Session: 03-03-01: Integrated Computational Materials Engineering (ICME)

Paper Number: 94753

94753 - Bayesian Analysis of Model Form Probabilities for Crystal Plasticity Models and Assessment of Slip Transfer Relations for Lamellar Grains in α+β Titanium Alloys 

Dual phase α+β Titanium alloys are widely used in aerospace applications as well as in medical implants. In particular, Ti-6Al-4V is commonly used in aerospace structural components due to its high strength-to-weight ratio, corrosion resistance, and high temperature performance. The mechanical properties of lamellar and Widmanstatten morphologies of a+b Titanium alloys is influenced by the mechanical properties of the constituent crystallographic phases in addition to the interactions between the phases. Due to the complex nature of these interactions, several widely disparate crystal plasticity modeling approaches have been proposed to quantitatively assess their mechanical response, all of which utilize certain idealizations to model the interactions at the interface between the two crystallographic phases. Since these idealizations are likely to induce uncertainties and biases in the predicted response, there exists a strong incentive to rigorously identify and assess them in order to aid in their deployment in practical applications. The difficulty in assessing crystal plasticity models for mechanical responses of α-β colonies is exacerbated by the dearth of direct measurements of grain-scale, because of the difficulty of preparing and testing small-scale samples containing a single colony. Our work aims to address the aforementioned gaps by developing a comprehensive three-step Bayesian Framework for the estimation of intrinsic single crystal properties along with quantified uncertainty as well as relative model probabilities of different crystal plasticity models for lamellar a+b colonies of Titanium alloys. The three-step Bayesian Framework first involves the establishment of inexpensive surrogate models to obtain quick predictions of the indentation property of interest. These surrogate models are trained on a dataset of indentation property values obtained using computationally expensive crystal plasticity finite element simulations. In order to minimize the overall computational expense incurred in development of the abovementioned dataset, this study utilizes an information gain based sequential design strategy to select additional simulations that have the highest potential to increase the model fidelity. In the second step of the Bayesian Framework, the intrinsic single crystal properties are obtained by calibrating the surrogate models against a dataset of experimentally obtained nanoindentation property measurements on grains in a polycrystalline sample that cover the relevant space of crystallographic orientations, with the help of Markov Chain Monte Carlo Sampling techniques. In the third step, the Markov Chain of configurations generated in the previous step is used to obtain an approximate estimate of the typically intractable model evidence, which is in turn normalized across all models under consideration to establish their relative model probabilities. The framework delineated and developed in this work is utilized in multiple case studies designed to compare crystal plasticity models for the colony morphology of Ti-6Al-4V. Moreover, the present work also assesses the relative efficacy of different geometric slip transfer criteria in explaining the overall mechanical response. The protocols developed herein possess broad applicability when it comes to assessing numerous crystal plasticity models with different underlying assumptions and model forms for high value complex alloy systems.

Presenting Author: Aditya Venkatraman Georgia Institute of Technology

Presenting Author Biography: I’m a fourth year Ph.D candidate in the George W. Woodruff School of Mechanical Engineering at Georgia Institute of Technology Atlanta. My advisor is Prof. Surya Kalidindi. My research interests are<br/>1. Crystal Plasticity and Molecular Dynamics<br/>2. Uncertainty Quantification and Propagation, Verification, Validation<br/>3. Machine Learning and Reduced Order Models<br/>4. Bayesian Calibration<br/>5. Nanoindentation<br/>My research broadly involves the development and deployment of novel Data Science and Uncertainty Quantification protocols for accelerating Computational Materials Science investigations. The aim of my research is the development of efficient and accurate tools with the potential to aid materials and product design efforts.

Authors:

Aditya Venkatraman Georgia Institute of Technology