Probabilistic Multi-Scale Damage Tolerance Modeling of Composite Patches for Naval Aluminum Alloys

The Office of Naval Research (ONR) Structural Reliability Program strives to assure “successful performance of a ship hull structure over its intended life. ” Due to loading and structural degradation given extreme operating environments, ship hulls may require repair or reinforcement during their lifetimes. One type of modification with a proven service record is to adhesively bond a composite overlay onto the metallic structure. (The system of a composite overlay bonded to an aluminum substrate is herein defined as a hybrid structure.) While in-service demonstration of this repair method establishes its successful application to ship structure, our understanding of the complex damage tolerance behavior and structural performance of these hybrid structural systems is lagging behind the implementation, as are standard reliability-based design procedures. Therefore, composite overlays are currently installed only as temporary repairs, and a thorough understanding of hybrid structure behavior under service loading and its long term performance is necessary to enable its reliable and widespread implementation. To investigate the reliability of hybrid structure, it is necessary to consider multiple damage mechanisms, including the progressive failure of the composite overlay, and the interactions between the damage mechanisms when predicting damage initiation and propagation in the hybrid structure. Additionally, the effects of the many complex sources of error, such as epistemic, aleatoric, and experimental uncertainty as well as model form error, must be evaluated and quantified. Performing physical experiments to carry out a comprehensive damage tolerance study that includes all potential configurations, sources of uncertainty, damage mechanisms, and loading conditions is prohibitive. Numerical modeling offers an alternative method to efficiently explore designs and investigate the effects of parameters on hybrid structure after validating a baseline model through experimental testing. Given the many types of damage mechanisms that affect the damage tolerance of hybrid structure, there is no single numerical method capable of accurately simulating all mechanisms simultaneously with the required fidelity level and within a feasible amount of computation time. Therefore, multi-scale modeling with varying levels of fidelity at each scale is required to develop the capability to comprehensively investigate the damage tolerance of hybrid structure. The goal of this research is to overcome many of these challenges through the development of multi-scale, physics-based models and methodologies that predict the damage tolerance and performance of hybrid structures. Through distinct models, customized for particular damage mechanisms, this approach captures widely varying physics, making it advantageous for complex problems such as hybrid structure performance. This effort integrates computational simulation at multiple scales with concurrent experimental testing to obtain material properties, fill in knowledge gaps pertaining to damage initiation and propagation, and provide validation data. Sensitivity analysis identifies the most influential parameters to patch performance enabling Navy implementation of this knowledge for effective design and optimization of patch configuration. Fundamental knowledge at multiple scales, informed by this research initiative, improve the understanding and guided efforts for reliable use of this repair technique. The technical approach consists of three concurrent and integrated components throughout the entire research effort: modeling and simulation (M&S) to develop predictive models and methodology across multiple scales, sensitivity analysis to identify the most influential parameters on damage tolerance performance, and experimental testing for characterization and model validation. The multi-scale models and methodology include the damage mechanisms of interlaminar and intralaminar composite overlay damage, plasticity, sensitization and crack growth in the metal, as well as disbond at the metal/polymer interface. Computational methodology encompasses both first principle calculation and numerical methods including Density Functional Theory (DFT), Peridynamics (PD), and Finite Element (FE) Analysis. Top down engineering requirements inform bottom up physics-based modeling and methodology development to simulate material science properties and structural performance. Computational model development, experimental testing, and sensitivity analysis was performed concurrently at all scales to account for the many types of parameter uncertainty, including model form error, experimental error, epistemic uncertainty, and aleatoric uncertainty, and to determine parameter influence on individual damage mechanisms as well as global damage tolerance. While this approach was demonstrated to be efficient and resulted in plug and play models that enable the evaluation of varying scenarios, several significant outcomes and recommendations should be considered in future work: • The parameter space is expansive, complex, and non-linear making it prohibitive, even with supercomputing resources, to build accurate surrogate models that encompass the entire space. Sensitivity analysis is also challenging given the difficulty in generating a surrogate model and the massive amount of sample data necessary to calculate converged data-driven Sobol Indices. Methodology to map the entire parameter space is needed to identify the dominant damage mechanisms and corresponding sensitive parameters in subspaces and their locations in the global space as well as the transitions between subspaces. • Damage should be quantified by the amount of energy absorbed by each individual damage mechanism and these values used to map out the parameter space. This information is readily extracted from the computational results, and damage energy can be correlated to the physical amount of damage in the structure. A maximum allowable amount of energy can then be set for each type of damage to ensure reliable patch performance. • One significant limitation in this research that must be considered in design, analysis, and future work is that all variables were defined as independent in the sensitivity analysis. Parameter correlation and dependency is inherent in this problem and must be investigated for improved implementation of sensitivity analysis results into design, analysis, and optimization procedures. • This study evaluated Sobol Indices for first order and total effects and identified parameters with a significant difference between the two. Higher order effects calculations using chosen parameter combinations are then needed to identify the interacting parameters. An efficient method to systematically identify these interacting parameter combinations is needed. Table of