Probabilistic Damage Characterization Using the Computationally-Efficient Bayesian Approach

This work presents a computationally-ecient approach for damage determination that quanti es uncertainty in the provided diagnosis. Given strain sensor data that are polluted with measurement errors, Bayesian inference is used to estimate the location, size, and orientation of damage. This approach uses Bayes' Theorem to combine any prior knowledge an analyst may have about the nature of the damage with information provided implicitly by the strain sensor data to form a posterior probability distribution over possible damage states. The unknown damage parameters are then estimated based on samples drawn numerically from this distribution using a Markov Chain Monte Carlo (MCMC) sampling algorithm. Several modi cations are made to the traditional Bayesian inference approach to provide signi cant computational speedup. First, an ecient surrogate model is constructed using sparse grid interpolation to replace a costly nite element model that must otherwise be evaluated for each sample drawn with MCMC. Next, the standard Bayesian posterior distribution is modi ed using a weighted likelihood formulation, which is shown to improve the convergence of the sampling process. Finally, a robust MCMC algorithm, Delayed Rejection Adaptive Metropolis (DRAM), is adopted to sample the probability distribution more eciently. Numerical examples demonstrate that the proposed framework e ectively provides damage estimates with uncertainty quanti cation and can yield orders of magnitude speedup over standard Bayesian approaches

Damage Characterization Method for Structural Health Management Using Reduced Number of Sensor Inputs

The development of validated multidisciplinary Integrated Vehicle Health Management (IVHM) tools, technologies, and techniques to enable detection, diagnosis, prognosis, and mitigation in the presence of adverse conditions during flight will provide effective solutions to deal with safety related challenges facing next generation aircraft. The adverse conditions include loss of control caused by environmental factors, actuator and sensor faults or failures, and damage conditions. A major concern in these structures is the growth of undetected damage (cracks) due to fatigue and low velocity foreign impacts that can reach a critical size during flight, resulting in loss of control of the aircraft. Hence, development of efficient methodologies to determine the presence, location, and severity of damage in critical structural components is highly important in developing efficient structural health management systems

Multiscale Modeling of Structurally-Graded Materials Using Discrete Dislocation Plasticity Models and Continuum Crystal Plasticity Models

A multiscale modeling methodology that combines the predictive capability of discrete dislocation plasticity and the computational efficiency of continuum crystal plasticity is developed. Single crystal configurations of different grain sizes modeled with periodic boundary conditions are analyzed using discrete dislocation plasticity (DD) to obtain grain size-dependent stress-strain predictions. These relationships are mapped into crystal plasticity parameters to develop a multiscale DD/CP model for continuum level simulations. A polycrystal model of a structurally-graded microstructure is developed, analyzed and used as a benchmark for comparison between the multiscale DD/CP model and the DD predictions. The multiscale DD/CP model follows the DD predictions closely up to an initial peak stress and then follows a strain hardening path that is parallel but somewhat offset from the DD predictions. The difference is believed to be from a combination of the strain rate in the DD simulation and the inability of the DD/CP model to represent non-monotonic material response

Strain-Based Damage Determination Using Finite Element Analysis for Structural Health Management

A damage determination method is presented that relies on in-service strain sensor measurements. The method employs a gradient-based optimization procedure combined with the finite element method for solution to the forward problem. It is demonstrated that strains, measured at a limited number of sensors, can be used to accurately determine the location, size, and orientation of damage. Numerical examples are presented to demonstrate the general procedure. This work is motivated by the need to provide structural health management systems with a real-time damage characterization. The damage cases investigated herein are characteristic of point-source damage, which can attain critical size during flight. The procedure described can be used to provide prognosis tools with the current damage configuration

Multiscale Analysis of Structurally-Graded Microstructures Using Molecular Dynamics, Discrete Dislocation Dynamics and Continuum Crystal Plasticity

A multiscale modeling methodology is developed for structurally-graded material microstructures. Molecular dynamic (MD) simulations are performed at the nanoscale to determine fundamental failure mechanisms and quantify material constitutive parameters. These parameters are used to calibrate material processes at the mesoscale using discrete dislocation dynamics (DD). Different grain boundary interactions with dislocations are analyzed using DD to predict grain-size dependent stress-strain behavior. These relationships are mapped into crystal plasticity (CP) parameters to develop a computationally efficient finite element-based DD/CP model for continuum-level simulations and complete the multiscale analysis by predicting the behavior of macroscopic physical specimens. The present analysis is focused on simulating the behavior of a graded microstructure in which grain sizes are on the order of nanometers in the exterior region and transition to larger, multi-micron size in the interior domain. This microstructural configuration has been shown to offer improved mechanical properties over homogeneous coarse-grained materials by increasing yield stress while maintaining ductility. Various mesoscopic polycrystal models of structurally-graded microstructures are generated, analyzed and used as a benchmark for comparison between multiscale DD/CP model and DD predictions. A final series of simulations utilize the DD/CP analysis method exclusively to study macroscopic models that cannot be analyzed by MD or DD methods alone due to the model size

Investigation of Fatigue Crack Initiation and Growth in Cast MAR-M247 Subjected to Low Cycle Fatigue at Room Temperature

MC carbide particles (with Hafnium and/or Tantalum as constituent metallic element, M) were observed to crack extensively in a cast polycrystalline nickel-base superalloy, MAR-M247, when subjected to low-cycle fatigue loading at room temperature. High resolution secondary electron images taken on the surface of a double edge notch test specimen revealed that approximately half the carbide particles cracked in the highly-strained notch section of the specimen. These images further illustrated that the average surface area of cracked particles was approximately three times that of the uncracked particles. Additional analysis illustrated that the cracks within a large number of particles aligned nearly perpendicular to the loading direction. However, high aspect ratio particles (with aspect ratio >3) were prone to incubate cracks aligned along its major axis, independent of the loading direction. Additionally, forward-scattered imaging often showed a high density of slip bands interaction with most of the particles which cracked. The life limiting crack growth in MAR-M247 was observed to be crystallographic in nature, as the crack grew along slip bands as measured by high-resolution electron backscatter diffraction, even after spanning many grains. Statistically representative microstructure models of MAR-M247 were generated and used in the crystal plasticity finite element simulations. As expected, there was a significant variation in the computed stress state among constituent carbide particles. The stress state of the carbide particles was found to be heavily influenced by the stress in surrounding grains and the orientation of the major axis of the particles with respect to applied load direction. For particles that intersect the free-surface, stress was found to be highly concentrated at the free surface and a positive correlation between the magnitude of free-surface area and the maximum principal stress was found. Additionally, high stress concentrations were observed in regions where carbide particles intersect grain boundaries

Scalable Implementation of Finite Elements by NASA _ Implicit (ScIFEi)

Scalable Implementation of Finite Elements by NASA (ScIFEN) is a parallel finite element analysis code written in C++. ScIFEN is designed to provide scalable solutions to computational mechanics problems. It supports a variety of finite element types, nonlinear material models, and boundary conditions. This report provides an overview of ScIFEi (\Sci-Fi"), the implicit solid mechanics driver within ScIFEN. A description of ScIFEi's capabilities is provided, including an overview of the tools and features that accompany the software as well as a description of the input and output le formats. Results from several problems are included, demonstrating the efficiency and scalability of ScIFEi by comparing to finite element analysis using a commercial code

Surrogate Modeling of High-Fidelity Fracture Simulations for Real-Time Residual Strength Predictions

A surrogate model methodology is described for predicting, during flight, the residual strength of aircraft structures that sustain discrete-source damage. Starting with design of experiment, an artificial neural network is developed that takes as input discrete-source damage parameters and outputs a prediction of the structural residual strength. Target residual strength values used to train the artificial neural network are derived from 3D finite element-based fracture simulations. Two ductile fracture simulations are presented to show that crack growth and residual strength are determined more accurately in discrete-source damage cases by using an elastic-plastic fracture framework rather than a linear-elastic fracture mechanics-based method. Improving accuracy of the residual strength training data does, in turn, improve accuracy of the surrogate model. When combined, the surrogate model methodology and high fidelity fracture simulation framework provide useful tools for adaptive flight technology

A Computationally-Efficient Probabilistic Approach to Model-Based Damage Diagnosis

This work presents a computationally-efficient, probabilistic approach to model-based damage diagnosis. Given measurement data, probability distributions of unknown damage parameters are estimated using Bayesian inference and Markov chain Monte Carlo (MCMC) sampling. Substantial computational speedup is obtained by replacing a three-dimensional finite element (FE) model with an efficient surrogate model. While the formulation is general for arbitrary component geometry, damage type, and sensor data, it is applied to the problem of strain-based crack characterization and experimentally validated using full-field strain data from digital image correlation (DIC). Access to full-field DIC data facilitates the study of the effectiveness of strain-based diagnosis as the distance between the location of damage and strain measurements is varied. The ability of the framework to accurately estimate the crack parameters and effectively capture the uncertainty due to measurement proximity and experimental error is demonstrated. Furthermore, surrogate modeling is shown to enable diagnoses on the order of seconds and minutes rather than several days required with the FE model

Probabilistic Prognosis of Non-Planar Fatigue Crack Growth

Quantifying the uncertainty in model parameters for the purpose of damage prognosis can be accomplished utilizing Bayesian inference and damage diagnosis data from sources such as non-destructive evaluation or structural health monitoring. The number of samples required to solve the Bayesian inverse problem through common sampling techniques (e.g., Markov chain Monte Carlo) renders high-fidelity finite element-based damage growth models unusable due to prohibitive computation times. However, these types of models are often the only option when attempting to model complex damage growth in real-world structures. Here, a recently developed high-fidelity crack growth model is used which, when compared to finite element-based modeling, has demonstrated reductions in computation times of three orders of magnitude through the use of surrogate models and machine learning. The model is flexible in that only the expensive computation of the crack driving forces is replaced by the surrogate models, leaving the remaining parameters accessible for uncertainty quantification. A probabilistic prognosis framework incorporating this model is developed and demonstrated for non-planar crack growth in a modified, edge-notched, aluminum tensile specimen. Predictions of remaining useful life are made over time for five updates of the damage diagnosis data, and prognostic metrics are utilized to evaluate the performance of the prognostic framework. Challenges specific to the probabilistic prognosis of non-planar fatigue crack growth are highlighted and discussed in the context of the experimental results