Smallest Representative Volume Element Research Articles

An upscaling approach for micromechanics based fatigue: from RVEs to specimens and component life prediction

A novel approach has been developed to estimate fatigue life at the specimen/component level from the simulation of relatively small Representative Volume Elements (RVE) of the polycrystalline microstructure. This technique estimates the statistical distribution of fatigue lives under general multiaxial loading conditions accounting for both microstructure and specimen size. The model relies on computational homogeneization where the crystal behavior follows a crystal plasticity model and simulations are performed using a FFT based solver. The simulation of the cyclic response of a set of different RVEs provides the statistical distribution of Fatigue Indicator Parameters for that RVE size, which can be accurately represented by an extreme value distribution as the Gumbel distribution. This distribution is upscaled to the actual size of the specimen or component of interest using a weakest link approach and is finally transformed into a distribution of fatigue lives using a simple fatigue-life expression fitted with experiments. The framework proposed estimates fatigue lives of specimens with millions of grains from the results obtained with RVEs containing only hundreds of grains and is able to reproduce the specimen size effect on fatigue life. The approach is first numerically validated and then used to predict the statistical distribution of fatigue life of a polycrystalline Ni-based superalloy showing very accurate results.

Discrete-element modeling of nacre-like materials: Effects of random microstructures on strain localization and mechanical performance

Natural materials such as nacre, collagen, and spider silk are composed of staggered stiff and strong inclusions in a softer matrix. This type of hybrid microstructure results in remarkable combinations of stiffness, strength, and toughness and it now inspires novel classes of high-performance composites. However, the analytical and numerical approaches used to predict and optimize the mechanics of staggered composites often neglect statistical variations and inhomogeneities, which may have significant impacts on modulus, strength, and toughness. Here we present an analysis of localization using small representative volume elements (RVEs) and large scale statistical volume elements (SVEs) based on the discrete element method (DEM). DEM is an efficient numerical method which enabled the evaluation of more than 10,000 microstructures in this study, each including about 5,000 inclusions. The models explore the combined effects of statistics, inclusion arrangement, and interface properties. We find that statistical variations have a negative effect on all properties, in particular on the ductility and energy absorption because randomness precipitates the localization of deformations. However, the results also show that the negative effects of random microstructures can be offset by interfaces with large strain at failure accompanied by strain hardening. More specifically, this quantitative study reveals an optimal range of interface properties where the interfaces are the most effective at delaying localization. These findings show how carefully designed interfaces in bioinspired staggered composites can offset the negative effects of microstructural randomness, which is inherent to most current fabrication methods.

Representative volume element for parallel fiber bundles: Model and size convergence

The simulation of textiles often occurs at the meso scale, where the individual tows are treated as a homogeneous continuum. To properly utilize such models, fiber-scale models are required to obtain homogenized tow mechanics and consider fiber-scale mechanisms. The current study demonstrates a representative volume element (RVE) for parallel fiber bundles using the discrete element method (DEM). A method for localization, homogenization, boundary conditions, and random packing generation is presented. An RVE size convergence study was conducted for six different loading cases. An RVE existed for all loading cases, and the smallest RVE which represented a reasonable response contained 162 fibers. Several concerns were highlighted which need to be considered when deciding on an acceptable RVE size for the current model, including loading rate, undulations in the response due to individual fiber slippage, and specimen to specimen variation due to initial fiber positions.

Modeling of metallic foam morphology using the Representative Volume Element approach: Development and experimental validation

This paper focuses on the development of an algorithm capable of generating morphologically-representative foam structures using the Representative Volume Element (RVE) approach. Stereology, a sampling method based on direct observations of the foam cross-sections, is used to characterize the pore size and shape distributions. Using the morphology generation algorithm, the smallest RVEs corresponding to the numerically-convergent foam morphologies are calculated for different foam porosities. To validate the foam generation algorithm, the pore size and shape distributions of the numerically-generated foams are compared to those of the titanium foams manufactured by the space holder method.

The Micromechanics of Biological and Biomimetic Staggered Composites

Natural materials such as bone, tooth and nacre achieve attractive properties through the “staggered structure”, which consists of stiff, parallel inclusions of large aspect ratio bonded together by a more ductile and tougher matrix. This seemingly simple structure displays sophisticated micromechanics which lead to unique combinations of stiffness, strength and toughness. In this article we modeled the staggered structure using finite elements and small Representative Volume Elements (RVEs) in order to explore microstructure-property relationships. Larger aspect ratio of inclusions results in greater stiffness and strength, and also significant amounts of energy dissipation provided the inclusions do not fracture in a brittle fashion. Interestingly the ends of the inclusions (the junctions) behave as crack-like features, generating theoretically infinite stresses in the adjacent inclusions. A fracture mechanics criterion was therefore used to predict the failure of the inclusions, which led to new insights into how the interfaces act as a “soft wrap” for the inclusions, completely shielding them from excessive stresses. The effect of statistics on the mechanics of the staggered structure was also assessed using larger scale RVEs. Variations in the microstructure did not change the modulus of the material, but slightly decreased the strength and significantly decreased the failure strain. This is explained by strain localization, which can in turn be delayed by incorporating waviness to the inclusions. In addition, we show that the columnar and random arrangements, displaying different deformation mechanisms, lead to similar overall properties. The guidelines presented in this study can be used to optimize the design of staggered synthetic composites to achieve mechanical performances comparable to natural materials.

Selection of representative volume elements for pore-scale analysis of transport in fuel cell materials

Pore-scale modeling has become a quite popular tool for evaluating the impact of material structure on fuel cell performance. However, the computational complexity of these models often limits simulations to analyze only a small volume of material, which is typically selected randomly from a much larger microstructure dataset. When considering the heterogeneous internal structure of fuel cell materials, it is highly unlikely that such a randomly selected volume (i.e., model domain) would adequately reflect the salient features of the material structure. The objective of this work is to utilize the recent advances in microstructure quantification to select small representative volume elements (RVEs) that accurately reflect the overall microstructure and transport properties of fuel cell materials. The micro-porous layer (MPL) in polymer electrolyte fuel cells is chosen for initial demonstration of the approach. Dual-beam focused ion beam scanning electron microscopy is utilized to obtain a 3-D structural dataset of the selected MPL sample. The RVEs are selected using the new approach of weighted sets of optimally selected statistical volume elements, and the key structure and transport metrics are evaluated using advanced microstructure algorithms developed in-house. Metric comparisons between the RVEs and the full dataset indicate that the RVEs selected by this approach offer a very good representation of the full dataset, albeit in a volume that is significantly smaller in spatial extent, therefore providing a computationally efficient and reliable model domain for pore-scale analyses.

A Nanoindentation Study of Photo-Induced Changes in Polymers Containing Azobenzene

Irradiation of materials by light of suitable photon energy can cause structural alterations of either permanent or temporary character that are reflected in their mechanical properties. Nanoindentation is particularly well suited to characterise small representative volume elements of materials with gradual or discrete changes of their mechanical properties. It is, therefore, an ideal technique for investigation of thin films, nanocomposites and other specimens with inhomogeneities in the nanometer to micrometer length scale that are either inherently existing in the material or externally stimulated. In this article, nanoindentation was applied to study the mechanical properties of pDR1 m surface relief gratings containing azobenzene. Hardness and elastic modulus increase after and during irradiation of the pDR1 m film correlated with an increase in the polymer density after light exposure. Permanent structural changes in the pDR1 m film are related to crosslinking and photo-isomerisation. In-situ nanoindentation under controlled periodic light illumination exhibits a week photomechanical switching and results finally in a permanent stiffer polymer network.

Failure Analysis of Cast Irons Under General Three-Dimensional Stress States

Observations of microscale behavior of cast irons indicate that considerable plastic flow occurs between microflaws prior to rupture. Therefore, the plastic limit load for small representative volume elements of material treated as structures should be a close approximation to the load at rupture. A representative volume element of cast iron is analyzed using limit analysis techniques to obtain bounds on the limit, or failure, surface under three dimensional average stress. Comparisons with other cast iron failure criteria and experimental data are made.