3D Representative Volume Element Research Articles

Loading rate effect of the interfacial tensile failure behavior in carbon fiber–epoxy composites toughened with ZnO nanowires

This paper attempts to study the loading rate effect of interface tensile failure behavior of carbon fiber-epoxy composites toughened with ZnO nanowires (ZnO NWs). ZnO NWs were grown onto woven carbon fiber fabrics through a two-step hydrothermal method, the growth time was carefully controlled to vary the nanowire length. Subsequently, a series of quasi-static and dynamic transverse fiber bundle (TFB) tensile tests were carried out under different loading velocities, ranging from 1 × 10−6 m/s on the universal testing machine to 9 m/s on the electromagnetic Hopkinson bar. A 2D representative volume element (RVE) model has been established to identify the load transfer and failure behavior of the ZnO NW modified interface. The results show that under quasi-static loading, the maximum TFB tensile strength improvement owing to ZnO NWs was about 36.9% and 16.5% when compared with the pristine fibers and the fibers with surface sizing. However, due to the loading rate enhancement of the interface bonding strength, the corresponding values were decreased to 13.9% and 5.0% under dynamic loading. Besides, nanowires with medium length are recommended, because too long nanowires shall reduce the matrix impregnation space between fibers, and the microcracks from the fiber/matrix interface can easily deflect into the matrix along the nanowires. This side-effect may neutralize the enhancement mechanism of ZnO NWs when their length increases to a certain extent.

Lath Martensite Microstructure Modeling: A High-Resolution Crystal Plasticity Simulation Study.

Lath martensite is a complex hierarchical compound structure that forms during rapid cooling of carbon steels from the austenitic phase. At the smallest, i.e., ‘single crystal’ scale, individual, elongated domains, form the elemental microstructural building blocks: the name-giving laths. Several laths of nearly identical crystallographic orientation are grouped together to blocks, in which–depending on the exact material characteristics–clearly distinguishable subblocks might be observed. Several blocks with the same habit plane together form a packet of which typically three to four together finally make up the former parent austenitic grain. Here, a fully parametrized approach is presented which converts an austenitic polycrystal representation into martensitic microstructures incorporating all these details. Two-dimensional (2D) and three-dimensional (3D) Representative Volume Elements (RVEs) are generated based on prior austenite microstructure reconstructed from a 2D experimental martensitic microstructure. The RVEs are used for high-resolution crystal plasticity simulations with a fast spectral method-based solver and a phenomenological constitutive description. The comparison of the results obtained from the 2D experimental microstructure and the 2D RVEs reveals a high quantitative agreement. The stress and strain distributions and their characteristics change significantly if 3D microstructures are used. Further simulations are conducted to systematically investigate the influence of microstructural parameters, such as lath aspect ratio, lath volume, subblock thickness, orientation scatter, and prior austenitic grain shape on the global and local mechanical behavior. These microstructural features happen to change the local mechanical behavior, whereas the average stress–strain response is not significantly altered. Correlations between the microstructure and the plastic behavior are established.

Finite element analysis and experiment study on the elastic properties of randomly and controllably distributed carbon fiber-reinforced hydroxyapatite composites

Randomly distributed carbon fiber-reinforced hydroxyapatite (RCF/HA) and controllably distributed carbon fiber-reinforced hydroxyapatite (CCF/HA) composites were firstly studied to design and prepare different required composite artificial bones with satisfying mechanical properties by combining experiment approach, theoretical prediction and finite element analysis (FEA). A plug-in was obtained by secondary development of ABAQUS for the FEA. A 3D representative volume element (RVE) for RCF/HA and CCF/HA can be easily generated using this tool. Stress and strain analyses of three directions of RVE were performed by ABAQUS with different fiber mass fractions and distributions. The elastic modulus of CF/HA composites were obtained. With 0.2 wt% fiber, the elastic modulus of RCF/HA and CCF/HA composites increased by 6.31% and 54.4% compared with that of HA, respectively. For CCF/HA composites, the elastic modulus increased significantly with the increasing fiber mass fraction in the E11 of the fiber. The results of experiment study and theoretical prediction were consistent with that of FEA. The maximum error between the FEA and experiment study was 2.84%, which confirmed that the RVE model was rational and accurate. The results indicated the fiber distribution can greatly affect the elastic modulus of the composites. In the future study, the controllably distributed fiber–reinforced composites would be a good choice because they can improve the mechanical properties as required. This study would endow possibility of designing and preparing the CF/HA bio-ceramics with satisfied mechanical properties by FEA and proper preparation parameter. It would also speed up application of clinical practice for CF/HA composites.

Particle distribution-dependent micromechanical simulation on mechanical properties and damage behaviors of particle reinforced metal matrix composites

A micromechanical simulation has been performed to study the effect of particle distribution on the mechanical properties and damage behaviors of particle reinforced metal matrix composites (PRMMCs). Two-dimensional (2D) representative volume elements with variable particle size, volume fraction and particle distribution were generated and subjected to finite element simulation. An enhanced continuum model, which incorporates dislocation punching effect at particle-matrix interfaces and Taylor-based nonlocal theory of plasticity in matrix, was used to simulate the mismatch in coefficients of thermal expansion strengthening and particle size-dependent strengthening. Additionally, constitutive damage behaviors were involved in simulating the crack initiation and evolution, considering the ductile damage in matrix and dislocation punching zone, as well as the particle cracking. Simulation results indicate that refining the particle size is helpful to improve the tensile strength and fracture resistance of PRMMCs, whereas the increase of particle clustering volume fraction or severity facilitates damage evolution and deteriorates the mechanical properties. Statistical analysis indicates a negative linear dependence between particle distribution homogeneity and the ductility, given a constant particle size and volume fraction.

Effect of the 3rd Dimension within the Representative Volume Element (RVE) on Damage Initiation and Propagation during Full-Phase Numerical Simulations of Single and Multi-Phase Steels.

In this research, the effect of 2D and 3D Representative Volume Element (RVE) on the ductile damage behavior in single-phase (only ferrite) and dual-phase (ferrite and martensite) steels is analyzed. Physical and fitting parameters of the constitutive model for bcc-ferrite and bcc-martensite phases are adapted from the already published work. Crystal plasticity (CP) based numerical simulations without damage consideration are run and, later, ductile damage criteria for the ferrite phase is defined for all cases. The results of the non-damage (-nD-) and damage (-D-) simulations are compared to analyze the global and local differences of evolving stresses and strains. It is observed that for the same model parameters defined in all cases, damage initiation occurs at the overall higher global strain in the case of 3D compared to 2D. Based on statistical data analysis, a systematic comparison of local results is carried out to conclude that the 3D RVEs provide better quantitative and qualitative results and should be considered for such full phase simulations. Whereas 2D RVEs are simple to analyze and provide appropriate qualitative information about the damage initiation sites.

Progressive damage analysis of an adhesively bonded composite T-joint under bending, considering micro-scale effects of fiber volume fraction of adherends

In this study, a numerical study on failure assessment and stress distribution on the adhesive region in a composite T-joint under bending load case is investigated using cohesive zone method (CZM). The Finite Element Model (FEM) has been verified with experimental results. To study the load transfer capability of the T-joint, five different adhesives are considered in the adhesive region and the effect of geometrical parameters such as stringer thickness, corner radius, and adherend thickness as well as micromechanical properties of reinforced fiber composite adherends are investigated. Effective properties of two composite adherends including Carbon-Epoxy (IM7/8552) and Glass-Epoxy (E-glass/Epon 828) with various fiber volume fractions are estimated using a 3D representative volume element (RVE) and employing period boundary conditions (PBC) through Python scripts in ABAQUS. The results show that the fiber volume fraction of composite adherends has a significant effect on failure behavior. For instance, increasing fiber volume fraction of carbon/epoxy composite from 0.4 to 0.7 resulted in a 78% increase in elastic stiffness and a 41% enhancement in maximum load-bearing capacity. Among different adhesive types used in this study, FM300 resulted in the strongest structure and S7752 led to a more ductile T-joint.

Effect of 3D Representative Volume Element (RVE) Thickness on Stress and Strain Partitioning in Crystal Plasticity Simulations of Multi-Phase Materials

Crystal plasticity simulations help to understand the local deformation behavior of multi-phase materials based on the microstructural attributes. The results of such simulations are mainly dependent on the Representative Volume Element (RVE) size and composition. The effect of RVE thickness on the changing global and local stress and strain is analyzed in this work for a test case of dual-phase steels in order to identify the minimal RVE thickness for obtaining consistent results. 100×100×100 voxel representative volume elements are constructed by varying grain size and random orientation distribution in DREAM-3D. The constructed RVEs are sliced in depth up to 1, 5, 10, 15, 20, 25, 30, 40, and 50 layers to construct different geometries with increasing thickness. Crystal plasticity model parameters for ferrite and martensite are taken from already published data and assigned to respective phases. Although the global stress/strain behavior of different RVEs is similar (<5% divergence), the local stress/strain partitioning in RVEs with varying thickness and grain size shows a considerable variation when statistically compared. It is concluded that two-dimensional (2D) RVEs can be used for crystal plasticity simulations when global deformation behavior is of interest. Whereas, it is necessary to consider three-dimensional (3D) RVEs, which have a specific thickness and number of grains for determining stabilized and more accurate local deformation behavior. This estimation will help researchers in optimizing the computation time for accurate mesoscale simulations.

Microstructure-based RVE modeling of ductile failure induced by plastic strain localization in tailor-tempered 22MnB5 boron steel

To differentiate the ductile fractures caused by deformation incongruities between phases, 22MnB5 boron steel sheets consisting of diverse bainite-martensite fractions were studied. The microstructural characteristics of each phase in tailor-tempered boron steel were examined in tandem with the ductile fracture morphologies after undergoing varied stress states. A micromechanical model was proposed, including microstructural reconstruction using a 2D representative volume element (RVE) approach and a constitutive formulation of a dislocation density-based strain hardening model. The microstructure-based RVE model can be utilized to study the effects of stress states and the influence of microstructural characteristics on the failure mode of tailor-tempered 22MnB5.

Void growth and morphology evolution during ductile failure in an FCC single crystal

Void growth and morphology evolution are studied using a 3D representative volume element with a spherical void embedded in an FCC single crystal. The plastic flow contours are studied to determine the scenarios leading to fully plastic flow and plastic flow with elastic region. Further, the effect of anisotropy on void growth is studied through three initial crystallographic orientations (ICOs) [100], [110], & [111] with respect to loading direction. Void growth and macroscopic stress variations with applied strain are obtained from our simulations. It is observed that the peak stress corresponds to rapid void growth initiation. The peak stress is found to be dependent on void volume fraction and ICO. Furthermore, an additional geometrical parameter, diagonal distortions $$(D_{d_{i}})$$ is introduced to classify the non-spheroidal void shapes observed in deformed anisotropic crystal.

Failures analysis of in-situ Al–Mg2Si composites using actual microstructure based model

In-situ Al–Mg2Si composites (0, 5, 10, 15, 20 wt% Mg2Si) were synthesized in an Al–Mg–Si system through gravity casting route. Influences of the Mg2Si addition (in terms of Mg and Si) on the mechanical properties, microstructural morphology, fracture behaviors, micro-mechanical response and failure initiation were systematically studied through experiments and mathematical modeling. Experimental results show that the primary Mg2Si formed in Al-10 wt% Mg2Si composite and the volume percentage and size of primary Mg2Si particles are increasing with an increase in Mg2Si concentration in the composite. The Mg2Si reinforcement significantly improves ultimate tensile strength (UTS), hardness and yield strength (YS) of the composite, but unwantedly the elongation decreased. Fracture surface analysis reveals that the composites have both the ductile and brittle mode of fracture and the amount of brittle fracture increased with an increase in reinforcing phase (Mg2Si) concentration. The fracture mode for the Mg2Si particles includes matrix yielding, decohesion, particle fracture. The deformation plasticity (Ramberg-Osgood) model was considered to investigate the micromechanical response under tension. Actual microstructure two-dimensional (2D) representative volume element (RVE) models have been developed to investigate the deformation and failure phenomenon of the composites. The FE analysis results have a great concurrence with the experimental one. It established that the composite's strength and failure initiation regions increased and the elongation decreased with an increase in Mg2Si concentration. It is noted that the eutectic Mg2Si morphology is the cause for failure initiation and then primary Mg2Si drive the final failure of the Al–Mg2Si composites.

Evaluation of the influence of voids on 3D representative volume elements of fiber-reinforced polymer composites using CUF micromechanics

This paper presents numerical results on the micromechanical linear analysis of representative volume elements (RVE) containing voids. The modeling approach is the micromechanical framework within the Carrera Unified Formulation in which fibers and matrix are 1D finite elements (FE) with enriched kinematics and component-wise capabilities. RVE models are 3D and consider all six stress components. Such a modeling strategy leads to a twofold reduction of the degrees of freedom as compared to 3D FE. The numerical assessments address the influence of the volume fraction and distribution of voids, including comparisons with data from the literature and statistical studies regarding homogenized properties and stress fields. The proposed modeling approach can capture the local effects due to the presence of voids, and, given its computational efficiency, the present framework is promising for nonlinear analysis, such as progressive failure.

Representative volume element generation and its size determination for discontinuous composites made from chopped prepregs

In the present study, the composites made from chopping prepregs in rectangular chips, called discontinuous composites derived from chopped prepreg (DCCP) were modeled for stiffness prediction. Standard mechanics approach with displacement boundary conditions is used for stiffness prediction. The minimum size of the representative volume element (RVE) for this material is determined. An algorithm based on the random sequential adsorption technique (RSA) has been exploited to generate the 3D RVEs. RVEs of five different aspect ratios of the cuboid-shaped inclusions are developed using this technique. The chips are completely randomly oriented with a constant volume fraction. A detailed study was carried out in each case by further generating the RVEs with different increasing sizes, and the smallest size of RVE with geometric periodicity was identified. Further, the characteristics of these RVEs have been investigated for different aspect ratios, varying the chip volume fraction for the influence of volume fraction on RVE size and the material properties. The efficacy of the developed approach is demonstrated through repetitiveness of the effective properties prediction for various scenarios studied. The resulting material showed isotropy in the plane where chips are distributed randomly while overall isotropy about 80% is seen in most of the RVEs studied.

Investigation of Yield Surfaces Evolution for Polycrystalline Aluminum after Pre-Cyclic Loading by Experiment and Crystal Plasticity Simulation.

This study aims at introducing the back stress of anisotropic strain-hardening into the crystal plasticity theory and demonstrating the rationality of this crystal plasticity model to describe the evolution of the subsequent yield surface of polycrystalline aluminum at the mesoscopic scale under complex pre-cyclic loading paths. By using two different scale finite element models, namely a global finite element model (GFEM) as the same size of the thin-walled tube specimen used in the experiments and a 3D cubic polycrystalline aggregate representative volume element (RVE) model, the evolution of the subsequent yield surface for different unloading cases after 30 pre-cycles is further performed by experiments and numerical simulations within a crystal plasticity finite element (CPFE) frame. Results show that the size and shape of the subsequent yield surfaces are extremely sensitive to the chosen offset strain and the pre-cyclic loading direction, which present pronounced anisotropic hardening through a translation and a distortion of the yield surface characterized by the obvious “sharp corner” in the pre-deformation direction and “flat” in the reverse direction by the definition of small offset strain, while the subsequent yield surface exhibits isotropic hardening reflected by the von Mises circle to be distorted into an ellipse by the definition of large offset strain. In addition, the heterogeneous properties of equivalent plastic strain increment are further discussed under different offset strain conditions. Modeling results from this study show that the heterogeneity of plastic deformation decreases as a law of fraction exponential function with the increasing offset strain. The above analysis indicates that anisotropic hardening of the yield surface is correlated with heterogeneous deformation caused by crystal microstructure and crystal slip. The crystal plasticity model based on the above microscopic mechanism can accurately capture the directional hardening features of the yield surface.

On the prediction of the bi-axial failure envelope of a UD CFRP composite lamina using computational micromechanics: Effect of microscale parameters on macroscale stress–strain behavior

A computational micromechanics based Finite Element (FE) analysis methodology is presented to predict the bi-axial failure envelope of a unidirectional (UD) carbon-epoxy composite ply. In order to estimate the effect of various microscale parameters that are influencing the macroscopic stress–strain behavior, under individual load cases, detailed numerical studies are conducted using a 3D RVE (Representative Volume Element) model. The constituent epoxy matrix plastic deformation in the RVE is captured using the linear Drucker-Prager plasticity model.The effect of the fiber–matrix interface damage, followed by frictional sliding of the constituent materials on the computed interface tractions is captured using the cohesive zone damage model combined with the Coulomb friction law, which is implemented into Abaqus using VUMAT. From the detailed FE analysis of the RVE under individual load cases, it is observed that the predicted macroscopic stress–strain behavior is sensitive to the fiber–matrix interface properties as well as the in-situ epoxy stress–strain behavior. Hence, using a coupled experimental-computational micromechanics approach the interface and the in-situ epoxy material properties are calibrated and validated. Using the calibrated interface and in-situ epoxy material properties, the bi-axial (transverse tension/transverse compression – in-plane shear) failure envelope of a UD composite ply is estimated. Comparing the predicted damage profiles and the failure envelope with the experimental results leads to good agreement and validates the proposed numerical methodology.

An ultra-simple universal model for the effective elastic properties of isotropic 3D closed-cell porous materials

In this paper, effective elastic properties of the isotropic 3D closed-cell porous materials are comprehensively investigated through finite element method simulations, theoretical formulations and experimental tests. 3D representative volume element models with randomly distributed non-overlapping Voronoi-structured voids of various porosities (from 0.01 to 0.99) are created to compute the effective bulk and shear moduli of the porous materials. An ultra-simple universal model (USUM) is developed to predict the effective shear modulus covering the entire porosities. The effective Young’s modulus and Poisson’s ratio of ultra-simple form are then formulated. The findings show that the theoretical estimates agree well with the numerical results for all the effective elastic properties. The uniaxial compression tests are implemented on the specimens of 3D printed porous nylon to measure the effective Young’s modulus. The results suggest that the theoretical predictions of the USUM agree very well with the effective Young’s moduli of the porous materials, covering a wide range of porosity.

Computational micromechanics of the effect of fibre misalignment on the longitudinal compression and shear properties of UD fibre-reinforced plastics

In this paper, 3D representative volume elements (RVEs) of UD carbon/epoxy composites are generated, taking into consideration a realistic misalignment of the fibres. To construct the RVE, a 2D distribution of the fibre sections is considered and then extruded in the longitudinal direction. Experimental measurements to the misalignments are modelled by perturbing the positions of the control points defined on the centreline of each fibre, representing the fibre path as a Bézier curve. The individual fibres are considered as linear elastic orthotropic whereas, the matrix is modelled as isotropic using a damage-plasticity model. The fibre/matrix interface is modelled using a cohesive formulation law. The IM7/8552 material was simulated using three loading conditions: longitudinal compression, longitudinal shear, and transverse shear. The results show clear correlation between fibre misalignment and compression strength, and stiffness. For shear loading, no effect is recorded. Under the three loading conditions, the predicted material properties and damage propagation are in agreement with the data available in the literature.

Distance map based micromechanical analysis of the impact of matrix heterogeneities on the yield stress of nodular cast iron

A method to construct 3D representative volume element (RVE) models of the nodular cast iron microstructure that accounts for the presence of heterogeneities in the matrix is proposed. The main advantage is the possibility to generate a wide spectrum of realistic distributions of the matrix heterogeneities in a simple and fast way. The method takes advantage of the fact that the spatial distribution of some of the matrix heterogeneities is intrinsically connected to the distribution of the graphite nodules, due to the nature of the solidification process. Accordingly, the graphite morphology is reconstructed first via X-ray computed tomography and subsequently used to estimate the distribution of the pearlite and of the Si micro-segregation – considered as case studies – by means of dedicated distance functions. The obtained 3D models are used to show that the spatial variation in the matrix plastic properties associated with the Si micro-segregation is not expected to influence the material yielding behavior significantly. In addition, it is shown that when the matrix pearlite content increases for a fixed overall C concentration, the corresponding decrease in the nodules’ volume fraction can account for as much as 1/3 of the obtained increment in the material macroscopic proof stress.

On Effective Mechanical Properties of Two-Dimensional Porous Materials

Two-dimensional (2D) representative volume element (RVE) has been widely used to simulate the effective behaviors of the materials with aligned pores. In this paper, the anisotropy indexes are defined for the 2D RVE model to quantitatively evaluate the extent of anisotropy of the model. A normalized procedure is then proposed to compute the effective moduli of the RVE models, which can further minimize the influence of anisotropy of the RVE models. The effective Poisson’s ratio of the porous materials is challengeable to be estimated well, and few analytical models can give good predictions. The theoretical models are proposed to approach the effective Young’s modulus and the effective Poisson’s ratio of the 2D porous materials covering the full range of porosity. It is numerically validated that the theoretical models give accurate predictions for the effective Young’s modulus and Poisson’s ratio of the 2D porous materials.

Microstructure-based numerical simulation of the mechanical properties and fracture of a Ti-Al3Ti core-shell structured particulate reinforced A356 composite

A microstructure-based numerical simulation is performed to understand the mechanical properties and fracture of a Ti-Al3Ti core-shell structured particulate reinforced A356 composite ((Ti-Al3Ti)cs/A356). A series of two-dimensional (2D) representative volume element (RVE) models are generated automatically by embedding Ti-Al3Ti core-shell structured particulates in an A356 matrix. Microstructure-based 2D RVE of monolithic Al3Ti particulate reinforced A356 composite (Al3Tip/A356) is also simulated for comparison. The ductile fracture of both Ti core and A356 matrix as well as the brittle fracture of the Al3Ti shell are considered. The simulation confirms that the high elongation of the (Ti-Al3Ti)cs/A356 composite is attributed to the uniform distribution of the overall ductile globular reinforcing particulates, which prevent a premature failure effectively by reducing local stress concentration both on and inside the core-shell structured particulates. The surrounding ductile phases of the Al3Ti shell blunt the crack tips effectively and, therefore, restricting the propagation of the cracks in a nominal strain range of 2.2%–6.1%. For both (Ti-Al3Ti)cs/A356 and Al3Tip/A356 composites, the simulation results are in good agreement with microstructural observations during an in-situ tensile test in a scanning electron microscope.

Investigating the elastic behavior of carbon nanocone reinforced nanocomposites

This paper deals with the evaluation of the effective mechanical properties of carbon nanocone centered composites using a 3D nanoscale representative volume element based on continuum mechanics. For extracting the effective material constants, the authors have taken the basis of theories of elasticity. The results constituting the effective Young's modulus of the composite and Poisson's ratio for different parameters stated above have been presented and validated with rule of mixtures. It can be clearly visualized from the results that the load-carrying capacities of carbon nanocones in the representative volume elements are quite significant and the same has been demonstrated with subsequent cases. Simulation-based modeling can show a considerable part in the improvement of carbon nanocone-based composites by providing results that help in appreciative of the performance of composites. Moreover, for a volume fraction of the CNC as 2.33% in a cylindrical representative volume element and a 19.2° apex angle of the cone, the stiffness of the composite can increase as many as 4.9 times of the matrix. Similarly for hexagonal and square, the increase is in terms of 4.3 and 3.01 times respectively. Cylindrical representative volume element is the best as it provides the maximum reinforcement in terms of effective Young's modulus of the composite. Carbon nanocone-based composites provide results that help in understanding the elastic behavior of composites.