Micromechanical Finite Element Model Research Articles

Micromechanical Modelling of the Deformation Mechanisms of Friction-Spun Yarn from Recycled Carbon Fibres

The growing use of carbon fibre-reinforced polymers (CFRP) results in an increased amount of CF waste from offcuts or end-of-life components. A promising method to reuse the waste fibre materials in a structural component with excellent mechanical properties is the processing of recycled CF (rCF) and thermoplastic fibres into hybrid yarns. Spinning of friction spun yarns consisting of more than 90% rCF and containing almost no thermoplastic fibres that are suitable for thermoset composites, currently leads to high fibre damage and low yarn quality and is, therefore, addressed in this project. The technology is reported in another paper. One of the limiting factors for drapability of textiles is the stretchability of continuous fibres and draping of the semi-finished textile products for complex geometries is still error-prone. Friction spun yarns exhibit significantly higher yarn elongations due to sliding mechanisms between the fibres. The deformation properties of friction spun yarns are significantly influenced by fibre-fibre interactions and depend on a variety of process and material parameters. In the following, micromechanical finite element models of the spun yarns are created by using beam elements. Monte Carlo method is used to model local variabilities in the yarns. The models are then used to simulate yarn behaviour under deformation and to investigate the influence of various process parameters.

A unique numerical iterative approach for modelling individual phase stress-strain curves in dual phase steel

Understanding the effects of martensite volume fractions (V m) in dual phase (DP) steel resulting from heat treatment is crucial for designing structures for mechanical impact resistance and optimizing manufacturing processes. DP steel’s material behaviour depends heavily on its microstructure properties. While stress-strain curves for individual phases in DP steels are often determined using empirical models, extensive experimental data is required to establish empirical model constants. This research aims to achieve two main objectives: firstly, to calibrate stress-strain curves for pure ferrite and pure martensite using limited experimental data using micromechanical adaptive iteration algorithm (MAIA). This calibration involves using stress-strain data from DP steels with varying V m during the calibration stage and additional data for verification. Secondly, to conduct a comprehensive sensitivity analysis of MAIA to assess its capabilities and limitations. Microstructure-based finite element (FE) models, simulated with ABAQUS/Standard, are employed to predict stress-strain curves under uniaxial tensile test conditions. The MAIA approach successfully calculated ferrite and martensite stress-strain curves that could predict plastic behaviour of DP steel with different V m, which agreed with experimental work. Key advantages of this approach include avoiding complex 3D microstructure geometries and requiring only two experimentally obtained stress-strain curves with different Vm for material constant calibration, along with another curve for validation. However, the experimental data selected for calibration must have a V m difference between 20%–50% and one of the DP steels must have a low martensite volume fraction. The FE micromechanical model could capture the effect of softening of martensite phase and strengthening of ferrite phase as compared to its bulk properties for DP steel. The effect of V m on strain hardening rate was also successfully captured. This technique comes with obvious shortcomings, such as excluding crystal plasticity behaviour, and change in chemical composition within the individual phase with varying martensite volume fraction.

Synergistic effect of carbon nanotube/graphene nanoplatelet hybrids on the elastic and viscoelastic properties of polymer nanocomposites: finite element micromechanical modeling

Synergistic effect of carbon nanotube/graphene nanoplatelet hybrids on the elastic and viscoelastic properties of polymer nanocomposites: finite element micromechanical modeling

Automatic generation of 3D micromechanical finite element model with periodic boundary conditions to predict elastic properties of bamboo fibre-reinforced composites

This study presents an automatic algorithm to generate a three-dimensional (3D) micromechanical finite element (FE) model to predict elastic behaviours of biocomposites reinforced with unidirectional (UD) continuous natural fibres such as bamboo fibres. The developed algorithm constructs a virtual FE framework by generating stochastic Representative Volume Elements (RVEs) of fibre-reinforced composites incorporating random fibre arrangement and random assignment of fibre radii. It also applies various loading scenarios and periodic boundary conditions to simulate elastic behaviours accurately. The algorithm generates 3D periodic RVEs by introducing boundary and corner fibres. All the 3D RVE models, representing different fibre-reinforced composites, various loading cases, and periodic boundary conditions, are automatically created using Python scripting with the Abaqus FE solver. The accuracy of the algorithm and virtual FE test model is validated through comparisons with analytical models and experimental results. The effects of different types of fibre radius assignment, fibre volume fraction, and fibre periodicity on the prediction of effective elastic properties are investigated. The study also establishes correlations between all elastic constants of bamboo fibre-reinforced composites and the fibre volume fraction.

Micromechanical analysis of composite materials considering material variability and microvoids

One of the main challenges for fiber-reinforced polymers (FRP) is the difficulty to predict their mechanical behavior. At the microscale, the properties of the constituents, their spatial distribution and the defects arising from manufacturing affect the mechanical behavior. In this work, statistically representative volume elements (SRVEs) are proposed based on a micromechanical finite element model to determine the effect of content, distribution and size of microstructural defects and, material uncertainties on the elastic mesoscale properties of FRPs. To that end, different cylindrical void sizes are considered as well as irregular shaped voids between fiber tows (inter-fiber voids). Fibers and voids are randomly distributed in a SRVE. An uncertainty quantification and management analysis is employed to obtain statistical descriptors of the effective mesoscale mechanical properties of FRPs. The results obtained are compared with analytical models. It is demonstrated that, for carbon fiber/epoxy composites, SRVEs with lateral dimensions equivalent to 15 times the average fiber diameter and a length of 0.01 mm along the longitudinal direction remain statistically representative with or without the presence of voids. The results show that the presence of voids reduces the transverse and shear elastic properties of FRPs. The smaller the voids are, the bigger is the reduction. Regarding the presence of inter-fiber voids, the reduction is lower. This trend is well predicted by the Mori–Tanaka mean field theory. However, the relative difference between the numerical and the analytical predictions increases for high void volume fractions. Regarding the effective longitudinal Young’s modulus, the rule of mixtures, the Mori–Tanaka mean field theory and the concentric cylinder assembly model provide similar predictions for the mean value, but the uncertainty is overestimated by the analytical models because the properties of the fibers take a single value for each calculation with the analytical model, while they more realistically change from fiber to fiber in the numerical SRVEs.

Investigating the mechanical performance of graphene reinforced polymer nanocomposites via atomistic and continuum simulation approaches

Graphene, having exceptional mechanical properties, is expected to improve the overall mechanical performance of polymer nanocomposites when inserted as a nanofiller. In this work, the mechanical properties of graphene-based cis-1,4-polybutadiene glassy polymer nanocomposites are investigated via a hierarchical multiscale approach, combining atomistic simulations and continuum mechanics. The global mechanical properties of the graphene-based polymer nanocomposites are computed via a rich enough set of remote applied deformations. On a localized level, the effective Young's modulus and Poisson's ratio are calculated in both the interphase and polymer matrix regions where the former shows greater rigidity. Finally, the properties of the different phases forming the heterogeneous polymer nanocomposite are used to develop a continuum three-phase micromechanical finite element model for predicting the overall mechanical behavior of the structure, which are found to be in very good agreement with the results from the atomistic MD simulations.

Dynamic 3D effects of single fiber tensile break within unidirectional composites including resin plasticity, residual stress, interfacial debonding and sliding friction

To study the dynamics of a single fiber tensile break within an S-Glass/epoxy composite and the associated effects of stress wave propagation in the fibers, interface and matrix, a 3D micromechanical Finite Element (FE) model with a hexagonal packing of parallel fibers is developed. The effects of a dynamic fiber break on energy dissipation associated with resin plasticity and interface debonding using cohesive traction laws are included. The 3D FE model also incorporates process-induced residual stresses that induces radial compression at the fiber-matrix interface due the mismatch in CTE and Poisson’s ratios between the fiber and matrix. During dynamic fiber failure where interface debonding occurs, radial compressive residual stresses lead to additional frictional energy dissipation in the debond region of the interface. A map of the dynamic stress concentration factor (SCF) values on the surface (along the axial as well as circumferential directions) of the fibers which are neighboring the fiber break is generated. A stability criterion based on an energy balance between elastic strain energy released by the fiber and energy dissipation (resin plasticity, interphase debonding and frictional sliding) is established to predict maximum fiber strength that initiates unstable debonding of the interface characteristic of axial splitting of the unidirectional composite loaded in tension. The FE modeling results also indicate that the dynamic fiber break introduces strain rates on the order of 106/s in the fiber and matrix, and up to 1012/s in the interphase.

Numerical simulation of mechanical behaviors and intergranular fracture of polycrystalline Nb3Sn and superconducting filaments

Given the importance of large-scale engineering applications of the superconducting compound Nb3Sn, both its use and performance under certain operating conditions have attracted the interest of applied superconductivity researchers and material scientists for several years now. Huge efforts are directed toward understanding the response to applied loads and predicting fracture damage within their internal microstructure; this is fundamental in the design of superconducting coils and magnets which must meet stringent requirements in terms of maximum thermal and electromagnetic loads. In this paper, the fracture behaviors in polycrystalline Nb3Sn and Nb3Sn filaments with composite structures are investigated using the micromechanical finite element (FE) models with Voronoi tessellation. First, the 2D and 3D Voronoi FE models of the polycrystalline Nb3Sn tensile tests are developed and validated to provide insight into the cracking behavior in the intergranular brittle fracture of polycrystalline Nb3Sn. A cohesive zone model is used to simulate crack propagation at the grain level model including grain boundary zones. It is found that the pre-existing cracks of polycrystals and martensitic phase transformation of grains significantly impact the fracture properties in polycrystalline Nb3Sn. Second, detailed FE models of powder-in-tube (PIT) and bronze route filaments with Voronoi structures for fracture analysis are then developed on the basis of experimental observations of sectional morphologies. The mechanism of crack initiation and propagation under tensile load have been investigated by analyzing the mechanical properties of each component and the characteristics of multi-scale composite structures of filaments. Furthermore, the damage situation is investigated in PIT filaments undergoing transverse compressive load. The proposed simulation method in this paper can be extended to the fracture and damage analysis of Nb3Sn superconducting wires with different layouts and fabrication processes.

A sequential mobile packing algorithm for micromechanical assessment of heterogeneous materials

A new non-uniform sequential mobile packing (NSMP) algorithm featuring an efficient collision detection scheme was developed to rapidly generate representative volume elements (RVEs) for advanced heterogeneous and/or composite material systems with either spherical or cylindrical inclusions and a broad range of microstructural characteristics (i.e., various inclusion orientations and sizes, and agglomerations). Statistical assessment of inclusion spatial dispersion using nearest neighbor-based and pair correlation functions revealed that the NSMP algorithm generated RVEs with realistic microstructures for all cases considered. Subsequent statistical finite element micromechanical modeling was conducted to compute the effective properties for each generated microstructure. A case study for a 3D-printed nanocomposite material revealed that a combination of aligned and misoriented rod inclusions was the most representative microstructure. Contour plots of normalized effective stiffness for the 3D-printed composites and normalized average hydrostatic stress in the matrix phase enabled comparison of RVEs with different microstructures. The material system with aligned rod inclusions benefited from simultaneous high effective stiffness and effective load transfer to the inclusions (at higher inclusion volume fractions), which is indicated by low average hydrostatic stress in the matrix. The microstructures comprising spherical inclusions exhibited moderate stiffness, while those with clustered misoriented rod inclusions had the lowest effective stiffness and load transfer to the inclusions. The NSMP algorithm can be used for further microstructural optimizations and assessments of renifornced or porous heterogeneous and/or composite materials using machine learning, while the generated contours can be used as general design guidelines.

Bidirectional hyperelastic characterization of brain white matter tissue.

Biomechanical study of brain injuries originated from mechanical damages to white matter tissue requires detailed information on mechanical characteristics of its main components, the axonal fibers and extracellular matrix, which is very limited due to practical difficulties of direct measurement. In this paper, a new theoretical framework was established based on microstructural modeling of brain white matter tissue as a soft composite for bidirectional hyperelastic characterization of its main components. First the tissue was modeled as an Ogden hyperelastic material, and its principal Cauchy stresses were formulated in the axonal and transverse directions under uniaxial and equibiaxial tension using the theory of homogenization. Upon fitting these formulae to the corresponding experimental test data, direction-dependent hyperelastic constants of the tissue were obtained. These directional properties then were used to estimate the strain energy stored in the homogenized model under each loading scenario. A new microstructural composite model of the tissue was also established using principles of composites micromechanics, in which the axonal fibers and surrounding matrix are modeled as different Ogden hyperelastic materials with unknown constants. Upon balancing the strain energies stored in the homogenized and composite models under different loading scenarios, fully coupled nonlinear equations as functions of unknown hyperelastic constants were derived, and their optimum solutions were found in a multi-parametric multi-objective optimization procedure using the response surface methodology. Finally, these solutions were implemented, in a bottom-up approach, into a micromechanical finite element model to reproduce the tissue responses under the same loadings and predict the tissue responses under unseen non-equibiaxial loadings. Results demonstrated a very good agreement between the model predictions and experimental results in both directions under different loadings. Moreover, the axonal fibers with hyperelastic characteristics stiffer than the extracellular matrix were shown to play the dominant role in directional reinforcement of the tissue.

Experimental and numerical study on SMA modified with an encapsulated polymeric healing agent

The present study aims at experimentally and numerically investigating the effect an encapsulated healing agent on the mechanical characteristics of a stone mastic asphalt (SMA). As a healing agent a thiol-containing urethane AR-polymer is used in this study. In order to gain a numerical insight into mechanical behavior of the capsules in SMA, a micromechanical finite element modeling is employed. The developed model allows capturing the stresses induced in the capsules at different load cases applied to the SMA on macro-scale. Particular attention is paid presently to the numerical evaluation of the local stress state that arises around capsules during compaction, operation, and also during crack initiation. SMA mixtures with various volumetric contents of healing capsules were manufactured and the capsules survival during mixture production was evaluated based on X-Ray Computed Tomography measurements. The effect of capsules on the self-healing properties of asphalt mixtures has furthermore been examined with repeated compressive strength tests. The obtained experimental results indicate that the absolute majority of capsules survive mixture production, and that their addition increases the SMA strength recovery during the healing period. The experimental and numerical results concerning capsules breakage are found to be in reasonable agreement. The developed micromechanical model may thus potentially provide a useful tool for optimization of capsules mechanical properties in order to improve their survival during mixture production as well as their timely activation.

Effective volume filling ratio of siliceous fillers within bituminous composites: experimental and micromechanical modelling

The effect of different volume filling ratios (VFR) of filler on the flexural creep stiffness and complex shear modulus of bituminous composites can be identified using BBR and DSR test setups. This research compares the findings of extensive experimental studies with the biphasic heterogeneous micromechanical finite element (FE) models to introduce the Effective Volume Filling Ratio (EVFR). The different VFRs from 10 to 40% were selected to fabricate asphalt mastic samples. The effects of loading regime, temperature, loading frequency, and VFR on the mechanical behavior of asphalt mastic were investigated, and practical formulations were proposed to determine the EVFR for both shear and bending stiffening. It was found that for VFR ≤ 20%, the differences between the FE and test results are negligible under both loading schemes. However, higher VFRs cause a further increase in the stiffening and percolation effects which produce more differences between the experimental and FE results.

Predictive Capability of a Finite Element Micro-Mechanical Model for Masonry Elements Reinforced Using CFRP

Different commercial Finite Element Codes proved to be able to describe the mechanical behavior of masonry materials externally reinforced by means of Carbon Fiber Reinforced Polymers (CFRP); the behavior of fracturing materials, characterized by low tensile strength, with adhered strips can be reproduced relying on parameters based on fracture mechanics and the theories of adhesion.In this report the comparison is made of previous experimental test results with numerical analysis, carried out on masonry panels reinforced with CFRP strips and subjected to out of plane actions. The comparison is especially addressed to the evaluation of the post peak branch; in addition to the slopes of the diagram in the pre-critic phase, available kinematic ductility and energy shares both prior and after the peak load were considered in order to interpret the capability of the micro-mechanical model implemented in the FEM Code to account for the local phenomena influencing the interaction between masonry and FRP strengthening systems.

Spherical indentation test for quasi-non-destructive characterisation of asphalt concrete

The indentation test is a promising technique for the viscoelastic characterisation of asphalt concrete (AC). Indentation measurements are primarily influenced by the material properties in the direct vicinity of the indenter-specimen contact point. Accordingly, it may become a useful alternative for the characterisation of thin asphalt layers as well as for a quasi-non-destructive AC characterisation in the field. In this study, the spherical indentation test is used to measure the linear viscoelastic properties of AC mixtures extracted from a road test section. The measured complex moduli are compared to those obtained by the shear box test and are found to exhibit a linear correlation. The measurements are further analysed using the Gaussian mixture model to assign each indentation test to either aggregate-dominated or mastic-dominated response. The measurements attributed to mastic-dominated response are found to be more sensitive to the temperature and AC’s binder properties as compared to the average measurements. Accordingly, the proposed test method may provide a promising tool to measure AC viscoelastic properties and monitor the changes in AC binder phase in a non-destructive manner. A finite element micromechanical model is used to identify a representative scale for the response measured in mastic-dominated tests as well as to quantify the effect of measured properties on the AC damage propensity.

Effect of dislocation network on precipitate morphology and deformation behaviour in maraging steels: Modelling and experimental validation

In maraging steels subjected to High Pressure Torsion (HPT), overaging (OA) leads to considerable reduction in ductility as compared to the overaged counterparts in the as-received (AR), hot-rolled state. Atom probe tomography has revealed a corresponding difference in morphology of Fe2Mo precipitates between the HPT+OA and the AR+OA conditions, the former being flat, disc shaped, while the latter are spherical. In order to reveal the role of the high dislocation density introduced during HPT on this change of precipitate morphology and consequent mechanical behaviour, phase field modelling study was carried out. It is shown that the increased solute mobility pathway provided by dislocations through pipe diffusion leads to the evolution of this new precipitate morphology in the otherwise slow diffusing species-Mo. Using a micromechanical finite element model, we correlate the changes in morphology to the differences in ductility in the overaged AR and HPT processed samples.

Synthesis, characterization, and modelling the behavior of in-situ ZrO2 nanoparticles dispersed epoxy nanocomposite

The cured epoxy has poor toughness owing to highly cross-linked nature. The present work reports inclusion of ZrO2 nanoparticles with epoxy via ultrasonic mixing process for improving the toughness. The developed nanocomposites are characterized using mechanical tests, fractographic analysis and dynamic mechanical thermal analysis (DMTA). The mode-1 fracture toughness (K1C), fracture energy (G1C), storage modulus (E') and glass transition temperature (Tg) for different filler concentration are evaluated. A theoretical explanation for improved ZrO2-epoxy nanocomposite behaviour is reported by analyzing the fracture parameters and morphology of fractured samples. A micromechanical finite element (FE) model is constituted for predicting macroscopic elastic properties of composites using numerical homogenization scheme. The model predicted location of fracture initiation under triaxial and uniaxial loading conditions. The SEM micrographs and modelling results collectively explained the fracture mechanism. The experimentation and modelling results are compared.

Micro-mechanical FE modelling and constitutive parameters calibration of masonry panels strengthened with CFRP sheets

This paper describes the development of a micro-mechanical Finite Element model apt to reproduce the behavior of masonry walls reinforced with Carbon Fiber Reinforced Polymer (CFRP) sheets, monotonically loaded by out of plane actions. According to the results of previous experimental programs carried out by the Authors, in the case of CFRP sheets bonded parallel to the bed joints, such walls behave like un-connected masonry portions (similar to strengthened masonry beams). For this reason, only such effective part was considered in both the experimental program (already published by the Authors) and the numerical simulations. Both simply bonded and anchored CFRP reinforcements have been considered in the paper.Particular attention was paid to the definition of the constitutive parameters, calibrated on the basis of several experimental campaigns previously performed by the Authors. Since fracture energy of bulk materials and adhesive tangential strength of the reinforcement are generally thought of as difficult to experimentally determine and can be affected by uncertainties, a sensitivity analysis concerning such parameters is described in the paper.The numerical predictions have been compared to the experimental outcomes in terms of load displacement diagrams, stress distribution and damage evolution; the proposed numerical model seems to well reproduce the general experimental behavior.

The Effect of Tempering Duration on the Creep Behavior of the P91 Steels at 600℃

High performance martensitic heat resistant steels are widely used in fossil fuel power plant industry due to because of their good creep resistance at high temperatures. In-depth understanding of the high temperature inelastic deformation mechanism of such steels is crucial to ensure the reliable, safe and efficient operation of the power plant [1]. The martensitic steels have a complex microstructure with a hierarchical arrangement, including a collection of packets in the prior austenite grain, blocks in the packet and laths along with dispersed nanoscale strengthening phases (e.g., MX precipitates and carbides). The purpose of this paper is to study the creep mechanisms with regard to the microstructure of the P91 martensitic steel at high temperature by means of experimental characterisation and finite element simulation. In the present paper, the effect of tempering duration on the creep response of the P91 steel at 600 oC was experimentally examined with the precipitate size identified. Apart from the standard heat treatment (holding at 1060℃ for 40 min and then at 760℃ for 2 h) for the as-received P91 steels, secondary tempering treatment has been applied with different tempering time periods, e.g., 0 h (T0), 10 h (T10) and 20 h (T20) at 780℃. In order to simulate the creep response, crystal plasticity based micromechanical finite element model was developed based on the measured microstructure [2]. The crystallographic slip at the block level is accounted for using an exponential type of constitutive flow rule and the precipitate size effect is represented in the crystal plasticity model through the use of an internal variable in association with the slip resistance. The results show that the secondary tempering duration can significantly affect the creep behavior of the martensitic steel (see Fig. 1). It is found that with increasing tempering time period the precipitate size increases, which could lead to detrimental effect on material’s creep resistance. Similar effect of the precipitate size on the creep response has also been shown in literatures [3]. The measured creep response of the P91 steels with different heat treatments at different stress levels can be predicted by the developed micromechanical model. The micromechanical modelling results show (see Fig. 2) that the accumulated equivalent plastic strain during the creep is strongly heterogeneous and the levels of the strain localization depend on the tempering duration.

Numerical study of the aggregate contact effect on the complex modulus of asphalt concrete

Asphalt concrete (AC) is a composite material consisting of binder, aggregates and air voids. The quantitative effect of aggregate-to-aggregate contact on the mechanical performance of AC is an important and complex issue, which has not been fully understood yet. To fill this gap, this study aims to characterize the aggregate contacts in AC and evaluate their effects on the viscoelastic behavior of AC through micromechanical finite element (FE) modeling. To this end, 3D microstructural models were generated through digital image processing (DIP) method and aggregate contacts were captured in the model via contact zone (CZ) elements. A CZ model was proposed and verified by a parametric study to identify the viscoelastic properties of CZ elements, while the viscoelastic properties of matrix phase were determined through laboratory tests. Steady-state dynamic (SSD) analysis was then conducted to investigate the macro-scale viscoelastic response of AC. It was found that the proposed modeling approach captures the measured response accurately. Accounting for aggregate contacts results in higher predicted AC dynamic moduli and lower phase angles, thus improving the agreement between modeling and experimental results. The numerical model developed in this study provides a promising approach for investigating the effect of aggregate contacts on the mechanical performance of AC.

Predicting the master curves of bituminous mastics with micromechanical modelling

The performance of asphalt mixtures is significantly affected by the viscoelastic properties of their mastic phase. The analytical approaches used to predict the properties of mastics from their constituents’ properties are limited in their accuracy and potential to handle non-linear material behaviour. An alternative micromechanical finite element modelling approach to calculate the master curves of mastics from the binder and filler phase properties is presented, where the representative volume elements of mastics consist of linear-viscoelastic bitumen matrices and elastic spherical filler particles. For validation, shear relaxation moduli of bitumen and bitumen-filler mastics are measured at °C°C. Additionally, the model is evaluated and compared with the existing analytical solutions. The results indicate that the proposed approach is advantageous as compared to the analytical solutions, as it allows predicting the mastics’ properties over wider temperature, frequency and material ranges at better agreement with the measurements while giving insight into the micromechanical behaviour.