Micromechanics-based Model Research Articles

Flexible and coatable insulating silica aerogel/polyurethane composites via soft segment control

We herein propose a facile approach to fabricate foldable and coatable silica aerogel polyurethane composites (APCs). For the flexibility control, the soft segment of polyurethane (PU) is manipulated. The change in soft segment length induces a difference in overall glass transition temperature of PU. When the silica aerogel content is increased, the PU with a shorter soft segment length shows brittle fracture behavior, while the PU with a longer soft segment length shows no breakage after bending. The thermal insulation properties of APCs were enhanced by 72% reduction in thermal conductivity upon 30 wt% aerogel loading and theoretically verified by a micromechanics-based thermal conductivity model considering the effects of interface and agglomeration. In addition, for the combustion behavior measurements, heat release rate and heat release capacity are substantially reduced for the APCs compared to neat PUs. Those enhanced thermal insulation properties may have a commercial impact on thermal insulation applications.

Static and kinematic damage characterization in structured sand

Damage is the key process controlling the behavior of cemented geomaterials, such as structured sand. Damage characterization of structured sand is studied based on granular material mechanics with the aid of discrete element method (DEM) simulation in this paper. Structured sand is viewed as a mixture of remolded and structured parts, whose behavior is defined by the collective responses of unbonded and bonded contacts, respectively. Based on the cross-scale links between macroscopic quantities (stress and strain) and microscopic quantities (contact force, contact position and relative motion of particles), stresses and strains of the two parts are assembled to arrive at the overall stress and strain of structured sand. The weights of the two parts in stress and strain assembling/partitioning emerge naturally as a stress-based static damage variable and a strain-based kinematic damage variable, respectively, which are then evaluated using the DEM simulation results. The static damage variable captures the role of remolded part in load-bearing structure of structured sand, while the kinematic damage variable describes the spatial geometric configuration of the two parts. Both damage variables increase with deviator strain in a sigmoidal pattern. Directional damage indexes indicate that damage is isotropic from the view of kinematic response, but it is anisotropic if examined from static point of view. The degree of anisotropy in static damage is influenced by external stress conditions and internal microstructure anisotropy. This study provides a physically robust and theoretically rigid framework for the development of a micromechanics-based constitutive model of structured sand.

Crack detection and localization in RC beams through smart MWCNT/epoxy strip-like strain sensors

In recent years, self-sensing structural materials have drawn enormous attention of scientific community due to their potential to enable continuous monitoring of the integrity of structures. The new paradigm of smart condition-based maintenance advocates the use of next-generation structures completely or partly constituted by self-sensing materials, that is, the structure or part of it also behaves as a sensor. In this context, the remarkable mechanical and electrical properties of multi walled carbon nanotubes (MWCNTs) have fostered an increasing number of applications as fillers for composites with multifunctional properties. Among a wide spectrum of potential applications, the development of skin-type piezoresistive distributed strain sensors shows great promise. Such sensors can be deployed onto large-scale structures, enabling a continuous monitoring of the strain state in the global area of the structure. In this paper, a theoretical study on the potential application of smart MWCNT/epoxy strip-like strain sensors for damage detection/localization/quantification in reinforced concrete (RC) beams is presented. A micromechanics-based finite element model is proposed for the electromechanical analysis of MWCNT/epoxy strips. Furthermore, a damage detection algorithm through model updating approach is introduced. To do so, an Euler–Bernoulli model for beams equipped with a smart MWCNT/epoxy strip is developed. Finally, two numerical case studies are presented including: a 2D concrete beam with multiple prescribed crack-like damages, and a 3D RC beam under four-point flexural conditions with non-prescribed cracking. Results show that the proposed smart strips are capable of exploiting the damage-induced variations in the electrical output to locate and quantify damages for real-time distributed structural health monitoring of RC beam structures.

A bi-material property based FE modelling method for progressive damage analyses of composite double-lap bolted joints

Abstract A bi-material property method was proposed to describe mechanical properties of the unidirectional composite lamina. It divided the lamina into the fiber layer and the resin layer, which have different material properties and are responsible for the intra-laminar and inter-laminar properties, respectively. Furthermore, a finite element modelling method with the composite lamina simulated by the bi-material property method was presented. Combined with a Hashin-type failure criterion and a micromechanics-based material degradation model, a novel progressive damage model (PDM) was constructed for typical double-lap bolted joints. To validate the novel PDM, four double-lap, single-bolt joints with various width-to-hole-diameter ratios were designed and quasi-static tensile tests of the joints were performed. Numerical results of the novel PDM show better agreements with the experimental outcomes than the traditional PDMs. Besides, the novel PDM can describe the inter-laminar damage more precisely via a more reasonable simulation for the inter-laminar property of the lamina, and can also obtain more accurate deformation of the hole along the thickness direction of the laminate. Furthermore, influences of the width-to-hole-diameter ratio W/D on failure behaviours of the double-lap, single-bolt joint were revealed, and an optimal width-to-hole-diameter ratio was recommended for engineering practice. Combined with our previous study on effects of the end-distance-to-hole-diameter ratio E/D, a failure mode map with varying W/D and E/D was determined for the double-lap bolted joint. It is helpful for designers to seek safer designs of composite bolted joints because the W/D and E/D are key geometrical parameters that significantly affect failure behaviours of the joints.

A micromechanics-based damage model for non-woven fiber networks

Non-woven materials are fiber networks consolidated by different bonding techniques. It has been found that interfiber bond fracture is a major damage mechanism in non-wovens and strongly affects mechanical strength and toughness. In this article, we present a micromechanically based damage model for non-wovens. The model is built upon modeling single bond breaking processes and linking local damage events to macroscopic behaviors. In this model, a nonlinear term is introduced to describe non-affine deformation of fibers at a bond. The traction load on a bonded interface is determined by considering local force balance and network constraints. A bond breaks when its traction load exceeds a critical value, and this local information is used to update the global damage state through a classical continuum damage mechanics framework. Spatial correlation of damage in the network is modeled using a non-local averaging scheme. The proposed model is applied to a commercial non-woven series. The model is able to reproduce experimentally observed behaviors including elasticity, non-linear hardening, peak load and damage localization under uniaxial tensile loading as a function of network density. Damage states predicted by the numerical simulations match well with in-situ imaging results demonstrating the predictive capability of the model. The proposed model bridges non-woven microstructure and macroscopic behaviors and thus can serve as an effective tool for future studies of the mechanics of fiber networks.

MWCNT/epoxy strip-like sensors for buckling detection in beam-like structures

Buckling of slender structures constitutes a hazardous failure mechanism that can yield partial or total collapses. Nonetheless, given that buckling failure is characterized by a highly non-linear and sudden loss of stability, most off-the-shelf monitoring systems fail to detect buckling and very few research works in the literature can be found in this regard. Recent advances in the field of Nanotechnology have fostered the development of innovative composite materials with multifunctional properties, offering vast possibilities in the field of Structural Health Monitoring. Along these lines, the present work proposes a novel concept of smart beams for buckling detection applications. This consists of the deployment of carbon nanotube-reinforced epoxy strip-like sensors on the upper and bottom faces of a beam-like structure. Carbon nanotube-reinforced composites exhibit strain self-sensing capabilities, that is to say, these composites provide measurable variations in their electrical properties under the action of mechanical strains. In this way, the proposed sensing strips not only act as mechanical reinforcements, but also confer self-diagnostic properties to the system. The failure detection principle of the proposed smart beams consists of the assessment of the bending-induced variations of the normal strains during buckling. To do so, the electrical resistance of the sensing strips is continuously monitored through a two-probe resistivity measurement scheme. The present research furnishes detailed numerical parametric analyses to investigate the effectiveness of the proposed smart beams to detect buckling under uniaxially compression, as well as to evaluate the influence of design parameters such as filler volume fraction, boundary conditions and electrodes layouts. The macroscopic behaviour of the smart beams is simulated by a micromechanics-based piezoresistivity model and a multiphysics finite element code. The numerical results demonstrate that the buckling failure can be tracked through sudden disturbances in the electrical output of the smart strips.

A micromechanical model for longitudinal compressive failure in unidirectional fiber reinforced composite

Abstract A micromechanics-based 2D numerical model is proposed to comprehensively trace the longitudinal compressive failure of unidirectional carbon fiber reinforced polymers (UD-CFRP), in which microscopic damage mechanisms (namely the fiber fracture, matrix plastic yield and fiber-matrix interface crack) are considered. With this model, the predicted compressive modulus, strength and failure pattern are in good agreements with the experimental results, which validate the effectiveness of the proposed model. It concludes that the longitudinal compressive failure is governed by the matrix damage rather than the fiber fracture and the interface crack triggers the matrix damage. In addition, the influence of some microscopic parameters, including the fiber volume fraction, initial fiber misalignment, initial fiber-matrix interface stiffness, interface strength and fracture energies, on the longitudinal compressive failure is disclosed. The compressive modulus increases with the fiber volume fraction while it is almost unaffected by the rest four parameters. The compressive strength increases with the increment of the initial interface stiffness or the decrement of the initial fiber misalignment while it is immune to the interface fracture energies. Moreover, a limited increment of the fiber volume fraction or the interface strength is beneficial for enhancing the compressive strength.

A 3-D mechanics-based particle shape index for granular materials

Particle shape plays an important role in the mechanical properties of granular materials. This paper studies the effect it has on particle rotations and stress via a mechanics-based 3-D particle shape index, which is based on an earlier 2-D particle shape index. A level set discrete element method (LS-DEM) simulation, with experimental validation, of a specimen of a natural sand with varying particle shapes, subject to triaxial compression, is analyzed. We show that particles whose shapes allow for more moment transmission—as characterized by the particle shape index—experience less deviation in rotation and contribute more to the macroscopic shear stress, and provide possible micromechanical explanations of these trends. The results have implications in the construction of micromechanics-based granular models and higher-order continuum models.

Time-Dependent Deformation and Damage Modeling of a SiC/SiC Composite

AbstractTime-dependent elevated temperature behavior of a two-dimensional (2D) woven melt-infiltrated Sylramic (SiC) ceramic matrix composite (CMC) is investigated. A micromechanics-based model tha...

Temperature dependent micromechanics-based friction model for cold stamping processes

Temperature rise in cold stamping processes due to frictional heating and plastic deformation of sheet metal alters the tool-sheet metal tribosystem. This is more prominent in forming advanced high strength steels and multi-stage forming operations where the temperature on the tool surface can rise significantly. The rise in temperature directly affects the friction due to break down of lubricant, change in physical properties of tribolayers and material behavior. This can result in formability issues such as workpiece-splitting, etc. Therefore, it is important to account for temperature effects on friction in sheet metal forming analyses. In this study, the temperature effect was included in a micromechanics-based friction model which allows calculation of local friction coefficients as a function of contact pressure, bulk strain and relative sliding velocity. The temperature influence on friction was introduced through material behavior of sheet metal, viscosity of lubricant and shear strength of boundary layer in the micromechanics-based model. The model validation has been done by comparing the calculated fractional real contact area with the experimental results. The model can be used in formability analyses and to predict optimum stamping press parameters such as the blank holder force and the press speed.

A Multiscale Model to Incorporate Texture Evolution into Phenomenological Plasticity Models

Crystal plasticity is a micromechanics-based model that is regularly used to simulate plastic spin during large deformation. Although crystal plasticity can provide an accurate description of local deformation behaviour, it is often computationally expensive and usually replaced by flow rule-based phenomenological models that do not capture this phenomenon. This work presents a phenomenological-based texture evolution (PBTE) model that allows for the enhancement of flow rule-based models to capture microstructural spin in a phenomenological manner. A numerical framework is presented for generating and calibrating the microstructural evolution for the PBTE model using crystal plasticity. The PBTE Model is calibrated and employed to predict the macroscopic mechanical response and the generated microstructural spin for single crystal FCC cube during non-proportional strain paths.

Micromechanical Multiscale Modeling of ITZ-Driven Failure of Recycled Concrete: Effects of Composition and Maturity on the Material Strength

Recycled concrete, i.e., concrete which contains aggregates that are obtained from crushing waste concrete, typically exhibits a smaller strength than conventional concretes. We herein decipher the origin and quantify the extent of the strength reduction by means of multiscale micromechanics-based modeling. Therefore, the microstructure of recycled concrete is represented across four observation scales, spanning from the micrometer-sized scale of cement hydration products to the centimeter-sized scale of concrete. Recycled aggregates are divided into three classes with distinct morphological features: plain aggregates which are clean of old cement paste, mortar aggregates, and aggregates covered by old cement paste. Macroscopic loading is concentrated via interfacial transition zones (ITZs)—which occur mutually between aggregates, old, and new cement paste—to the micrometer-sized hydrates resolved at the smallest observation scale. Hydrate failure within the most unfavorably loaded ITZ is considered to trigger concrete failure. Modeling results show that failure in either of the ITZs might be critical, and that the failure mode is governed by the mutual stiffness contrast between aggregates, old, and new paste, which depend, in turn, on the concrete composition and on the material’s maturity. The model predicts that the strength difference between recycled concrete and conventional concrete is less pronounced (i) at an early age compared to mature ages, (ii) when the old cement paste content is small, and (iii) when recycling a high-quality parent concrete.

Cyclic plastic behavior of unidirectional SiC fibre-reinforced copper composites under uniaxial loads: An experimental and computational study

Silicon carbide continuous fiber-reinforced copper matrix composites (Cu/SiCf) offer huge potential as heat sink material for high-heat-flux applications at elevated temperatures (>300 °C) owing to the beneficial combination of strong, stiff and refractory SiC fibers with a highly conductive and ductile copper matrix. As high-heat-flux components are normally subjected to large temperature fluctuations combined with thermal strain variations, degradation of the Cu/SiCf composites caused by fatigue damages under cyclic loads may affect the structural integrity of the component. In this study, the robustness of the Cu/SiCf composites under cyclic loads at different temperatures was evaluated by means of uniaxial cyclic loading tests. The stability of the cyclic deformation hysteresis curves was used as a measure of material’s durability. The experimentally observed global deformation behavior was interpreted with the help of a micromechanics-based theoretical model. It was shown that the Mori-Tanaka type mean field theory could describe the cyclic loading behavior of the composite quite well with a good fitting quality between the measured and simulated saturated cyclic curves. The effects of fiber content, applied strain range and test temperature are discussed.

Bending of an elastoplastic Hencky bar-chain: from discrete to nonlocal continuous beam models

The static behavior of an elastoplastic one-dimensional lattice system in bending, also called a microstructured elastoplastic beam or elastoplastic Hencky bar-chain (HBC) system, is investigated. The lattice beam is loaded by concentrated or distributed transverse monotonic forces up to the complete collapse. The phenomenon of softening localization is also included. The lattice system is composed of piecewise linear hardening–softening elastoplastic hinges connected via rigid elements. This physical system can be viewed as the generalization of the elastic HBC model to the nonlinear elastoplasticity range. This lattice problem is demonstrated to be equivalent to the finite difference formulation of a continuous elastoplastic beam in bending. Solutions to the lattice problem may be obtained from the resolution of piecewise linear difference equations. A continuous nonlocal elastoplastic theory is then built from the lattice difference equations using a continualization process. The new nonlocal elastoplastic theory associated with both a distributed nonlocal elastoplastic law coupled to a cohesive elastoplastic model depends on length scales calibrated from the spacing of the lattice model. Differential equations of the nonlocal engineering model are solved for the structural configurations investigated in the lattice problem. It is shown that the new micromechanics-based nonlocal elastoplastic beam model efficiently captures the scale effects of the elastoplastic lattice model, used as the reference. The hardening–softening localization process of the nonlocal continuous model strongly depends on the lattice spacing which controls the size of the nonlocal length scales.

An integrated process–structure–property modeling framework for additive manufacturing

One goal of modeling for metal Additive Manufacturing (AM) is to predict the resultant mechanical properties from given manufacturing process parameters and intrinsic material properties, thereby reducing uncertainty in the material built. This can dramatically reduce the time and cost for the development of new products using AM. We have realized the seamless linking of models for the manufacturing process, material structure formation, and mechanical response through an integrated multi-physics modeling framework. The sequentially coupled modeling framework relies on the concept that the results from each model used in the framework are contained in space-filling volume elements using a prescribed structure. This framework is implemented to show a prediction of the decrease in fatigue life caused by insufficient fusion resulting from low laser power relative to the hatch spacing. In this demonstration, powder spreading and thermal-fluid flow models are used to predict the thermal history and void formation in a multilayer, multi-track build with different processing conditions. The results of these predictions are passed to a cellular automaton-based prediction of grain structure. Finally, the predicted grain and void structure is passed to a reduced-order micromechanics-based model to predict mechanical properties and fatigue life arising from the different processing conditions used in the process model. The simulation results from this combination of models demonstrate qualitative agreement with experimental observations from literature, showing the appealing potential of an integrated framework.

Microstructural damage based micromechanics model to predict stiffness reduction in damaged unidirectional composites

Prediction of the residual stiffness of the carbon fiber reinforced polymer composite, subjected to fatigue loading, can be performed using some of the phenomenological models. However, it is still a challenge to find the stiffness based on the known microstructural damage state (that was developed irrespective of the load history). In this work, two micromechanics-based models were developed to predict reduction in the stiffness of the damaged composite. Fiber crack density and interface debonding was used to define the microstructural damage state of the composite. These models account for the fiber crack density in the form of change in either geometry (equivalent ellipsoid model) or material property of the fiber (reduced stiffness model). The microstructural damage state in the unidirectional carbon fiber reinforced polymer composite, obtained from the on-axis tension–tension fatigue loading, was used to validate the models. The results from reduced fiber stiffness model were compared against experiment and finite element analysis for the given microstructural damage. The stiffness obtained using reduced fiber stiffness model was in good agreement with that obtained from the experiment. However, reduced fiber stiffness model underestimated reduction in stiffness compared to finite element analysis.

A Review on Water Vapor Pressure Model for Moisture Permeable Materials Subjected to Rapid Heating

This paper presents a comprehensive review and comparison of different theories and models for water vapor pressure under rapid heating in moisture permeable materials, such as polymers or polymer composites. Numerous studies have been conducted, predominately in microelectronics packaging community, to obtain the understanding of vapor pressure evolution during soldering reflow for encapsulated moisture. Henry's law-based models are introduced first. We have shown that various models can be unified to a general form of solution. Two key parameters are identified for determining vapor pressure: the initial relative humidity and the net heat of solution. For materials with nonlinear sorption isotherm, the analytical solutions for maximum vapor pressure are presented. The predicted vapor pressure, using either linear sorption isotherm (Henry's law) or nonlinear sorption isotherm, can be greater than the saturated water vapor pressure. Such an “unphysical” pressure solution needs to be further studied. The predicted maximum vapor pressure is proportional to the initial relative humidity, implying the history dependence. Furthermore, a micromechanics-based vapor pressure model is introduced, in which the vapor pressure depends on the state of moisture in voids. It is found that the maximum vapor pressure stays at the saturated vapor pressure provided that the moisture is in the mixed liquid/vapor phase in voids. And, the vapor pressure depends only on the current state of moisture condition. These results are contradictory to the model predictions with sorption isotherm theories. The capillary effects are taken into consideration for the vapor pressure model using micromechanics approach.

Statistical Micromechanics-Based Modeling for Low-Porosity Rocks under Conventional Triaxial Compression

Statistical Micromechanics-Based Modeling for Low-Porosity Rocks under Conventional Triaxial Compression

A progressive fatigue damage model for composite structures in hygrothermal environments

An improved progressive fatigue damage model (PFDM) involving hygrothermal effects was proposed to predict fatigue failure of composite structures in hygrothermal environments. In the improved PFDM, a unified model was established to evaluate the variation of composite material properties caused by hygrothermal environments. The hygrothermal-induced material properties were utilized in the stress analysis model, material degradation models and fatigue failure criterion. The hygrothermal strains were introduced into the constitution equation to account for the hygrothermal effects. A residual-strain-based gradual material degradation model and a micromechanics-based sudden material degradation model were enhanced to describe the damage of composite materials in hygrothermal environments. Besides, fatigue tests and progressive fatigue damage analyses of an open-hole laminate were performed in hygrothermal environments. The good consistency between the numerical and experimental results validated the improved PFDM. Both the experimental and numerical outcomes indicate that the effective moisture equilibrium considerably reduces the compressive strength and compressive fatigue life of the open-hole laminate made of T800 carbon/epoxy composites.

A Micromechanics-Based Elastoplastic Damage Model for Rocks with a Brittle–Ductile Transition in Mechanical Response

As confining pressure increases, crystalline rocks of moderate porosity usually undergo a transition in failure mode from localized brittle fracture to diffused damage and ductile failure. This transition has been widely reported experimentally for several decades; however, satisfactory modeling is still lacking. The present paper aims at modeling the brittle–ductile transition process of rocks under conventional triaxial compression. Based on quantitative analyses of experimental results, it is found that there is a quite satisfactory linearity between the axial inelastic strain at failure and the confining pressure prescribed. A micromechanics-based frictional damage model is then formulated using an associated plastic flow rule and a strain energy release rate-based damage criterion. The analytical solution to the strong plasticity-damage coupling problem is provided and applied to simulate the nonlinear mechanical behaviors of Tennessee marble, Indiana limestone and Jinping marble, each presenting a brittle–ductile transition in stress–strain curves.