Microstructure-sensitive design of a compliant beam

Abstract

We show that mechanical design can be conducted where consideration of polycrystalline microstructure as a continuous design variable is facilitated by use of a spectral representation space. Design of a compliant ÿxed-guided beam is used as a case study to illustrate the main tenets of the new approach, called microstructure-sensitive design (MSD). Selection of the mechanical framework for the design (e.g., mechanical constitutive model) dictates the dimensionality of the pertinent representation. Microstructure is considered to be comprised of basic elements that belong to the material set. For the compliant beam problem, these are uni-axial distribution functions. The universe of pertinent microstructures is found to be the convex hull of the material set, and is named the material hull. Design performance, in terms of speciÿed design objectives and constraints, is represented by one or more surfaces (often hyperplanes) of ÿnite dimension that intersect the material hull. Thus, the full range of microstructure, and concomitant design performance, can be exploited for any material class. Optimal placement of the salient iso-property surfaces within the material hull dictates the optimal set of microstructures for the problem. Extensions of MSD to highly constrained design problems of higher dimension is also described.

The triple junction hull: Tools for grain boundary network design

“…For example, the texture set and texture hull originally defined in (Adams et al, 2001), are denoted using our scheme as M (1) S and M (1) H respectively.…”

“…This represents a subset of m (3) H , which we denote m (3) H , and whose size, relative to m (3) H provides an estimate for how much of the grain boundary network design space is accessible through the control of texture alone. In order to measure m (3) H , we must first introduce the concepts of the texture set and texture hull 4 (Adams et al, 2001(Adams et al, , 2012Fast et al, 2008) and provide their mathematical definitions in the context of the hyperspherical harmonic expansion.…”

“…In the context of texture and grain structure in polycrystalline materials, microstructure design tools now allow the designer to explore a complete set of physically realizable microstructures and identify those that meet various performance objectives and design constraints (Adams et al, 2001(Adams et al, , 2012. These tools have been used to address design problems in which elastic and plastic properties are concerned (Adams et al, 2001;Fast et al, 2008;Houskamp et al, 2007;Kalidindi and Houskamp, 2007;Kalidindi et al, 2004;Lyon and Adams, 2004;Saheli et al, 2005;Sintay and Adams, 2005).…”

“…These tools have been used to address design problems in which elastic and plastic properties are concerned (Adams et al, 2001;Fast et al, 2008;Houskamp et al, 2007;Kalidindi and Houskamp, 2007;Kalidindi et al, 2004;Lyon and Adams, 2004;Saheli et al, 2005;Sintay and Adams, 2005). However, their application to other properties of scientific and engineering interest, such as fracture and corrosion, which depend upon the structure of the grain boundary network, remains to be addressed.…”

Texture mediated grain boundary network design in two dimensions

“…6,7 This design formalism is referred to as microstructure sensitive design for performance optimization (MSDPO). Whereas the materials designer formerly had a finite (and rather incomplete) catalogue of observed microstructures and forward models at his/her disposal, the advent of these new microstructure design tools has allowed for the consideration of material structure as a continuous design variable and the rigorous solution of complex inverse design problems.…”