institut für Strukturmechanik
Tag:Bayesian method; Fracture mechanics; Phase-field modeling; Polymer nanocomposites; Uncertainty analysis
GND Keyword:Bruch; Unsicherheit; Rissausbreitung; Bayes; Sensitivitätsanalyse
Dewey Decimal Classification:600 Technik, Medizin, angewandte Wissenschaften / 620 Ingenieurwissenschaften
500 Naturwissenschaften und Mathematik / 510 Mathematik / 518 Numerische Analysis
BKL-Classification:31 Mathematik / 31.73 Mathematische Statistik
51 Werkstoffkunde / 51.32 Werkstoffmechanik
Licence (German):License Logo Creative Commons 4.0 - Namensnennung-Keine kommerzielle Nutzung-Weitergabe unter gleichen Bedingungen (CC BY-NC-SA 4.0)