Size effects in elastic-plastic functionally graded materials

TL;DR

This paper introduces a strain gradient plasticity model for functionally graded materials, revealing size-dependent strengthening effects and the influence of microstructural features on mechanical response.

Contribution

It develops a novel strain gradient plasticity formulation for FGMs with spatially varying properties, incorporating homogenization and analyzing size effects through numerical boundary value problems.

Findings

Micro-size FGMs exhibit increased stiffness with decreasing thickness.

Indentation hardness significantly increases as indenter size decreases.

High dislocation densities near cracks elevate local stresses.

Abstract

We develop a strain gradient plasticity formulation for composite materials with spatially varying volume fractions to characterize size effects in functionally graded materials (FGMs). The model is grounded on the mechanism-based strain gradient plasticity theory and effective properties are determined by means of a linear homogenization scheme. Several paradigmatic boundary value problems are numerically investigated to gain insight into the strengthening effects associated with plastic strain gradients and geometrically necessary dislocations (GNDs). The analysis of bending in micro-size functionally graded foils shows a notably stiffer response with diminishing thickness. Micro-hardness measurements from indentation reveal a significant increase with decreasing indenter size. And large dislocation densities in the vicinity of the crack substantially elevate stresses in cracked FGM components. We comprehensively assess the influence of the length scale parameter and material gradation profile to accurately characterize the micro-scale response and identify regimes of GNDs relevance in FGMs.