Size effects in elastic-plastic functionally graded materials

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 mechanismbased 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.

Phase field modelling of crack propagation in functionally graded materials

“…For example, the extension to metal-based elastic-plastic FGMs is immediate in the absence of plastic-damage coupling, provided that plastic size effects are accounted for [39]. Similarly, the framework can easily accommodate other homogenization schemes, such as those proposed for functionally graded composites integrating carbon nanotubes [40,41].…”

On the Finite Element Implementation of Functionally Graded Materials

“…Typically, the information available is the spatial variation of the volume fractions of constituent materials, which is provided as input to the production technique [16]. The macroscopic material property variation does not tend to mirror the volume fraction profile, but one can estimate the former from the latter by using homogenization laws [17]. However, the micromechanical assumptions upon which these theoretical mixing laws are built may hinder an accurate characterization of the macroscopic variation of material properties.…”

Numerical investigation of the dynamic behavior of a Ti/TiB functionally graded material using Split Hopkinson Pressure Bar test

“…The effect of material parameters such as constituent volume fraction (Vc), size, shape, particle distribution on the elastoplastic deformations, failure mechanisms, and microstructure heterogeneity of FGMs under quasi-static loading have been widely studied. [13][14][15][16][17][18][19][20][21] For example, Kubair and Lakshmana 22 carried out a numerical study of initiation and growth of damages in layered composites structures with a functionally graded core. The simulation indicated that the energy absorption due to the damage process is modified by the presence of the functionally graded core, Moreover, Gunes et al 23 analyzed the elastic and elastoplastic behavior of functionally graded circular plates under low-velocity impact loading using experimental and computational techniques.…”