Representative Volume Element Model Research Articles

Numerical simulation on mechanical properties and damage behavior of CFRP with self-healing microvascular channels

In this study, 3D representative volume element models with microchannels were established based on measured data. And the periodic boundary conditions were moderately modified to adapt to the actual constraints of the studied object. The effects of different microvascular parameters on the tensile and compressive properties of composites were studied. And the damage pattern of carbon fiber as the main load-bearing phase under the force was analyzed. The models were verified by tensile testing and micromorphology experiments. The research results are of application to the design and analysis of CFRP laminates containing similar microchannel structures.

Micromechanical analysis of high fibre volume fraction polymeric laminates using micrograph-based representative volume element models

This work develops RVE-based finite element (FE) models to understand how the microstructure of Ultra-High-Molecular-Weight Polyethylene (UHMWPE) composites affects the overall mechanical behaviour of the laminate. The models represent a [0/90] configuration with a random fibre packing sequence through the thickness of each ply, as well as a variation in the cross-sectional shape of the fibres, both obtained from laminate cross section micrograph images. The uncertainty of interface properties and its effects on the overall mechanical response is also investigated. The response of the fibre is assumed to be viscoelastic-plastic and transversely isotropic and the three-dimensional constitutive behaviour is implemented through a user-defined subroutine in the LS-DYNA explicit FE code. Constituent properties are calibrated using experimental results on UHMWPE single fibres and a generic thermoplastic polyurethane resin material. The numerical results generated by the RVE models are validated against experimental results found in the open literature. Special focus was given to the in-plane shear and out-of-plane compression response of UHMWPE laminates. Our results can be used as inputs in a homogenised continuum level model, to express the effect of uncertainties which propagate from the microstructure to the macro-scale response.

Investigation on carbon nanoparticle (CNP)-polymer sensors for fatigue monitoring of fiber-reinforced composites

Carbon nanoparticle (CNP)-polymer sensors are good candidates for monitoring structural damage. A combined numerical-analytical approach with considering the stiffness degradation of composite is proposed to calculate the resistance variations with the cyclic loads. The electro-mechanical behavior of the sensor can be simulated through the finite element analysis of a random representative volume element model and the equivalent resistance calculation of microcircuit. Then, taking the glass fiber-reinforced composite coated with the CNP-epoxy resin as example, its electro-mechanical behavior under tension-tension cyclic loading is investigated experimentally and numerically. Furthermore, by microscopic analysis, the fatigue damage monitoring mechanism of the sensor is revealed.

Study on progressive damage performance of basalt‐fiber wound composite tube

AbstractFor filament wound composite tubes made of basalt fiber‐reinforced polymer (BFRP), damage performances were simulated and load capacity was evaluated with a multi‐scale homogenization method based on properties of component materials, fiber volume fraction and the winding process. Considering about both the intra‐layer and inter‐layer damage properties, a representative volume element (RVE) was defined in the structural layer of the pipe wall firstly. Equivalent mechanical properties of the structural layer were then obtained by simulating damage evolution of the RVE under tension, compression and the shear load. In order to verify the RVE model, tensile tests of the specimens that were cut out of the BFRP tube in both longitudinal and circumferential directions were implemented. The predicted load–displacement curves of the RVE were in good agreement with the corresponding experimental results. Finally, the tube wall was simplified into a three‐layer structure including inner lining layer, equivalent structural layer and outer protection layer. Damage evolutions of the tube were calculated under basic loads, borne typically by the oil and gas pipeline, such as internal pressure, tension, bending and torsion. The results lead to a better understanding of the load‐bearing capacity of the BFRP tube and promote the application of the BFRP in the oil and gas field.

A highly efficient explicit constitutive model for linear viscoelastic closed-cell porous materials

In this paper, a highly efficient explicit constitutive model for linear viscoelastic closed-cell porous materials is proposed based on micromechanics and homogenization method in the time domain. The deformation first is additively divided into volumetric and deviatoric parts and then the viscoelastic behaviors are decomposed into the time-dependent and time-independent parts. Finite element simulations based on representative volume element models are utilized to numerically verify the constitutive model. The effects of the void-shape, porosity, elastic and viscous parameters of the matrix, strain rate, and angular frequency on the effective linear viscoelastic responses are studied. The results demonstrate that the constitutive model can provide accurate estimation of the effective linear viscoelastic properties for the closed-cell porous materials in both time and frequency domains. The 3D printed nylon porous materials with various porosities are employed to experimentally validate the constitutive model through simple uniaxial compression tests, stress relaxation uniaxial compression tests, and uniaxial compression tests with different strain rates. The results reveal that the constitutive model can also predict well the behaviors of linear viscoelastic closed-cell porous materials with different porosities in the time domain under various loading conditions.

Mechanical characterization of additively-manufactured metallic lattice structures with hollow struts under static and dynamic loadings

Inspired by the natural hollow structures, periodic lattice structures composed of hollow struts and spheres were designed and fabricated by selective laser melting (SLM) process with 316L stainless steel. Two architecture configurations with Body-Centered Cubic (BCC) and Face-Centered Cubic (FCC) symmetry were taken into consideration. Finite element (FE) simulations based on representative volume element (RVE) models and cell-assembly models were conducted to investigate the elastic response and large deformation behavior of the hollow lattice materials, respectively. Afterwards, compression experiments were carried out on an electronic universal machine and a drop hammer (DH) system to explore the quasi-static and dynamic mechanical response of the lattice specimens. The complete deformation evolutions of the lattice samples under different loading velocities were captured through high-resolution photography and inspected by the digital imaging correlation (DIC) analysis. Both the experimental research and numerical simulations demonstrated that the hollow beam cross-sections contributed to the stable crushing response of the proposed lattice structures under either quasi-static or dynamic compression. Accordingly, the post-yield behavior of the tested lattice structures was quite smooth without any fluctuations. Meanwhile, the specific strength and energy absorption of the hollow lattice structures were found to be superior to many existed lattice materials with solid struts, and comparable with the reported triply periodic minimal surface (TPMS) lattice structures. Finally, the effect of the geometric characteristic parameters on the specific mechanical properties of the lattice structures was discussed according to the supplemental analysis by numerical simulations.

Testing and multiscale modeling of a foam-based lung surrogate subjected to underwater shock loading

A combined experimental and computational study was conducted to investigate the structural response of a foam-based lung simulant subjected to underwater pressure wave. In the physical experiments, a lung surrogate made from porous medium was exposed to underwater pressure wave in an impact force - driven testing tube. The pressures in the water and surrogate deformation profile were recorded throughout the event. A numerical model of the underwater shock tube was developed using finite element (FE) method and validated against experimental data. An arbitrary Lagrangian-Eulerian (ALE) fluid–structure coupling algorithm was then utilized to simulate the interaction between the underwater pressure wave and the lung surrogate. Based on the numerical model, a multiscale modeling strategy was used to link the surrogate responses in macro and micro scales. The modeling process consists of two steps, namely (1) macro scale FE modeling to predict the overall surrogate reponse; and (2) micro scale Representative Volume Element (RVE) modeling for the detailed microstructure response. The strain tensors computed in Step (1) were applied to the RVE as the boundary condtions in Step (2) to calculate its response in the micro scale. With this multiscale modeling approach, a parametric study was carried out to study the influence of waveform on the RVE strain response. The results indicate that for current input pressure levels, the strain response within the foam surrogate model is more sensitive to the overpressure than the duration of pulse. The modeling approach developed in this work can potentially serve as a basis for further numerical models to gain a deeper insight into the mechanism of underwater blast-induced lung injury.

Energy Absorption Characteristics and Elastoplastic Damage Response of Hybrid Epoxy/Coir Fibre-Reinforced Aluminum 6063 Tubes in Axial Deformation

Occupant safety is one of the critical performance criteria established in the aerospace industry. Several composite materials have been developed but the energy absorption properties are not yet satisfactory. This study investigates the energy absorption characteristics of aluminum tubes reinforced with coir-fiber/epoxy system at varying proportions (10-90%) according to the specifications of hybrid tube thickness compositions (10T, 15T, 20T) towards evolving a criterion for optimal performance. Finite element analysis was conducted in ABAQUS to determine the load–displacement response and the crashworthiness properties of the tubes while a representative volume element (RVE) model was formulated to obtain the elastic properties of the reinforcement phase. The results indicated that the incidence of high peak forces Pmax is related to tube thickness variations where the 20T tubes were found to give the best performance, while the 15T tubes showed a superior performance under progressive crushing and presented the best responses for specific energy absorption (SEA). A multi-objective optimization plan was implemented and through the Pareto fronts, tube configurations (C20T60F), (C15T70F) and (C20T40F) were found to be most consistent with the design criteria. Results from experimental validation were found to be in close agreement with numerical predictions and satisfied the overall objective of achieving a good balance in lightweight design for crashworthiness applications.

Modelling of the intergranular fracture of TWIP steels working at high temperature by using CZM–CPFE method

Grain boundaries (GBs) of metallic materials will become the weakest and most vulnerable place when the materials deform at high temperature. This could directly affect deformation flow, plastic strengthening, the initiation and propagation of microcracks, and finally the fracture failure of materials. In this research, to reveal the high temperature deformation mechanisms of twinning–induced plasticity (TWIP) steels, the crystal plasticity finite element method (CPFEM) was employed to model the mechanical response of grain interiors. The cohesive zone model (CZM) of the bi–linear traction separation law (TSL) was developed to describe the damage and failure of GBs. By combining CZM and CPFEM, an analysis method was proposed to investigate the effect of the microstructure morphology, orientation and size of grains, and temperature. Furthermore, the damage initiation, accumulation and fracture at GBs were represented by the representative volume element model based on the CZM–CPFE method to explore the influences of GB angle, grain size and local microvoids (including the location and size) on the GB cracking. The stress damage cloud maps, the distribution of quadratic stress damage initiation criterion (QUADSCRT) and the scalar stiffness degradation (SDEG) describing the damage and fracture along the GBs were used to articulate the relationships of GB angle, size effect, local microvoids and the expected failure strain. The results show that low angle grain boundaries (LAGBs), the small average grain size (<21.2 μm), microvoids at the horizontal GBs and microvoids with a diameter below 1.5 μm can delay the initiation of microcracks and fracture failure along the GBs. The predicted damage and failure of GBs and the intergranular cracking characteristics in plastic deformation of TWIP steels at high temperature were corroborated by microscopic in–situ SEM experiments, in which the deformation characteristics inside the grains, and microcrack initiation and propagation near GBs were observed at 500 and 750°C. This research enhances the understanding of intergranular fracture, mechanical response and microstructure evolution of TWIP steels worked at different temperatures, and also provides a new way and strategy for studying the deformation behaviours of TWIP steels considering GB properties.

Thermal-damage suppression of composite material by anti-lightning NCF/CIPCF film

Lightning strike protection (LSP) design is significant for carbon fiber reinforced plastic (CFRP), which is sensitive to lightning strikes. An anti-lightning film reinforced by nickel-coated carbon fibers/carbonyl iron powders conductivity framework (NCF/CIPCF) is designed for lightning protection of CFRP laminates. Representative volume element (RVE) models of NCF/CIPCF film are established according to random sequential addition (RSA) method. Material properties are obtained based on homogenization theory. This numerical method is validated by calculations of electrical resistivity and thermal conductivity. Subsequently, lightning damage analysis of CFRP laminates with different protections is conducted based on thermal-electric coupling method and temperature dependent ablation criteria, which aims to evaluate the suppression effects of lightning damage by this film. Results show that damage area and depth of CFRP laminates are effectively controlled by NCF/CIPCF film, which is slightly superior to aluminum at the same weight. NCF/CIPCF anti-lightning film is light and easy to repair and replace, which can be considered as an excellent and promising method in LSP design of aircraft.

An Experimentally Based Micromechanical Framework Exploring Effects of Void Shape on Macromechanical Properties.

A micromechanical simulation approach in a Multi-Scale Modeling (MSM) framework with the ability to consider manufacturing defects is proposed. The study includes a case study where the framework is implemented exploring a cross-ply laminate. The proposed framework highlights the importance of correct input regarding micromechanical geometry and void characteristics. A Representative Volume Element (RVE) model is developed utilizing true micromechanical geometry extracted from micrographs. Voids, based on statistical experimental data, are implemented in the RVE model, and the effects on the fiber distribution and effective macromechanical properties are evaluated. The RVE algorithm is robust and maintains a good surrounding fiber distribution around the implemented void. The local void fraction, void size, and void shape affect the effective micromechanical properties, and it is important to consider the phenomena of the effective mechanical properties with regard to the overall void fraction of an RVE and the actual laminate. The proposed framework has a good prediction of the macromechanical properties and shows great potential to be used in an industrial implementation. For an industrial implementation, weak spots and critical areas for a laminate on a macro-level are found through combining local RVEs.

Development of modeling to investigate polyurethane pad hardness in chemical mechanical planarization/polishing (CMP) process

In chemical mechanical polishing (CMP) for IC fabrication, porous pads are critical for achieving extremely consistent throughput in CMP process. The pad hardness, porosity of pad, and pore sizes in the thermoplastic polyurethanes foam fabrication procedure determine the properties of CMP pads. This paper aims to develop a methodology for modeling macro and micro pad hardness. The IC1000 CMP pad has been analyzed with a developed image processing method to determine porosity and pores size. In addition, nano-indentation tests are used to determine physical properties of micro-solid components. For macro hardness analysis, five different sizes of three-dimensional representative volume elements (RVE) have been investigated using the random sequential adsorption technique. Furthermore, simulation of macro pad hardness of RVE models are completed with finite element method. Results of this study not only achieves macro hardness of CMP pad simulation as 3% errors as compared with developed micro-indentation test, but also complete three dimensional porous pad modeling with RVE.

Hyperelastic behaviors of closed-cell porous materials at a wide porosity range

In this paper, the constitutive model proposed in the previous work for neo-Hookean materials with spherical voids and an explicit homogenization solution named Shrimali-Lefèvre-Lopez (SLL) model for isotropic porous elastomers are adopted to theoretically predict the macroscopic effective hyperelastic responses of the closed-cell porous materials with rubber-like incompressible neo-Hookean matrix at finite deformations. Representative volume element (RVE) models with randomly distributed non-overlapping polyhedral voids are employed to numerically validate the theoretical models at a wide porosity range from 0.05 to 0.9. Various deformations including hydrostatic deformations, pure shear deformations, uniaxial deformations and plane strain deformations are applied to the theoretical and RVE models. The results show that the theoretical models can well estimate the effective hyperelastic properties of the porous materials under all deformation conditions considered, and our theoretical model is complementary with the SLL model for predicting different effective properties under given deformation. The constitutive models are also validated experimentally by comparing with the experimental data from the literature.

Parameter optimization of particle-reinforced adhesive bonded joints based on the response surface method

We investigated the effects of process parameters on the quality of alumina-reinforced adhesive bonded joints. Single-lap joints of 1.5-mm-thick aluminum alloy 5182 sheets were prepared by adhesive bonding with particulate composite adhesive. The multivariate regression models between process parameters (particle size, adhesive layer thickness, and mass fraction) and response values (failure load, energy absorption value) were established, and the models were verified by experiments. The adhesive layer was modeled using the ABAQUS CPS4R mesh element. The representative volume element (RVE) model was then established to simulate the failure of adhesively bonded joints during tensile tests. The findings indicate that particle size has the biggest impact on the failure load of the joints, and particle mass fraction has the highest influence on the energy absorption value of the joints. The optimum process parameters ranges are: particle size of 0.046 mm, adhesive layer thickness of 0.6 mm, and mass fraction of 5%. As per finite element analysis, the failure load and tensile modulus of the adhesive layer decrease as particle size and particle volume fraction increase.

Axial crushing response of carbon/glass hybrid composite tubes: An experimental and multi-scale computational study

This study focuses on the axial crushing behavior of double hat-shaped composite tubes prepared using plain woven fabrics reinforced by carbon fibers, glass fibers and their intra-layer hybrids. A multi-scale modelling strategy was adopted to study the crushing response of composite structures. The Chamis model was used to calculate the effective properties of carbon and glass yarns at the micro-scale level. At the meso-scale level, representative volume element (RVE) models were constructed considering the real fabric pattern. Intra-layer hybridized lamina properties can be obtained using RVE models subjected to typical loading cases. The results were validated through tension, compression and in-plane shear tests. At the macro-scale level, we used a stacked-shell strategy to create the axial crushing finite element models. The effect of intra-layer hybrid on the crushing failure mechanisms of composite tubes was analyzed and compared to that of non-hybrid carbon fiber reinforced polymers (CFRP) or glass fiber reinforced polymers (GFRP) tubes.

Quantitative analyses on geometric shape effect of microdefect on fatigue accumulation in 316L stainless steel

Geometric shapes of microdefects are closely associated with the local deformation potentially inducing crack initiation. The main goal of this attempt is to explore and quantitatively analyze the close link between varying shapes of microdefects and fatigue accumulation in 316L stainless steel. In the perspective of crystal plasticity finite element method (CPFEM), we systematically build representative volume element (RVE) models designated with three typical geometric shapes of microdefects including rectangle, circle and rhombus, aiming to quantitatively reveal the underlying mechanism of fatigue accumulation in the presence of defects. Results show that crack initiation from multiple sites around microdefects is more likely dependent of the geometric shape of microdefect, as well as the heterogenous property of microstructure. Statistical probability analyses indicate that, compared to rectangular and circular defects, rhombic microdefect results in a higher degree of deformation that is prone to crack initiation at critical location. These numerical findings are consistent with experimental observation, providing quantitative reference for the design of polycrystalline materials.

Study on stress distribution of SiC/Al composites based on microstructure models with microns and nanoparticles

Abstract The simulation model represents the microstructure that can accurately analyze and predict composites’ micro-stresses and mechanical properties. The conventional representative volume element (RVE) model can only contain one single-particle form. It makes that all the particles in the simulation model have the same shape, which is significantly different from actual particles. In the present study, four typical particle-modeling methods were adopted to establish geometric models to analyze the particle morphology and RVE size selection rules. Particles with the same granularity and similar volume were selected to generate RVE models with randomly distributed particles to predict the mechanical properties and analyze the micro-stress. The micro-stress distribution of the matrix and particles conformed to the rule of normal distribution, while the stress of the interphase does not conform to this law. The particle morphology has a negligible effect on the stress distribution of the matrix; however, it has a significant influence on the stress distribution of particles and interphases, especially during plastic deformation. Furthermore, the micro-stress of composites containing nanoparticles also conforms to the above law, but the stress of the interphase is more minor, and the stress of particles is more dispersed than composites with micron particles.

Investigation into the influence of CNTs configuration on the thermal expansion coefficient of CNT/Al composites

A 3D representative volume element (RVE) model was developed to analyze the effective thermal expansion coefficient (CTE) of carbon nanotube reinforced aluminum (CNT/Al) composites. The influences of geometric configuration, orientation and volume fraction of CNTs on CTE of the CNT/Al composites were investigated. The results show that the orientation of CNTs significantly influences the stress and strain distributions around CNTs, and when CNTs are parallel to the load direction, the constraint effect of CNTs on the matrix is the largest. Furthermore, the configuration of CNTs also plays an important role in reducing thermal expansion behavior of CNT/Al composites, and the bundled configuration exhibit the lowest CTE. In particular, with the increase of the number of CNTs in each bundle, the CTE decreases and then tends to be unchanged. When the volume fraction of CNTs is 5%, and the number of CNTs in each bundle is 25, the CTE of the composite reaches 5.12 × 10−6/°C, which is 76% lower than the CTE of the matrix. A linear decrease of the CTE of CNT/Al composites is observed as the CNT volume fraction increases. Overall, this work establishes a comprehensive understanding of factors affecting the CTE, and the obtained findings could provide a good theoretical basis for designing low CTE CNT/Al composites.

Meso-scale Finite Element (FE) modelling of biaxial carbon fibre non-crimp-fabric (NCF) based composites under uniaxial tension and in-plane shear

Non-crimp-fabrics (NCF) are promising materials in aerospace applications. The complex internal structure of NCF composites could influence the in-plane performances, which needs to be comprehensively studied. The novel three-dimensional (3D) meso-scale repeated unit cell (RUC) models were proposed for biaxial NCF composites based on the Finite Element (FE) method to conduct a systematic parameter study, including layup sequence, out-of-plane tow waviness, resin-rich areas, transverse tow placements and delamination. The meso RUC model could effectively predict the homogenised uniaxial tensile and in-plane shear properties of biaxial NCF composites based on their meso-scale constituent and material properties. A multiscale framework was also developed for biaxial NCF composites. A micromechanical representative volume element (RVE) model provided homogenised mechanical properties for tows, and a macroscopical FE model validated the test results using the homogenised results obtained from meso RUC models. The numerical results were in good agreement with the experiment results. Therefore, the multiscale framework provides an insight into the critical parameters influencing the in-plane properties of NCF composites and an analysis tool for NCF material design.

Fatigue failure mechanism analysis and life prediction of short fiber reinforced polymer composites under tension-tension loading

Short fiber reinforced polymer (SFRP) composites have won extensive applications in the automotive industry. For precisely expounding the fatigue failure mechanism and predicting the fatigue life of SFRP composites, a novel micromechanical fatigue model of SFRP dominated by the fiber–matrix interface is proposed. A newly designed three-layer reinforcement structure is introduced to construct the representative volume element (RVE) model. The numerical analysis is performed under the envelope load damage framework and verified via fatigue tests and in situ X-ray imaging. Results show that the progressive fatigue damage of each constituent can be quantitatively analyzed. Moreover, the S-N data of SFRP featuring specific orientation tensor and stress ratio is well predicted, which can be applied to reduce the fatigue test costs and improve the durability of SFRP components.