Utilization of a Linear Solver for Multiscale Design and Optimization of Microstructures

Abstract

Microstructures have a significant effect on the performance of critical components in numerous aerospace metallic material applications. Examples include panels in airframes that are exposed to high temperatures and sensors used for vibration tuning. This paper addresses the techniques to optimize the microstructure design for polycrystalline metals. The microstructure is quantified with the orientation distribution function that determines the volume densities of crystals that make up the polycrystal microstructure. The orientation distribution function of polycrystalline alloys (e.g., hexagonal close-packed titanium) is represented in a discrete form, and the volumeaveraged properties are computed through the orientation distribution function. The optimization is performed using the space of all possible volume-averaged macroproperties (stiffness and thermal expansion). A direct linear solver is employed to find the optimal orientation distribution functions. The direct solver is capable of finding exact solutions even for problems with multiple or infinite solutions. It is first applied to the optimization of the panel-buckling problem. The objective of the buckling optimization problem is to find the best microstructure design that maximizes the critical buckling temperature. The optimum solution computed with this approach is found to be same as the optimum solution of a global approach that uses a genetic algorithm. The linear solver methodology is extended to plastic properties and applied to explore the design of a Galfenol beam microstructure for vibration tuning with a yielding objective. The design approach is shown to lead to multiple optimum solutions.

Crystal Plasticity Modeling and Experimental Validation with an Orientation Distribution Function for Ti-7Al Alloy

“…The present work introduces the ODF based methodology using a local basis [34] and focuses on an inverse problem for crystal plasticity modeling of Ti-Al alloys (Ti-0Al and Ti-7Al) using the technique. The single crystal constitutive model presented by Anand and Kothari [35] is used to model the crystal plasticity of the microstructure, and the ODF evolution is modeled using a conservation equation.…”

Stochastic Design Optimization of Microstructural Features Using Linear Programming for Robust Design

“…To illustrate this, we first identify all possible ODF solutions, given the values of the stiffness parameters C 11 C 12 510.9785 329.0219 GPa using the deterministic solver explained in Ref. [2]. The solver is capable of finding multiple/infinite solutions using the null space of the linear system relating ODF to properties.…”

“…The null space approach is explained in detail by the authors in Ref. [2]. Using the given input information, we compute the multiple ODF solutions by implementing the null space approach.…”

“…Introduction M ICROSTRUCTURE design has been typically addressed as a deterministic optimization problem in which features such as volume fractions of various phases are controlled to achieve the desired property. Several issues arise: First, multiple microstructures can lead to the desired property, and some microstructures are easier to manufacture than others [1,2]. Thus, the deterministic optimizer has to be capable of predicting nonunique solutions.…”

Multiscale Optimization of Nanocomposites with Probabilistic Feature Descriptors

“…Here, the 3D rotation is based on the unique association of an orientation with an axis of rotation, n, and a rotation angle, θ, about the axis. The details for the Rodrigues parameterization and ODF representation can be found in our earlier studies [40,41]. Because the SWNT-epoxy lattice is transversely isotropic and contains hexagonal symmetry, the 3D orientation space can be reduced to a small subset called the fundamental region that accounts for hexagonal symmetry.…”