Micromechanical Method Research Articles

Continuum damage mechanics-based finite-volume homogenization of unidirectional elastoplastic fiber-reinforced composites

The Finite-Volume Direct Averaging Micromechanics (FVDAM) method has been further extended to predict nonlinear behaviors of unidirectional boron/aluminum (B/Al) composites, induced by plastic deformation and ductile damage for the first time. The latter is considered by gradual stiffness degradation via the continuum damage mechanics (CDM) model. The convergence of homogenized and local response generated by the new FVDAM damage framework has been demonstrated by considering the hexagonal and square repeating unit cells (RUC) with different mesh discretizations under transverse tensile, transverse shear and axial shear loading paths. Then, the reliability of the developed approach to predict the nonlinear response of B/Al composites has been verified extensively vis-à-vis the experimental response available in the literature, under monotonic loading path with various off-axis angles. To accurately capture the experimental response, an RUC with actual microstructure characterized by a random fiber distribution is constructed and utilized in the numerical simulations. In addition, the developed model is also applied to predict the cyclic response of B/Al composites with different off-axis angles in further support of the theory’s potential to capture the macroscopic behaviors of B/Al composites under complex loading conditions.

Refined nonlinear micromechanical models using artificial neural networks for multiscale analysis of laminated composites subject to low-velocity impact

The parametric high fidelity generalized method of cells (PHFGMC) is an advanced micromechanical method that can be used for the nonlinear and failure analysis of several composite materials. The computational effort required for studying the nonlinear and damage multiaxial behavior is relatively small, depending on the size of the discretized repeating unit cell (RUC). However, it is computationally challenging, if not impossible, to integrate refined nonlinear micromechanical models within a multiscale analysis of composite structures. This is due to the thousands or more RUC models required at the integration points within a multiscale finite-element (FE) model of laminated structures. To that end, we propose a new artificial neural network (ANN) based micromechanical modeling framework, termed ANN-PHFGMC, for exploring the nonlinear behavior of fiber-reinforced polymeric (FRP) materials. Pre-simulated mechanical stress–strain responses and behaviors are determined using the PHFGMC to generate a multiaxial training database for the ANN micromodel. The simulated training data is founded on the PHFGMC-RUC results based on a hexagonal RUC. The PHFGMC effective stress–strain responses for different applied multiaxial strain paths are divided into two sets of data; one for the training and the other for verifying the trained ANN-PHFGMC model. The resulting trained ANN-PHFGMC is accurate, with less than 5% error in the verified predictions. The ANN-PHFGMC can be used as a stand-alone or embedded as a surrogate proxy model within a multiscale analysis of composite structures. Next, the ANN-PHFGMC model is integrated within a commercial explicit FE code for low-velocity impact (LVI) analysis of laminated composite plates. Multiscale LVI analyses are performed for two composite plates with different layups. Further, results are compared to experimental data to demonstrate the new model's ability to integrate refined nonlinear micromechanical models within a multiscale analysis.

Micromechanical BEoL robustness evaluation methods enabling loading condition customization and acoustic emission damage monitoring

For micromechanical robustness evaluation methods, it is advantageous if the mechanical loading conditions applied can be controlled as precisely as possible. For microchips, this is required to determine the robustness under specific conditions, e.g. during assembly or characteristic application/usage scenarios. In this work, three different micromechanical BEoL (Back End of Line) robustness evaluation methods are presented which should enable a more precise and flexible mechanical load induction and damage identification. They have been subsequently developed. Three main aspects characterize the customization of the developed approaches:•The design and testing of customized micro-tools to precisely apply mechanical load to individual Cu-pillars.•The implementation of an AE (Acoustic Emission) monitoring approach to detect minor damages during mechanical loading. This strategy also enabled the development of sub-critical loading experiments for which AE signals served as a damage indicator and mechanical loading was aborted upon the detection of AE events.•The development of a new measurement setup and approach to enable the solder attach of individual Cu-pillars to a mechanical testing system.The applications of these approaches should enable the induction of customized mechanical loading conditions and the identification of failure modes and damage initiation locations.

High pressure micromechanical force method to assess the non-plugging potential of crude oils and the detection of asphaltene-hydrate mixed agglomerates

A hydrate prevention strategy taking advantage of crude oil that exhibit hydrate non-plugging tendency is a viable option in oilfield production conditions, or during transient operations. For that reason, it is important to accurately evaluate crude oils for their potential as non-plugging oils in a small-scale apparatus, such as a High-Pressure Micromechanical Force (HP-MMF) system, before continuing to large-scale testing. HP-MMF is an interfacial method that has been applied to measure gas hydrate interparticle cohesive force to gain insight into the hydrate agglomeration tendencies of crude oils. Herein, methane/ethane hydrate cohesive force measurements in the presence of small concentrations of crude oil were performed in the HP-MMF. Direct observations from the HP-MMF revealed, for the first time, the appearance of asphaltene precipitates that interact with the gas hydrate particles to produce an asphaltene-hydrate mixed agglomerate. A new HP-MMF method has been developed that enables representative sampling and evaluation of the effect of crude oil samples on the cohesive force between two gas hydrate particles in the HP-MMF. The method has been tested with two crude oils, where lower cohesive force results are demonstrated by the presence of small concentrations (<5 vol% in model oil) of Crude A and C compared to the baseline system of pure model oil. Hence, indicating the presence of natural anti-agglomerants (AAs) that contribute to the non-plugging behavior of these crude oils. These studies show that the HP-MMF is a convenient tool to assess the non-plugging potential of crude oils at realistic (high pressure, low temperature) conditions, requiring only small oil sample volumes. The HP-MMF method developed in this work is demonstrated to be a unique tool that can be utilized for the detection of asphaltene-hydrate mixed agglomerates. These new findings provide important insights for asphaltene precipitation in the presence of gas hydrates, that can create catastrophic agglomeration in the flowlines.

Locally resonant porous phononic crystal sensor for heavy metals detection: A new approach of highly sensitive liquid sensors

In this research, a novel and highly sensitive phononic crystal (PnC) sensor is presented for the detection of CdBr2 concentrations at a low scale (ppm) which is considered a highly toxic heavy metal ion in freshwater. The proposed sensor is composed of two thin layers of rubber covering both the top and bottom surfaces of a one-dimensional ternary porous silicon (PSi) PnC. As a result, the whole designed structure is arranged as {rubber/[PSi1/PSi2/PSi3]N/rubber}. The appearance of local resonant modes is due to the presence of two thin rubber layers as a cap layer of the PnC design. In particular, the spectral position of the modes is significantly tuned when filling the PSi layers with CdBr2 ions. It is worth mentioning that the novelty of this work is mainly focused on three axes. The first one is the use of locally resonant PnCs (not conventional defective ones) as highly sensitive biosensors. The second one, the liquid of interest here is considered a dangerous aqueous solution with a very low scale (ppm). The last promising point, we proposed the pores inside Si layers are filled with a liquid material in contrast to most of the micromechanics methods of composite materials that supposed the pores are empty (just voids are inside). To realize the best performance of this sensor, an optimization strategy of some related parameters such as the rubber layer thickness, the geometry of the PnC, and the unit cell number was conducted. In this regard, the proposed sensor provides promising values of sensitivity, quality factor, detection limit, and damping rate of 47.25 Hz/ppm, 2756.2, 82 ppm, and 0.00018, respectively. Therefore, the present design could be of serious contribution to liquid sensors and bio-sensing applications due to its simplicity, novelty, and high performance.

Micromechanics Modeling of Transverse Tensile Strength for Unidirectional CFRP Composite

Transverse tensile strength of unidirectional (UD) composites plays a key role in overall failure of fiber-reinforced composites. To predict this strength by micromechanics, calculation of actual stress in constituent matrix is essentially required. However, traditional micromechanics models can only give the volume-averaged homogenized stress rather than an actual one for a matrix, which in practice will cause large errors. In this paper, considering the effect of stress concentration on a matrix, a novel micromechanics method was proposed to give an accurate calculation of the actual stress in the matrix for UD composite under transverse tension. A stress concentration factor for a matrix in transverse tensile direction is defined, using line-averaged pointwise stress (obtained from concentric cylinder assemblage model) divided by the homogenized quantity (obtained from a bridging model). The actual stress in matrix is then determined using applied external stress multiplied by the factor. Experimental validation on six UD carbon fiber-reinforced polymer (CFRP) specimens indicates that the predicted transverse tensile strength by the proposed method presents a minor deviation with an averaged relative error of 5.45% and thus is reasonable, contrary to the traditional method with an averaged relative error of 207.27%. Furthermore, the morphology of fracture section of the specimens was studied by scanning electron microscopy (SEM). It was observed that different scaled cracks appeared within the matrix, indicating that failure of a UD composite under transverse tension is mainly governed by matrix failure. Based on the proposed approach, the transverse tensile strength of a UD composite can be accurately predicted.

Electrical Transport Properties of Few-Layer SnS2 Field-effect Transistors

After the discovery of graphene in 2004, two dimensional (2D) materials have fascinated a lot of view due to the excellent properties. Nowadays, the research on 2D materials has spread to other graphene-like layer structured materials, especially transition metal dichalcogenides (TMDCs). Tin disulfide (SnS2) is a kind of TMDCs with a sizable bandgap. Here we introduce few-layer SnS2 field-effect transistors (FETs) fabricated using micromechanical exfoliation method. The FETs show n-type behavior, the on/off ratio exceeding 0.54×104 and the carrier mobility is 0.61 cm2V−1s−1. The electronic and optical characteristics of SnS2 flakes with a finite bandgap illustrate their potential applications in optoelectronics device.

Micromechanical damping analysis of composite materials using linear viscoelasticity vs the strain energy approach

The phenomenological strain energy approach for predicting composite damping properties is widely used because of its simplicity. The composite dissipated energy is approximated as the volume average of the local (constituent) loss factor times the local strain energy. Thus, any micromechanics method (e.g., finite element or the high-fidelity generalized method of cells used herein) that can predict the local fields (and thus the strain energy) within a composite can be used to approximate the effective damping properties. In this paper, two more physics-based approaches, the correspondence principle and explicit viscoelastic modeling, are implemented within the two-scale high-fidelity generalized method of cells micromechanics theory and compared with the widely-used strain energy approach. It is shown that all three approaches provide quite similar predictions for the effective damping properties of unidirectional composites. Finally, the presented two-scale micromechanics theory is applied to predict the effective anisotropic damping properties of 2D and 3D woven composites.

Investigation of the Mechanical Properties for Polymer Reinforced by Nanoparticles with Considering Viscoelasticity of the Matrix

Investigation of the Mechanical Properties for Polymer Reinforced by Nanoparticles with Considering Viscoelasticity of the Matrix

BEoL stack robustness investigations utilizing Cu-pillar immobilization and micromechanical loading methods

Under harsh application conditions in fields such as aerospace or automotive, it is crucial that the mechanical robustness of microchip components is ensured at any time. To obtain this, thorough and highly specialized testing approaches have to be deployed already in the design phase. The general strategy of these approaches is to induce (thermo-)mechanical load to a given system or component under well controlled conditions and assess the resulting effects. The testing methods should emulate the mechanical application conditions as closely as possible to identify the most damage prone areas of the system and to obtain an understanding of the occurring damage processes. In this work, the development and deployment of two different testing methods to evaluate mechanical BEoL (Back end of Line) stack robustness by inducing micromechanical load to superjacent Cu-pillars are introduced. In flip chip applications, Cu-pillars are immobilized by a solder connection as well as underfill material. Compared to previously developed methods, it was attempted to realize mechanical scenarios which are closer to assembly or application conditions. Therefore, the methods presented in this work can be regarded as subsequent developments of e.g. the Cu-pillar shear-off approach presented in Silomon et al. (2021). The details are discussed in more depth in Silomon et al. (2022). Specifically, a mechanical immobilization approach utilizing an indenter tip with a cavity was developed as well as a soldering approach utilizing a Cu indenter tip as a soldering bolt and a landing pad simultaneously. The approaches were deployed on a high-end microchip sample which has been introduced and investigated in Silomon et al. (2021).Two different mechanical loading conditions were emulated utilizing the developed approaches. These conditions are relevant at different points in the life cycle of a microchip and could not be induced utilizing previously developed methods. Oscillating load as an emulation of thermal expansion and contraction or vibration (application conditions) as well as tensile loading as an emulation of assembly conditions were induced. Applying mechanical load to individual Cu-pillars utilizing the different methods enabled the determination of the failure conditions and subsequent analysis led to the identification of the respective damage mode. Additionally, sub-critical experiments utilizing AE (acoustic emission) signal monitoring as a damage indicator were conducted to determine the exact location of damage initiation. This was achieved by subsequent damage assessment measurements utilizing optical microscopy, nXCT as well as SEM/FIB analyses. Applying this workflow, it was possible to describe the damage modes as well as to identify the most damage prone areas for the specific loading conditions induced by the two different developed mechanical loading methods.

A comparative study of micromechanics models to evaluate effective coefficients of 1-3 piezoelectric composite

In present paper a micromechanics method is developed to evaluate effective coefficients of piezoelectric fiber reinforced composites. Exact solution is derived for effective elastic, piezoelectric and dielectric coefficients of such piezocomposite subjected to the applied load in the direction transverse to the fiber orientation. Simultaneously, based on the finite element method a numerical study is performed on a representative volume element of the piezocomposite containing fibers in square packing arrangement. From results, it is observed that the method developed in present study provides better results for the effective coefficients susceptible to the fiber packing arrangements.

Deep learning method for predicting the strengths of microcracked brittle materials

The strengths of brittle or quasi-brittle materials strongly depend on the interaction of distributed microcracks. Traditional micromechanics methods are difficult to exactly predict the strengths of materials containing a large number of microcracks. In this paper, a micromechanics-based deep learning method is proposed to predict the strengths of two-dimensional microcracked brittle materials. Utilizing a numerical method based on Kachanov’s theory of microcrack interaction, we generate a data set containing a large number of images of two-dimensional microcracked specimens and their load-bearing capacity under various in-plane loading. A deep neural network is formulated based on this data set to establish the implicit mapping between the load-bearing capacity of the specimens and the spatial distribution of microcracks. Numerical experiments demonstrate that the trained deep neural network can accurately and efficiently predict the load-bearing capacity of microcracked brittle materials.

Optimal Data-Generation Strategy for Machine Learning Yield Functions in Anisotropic Plasticity

Trained machine learning (ML) algorithms can serve as numerically efficient surrogate models of sophisticated but numerically expensive constitutive models of material behavior. In the field of plasticity, ML yield functions have been proposed that serve as the basis of a constitutive model for plastic material behavior. If the training data for such ML flow rules is gained by micromechanical models, the training procedure can be considered as a homogenization method that captures essential information of microstructure-property relationships of a given material. However, generating training data with micromechanical methods, as for example, the crystal plasticity finite element method, is a numerically challenging task. Hence, in this work, it is investigated how an optimal data-generation strategy for the training of a ML model can be established that produces reliable and accurate ML yield functions with the least possible effort. It is shown that even for materials with a significant plastic anisotropy, as polycrystals with a pronounced Goss texture, 300 data points representing the yield locus of the material in stress space, are sufficient to train the ML yield function successfully. Furthermore, it is demonstrated how data-oriented flow rules can be used in standard finite element analysis.

Elastic modulus and Poisson’s ratio of graphene nanoplatelet/glass fiber-reinforced polymer hybrid composites subjected to off-axis loading

Effective elastic properties of the graphene nanoplatelet (GNP)/unidirectional glass fiber (GF)-reinforced polyimide composites subjected to off-axis loading are predicted using a closed-form hierarchical micromechanical approach. The effects of volume fraction, agglomeration and non-flat structure of GNPs, graphene/polymer interfacial region, and fiber volume fraction on the off-axis elastic modulus and off-axis Poisson’s ratio are investigated. In order to verify the accuracy of the present micromechanical method, predictions are compared with the experimental data. Adding GNPs into the polymeric resin increases the elastic modulus of all off-axis coupons. When flat GNPs are uniformly dispersed in the polyimide resin, much more improvement in the off-axis elastic properties is achieved. The results indicate that agglomeration and non-flat structure of the GNP can drastically decrease the off-axis elastic modulus. It is observed that the off-axis elastic response of hybrid composites may be sensitive to the material property and thickness of the interfacial region.

Experimental study of quasi-static and dynamic tensile behavior of epoxy resin under cyclic hygrothermal aging

Fiber-reinforced polymer (FRP) structures used in aviation are typically exposed to cyclic hygrothermal environments in which they may be subjected to impact loads that threaten flight safety. Although the effects of hygrothermal aging on the mechanical behavior of FRPs have been extensively explored, few authors have discussed the impact-induced behavior of composites after long-term hygrothermal aging, and hardly any study has examined the effect of the strain rate of neat epoxy resin after hygrothermal aging. This study examines the quasi-static and dynamic tensile properties of TDE86 epoxy resin under cyclic hygrothermal aging for the first time. The resin specimens were aged for 0, 1, 7, 14, 28, 56, 70, and 140 days, representing specimens that were unaged, and had been in service for one month, six months, one year, two years, four years, five years, and 10 years respectively. The strain rate at which they were tested ranged from 7.5 × 10−6 s−1 to 1000 s−1. This yielded the hygroscopic law, the process of evolution of crack-induced damage, and the viscoelastic behavior of the specimens, including the hygrothermal effect and the effect of the strain rate of the epoxy resin. This information can be used to predict the hygrothermal behavior of FRPs based on the micromechanics method.

The in situ matrix cracking behavior in cross-ply laminates under out-of-plane shear loading

The in situ effect on cross-ply laminates under out-of-plane shear loading is firstly studied with a two-dimensional RVE-based computational micromechanics method. High fidelity simulations of the interface de-bounding and crack propagation in laminates are performed, which shows good consistency with experimental observation. The matrix cracking behaviors and micro-mechanical response demonstrate that an in situ effect exists in cross-ply composites under out-of-plane shearing. Specifically, thinner ply laminates provide higher shear strength and stronger damage resistance due to the delay effect of transverse cracking and delamination. The analytical predictions on interlaminar shear strength of cross-ply laminates agree well with the existing theoretical criteria. A parametric study is performed to explore the possibility of acquiring stronger fiber-reinforced composites. The coupled load analysis sheds useful insights on the failure mechanism and optimization design of multi-layer composites.

Elastic Characterization of Shale at Microscale: A Comparison between Modulus Mapping, PeakForce Quantitative Nanomechanical Mapping, and Contact Resonance Method

Summary Because of the extremely high resolution and little damage to the sample, micromechanical mapping methods have been widely used for elastic characterization of shale at microscale. However, few studies have investigated connections and differences among commonly used micromechanical mapping methods. The influencing factors of micromechanical tests, such as sample preparation, experimental setup, and data processing, have not yet been sufficiently discussed. In the presented paper, three representative micromechanical mapping methods, including modulus mapping (MM), PeakForce quantitative nanomechanical mapping (PFQNM), and contact resonance (CR) method, were systematically compared from theory to application. The fundamental principles of the three methods were introduced, and connections in theoretical background were discussed. A shale sample from the Yanchang Formation in the Ordos Basin was selected for elastic characterization. Mechanical tests were performed on a fixed area on the sample surface by using different methods. The modulus distribution images obtained by the three methods intuitively exhibited microheterogeneity in shale. The influences of scanning frequency, peak force frequency, and force setpoint were analyzed based on the test results. The comparison of the contact area revealed that MM possessed the lowest spatial resolution with the experimental setup, and the CR method was less sensitive to the surface condition than PFQNM. The effectiveness of the data processing method was demonstrated through scale dependency analysis, and the limitations of the test methods were discussed. This work may contribute to improved understanding and selection of micromechanical mapping methods and experimental design of elastic characterization of shale.

Mechanical properties and wear resistance of Fe–Ni–Cu-based metal matrix composites reinforced with hollow corundum microspheres

This paper focuses on the development of composite materials based on the Fe–Ni–Cu alloy with hollow corundum microspheres (HCM). The composites were produced by means of powder metallurgy: by mixing initial metallic powders in various types of mixers followed by hot pressing. Compact samples of Fe–Ni–Cu + HCM composites featured high relative density and microstructure homogeneity. The introduction of HCM leads to a decrease in strength to 30 % (from 1125 MPa to 800 MPa at a HCM concentration of 15 vol.%). However, resulting composite materials retained high plasticity. It was established by the micromechanical modeling method that such composites have stress concentration regions not at the interface between HCM and the matrix, but on the inner surface of microspheres. On the contrary, the adjacent matrix volume around HCM features stress relaxation and «unloaded» regions formed. HCM introduction into the matrix based on the Fe–Ni–Cu alloy increases wear resulting from friction on M300 concrete by 50–170 % with a grain size of 70–100 μm and by 160–325 % with a grain size of 100–140 μm. During friction, HCMs act as a reservoir for debris (concrete particles), so the matrix surface remains free of wear products and directly contacts the material processed. The heavy wear of composites with HCM makes them promising for use as a binder in diamond tools designed for the dry cutting of concrete and reinforced concrete.

Using Scalable Graphene via Press-and-Peel: A Robust and Storable Tape.

The independent expertise required by the preparation and application of graphene has brought a challenge to the more fluent development of graphene devices. We combine the advantages of chemical vapor deposition and micromechanical exfoliation methods of synthesizing graphene to develop a "graphene tape" for the fast utilization of graphene, which is robust, storable, and user-friendly. Prepared by pretransferring graphene to the surface of a polymer carrier film with weak interfacial adhesion, this graphene tape enables the acquisition, patterning, and layer-by-layer epitaxy of scalable graphene on a target substrate through simple cutting, pressing, and peeling off. Multiple characterizations demonstrate its comparable quality with as-synthesized graphene even after stored for over 30 days, overcoming the time and space limitations of acquiring a graphene sample. We believe that this graphene tape can bridge the current gap between graphene synthesis and applications and promote industrial progress of graphene-based devices in the post-Moore era.

Effective time-dependent behavior of three-phase polymer matrix smart composites

This study presents a mathematical framework to predict the effective time-dependent behavior of three-phase smart composites with typical 0-3, 1-3, and 2-2 connectivities. A composite is composed of magnetostrictive and piezoelectric reinforcements that both show nonlinear multiphysics coupling and a polymer matrix that exhibits viscoelastic behavior. For dealing with nonlinear and time-dependent problems, a tangent linearization is employed to linearize the nonlinear constituents and a time-integration algorithm is applied to numerically determine the viscoelastic response of the matrix. A unified constitutive equation can be subsequently formulated to cover various phase constitutive laws following by a simplified unit-cell micromechanics model to set up a composite constitutive relation. The presented formulation is validated by limited experimental data available in literatures. Numerical results show that inclusion of a polymer matrix in a smart composite causes magnetoelectric coupling to be creep due to strain-mediated coupling among these three phases. The established unit-cell micromechanics model can be further integrated into a finite element framework to analyze composite structures, which is a great merit in a variety of practical applications. It will do so by implementing the presented micromechanics method at every integration point.