Stochastic J-integral and reliability of composite laminates based on a computational methodology combining experimental investigation, stochastic finite element analysis and maximum entropy method

The present thesis concerns itself with the stochastic fracture behavior and the reliability of laminated composites. A computational approach combining the Stochastic Finite Element Method (SFEM), the Maximum Entropy Method (MEM), and experimental investigation has been developed. Using this approach, the fracture parameters including the Stress Intensity Factor (SIF), the Energy Release Rate (ERR) and the J-Integral have been determined based on the experimental data for the properties of the composite material. The material parameters and the fracture parameters have been quantified in terms of the respective mean values, the standard deviations, the coefficients of variation, and the true analytical probability distributions. For this purpose, the analytical distributions are obtained using the maximum entropy method. The fracture behavior of laminates made of the NCT 301 graphite-epoxy composite material has been studied and further, a parametric study encompassing the effects of the laminate configuration, the number of stochastic simulations, the geometrical parameters of the laminate, and the crack length has been conducted. Relevant design aspects are synthesized based on the parametric study. The significance of the J-Integral in more accurately describing and quantifying the stochastic characteristics of fracture behavior than the ERR and the SIF is established. The formulation for the reliability analysis for the probabilistic design of laminates has been developed based on the interference theory of mechanical reliability. The formulation has been applied for the case of stress-based fracture criterion and demonstrated for the orthotropic laminates made of NCT 301 graphite-epoxy composite material. For this purpose, the fracture toughness values of the orthotropic laminate are obtained from the in-plane fracture toughness tests using Single Edge Notched (SEN) tension specimens of the laminate. Aspects related to the reliability-based probabilistic design are highlighted. Further, the effects of loading on the reliability of the orthotropic laminates are evaluated.