Uncertainty Quantification for Ti-7Al Alloy Microstructure with an Inverse Analytical Model (AUQLin)

Area of Science:

• Materials Science
• Computational Mechanics
• Statistical Physics

Background:

• Material properties at the macro-scale are influenced by underlying microstructural characteristics.
• Understanding and quantifying the stochasticity (randomness) of microstructures is crucial for predicting material behavior.
• Existing methods may not fully capture the link between macro-scale property variations and microstructural randomness.

Purpose of the Study:

• To develop an analytical uncertainty quantification (UQ) model, AUQLin, for inferring microstructural stochasticity from macro-scale material property variations.
• To establish a framework for inverse problems linking macroscopic observations to microscopic uncertainties.
• To provide a computationally efficient method for material uncertainty analysis.

Main Methods:

• Modeling material property uncertainty using an analytical algorithm.
• Solving uncertainty propagation to the microstructure via an inverse problem employing the transformation of random variables principle.
• Addressing the underdetermined linear system from the inverse problem by solving an optimization problem to minimize discrepancies with experimental data.

Main Results:

• The developed inverse problem yields multiple solutions for microstructural statistical features.
• An optimization approach successfully selects the most plausible microstructural solution.
• The computed microstructural uncertainty demonstrates a strong agreement with experimental microstructure data.

Conclusions:

• The AUQLin model effectively bridges the gap between macro-scale material properties and microstructural stochasticity.
• The inverse problem approach combined with optimization provides a robust method for uncertainty quantification in materials.
• The study validates the model's predictive capability against experimental observations, highlighting its potential for materials design and analysis.