Micromechanics-based Model Research Articles

Probabilistic-based investigation on tensile behavior of engineered cementitious composites (ECC): A macro-scale stochastic model

Micromechanics-based models are extensively used to simulate the tensile behavior of engineered cementitious composites (ECC). However, obtaining the micromechanical parameters in these models requires complicated experiments. This study proposes a macro-scale stochastic model to straightforwardly simulate the tensile behavior of ECC based on the strength criterion of strain-hardening. Specifically, the model simulates the multiple cracking of ECC as a stochastic process, in which the strength criterion is used to determine the formation of a crack. The failure probability distribution of the cracks is calculated by using statistical parameters of cracking strength and fiber bridging strength. Afterward, the crack number and tensile strain capacity of ECC are derived from the expectation of the failure probability distribution. Results show that the model predicts the crack number and tensile strain capacity of ECC with errors lower than 9.4% and 14.9%, respectively. Parametric analysis reveals that the crack number increases with the increasing difference value between cracking strength and fiber bridging strength. The stochastic model provides a comprehensive understanding on the multiple cracking of strain-hardening materials.

Development of engineered cementitious composite with moderate tensile properties using polyester fibers

In recent years, the use of reinforced cementitious composites has increased manifold for structural rehabilitation purposes. The present study concerns the development of a special variant of ECC, which is low-cost but has moderate tensile strength and ductility. Widely available polyester fiber was chosen, which was about ten times cheaper but about four times weaker than the preferred but expensive PVA fibers. Micromechanics-based mathematical model was used for fiber optimization to attain the multiple and strain hardening phenomena of the ECC. Different ECC mixes were prepared to investigate the effect of the matrix toughness on the tensile properties of ECC. ECC, with a strong matrix, failed to attain multiple cracking after 28-days of tensile testing because the fracture toughness exceeded the fiber bridging energy. The matrix was made weaker by increasing the amount of fly ash, and the desired strain hardening phenomena was achieved after 28-days of tensile testing. A low-cost ECC was developed, which used 3% polyester fiber by volume; the tensile strength and strain capacity of ECC was 2.17 MPa and 1.88%, respectively.

The damage mechanism of the metastable β-titanium alloy Ti5321 with specific microtexture using synchrotron X-ray microtomography

In order to investigate damage mechanism of metastable β-titanium alloy Ti5321 with bimodal microstructure and specific microtexture, in situ tensile test was performed facilitating with synchrotron X-ray microtomography. The damage evolution of metastable β-titanium alloy Ti5321 can be predicted in three dimensions by proper micromechanics-based modelling methods, the Rice and Tracey model and Huang model. Through comparisons of the Rice and Tracey model and Huang model validated using the values of stress triaxiality calculated from experimental data and Finite Element (FE) simulations, the prediction accuracy of growth rates of voids can be enhanced. The results also show that the void growth is strongly related to microtexture of α plates. It is found that the growth path of largest voids is along α plates which have their c-axes with similar inclination angle of ∼45° from rolling direction (RD). Electron backscatter diffraction (EBSD) was also used to reveal the damage mechanism. This result is important enlightenment for study of damage mechanism of metastable β-titanium alloys.

A micromechanical fatigue damage model for quasi-brittle rocks subjected to triaxial compressive cyclic loads

This paper is devoted to a novel micromechanics-based damage constitutive model for describing the mechanical behavior of quasi-brittle rocks under cyclic loading considering the effects of confining pressure. The proposed model is successfully employed to simulate cyclic loading tests under various confining pressures and upper limit stresses. Inspired by previous studies that focus on time-dependent creep deformation of quasi-brittle materials, the number of cyclic loading is regarded as equivalent to time scale. In the same spirit, the scalar-valued internal damage variable used to describe the degradation of rock materials is decomposed into two parts, namely an instantaneous component due to monotonic loading, and a fatigue-related component attributed to cyclic loading. Within the framework of irreversible thermodynamics, we present a Coulomb-type friction criterion and a strain energy release rate-based damage criterion. To describe the evolution of fatigue damage, we also propose a damage criterion based on the microstructure evolution. By the use of returning mapping procedure, the constructed model is applied to simulate two representative quasi-brittle rocks, namely sandstone and argillaceous quartz siltstone, and successfully captures all significant behavior features.

An enhanced boundary lubrication friction model for sheet metal forming

A new micromechanics-based friction model a under boundary lubrication is proposed to enhance an existing surface asperity-based friction model. The study presents a formulation of equilibrium between the plastically deformable workpiece and contact tool, and the newly proposed geometrical modeling of the tool surface to implement the plowing effect. Under this scheme, the contact tool is modeled based on the primary summits in the tool height distribution identified by a measured wavelength, which avoids the dependency on the accurate measurement of summit profiles. Also, the model can consider the micro-scale interaction between metal workpiece and tool surface. The developed micromechanics-based friction model is validated by comparing the calculated nominal friction coefficients of advanced high-strength steels (AHSS) at different contact pressures with those of experiment. Finally, the friction model is implemented in finite element (FE) software to simulate two forming processes: U-draw/bending and an in-line incremental die forming. The predicted forming force and springback in the sheet metal forming agree well with the experimentally measured ones, which verifies the accuracy and numerical efficiency of the proposed friction model and its numerical implantation.

A new fiber-bridging constitutive model for quantifying the matrix carbonation and fiber-to-matrix interface healing in PVA fiber-reinforced SHCC

Predicting fiber-bridging constitutive law is conducive to the rational design of strain-hardening cementitious composites (SHCCs). However, non-uniform carbonation along depths and fiber-to-matrix interface debonding and healing may significantly affect fiber-bridging behavior, which is seldom considered in current models. Therefore, a new micromechanics-based analytical model quantifying the carbonation-induced depth dependency and the healing-induced interfacial enhancement is developed. Particularly, to quantify the carbonation effect, the quantitative relationships between the interfacial properties (Gd, τ0, and β) and depth y are characterized by Fick’s Law of diffusion. To quantify the interface debonding and healing, the debonding crack lengths are calculated based on preloading level; new interfacial properties (Gd’, τ0′, and β’) are assigned to the debonded-and-healed interface segment; complex two-way fiber pullout scenarios during reloading are determined based on thorough classification. This new model is validated by the tensile test results of SHCCs with pristine and SiO2-coated PVA fibers under monotonic loading and reloading. The modeling results can reflect the multiple peculiar phenomena in SHCCs service, i.e., the overestimation of fiber-bridging strength of partially carbonated MgO cementitious matrix, the healing-induced fiber-bridging tensile strength enhancement, and the coating-induced higher PVA fiber-bridging recovery.

A Coupled Electro-Mechanical Homogenization-Based Model for PVDF-Based Piezo-Composites Considering α → β Phase Transition and Interfacial Damage.

Polyvinylidene fluoride or polyvinylidene difluoride (PVDF) is a piezoelectric semi-crystalline polymer whose electro-mechanical properties may be modulated via strain-induced α → β phase transition and the incorporation of polarized inorganic particles. The present work focuses on the constitutive representation of PVDF-based piezo-composites developed within the continuum-based micromechanical framework and considering the combined effects of particle reinforcement, α → β phase transition, and debonding along the interface between the PVDF matrix and the particles under increasing deformation. The micromechanics-based model is applied to available experimental data of PVDF filled with various concentrations of barium titanate (BaTiO3) particles. After its identification and predictability verification, the model is used to provide a better understanding of the separate and synergistic effects of BaTiO3 particle reinforcement and the micromechanical deformation processes on the electro-mechanical properties of PVDF-based piezo-composites.

Micromechanics-based variational phase-field modeling of Brazilian splitting tests

The simulation of the Brazilian splitting test can be challenging due to the presence of stress concentrations near the load points, which can lead to numerical problems and convergence issues. This paper aims to realistically model the Brazilian splitting test on mortar samples under monotonic loading, employing a micromechanics-based variational phase-field formulation. A micromechanics-based phase-field model connects the field variables at the macroscale and the physical dissipative mechanisms at the microcrack level, associating plasticity with the sliding of closed microcracks and damage with the growth of open microcracks. The distinction between these two mechanisms aids crack initiation and helps to overcome convergence issues. To further support convergence, a viscoplasticity regularization is embedded in the micromechanics-based phase field model. First, the homogeneous response of a single volume element is presented to demonstrate the effect of the viscosity parameter, and to provide insight of different failure modes that the model predicts. The model is next calibrated against experimental results. Hereto, Brazilian splitting tests have been performed using Digital Image Correlation technique. The calibrated numerical model predicts shear fracture mechanisms involved in the Brazilian splitting test and this has been further explained by studying the effect of confining pressure on modulated failure modes in the model. The calibrated parameters are then used for other samples with the same material but a different size and boundary conditions to assess the validity of the model and its prediction capabilities. Results show that the numerical failure prediction is consistent with the experiment. Overall, the calibration and comparison of numerical and experimental results confirm the validity and reliability of the simulation model and its ability to predict material behavior and fracture modes under different boundary conditions.

Micromechanics-Based Modeling of SiC/SiC Ceramic Matrix Composites and Structures

The behavior and response of ceramic matrix composites (CMCs), in particular silicon carbide fiber reinforced silicon carbide matrix (SiC/SiC), is affected by many factors such as variation of fiber volume fraction, residual stresses resulting from processing of the composites at high temperature, random microstructures, and the presence of matrix flaws (e.g., voids, pores, cracks etc.) as well as general material nonlinearity and heterogeneity that occurs randomly in a composite. Residual stresses arising from the phase change of constituents are evaluated in this paper and it is shown that they do influence composite strength and need to be properly accounted for. Additionally, the microstructures (location of fiber centers, coating thickness etc.) of advanced CMCs are usually disordered (or random) and fiber diameter and strength typically have a distribution. They rarely resemble the ordered fiber packing (square, rectangular, or hexagonal) that is generally assumed in micromechanics-based models with periodic boundary conditions for computational expediency. These issues raise the question of how should one model such systems effectively? Can an ordered hexagonal packed repeating unit cell (RUC) accurately represent the random microstructure behavior? How many fibers need to be included to enable accurate representation? Clearly, the number of fibers within an RUC must be limited to insure a balance between accuracy and efficiency. NASA’s in-house micromechanics-based code MAC/GMC provides a framework to analyze such RUCs for the overall composite behavior and the FEAMAC computer code provides linkage of MAC/GMC to the commercial FEA code, ABAQUS. The appropriate level of discretization of the RUC as well as the analysis method employed, i.e., Generalized Method of Cells (GMC) or High Fidelity Generalized Method of Cells (HFGMC), is investigated in this paper in the context of a unidirectional as well as a cross-ply laminated CMC. Results including effective composite properties, proportional limit stress (an important design parameter) and fatigue are shown utilizing both GMC as well as HFGMC. Finally, a few multiscale analyses are performed on smooth bar test coupons as well as test coupons with features such as open-hole and double notches using FEAMAC. Best practices and guidance are provided to take these phenomena into account and keep a proper balance between fidelity (accuracy) and efficiency. Following these guidelines can account for important physics of the problem and provide significant advantages when performing large multiscale composite structural analyses. Finally, to demonstrate the multiscale analysis framework, a CMC gas turbine engine vane structure is analyzed involving a progressive damage model.

Enhancing understanding of fracture mechanisms in brittle rocks under static and cyclic loads: Experimental insights and theoretical model

The present study investigates the fatigue behavior of granite and red sandstone under coupled static and cyclic loading. Experimental results reveals a three-stage evolution trend for the deformation modulus, Young's modulus, peak strain, residual strain, dissipated energy as a function of the absolute cycle. Acoustic emission (AE) rate also exhibits a three-phase stage, including the initial phase, uniform velocity phase, and accelerated phase. To explain the mechanical responses and fracture mechanisms related to rock fatigue, this study built a micromechanics-based damage model that adopts a modified Paris law and considers both the effect of static stress and stress amplitude. The theoretical model successfully reflects the effect of static loading history and reproduces the three-stage evolution of residual strain during rock fatigue. The SIF deduced by the theoretical model exhibits a distinct behavior: it initially decreases during the first few cycles, stabilizes at a lower value, and subsequently undergoes a significant increase as it approaches the final cycles. The internal cause behind the three-stage evolution of crack growth rate, AE rate, and mechanical properties is attributed to subcritical crack growth during cyclic loading. Finally, the theoretical model successfully characterizes the effect of static stress and stress amplitude of cyclic loads on fatigue damage evolution.

Micromechanics-based constitutive modeling of hard-magnetic soft materials

Soft materials exhibit large deformation material nonlinearity when stretched and possess enhanced elongation-at-break strain prior to rupture. As a result, these materials can cater to several state-of-the-art biomedical and microfluidic applications that require cross-domain energy transduction. Furthermore, they are often impregnated with external multi-functional filler materials (e.g., hard-magnetic particles) to result in hard-magnetic soft materials (hMSM). This gives rise to an inherent complexity owing to the multi-physics coupling due to magnetics and solid dynamics (along with geometric and material nonlinearities), which demands a rigorous magneto-mechanical model for a thorough understanding of their large deformation mechanical behavior under magneto-mechanical loads. It is also mandatory to understand their rate-dependent, hyperelastic, and flow behavior that is omnipresent during their deformation process. This paper focuses on the development of a novel thermodynamically-consistent micromechanics-based constitutive model that incorporates all these attributes using the finite deformation theory. A statistical mechanics-based approach has been undertaken to model the mechanics of the elastomer matrix. The plastic behavior due to the elastomer and the dispersed magnetic phases has been further accounted using a double-yield function with a micromechanical approach. The developed model shows a good agreement for a wide range of hMSM subjected to a variety of complex loading conditions. Finally, a parametric study has been carried out to provide physical insights into the different model parameters.

Modeling the multiaxial fracture behavior of Ti–6Al–4V alloy sheets at a high temperature using improved damage modeling

In this study, the mechanical responses of Ti–6Al–4V alloy sheets at a high temperature under multi-axial loading were investigated using a micromechanics-based damage model within a continuum finite element (FE) framework. Tensile tests at three strain rates and a high temperature were conducted to analyze the plastic and ductile damage properties of the Ti–6Al–4V alloy sheets. Additionally, hot Nakajima tests were conducted on specimens with three different shapes to evaluate the improvement in formability at a high temperature. Moreover, the dimples on the fractured surfaces of the experimental samples were qualitatively analyzed. Simultaneously, corresponding FE simulations were conducted to predict the ductile damage behavior of the Ti–6Al–4V alloy sheets at a high temperature using a modified Gurson−Tvergaard−Needleman model. The predicted results and the displacements at the onset of failure were compared with the corresponding experimental data.

Comprehensive inter-fibre failure analysis and failure criteria comparison for composite materials using micromechanical modelling under biaxial loading

Inter-fibre failure analysis of carbon fibre-reinforced polymer (CFRP) composites, under biaxial loading conditions, has been a longstanding challenge and is addressed in this study. Biaxial failure analysis of IM7/8552 CFRP unidirectional (UD) composites is conducted under various stress states. Two widely accepted failure criteria, the interactive Tsai-Wu and non-interactive Hashin failure criteria, are comprehensively assessed with finite element-based micromechanical analysis. High-fidelity three-dimensional representative volume elements (RVEs) are subjected to biaxial loadings with imposed periodic boundary conditions. Carbon fibres are assumed to be transversely isotropic and linearly elastic. The Drucker-Prager plastic damage constitutive model and cohesive zone model are utilised to simulate the mechanical response of the matrix and fibre-matrix interface, respectively. Coulomb friction is assumed between the fibres and matrix after interface failure. Two sets of biaxial loading scenarios (i.e. transverse stress dominated and shear stress dominated) with the associated failure modes are selected for the failure analysis and assessment of these failure criteria. A data-driven failure envelope for the composites under biaxial loadings is developed using a univariate cubic spline function. Failure mode transition points are determined under biaxial loadings. It is found that the micromechanics-based numerical model is effective in assessing these two existing criteria.

Investigation on the effect of interface properties on compressive failure behavior of 3D woven composites through micromechanics-based multiscale damage model

In this paper, the effect of interface properties on the compressive failure behavior of 3D woven composites (3DWC) is investigated by incorporating a micromechanics-based multiscale damage model (MMDM). The correlation between the mesoscopic stress of yarns and microscopic stress of constituents is established by defining a stress amplification factor. With the microscopic stresses, the fiber breakage and matrix failure can be separately evaluated at the microscale, without assuming the yarns as transversely isotropic homogeneous materials. Especially, the interfacial debonding between yarns and matrix is also a dominant damage mode within 3DWC. Given that there is still a lack of studies on the influence of interfacial properties on the compressive failure behavior of 3DWC, it is meaningful to perform numerical parametric studies to reveal how the interface properties contribute to the damage mechanisms of 3DWC under compressions. The predicted results indicate that with the increase of interface strengths and fracture toughness, the compressive resistance of 3DWC can be significantly improved, resulting in higher strength and failure strain. Additionally, the studied 3DWCs with weak, medium and strong interfaces exhibit different damage development processes.

A Micromechanics-Based Model of Direct Tensile Fracture in Brittle Rocks under Confining Pressure

A novel micromechanics-based model in brittle rocks is presented during the confined tensile fracture. This model is formulated by using the stress intensity factor of crack under distinct loading modes in the fracture mechanics theory. The confined tensile fracture mechanisms with and without initial crack friction are established. The development process from the confined tensile fracture without initial crack friction to that with initial crack friction is studied. The stress–strain constitutive relationship describing the transformation mechanism from the unloading of axial stress at a compressive state to the loading of axial stress at a tensile state is also studied during the confined tensile fracture. The tension–compression transformation mechanism codetermined by the friction of the initial crack, the angle of initial crack inclination, and the confining pressure is proven. With the decrease of the angle of initial crack inclination or the increase of the confining pressure, the confined tensile fracture constitutive model tends to be dominated by the tensile fracture mechanism with initial crack friction. The confined tensile fracture of brittle rocks tends to happen at the larger angle of initial crack inclination. The reasonableness of the presented model is checked by contrasting the experimental data. Effects of the friction, density, inclination angle and size of the initial crack, and the confining pressure on the tensile relation curve of strain and stress, the tensile relation curve of crack length and stress, the tensile elastic modulus, the tensile stress of crack initiation, and the tensile strength are discussed.

A critical examination of force–extension relationship for freely jointed chain model

The pioneering paper by Kuhn and Grün (1942) provided a thorough understanding of the finite extensibility of the freely-jointed chain model in polymer science. In their work, the relative number of conformations are evaluated through the introduction of a non-Gaussian probability distribution for the free (subjected to zero force) chains. However, Flory (1969) pointed out that this distribution does not truly describe the probability for the end-to-end vector of the chain. To tackle this issue, a corrected probability distribution was proposed and compared with the original form. Despite this improvement, numerous research studies still rely upon the original formulation of Kuhn and Grün, without being aware of Flory’s correction. The present work attempts to clarify the fundamental difference between the two probabilities through recognition of the distinct underlying ensembles. Then, the influence of this correction is studied on the force–extension relationship of the individual chain, as well as on some well-known micromechanics-based network models. Finally, it is demonstrated that misuse of the probability distribution can lead to significant discrepancy in the force–extension relationship of a coil-rod chain, a model for the building element of some biopolymer gels.

Improvement of the compressive strength of recycled aggregate concretes and relative effects on durability properties

The present paper deals with the problem of the compensation of the mechanical properties of recycled aggregate concretes (RAC) by adjusting the effective water-to-cement ratio. For this purpose, two substitution rates (60% and 100%) of natural aggregates by recycled ones are first considered and the loss rates of the compressive strength and the elastic modulus of the relative RAC are quantified. In the second part, the improvement of the 28 days compressive strength thanks to the water-to-cement ratio adjustment is proceeded and the effect of this process on the mechanical (elastic modulus), physical and durability properties (water accessible porosity, total shrinkage, chloride diffusion and carbonation) is quantified and presented for discussion. Among many other results, the compensation of the compressive strength (by adjusting the effective water-to-cement ratio from 0.42 to 0.35 for instance) is reported to be insufficient to compensate simultaneously the physical, mechanical and durability properties of the resulting recycled aggregate concrete. Finally, a micromechanics-based model is developed and fed with experimental data collected on the microstructure at different scales. Compared to the macroscopic mechanical properties, the predictions of the established model are shown to express with a good accuracy the effective elastic properties of RAC undergoing the compensation process.

Experimental and numerical studies on kevlar composites

The composite materials are finding its application in various engineering field owing to its light weight and high strength. Among various types of composites, a laminated polymer composite which is prepared using kevlar-49 (K49) as the reinforcement material in the form of woven fibres stacked together with the addition of epoxy resin as matrix material. Vacuum bag moulding method is used to fabricate the laminated Kevlar reinforced composites. The mechanical tests such as tensile and compression are performed to characterize the composites. The experimental results obtained for laminated K49 reinforced composites (KRC) have been verified with the aid of micromechanical model. The results of mechanical characterization such as tensile and compressive are experimentally determined and compared with the theoretical predictions. The scanning electron microscope images from selected specimens were also briefed to understand about the fracture mechanism of the laminate. The micromechanics-based models such as the Modified Rule of Mixtures (MROM) and Xu-Reifsnider (XR) models has been employed to predict the mechanical properties of KRC.

A micromechanical damage-healing model for encapsulation-based self-healing polymer composites under tensile loading

In this study, a novel micromechanics-based damage model is proposed for the damage evolution of a two-component microencapsulated-based self-healing polymer composite. In this way, a representative volume element (RVE) including an epoxy matrix with randomly distributed poly(methyl methacrylate) (PMMA) microcapsules is modeled in DigimatTM software and analyzed in Abaqus®. A new technique is developed to investigate the progressive damage by pre-inserted cohesive elements along all element boundaries of the epoxy matrix, PMMA shell, and capsule-matrix interfaces with the bilinear traction–separation law. Moreover, the impact of interface bonding strength, interface fracture energy, and PMMA microcapsules volume fraction on the load-carrying capacity of the RVEs under uniaxial tension loading was studied. The results indicated that the tensile strength of the self-healing polymer composite increased as the interfacial strength and fracture energy increased from 10 to 60 MPa and 100 to 1000 J/m2, respectively. Furthermore, the higher volume fraction of 5% PMMA microcapsules results in a lower load-carrying capacity of self-healing polymer composite with a strength of 4.9 N. A similar trend of Young’s modulus was observed for microcapsule-loaded epoxy composite compared to the pristine epoxy matrix. The micromechanical model has proper accuracy in predicting the tension behavior of self-healing composite in comparison to experimental results. Finally, two healing strategies are considered for the damaged RVE.

Experimental investigation and micromechanics-based damage modeling of tensile failure of polymer concrete reinforced with recycled PET bottles

Epoxy-based polymer concretes (PCs) behave in a quasi-brittle manner and suffer from low tensile strength. Adding different kinds of fillers has been widely used to improve the ductility of these materials and change the failure mechanisms. In this study, we used polyethylene terephthalate (PET) fillers from recycled bottles to enhance the tensile strength and ductility of PCs and prevent sudden brittle failure. Two different sizes of fillers (i.e., fine and coarse) are considered and the Brazilian disk configuration is used to measure the indirect tensile strength of reinforced PCs. Experimental results showed that the addition of coarse PET fillers to the PC has more significant effects on tensile strength and failure mechanism than fine PET fillers. Then, micromechanical damage analyses are conducted via finite element simulations of two-dimensional representative volume elements. The effects of void content and recycled PET fillers on the tensile strength and ductility of reinforced PCs were studied in the micromechanical simulations. Since the Brazilian disk examines the indirect tensile behavior, a relationship was proposed between the direct micromechanical tensile strength and the indirect macro mechanical tensile strength. The new procedure is experimentally validated for the prediction of the tensile strength of both reinforced and unreinforced PCs.