Micromechanical Finite Element Research Articles

Studying the effect of design microscale factors on the thermoelastic response of carbon nanotube-reinforced metal nanocomposites using the finite element micromechanics method

Studying the effect of design microscale factors on the thermoelastic response of carbon nanotube-reinforced metal nanocomposites using the finite element micromechanics method

The role of constitutive properties on the longitudinal compressive strength of composites

The longitudinal compressive strength of fibre-reinforced composites is often a limiting factor for structural design. This paper uses micromechanical finite-element analyses to examine how the constitutive properties of the matrix, fibres, and interface affect the composite’s strength. For a typical carbon/epoxy composite, the matrix shear strength has a larger effect than the modulus; a linear-elastic perfectly-plastic approximation of the matrix shear curve may overestimate the composite’s strength by over 15%. A pressure-dependent and dilatant matrix plasticity response may strengthen the composite by 30%, considering current uncertainties in friction and dilation angles of epoxy matrices. The finite shear modulus of carbon fibres may weaken the composite by more than 10%. Considering a cohesive interface using traction–separation laws significantly affects the predicted response of the composite, even for interfaces stronger than the matrix. Opportunities for improving the characterisation, modelling and performance of the constituents in terms of matrix plasticity, fibre shear modulus, and interface response are discussed.

Identifying multiple synergistic factors on the susceptibility to stress relaxation cracking in variously heat-treated weldments

The 347H austenitic stainless steel has been widely used for pressure vessels and pipeline (PVP) applications due to its excellent creep and corrosion resistance, which fit ideally to the harsh conditions in petrochemical industries, fossil fuel or nuclear power plants, and modern energy storages. However, a failure mode has been commonly observed with cracks emerging at the heat affected zone (HAZ) of weldments during post-weld heat treatment (PWHT) or under intermediate to high temperature service conditions. This phenomenon is termed as Stress Relaxation Cracking (SRC) since the purpose of PWHT is to relieve the welding-induced residual stress fields, or as Stress Age Cracking (SAC) if failure happens during service. A leading literature explanation of this failure suggests that the residual stress relaxation and the precipitation dissolution and/or re-precipitation occur in the same temperature range, which can lead to locally high strains and thus to crack at the grain boundaries. Since in situ spatial measurements of residual stress fields, microstructural evolution, and failure processes are nearly infeasible, this work recourses to a micromechanical finite element framework that models the high temperature failure as the nucleation and growth of grain boundary cavities, whereas various parameters such as thermomechanical loading history and its evolution, the competition of grain-interior dislocation creep and grain-boundary diffusion in failure lifetime, and microstructural heterogeneities (such as the precipitate free zone near grain boundaries) can be quantitatively incorporated. It can be concluded from these microstructure-explicit simulations that an accurate knowledge of residual stress evolution and a carefully calibrated set of material constitutive parameters are the essential prerequisites for lifetime predictions. The understanding of individual governing factors also leads to a mechanistic interpretation of the observed SRC susceptibility C-curves. These results suggest that the criticality of residual stress evolution, but not the precipitation-induced local strains, be the leading factor for SRC.

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.

Ductile rupture under cyclic loadings at high triaxiality: The influence of strain hardening and elasticity

Previous works (Devaux et al., 1997; Cheng et al., 2017) have emphasized the effects of strain hardening and elasticity upon ductile rupture of metals under cyclic loading conditions. This work pursues the study and modelling of these two effects by distinct theoretical methods, each coupled with micromechanical finite element simulations of the behaviour of some “representative cell”. For the effect of strain hardening, we employ Morin et al. (2017)’s approach, based on the theory of sequential limit-analysis (Yang, 1993; Leu, 2007; Leblond et al., 2018). This approach is applied to various types of hardening of the metallic matrix: isotropic, linear kinematic, nonlinear kinematic with one or two kinematic variables (Armstrong and Frederick, 2007) , and even a simplified version of Chaboche (1991)’s model accounting for complex cyclic effects. Numerical micromechanical simulations of a hollow sphere made of elastic–plastic materials obeying the various hardening laws considered, and subjected to cyclic loadings at high triaxiality, fully confirm the predictions of the model developed, provided elasticity is made negligible by using an artificially high value of Young’s modulus. When a realistic value is employed, however, the agreement between theoretical predictions and numerical results is degraded, thus emphasizing again the importance of the effect of elasticity in cyclic ductile rupture. To deal with this effect we derive, apparently for the first time, an evolution equation of the porosity accounting for (compressible) elasticity. However, numerical micromechanical simulations reveal that simply using this new evolution law, while keeping all other aspects of the model unchanged, remains insufficient to get a good match of theoretical and numerical results. Such a match is achieved by introducing the ad hoc hypothesis that the yield criterion and flow rule derived from sequential analysis still apply in the presence of elasticity, but with some “effective porosity” slightly differing from the true one through some heuristic, adjustable factor.

Modelling, optimization, and testing of novel cuboidal spherical plate lattice structures

ABSTRACT This study investigates the mechanical behavior of a novel set of Cuboidal Spherical Plate Lattice (CSPL) materials. The procedure of constrained-domain topology optimization is implemented with the aim of enhancing stiffness. The micromechanical finite element homogenization approach is used to evaluate the effective elastic-plastic properties of the CSPLs and their topologically optimized counterparts, TOCSPLs (Topologically Optimized Cuboidal Spherical Plate Lattices). The TOCSPLs demonstrate higher uniaxial, shear, and bulk moduli compared to the CSPLs, with an increase of 31%, 14%, and 36% respectively. Moreover, there is an increase in the yield strengths under uniaxial, shear, and hydrostatic loading conditions, with enhancements of 103%, 55%, and 62%, respectively. The topologies are additively manufactured through Fused Deposition Modeling (FDM) out of ABS thermoplastic material. The quasi-static compression experiments demonstrate the superiority of TOCSPL 111+100 over the other topologies in terms of uniaxial modulus. The suffix 111+100 denotes the crystallographic planar orientations in which the solid plate-like disks were formed within a cubic system. The topologies proposed herein outperform certain types of Triply Periodic Minimal Surface, honeycomb, truss-, and plate-based lattice materials. The proposed topologies offer a compelling justification for their utilization in applications that require load-bearing and impact absorption capabilities.

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.

Effect of interface on elastic and toughening behavior in poly lactic acid/thermoplastic starch blends: Micromechanical finite element analysis

AbstractIt is frequently emphasized that the action of interfacial adhesion is a critical parameter to improve the stiffness and toughness of polylactic acid/thermoplastic starch (PLA/TS) blends. In this work, the micromechanical behavior of PLA/TS blends with droplet morphology selected from literature is predicted and analyzed systematically by finite element analysis. A quantitative assessment of the effect of interface (perfect or imperfect) on the elastic behavior and craze initiation for toughening of PLA/TS blends is presented. For the elastic behavior, the PLA phase is the blend's load‐bearing component as the TS is more compliant than PLA, so an interface perfectly bonded reduces the blend's elastic modulus when compared to the modulus obtained if the interface is weakly bonded. Regarding the toughening behavior, as a compliant phase, the TS has the potential to nucleate stable crazes in the host PLA matrix independently of the degree of interfacial adhesion because the highly stressed region lies near the equator of the particle; nonetheless, the critical stress for craze initiation is very sensitive to the TS particle size. On the other hand, as the TS is less capable than PLA to develop large hydrostatic stresses, the TS has a low potential to dissipate energy by cavitation.

Numerical vibroacoustic analysis of multi-layered composite structure under hygrothermal loading using coupled FEM-IBEM micromechanical model

The vibroacoustic responses of multi-layer composite shallow shell panels subjected to harmonic mechanical excitation in hygrothermal environment is numerically investigated. A homogenized micromechanical finite element (FE) based on the higher-order mid-plane kinematics replicating quadratic function as well as the through the thickness stretching effect together with the indirect boundary element (IBE) scheme has been first time employed. The isoparametric Lagrangian element with zero-order Hermitian interpolation function (10 degrees of freedom per node) is used for structural model discretization to attain the hygro-thermo-elastic natural frequencies via Hamilton’s principle. The uniqueness of the model is the incorporation of the effective material properties under combined hygrothermal loading via a micromechanics approach. An IBE method is then implemented to attain structure-surrounding coupling and the Helmholtz wave equation is solved to compute the sound radiation responses. The effectiveness of the model is tested by converging it with the similar analytical/numerical results as well as the experimentally acquired data for vibrational as well as acoustic responses. The present scheme is further hold out for solving diverse numerical illustrations. The geometrical parameters, volume fraction of fiber, layup, and support conditions alongside the hygrothermal load is found to have significant influence on the hygro-thermo-acoustic characteristics. The functional inferences will assist in designing the imminent multi-layered structures that serve under the influence of severe hygrothermal loading during high-performance engineering applications.

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.

A multiscale deep learning model for elastic properties of woven composites

Time-consuming and costly computational analysis expresses the need for new methods for generalizing multiscale analysis of composite materials. Combining neural networks and multiscale modeling is favorable for bypassing expensive lower-scale material modeling, and accelerating coupled multi-scale analyses (FE2). In this work, neural networks are used to replace the time-consuming micromechanical finite element analysis of unidirectional composites, representing the local material properties of yarns in woven fabric composites in a multiscale framework. Leveraging the fast multiscale data generation procedure, we presented a second neural networks model to estimate the elastic engineering coefficients of a particular weave architecture based on a broad range of dry resin and fiber properties and yarn fiber volume fraction. As an outcome, this paper provides the user with a generalized, neural network-based approach to tackle the balance of computational efficiency and accuracy in the multiscale analysis of elastic woven composites.

Porous single crystals under triaxial creep loadings: A data-driven modelling approach

The evolution of porosity plays an important role during failure processes in metallic materials at room and elevated temperatures. Recent experiments showed that void growth and coalescence may lead to the creep rupture of single crystal materials, mainly through plastic flow. It is highly challenging to accurately model the combined effects of multiple controlling factors, such as crystal orientation, matrix hardening behaviour, void shape and stress state. In this work, a neural network surrogate model was constructed to predict the behaviour of single crystals containing voids under creep loadings. Training of the neural network model was performed using 3D micromechanical finite element simulation results. A detailed assessment was carried out to examine the interpolation ability of the neural network model with respect to the crystal orientation, stress triaxiality and Lode parameter, as well as its extrapolation ability. Within the interpolation range, the neural network predictions of the deformation behaviour and porosity evolution of porous single crystals agree well with the finite element results of test dataset. The characteristic quantities, including the effective steady state strain rate, critical time and effective strain for the onset of tertiary creep, were predicted within 20% error with respect to the micromechanical simulation results for most of cases considered. Finally, the extrapolation ability of the model in predicting deformation behaviour of porous single crystal is good for the stress triaxiality lower than 1/3. However, the prediction of deformation and void evolution is deteriorated for the stress triaxiality larger than the range of value used for the training.

Lower hardness than strength: The auxetic composite microstructure of limpet tooth.

The limpet tooth is widely recognized as nature's strongest material, with reported strength values up to 6.5 GPa. Recently, microscale auxeticity has been discovered in the leading part of the tooth, providing a possible explanation for this extreme strength. Utilizing micromechanical experiments, we find hardness values in nanoindentation that are lower than the respective strength observed in micropillar compression tests. Using micromechanical modeling, we show that this unique behavior is a result of local tensile strains during indentation, originating from the microscale auxeticity. As the limpet tooth lacks ductility, these tensile strains lead to microdamage in the auxetic regions of the microstructure. Consequently, indentation with a sharp indenter always probes a damaged version of the material, explaining the lower hardness and modulus values gained from nanoindentation. Micropillar tests were found to be mostly insensitive to such microdamage due to the lower applied strain and are therefore the suggested method for characterizing auxetic nanocomposites. STATEMENT OF SIGNIFICANCE: This work explores the micromechanical properties of limpet teeth, nature's strongest biomaterial, using micropillar compression testing and nanoindentation. The limpet tooth microstructure consists of ceramic nanorods embedded in a matrix of amorphous SiO2 and arranged in a pattern that leads to local auxetic behavior. We report lower values for nanoindentation hardness than for compressive strength, a unique behavior usually not achievable in conventional materials. Utilizing micromechanical finite element simulations, we identify the reason for this behavior to be microdamage formation resultant of the auxetic behavior, sharp indenter tip and lack of ductility of the limpet tooth microstructure. This formation of microdamage is not expected in micropillar compression tests due to lower locally imposed strain.

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.

Investigation of asphalt pavement crack propagation based on micromechanical finite element: A case study

Cracking is a prevalent issue in expressway pavements in Shanxi Province, exhibiting various types. Based on field investigations, the primary types of asphalt pavement cracks observed in Shanxi expressways can be categorized as top-down crack (TDC, surface crack) and reflection crack (bottom-top crack). These two types differ significantly in terms of cracking mechanisms, development modes, treatment methods, and impact severity. This paper aims to simulate the initiation and propagation processes of top-down cracks and reflection cracks using the finite element method, aiming to provide a basis for distinguishing between the two. In this paper, a microstructure numerical model of a three-phase asphalt concrete pavement is established. Finite element software is utilized to simulate the initiation and propagation of top-down cracks and reflection cracks on asphalt pavement, while investigating the influence of various factors on crack propagation. The findings demonstrate that top-down cracks exhibit multi-point cracking on the pavement surface, resulting in a tortuous and discontinuous development process. Conversely, reflection cracks display significant stress concentration at the crack tip, leading to propagation even under loads significantly lower than the material's tensile strength, following a single propagation path. Aggregate distribution form, preset crack length, tensile strength of ITZ, and load distribution form do not have a significant effect on the primary cracking mode. However, they do influence the crack initiation point, cracking load, and propagation path to some extent.

Micromechanical Finite Element Simulation of Low Cycle Fatigue Damage Occurring During Sliding Wear Test of ECAP-Processed AA7075 Alloy

Micromechanical Finite Element Simulation of Low Cycle Fatigue Damage Occurring During Sliding Wear Test of ECAP-Processed AA7075 Alloy

Fracture properties of thin brittle MTM clay coating on ductile HEC polymer substrate

Thin clay coatings can be deposited from water dispersions for the purpose of improved gas barrier properties and fire retardancy of polymeric materials. Mechanical properties of the coatings are difficult to assess, since they are very thin (≈1µm). In-situ tests using a micro tensile stage in a scanning electron microscope reveal a thickness-dependent microcracking mechanism, and Weibull parameters for coating fracture are extracted. Complex fracture events are identified, related to a weak clay coating-polymer substrate interface. A micromechanical finite element formulation provides values of 5 MPa for interfacial shear strength and 1 J/m2 for interfacial fracture toughness. From the multiple cracking behavior of the clay coating, a clay strength ≈ 225 MPa is estimated by the Weibull strength parameter from fragmentation diagrams. The method may be extended to other combinations of brittle coating-ductile substrates.

Mediating compositional machining difference of UD-CFRP in orthogonal cutting by epoxy coating

The intrinsically different mechanical properties between fiber and matrix result into heterogeneous deformation behavior of unidirectional carbon fiber reinforced polymer (UD-CFRP) composites under mechanical loading. And how to minimize even eliminate the compositional machining difference is central for enhancing the machinability of UD-CFRP composites. In the present work, we propose a novel cutting strategy of applying an epoxy coating onto the pre-machined surface, i.e., epoxy coating cutting (ECC), for mediating the compositional machining difference accompanied with promoted machinability of UD-CFRP composites. Experimental results of both ECC and conventional cutting (CC) illustrate the alternation of cutting force, chip formation and machined surface quality by applying epoxy coating. Corresponding micromechanical finite element simulations of ECC reveal that the introduced restraining effect by epoxy coating is effective in prolonging the failure resistance of matrix, and thus minimizing the machining difference between fiber and matrix. The dependence of the mediating effect of epoxy coating on coating thickness is further evaluated by numerical simulations and corresponding experiments. Current findings provide novel insights and a practical guidance for rationally mediating the compositional machining difference of CFRP composites by employing the ECC strategy.