Higher Length Scales Research Articles

Transformation Surfaces of a Textured Pseudoelastic Polycrystalline Cu-Zn-Al Shape Memory Alloy

Pseudoelasticity is a useful regime of behavior for industrial applications of shape memory alloys. The complexity of the physical phenomena of pseudoelastic shape memory behavior requires micromechanical methods of scale transition to model at higher length scales using crystallographic information. Using a self-consistent model to transition from single crystal to polycrystal behavior, we present results for computed surfaces of constant effective transformation strain for random, drawn, tension, compression and rolled textures of a polycrystalline Cu-Zn-Al shape memory alloy in the pseudoelastic regime. These results are relevant to the development of macroscopic transformation surfaces in stress space. A feature of the results is that normality of transformation strain rate to surfaces of constant macroscopic transformation strain is observed for the most part, apart from regions of high curvature that bridge different segments of the transformation surface.

Application of image processing for simulation of mechanical response of multi-length scale microstructures of engineering alloys

Microstructures of engineering alloys often contain features at widely different length scales. In this contribution, a digital image processing technique is presented to incorporate the effect of features at higher length scales on the damage evolution and local fracture processes occurring at lower length scales. The method is called M-SLIP: Microstructural Scale Linking by Image Processing. The technique also enables incorporation of the real microstructure at different length scales in the finite element (FE)-based simulations. The practical application of the method is demonstrated via FE analysis on the microstructure of an aluminum cast alloy (A356), where the length scales of micropores and silicon particles differ by two orders of magnitude. The simulation captures the effect of nonuniformly distributed micropores at length scales of 200 to 500 µm on the local stresses and strains around silicon particles that are at the length scales of 3 to 5 µm. The procedure does not involve any simplifying assumptions regarding the microstructural geometry, and therefore, it is useful to model the mechanical response of the real multi-length scale microstructures of metals and alloys.

Numerical and analytical study to estimate the effect of two length scales upon the permeability of a fibrous porous medium

A fibrous porous medium with two length scales is modeled as a bed of porous cylinders aligned perpendicular to the flow of viscous fluid. The flow behavior is described using Stokes and Darcy flow equations in the regions around (higher length scale) and within the cylinders (lower length scale) respectively. The typical ratio of higher and lower length-scale regions enable us to invoke lubrication approximation and simplify the equations to develop a closed form solution for the overall permeability of this dual-scale porous medium. A parametric analysis is performed to explore the dependence of permeability on factors such as the volumetric ratio of higher and lower length-scale regions, permeability and size of inclusions in the smaller length-scale region. The analytical model is compared with the numerical results and the trend is compared with the experiments.