Micromechanical Finite Element Analysis Research Articles

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.

Strain-rate dependent mixed-mode traction laws for glass fiber-epoxy interphase using molecular dynamics simulations

In this paper, we establish a methodology to predict strain rate-dependent mixed-mode traction-separation responses (i.e., traction laws) for glass-epoxy composite interphase using molecular dynamics (MD) simulations. Glass-epoxy interphases with monolayer glycidoxypropyltrimethoxy silane are prepared by varying silane number density from 0.0 nm−2 to 3.9 nm−2 following the epoxy-amine diffusion and curing reactions. To established the effects of strain rate and mode-mixity on the interphase traction laws, the nano-meter size interphase domain is loaded in various mode-mixity (θ=0°(Mode−II),15°,30°,45°,60°,and90°(Mode−I)) with full range of strain rates from quasit-static to high strain rate (∼1e16/s) where a theoretical plateau strength limit is predicted. Following our previous work on Mode-I [Chowdhury et al., Composites Part B 237 (2022) 109877], mathematical model is developed for Mode-II as function of strain rate for different interphase structures (i.e., silane number density). The continuum equivalent bi-linear cohesive traction law is developed using the MD results to determine the mode-mixity quadratic functions and associated exponents for peak tractions, energy absorption, crack initiation and crack opening displacement from the mixed-mode simulations data. The MD predicted traction laws can be used to model interphase in micromechanics finite element analysis to bridge the length scale for the prediction of fiber-matrix debonding in composites.

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.

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.

Aluminum Matrix Composites with Weak Particle Matrix Interfaces: Effective Elastic Properties Investigated Using Micromechanical Modeling.

The impact of weak particle-matrix interfaces in aluminum matrix composites (AMCs) on effective elastic properties was studied using micromechanical finite-element analysis. Both simplified unit cell representations (i.e., representative area or volume elements) and “real” microstructure-based unit cells were considered. It is demonstrated that a 2D unit cell representation provides accurate effective properties only for strong particle-matrix bond conditions, and underpredicts the effective properties (compared to 3D unit cell computations) for weak interfaces. The computations based on real microstructure of an Al–TiB2 composite fabricated using spark plasma sintering (SPS) show that, for weak interfaces, the effective elastic properties under tension are different from those obtained under compression. Computations show that differences are the result of the local stress and strain fields, and contact mechanics between particles and the matrix. Preliminary measurements of the effective elastic properties using the ultrasonic pulse-echo technique and compression experiments support the trends observed in computational analysis.

Effects of void content on flexural properties of additively manufactured polymer composites

Mechanical characterizations are inevitable to the research and development in additive manufacturing (AM). Most mechanical tests for composite materials are relatively expensive, time-consuming, and challenging. Therefore, three-point flexural testing is widely adopted as it offers an easy and fast method to assess AM composite's performance. The correlations between the flexural and other mechanical properties in AM composites are, however, not understood. In this work, multiscale modeling is utilized to connect micro-scale composite properties to macro-scale flexural simulations and experiments. Two AM composite samples of continuous carbon fiber-reinforced polyetheretherketone (PEEK) are considered. The void volume fractions in these samples are ~10 and 5%, typical of the composite's AM process. First, elastic constants for the two samples, considering their porosity, are predicted via micro-mechanical finite element analysis (FEA). A test model is then constructed to carry out detailed macro-scale FEA stress analysis in flexural tests. Specifically, flexural strength of AM composites is correlated to their tensile and compressive strengths. The findings of this study can pave the way for rapid characterization, process optimization, and new materials development in AM composites.

Micromechanical Modeling of Anisotropy and Strain Rate Dependence of Short-Fiber-Reinforced Thermoplastics

The anisotropy and strain rate dependence of the mechanical response of short-fiber-reinforced thermoplastics was studied using a straightforward micromechanical finite element analysis of representative volume elements (RVEs). RVEs are created based on the fiber orientation tensor, which quantifies the processing-induced fiber orientation distribution. The matrix is described by a strain rate-dependent constitutive model (the Eindhoven glassy polymer (EGP) model), which accurately captures the intrinsic response of amorphous polymers. The micromechanical results indicate that the influence of strain rate and that of the loading direction on the yield stress are multiplicatively decouplable, which confirms previous experimental observations. Moreover, it is demonstrated that the yield stress, to a good approximation, can be directly linked to the fiber orientation in the direction of loading. This leads to a new relation that uniquely links the rate dependence of the yield stress to the fiber orientation in loading direction.

Micromechanical finite element analysis of effect of multilayer interphase on crack propagation in SiC/SiC composites

The current study presents a micromechanical methodology to analyze the cracking behavior of a SiC/SiC composite with multilayer interphase using finite element method. To capture the constituent level damage initiation and propagation within the multilayer interphase, an axisymmetric unit-cell model was developed by discreetly modeling the fiber, the matrix, and the sublayers of interphase. Moreover, the cracking inside the interphase and debonding at the interfaces between different constituents were taken into account. The extended finite element method (XFEM) was applied to model the cracking inside the interphase and matrix. The cohesive surface approach was employed to describe the debonding behavior at all the interfaces. Adopting the proposed numerical approach, detailed local stress state and cracking behavior of SiC/SiC composites with multilayer interphase were analyzed. The results show that the multilayer interphase has a significant effect on the cracking behavior. Moreover, the growth length of secondary cracks had been demonstrated to be a useful parameter that is capable of connecting composites level behaviors and constituent level damages. From the various numerical methods used, the finite element simulation in conjunction with the XFEM and the cohesive surface approach is a precise and consistent way to analyze the crack propagation and prediction of failure for composites with multilayer interphase. The research provides a fundamental method for promoting the interphase design of SiC/SiC composites.

Investigation on mechanical properties and deformation behavior of copper-based three-phase metal matrix composite: Experimental and micro-macro-mechanical finite element analysis

The present study involved development of copper-based metal matrix composite, reinforced with waste EN 31 steel chips and TiB2 ceramic particles. Waste EN 31 steel chips and TiB2 ceramic particles were ball-milled for 100 h to obtain a single entity. The composite material was produced with a stir-casting technique, followed by a squeeze pressure process. The addition of Cu + 10 wt% of waste steel chips + 5 wt% of TiB2 improved the tensile strength of the copper matrix by about 68.35%. Furthermore, the addition of Cu + 5 wt% of waste steel chips + 10 wt% of TiB2 and Cu + 12.5 wt% of waste steel chips + 2.5 wt% of TiB2 increased the hardness and toughness of the copper matrix by about 133.33% and 28.57%, respectively. The addition of Cu + 10 wt% waste steel chips + 5 wt% of TiB2 ensured minimal corrosion weight loss in the metal matrix composite as a result of low porosity and a strong bond between the molecules. Further, representative volume element (size: 225 × 225 × 225 nm)-based finite element analysis was done to explain the micro-mechanical deformation, interfacial strength of matrix-particle interaction and damage behavior of Cu + 10 wt% of waste steel chips + 5 wt% of TiB2 metal matrix composite. A user material sub-routine model was also written and implemented with the help of FORTRAN subroutines to simulate the macro-mechanical tension test process of Cu + 10 wt% waste steel chips + 5 wt%TiB2 metal matrix composite. The results revealed a good agreement between the micro-mechanical and macro-mechanical finite element analysis models on the one hand and the experimental results on the other. Further, the representative volume element (with matrix and particles) showed about 59% and 66.5% higher tensile strength compared to the matrix–particle interface and the matrix (without particles), respectively. The percentage difference between the micro-mechanical finite element analysis and the experiments as well as the macro-mechanical finite element analysis and the experiments was found to be 5.58% and 9.64%, respectively. The finite element analysis results established that the waste steel chip powder particles exhibited greater stress than the TiB2 powder particles.

Crack density-based semi-quantitative estimation for leak rate of composite laminates with thin-plies

To predict the leakage of composite fuel tanks due to matrix cracks, this paper proposes novel simulation schemes: (1) A semi-quantitative leak rate estimation method is developed based on the crack intersection area; (2) The semi-analytical damaged constitutive model is obtained by a small amount of micro-mechanical finite element analysis (FEA); (3) The mixed mode crack density is estimated by using the FEA of laminates, which involves the progressive damaged properties; (4) The crack intersecting area is estimated based on the crack density and the crack opening displacement (COD), which is considered as the product of the average unit COD and the strain component. Two sets of simulations are set at room temperature to validate the method in detail, to verify the mechanics of leakage due to the matrix cracks, and to find out the effect of the thin-plies on the leakage. This paper aims at providing new simulation schemes for damaged constitutive model, crack density prediction and leak rate estimation of the composite laminates.

Computational micromechanical modeling of transverse tensile damage behavior in unidirectional glass fiber-reinforced plastic composite plies: Ductile versus brittle fracture mechanics approach

A detailed micromechanical finite element analysis methodology is presented to predict the transverse tensile (fiber perpendicular) failure behavior of a unidirectional (UD) glass fiber-reinforced plastic composite ply. In order to understand the constituent-level stress–strain and damage behavior, finite element analysis is accomplished using representative volume element (RVE) that consists of random fiber distribution as observed in the microscopic image of an actual composite ply. For modeling the fiber/matrix interface failure behavior, cohesive zone module (cohesive surface/cohesive element) of Abaqus® is used. In order to capture the epoxy matrix stiffness and strength degradation, the following two different approaches are used: (i) initially, the linear Drucker–Prager plasticity model in combination with a ductile fracture criterion is used; (ii) later, a brittle failure approach such as the quadratic normal stress criterion within the framework of eXtended finite element method is used. From the detailed micromechanical analysis of the RVE, it is observed that the initial damage in the RVE occurs in the form of fiber/matrix interface decohesion. With increasing tensile load, interface crack propagates and creates a stress concentration region in the matrix material, adjacent to the crack tip. Further load application causes both interface crack tip and matrix stress concentration to move away from the load application direction. As soon as the interface crack tip reaches approximately 60° to 70° away from the load application direction, the conjunction of the matrix damage with the interface crack leads to the RVE final failure. The predicted average stress–strain curves from the above-mentioned two different epoxy matrix failure criterions (ductile and brittle) correlate very well with the experimental results, indicating that the brittle failure behavior of a UD fiber-reinforced plastic composite ply under transverse tensile load is mainly controlled by the fiber/matrix interface properties.

Micromechanical Modeling of Damage Evolution and Mechanical Behaviors of CF/Al Composites under Transverse and Longitudinal Tensile Loadings.

This paper investigates the progressive damage and failure behavior of unidirectional graphite fiber-reinforced aluminum composites (CF/Al composites) under transverse and longitudinal tensile loadings. Micromechanical finite element analyses are carried out using different assumptions regarding fiber, matrix alloy, and interface properties. The validity of these numerical analyses is examined by comparing the predicted stress-strain curves with the experimental data measured under transverse and longitudinal tensile loadings. Assuming a perfect interface, the transverse tensile strength is overestimated by more than 180% and the transverse fracture induced by fiber failure is unrealistic based on the experimental observations. In fact, the simulation and experiment results indicate that the interface debonding arising from the matrix alloy failure dominates the transverse fracture, and the influence of matrix alloy properties on the mechanical behavior is inconspicuous. In the case of longitudinal tensile testing, however, the characteristic of interface bonding has no significant effect on the macroscopic mechanical response due to the low in-situ strength of the fibers. It is demonstrated that ultimate longitudinal fracture is mainly controlled by fiber failure mechanisms, which is confirmed by the fracture morphology of the tensile samples.

Micromechanical FE Analysis of SiCf/SiC Composite with BN Interface

The current study presents a micromechanical Finite Element Analysis (FEA) methodology to predict the room temperature transverse tensile failure behavior of a SiCf/SiC composite (Silicon Carbide Fiber/Silicon Carbide Matrix) with Boron Nitride (BN) fiber coating. In order to accurately capture the constituent level damage initiation and propagation, three-dimensional Representative Volume Element (RVE) models are generated by discreetly modeling the fiber, the matrix, and the coating material. In addition, various geometrical parameters such as the random distribution of the fibers, the fiber-coating, and the matrix-coating interface decohesions were taken into account. For modeling the fiber-coating and the matrix-coating interface interactions, cohesive surface approach within the cohesive zone module of Abaqus® was used. In order to capture the coating and the matrix material fracture behavior, the eXtended Finite Element Method (XFEM) approach was employed. Using the proposed numerical methodology, detailed local stress-strain and damage analysis lead to an observation that the chosen interface interactions have a predominant effect on the RVE damage behavior. Moreover, local fiber placement and the RVE size have a significant influence on the damage initiation threshold and hence the predicted strength and failure strain of the RVE.

Theoretical aspects of selecting repeated unit cell model in micromechanical analysis using displacement-based finite element method

Repeated Unit Cell (RUC) is a useful tool in micromechanical analysis of composites using Displacement-based Finite Element (DFE) method, and merely applying Periodic Displacement Boundary Conditions (PDBCs) to RUC is almost a standard practice to conduct such analysis. Two basic questions arising from this practice are whether Periodic Traction Boundary Conditions (PTBCs, also known as traction continuity conditions) are guaranteed and whether the solution is independent of selection of RUCs. This paper presents the theoretical aspects to tackle these questions, which unify the strong form, weak form and DFE method of the micromechanical problem together. Specifically, the solution’s independence of selection of RUCs is dealt with on the strong form side, PTBCs are derived from the weak form as natural boundary conditions, and the validity of merely applying PDBCs in micromechanical Finite Element (FE) analysis is proved by referring to its intrinsic connection to the strong form and weak form. Key points in the theoretical aspects are demonstrated by illustrative examples, and the merits of setting micromechanical FE analysis under the background of a clear theoretical framework are highlighted in the efficient selection of RUCs for UniDirectional (UD) fiber-reinforced composites.

Micromechanical Finite Element Analysis of the Effects of Martensite Particle Size and Ferrite Grain Boundaries on the Overall Mechanical Behavior of Dual Phase Steel

This paper focuses on micromechanical finite element (FE) modeling of the effects of size and morphology (particularly elongation or aspect ratio (AR) along the loading direction) of martensite particles and the ferrite grains on the overall mechanical behavior of dual-phase (DP) steels. To capture the size-effect of the martensite particles and ferrite grains, the core and mantle approach is adapted in which a thin interphase of geometrically necessary dislocations (GNDs) is embedded at the martensite–ferrite boundaries. It is shown that as the martensite particles size decreases or their aspect ratio increases, both the strength and ductility of DP steel increase simultaneously. On the other hand, as the ferrite grain size decreases or its aspect ratio increases, the overall strength increases on the expense of the ductility. The conclusions from this study can be used in guiding the microstructural design of DP steels.

Micromechanical finite element analysis of the effects of martensite morphology on the overall mechanical behavior of dual phase steel

Strong and ductile dual-phase (DP) steels are an important class of advanced high strength steels that are commonly used by the automotive industry. Micromechanical computational modeling is imperative for guiding the material design of DP steels with simultaneous enhancements in strength and ductility. In this study, the effect of the morphology of the martensite hard phase on the overall stress-strain response of DP steels is studied. Through generating realistic virtual representative volume elements (RVEs) and adapting a microstructural-based approach using a finite deformation elastic-viscoplastic constitutive model, it was possible to conduct various parametric studies of the effects of martensite phase on the strength and ductility of DP steel. Morphological parameters of the martensite phase that are studied include (1) effect of aspect ratio (equiaxed versus elongated), (2) effects of the combination of various aspect ratio within an RVE, and (3) effect of interconnectivity between martensite particles and its thickness. It is shown that elongated martensite particles lead to a better overall performance than that of equiaxed martensite particles. It is found that by having the martensite phase interconnected, both strength and ductility increase. Furthermore, it is shown that the increase in the volume fraction of equiaxed martensite particles within microstructures of elongated particles reduces the strength and ductility simultaneously. Overall, it is concluded that the morphology of the martensite phase in DP steels impacts more the ductility than strength.

A physically based model for kink-band growth and longitudinal crushing of composites under 3D stress states accounting for friction

A material model to predict kink-band formation and growth under a 3D stress state is proposed. 3D kinking theory is used in combination with a physically based constitutive law of the material in the kink-band, accounting for friction on the microcracks of the damaged material. In contrast to existing models, the same constitutive formulation is used for fibre kinking and for the longitudinal shear and transverse responses, thereby simplifying the material identification process. The full collapse response as well as a crush stress can be predicted. The model is compared with an analytical model, a micromechanical finite element analysis and crushing tests. In all cases the present model predicts well the different stages of kink-band formation and crushing.

다공성 복합재의 파손 강도 예측을 위한 미시역학 전산 해석

Porosity in polymer matrix composites increases rapidly during thermochemical decomposition at high temperatures. The generation of pores reduces elastic moduli and failure strengths of composite materials, and gas pressures in internal pores influence thermomechanical behaviors. In this paper, micromechanical finite element analysis is carried out by using two-dimensional representative volume elements for unidirectionally fiber-reinforced composites with porous matrix. According to the state of the pores, effective elastic moduli, poroelastic parameters and failure strengths of the overall composites are investigated in detail. In particular, it is confirmed that the failure strengths in the transvers and through-thickness directions are predicted much more weakly than the strength of nonpored matrix, and decrease consistently as the porosity of matrix increases.

Micro-mechanical finite element analysis of Z-pins under mixed-mode loading

This paper presents a three-dimensional micro-mechanical finite element (FE) modelling strategy for predicting the mixed-mode response of single Z-pins inserted in a composite laminate. The modelling approach is based upon a versatile ply-level mesh, which takes into account the significant micro-mechanical features of Z-pinned laminates. The effect of post-cure cool down is also considered in the approach. The Z-pin/laminate interface is modelled by cohesive elements and frictional contact. The progressive failure of the Z-pin is simulated considering shear-driven internal splitting, accounted for using cohesive elements, and tensile fibre failure, modelled using the Weibull’s criterion. The simulation strategy is calibrated and validated via experimental tests performed on single carbon/BMI Z-pins inserted in quasi-isotropic laminate. The effects of the bonding and friction at the Z-pin/laminate interface and the internal Z-pin splitting are discussed. The primary aim is to develop a robust numerical tool and guidelines for designing Z-pins with optimal bridging behaviour.

Analysis of tool-particle interactions during cutting process of metal matrix composites

Metal matrix composites (MMCs) have become common materials that are employed in different industrial applications due to their outstanding strength and wear resistance. However, machining MMCs is considered to be a challenging process. This paper presents a micro-mechanical finite element analysis developed for simulation of MMC machining. Unlike the previously developed FE models, this model simulates the behavior of all main components that distinguish the MMC, namely the matrix, particles, and the particle-matrix interface, during the process. As a result, various aspects of the process, such as debonding and fracture in the particles and different scenarios of tool-particle interactions can be studied using the proposed model. The predicted forces were compared to the measured ones and used to verify the presented model. The developed model is successful in providing a broad understanding of MMC machining process.