Representative elementary volume

About: Representative elementary volume is a research topic. Over the lifetime, 4105 publications have been published within this topic receiving 86863 citations.

Micromechanics-based thermoelastic model for functionally graded particulate materials with particle interactions

Abstract: Thermoelastic behavior of functionally graded particulate materials is investigated with a micromechanical approach. Based on a special representative volume element constructed to represent the graded microstructure of a macroscopic material point, the relation between the averaged strains of the particle and matrix phases is derived with pair-wise particle interactions, and a set of governing equations for the thermoelastic behavior of functionally graded materials is presented. The effective coefficient of thermal expansion at a material point is solved through the overall averaged strain of two phases induced by temperature change under the stress-free condition, and is shown to exhibit a weak anisotropy due to the particle interactions within the graded microstructure. When the material gradient is eliminated, the proposed model predicts the effective coefficient of thermal expansion for uniform composites as expected. If the particle interactions are disregarded, the proposed model recovers the Kerner model. The proposed semi-analytical scheme is consistent and general, and can handle any thermal loading variation. As examples, the thermal stress distributions of graded thermal barrier coatings are solved for two types of thermal loading: uniform temperature change and steady-state heat conduction in the gradation direction.

Effect of carbon nanotube orientation on the mechanical properties of nanocomposites

Abstract: Carbon nanotubes (CNTs) have been regarded as ideal reinforcements of high-performance composites with enormous applications. In this paper, nano-structure is modeled as a linearly elastic composite medium, which consists of a homogeneous matrix having hexagonal representative volume elements (RVEs) and homogeneous cylindrical nanotubes with various inclination angles. Effects of inclined carbon nanotubes on mechanical properties are investigated for nano-composites using 3-D hexagonal representative volume element (RVE) with short and straight CNTs. The CNT is modeled as a continuum hollow cylindrical shape elastic material with different angles. The effect of the inclination of the CNT and its parameters is studied. Numerical equations are used to extract the effective material properties for the hexagonal RVE under axial as well as lateral loading conditions. The computational results indicated that elastic modulus of nano-composite is remarkably dependent on the orientation of the dispersed SWNTs. It is observed that the inclination significantly reduces the effective Young’s modulus of elasticity under an axial stretch. When compared with lateral loading case, effective reinforcement is found better in axial loading case. The effective moduli are very sensitive to the inclination and this sensitivity decreases with the increase of the waviness. In the case of short CNTs, increasing trend is observed up to a specific value of waviness index. It is also found from the simulation results that geometry of RVE does not have much significance on stiffness of nano-structures. The results obtained for straight CNTs are consistent with ERM results for hexagonal RVEs, which validate the proposed model results.

Crystal plasticity modeling of cyclic deformation for a polycrystalline nickel-based superalloy at high temperature

Abstract: Cyclic deformation at elevated temperature has been modeled for a polycrystalline nickel-based superalloy using the crystal-plasticity constitutive formulations. Finite element analyses were carried out for a representative volume element (RVE), consisting of randomly oriented grains and subjected to periodic boundary constraints. Model parameters were determined by fitting the strain-controlled cyclic test data at 650 °C for three different loading rates. Simulated results are in good agreement with the experimental data for both stress–strain loops and cyclic hardening behavior. The model was utilized to predict the stress relaxation behavior during the hold periods at the maximum and minimum strain levels, and the prediction compares well with the experimental results. Localized stress and strain concentrations were observed due to the heterogeneous nature of grain microstructure and the mismatch of the mechanical properties of individual grains.

Transformation-Induced, Geometrically Necessary, Dislocation-Based Flow Curve Modeling of Dual-Phase Steels: Effect of Grain Size

Abstract: The flow behavior of dual-phase (DP) steels is modeled on the finite-element method (FEM) framework on the microscale, considering the effect of the microstructure through the representative volume element (RVE) approach. Two-dimensional RVEs were created from microstructures of experimentally obtained DP steels with various ferrite grain sizes. The flow behavior of single phases was modeled through the dislocation-based work-hardening approach. The volume change during austenite-to-martensite transformation was modeled, and the resultant prestrained areas in the ferrite were considered to be the storage place of transformation-induced, geometrically necessary dislocations (GNDs). The flow curves of DP steels with varying ferrite grain sizes, but constant martensite fractions, were obtained from the literature. The flow curves of simulations that take into account the GND are in better agreement with those of experimental flow curves compared with those of predictions without consideration of the GND. The experimental results obeyed the Hall-Petch relationship between yield stress and flow stress and the simulations predicted this as well.