Micromechanical analysis of friction anisotropy in rough elastic contacts

AbstractComputational contact homogenization approach is applied to study friction anisotropy resulting from asperity interaction in elastic contacts. Contact of rough surfaces with anisotropic roughness is considered with asperity contact at the micro scale being governed by the isotropic Coulomb friction model. Application of a micro-to-macro scale transition scheme yields a macroscopic friction model with orientation- and pressure-dependent macroscopic friction coefficient. The macroscopic slip rule is found to exhibit a weak non-associativity in the tangential plane, although the slip rule at the microscale is associated in the tangential plane. Counterintuitive effects are observed for compressible materials, in particular, for auxetic materials

Multi Scale Modeling of The Elastic Properties of Polymer-Clay Nanocomposites

RÉSUMÉ Les Nanocomposites Polymères-Argiles (NPA) sont reconnus pour leur capacité à améliorer les propriétés mécaniques de polymères bruts, et ce, même dans le cas de faibles fractions volumiques de nano-argiles. Cette amélioration est attribuable aux rapports de forme élevés ainsi qu'aux propriétés mécaniques des nano-argiles. En outre, la zone d'interphase résultant d'une modification des chaînes de polymère à proximité des nano-argiles joue un rôle important dans la rigidité de NPA. Plusieurs approches analytiques existent pour la prédiction des propriétés élastiques de NPA, allant des modèles simplifiés en deux étapes aux modèles plus sophistiqués. Il n'existe toutefois aucune étude ayant déjà vérifié l'exactitude de ces modèles. Par ailleurs, les modèles numériques servant à évaluer leurs homologues analytiques sont encore loin de pouvoir modéliser la microstructure réelle de NPA. Par exemple, la majorité des modèles n'ont pas tenu compte de la microstructure tridimensionnelle de particules aléatoirement réparties, du rapport de forme élevé des nano-argiles, ou de l'intégration explicite de phases constitutives. Plus important encore, la plupart des études numériques ont été développées sans tenir compte du Volume Élémentaire Représentatif (VER) en raison du coût énorme de calculs imposé par ce dernier. Par conséquent, l'exactitude des résultats de référence ainsi obtenus est contestable. Le but principal de cette thèse était d’évaluer l'exactitude des modèles d'homogénéisation pour la prédiction de comportement mécanique de NPA. Dans un premier temps, la validité des modèles micromécaniques analytiques couramment utilisés pour la prédiction de propriétés élastiqués de NPA exfoliés a été évaluée à l'aide de simulations Éléments Finis (EF) tridimensionnelles. Une attention particulière a été accordée à l'interphase autour des nano-argiles. La stratégie de modélisation était une procédure en deux étapes se basant sur la notion de Particule Effective (PE). Dans cette approche de modélisation, les renforts multicouches ont été remplacés par des particules homogènes à effets équivalents. L'exactitude des modèles numériques dans des limites de tolérances prédéfinies était garantie grâce à la détermination du VER. Cette étude a révélé que la méthode de Mori-Tanaka est la plus fiable à utiliser parmi les modèles en deux étapes pour les valeurs typiques de paramètres de NPA exfoliés (contraste de module, rapport de forme et la fraction volumique). Les propriétés mécaniques de l'interphase ainsi que son épaisseur ont été estimées à partir d'une comparaison entre une étude paramétrique numérique et des résultats expérimentaux.----------ABSTRACT Polymer-Clay Nanocomposites (PCN) are known to improve the mechanical properties of bulk polymers, even for modest clay loadings. This enhancement is due to the High aspect ratio and mechanical properties of the nanoclay platelets. Additionally, the interphase zone created by altered polymer chains in the vicinity of the nanoclays plays an important reinforcing role. Several analytical approaches exist for predicting the elastic properties of PCN, ranging from simplified two-step models to more complex one-step methods. However, no thorough study has yet rigorously verified the accuracy of these models. On the other hand, the numerical models that are commonly used to evaluate the analytical models are still far from modeling the real PCN microstructure reported in the literature. For example, most of the models have failed to model the detailed 3D microstructure considering randomly positioned reinforcing particles, the large nanoclay aspect ratio and the explicit incorporation of the constituent phases. More significantly, most of numerical studies have been reported without a thorough determination of the appropriate Representative Volume Element (RVE) due its computational burden, resulting in benchmark results of questionable accuracy. The main purpose of this thesis was to evaluate the accuracy of homogenization models for predicting the mechanical behavior of nanoclay nanocomposites. First, the validity of commonly used analytical micromechanical models for the prediction of exfoliated PCN elastic properties was evaluated with the help of 3D Finite Element (FE) simulations. In particular, special attention was devoted to the interphase around the nanoclays. The modeling strategy was a two-step procedure relying on the Effective Particle (EP) concept, in which the multi-layer reinforcing stacks were replaced by homogenized particles. The accuracy of the numerical models was guaranteed, within a given tolerance, by rigorous determination of the RVE. It was found that the Mori-Tanaka model was the most reliable method to be used in two-step models for the possible ranges of modulus contrasts, aspect ratios and volume fractions typical of exfoliated PCN. The properties and the thickness of the interphase were estimated from comparison between a numerical parametric study and experimental results. The importance of incorporating the interphase for predicting the axial Young's modulus was highlighted. Second, the evaluation was extended to a wider class of models applicable to both intercalated and exfoliated morphologies

A nonlinear multiscale finite element model for comb-like sandwich panels

Modern composite materials and lightweight construction elements are increasingly replacing classic materials in practical applications of mechanical and civil engineering. Their high prevalence creates a demand for calculation methods which can accurately describe the mechanical behavior of a composite structure, while at the same time preserving moderate requirements in terms of numerical cost. Modeling the full microstructure of a composite by means of the classical finite element method quickly exceeds the capabilities of today’s hardware. The resulting equation systems would be extremely large and unsuitable for solution due to their enormous calculation times and memory requirements. Homogenization methods have been developed as a remedy to this issue, in which the complex microstructure is replaced by a homogeneous material using averaged mechanical properties that are determined via experiments or by analytical or numerical investigation. However, classical homogenization methods usually fail as soon as nonlinear system behavior is introduced and the effective properties, which are presumed to be constant, begin to change during the course of a simulation. In this work, a coupled global-local method will be presented specifically for sandwich panels with axially stiffened or honeycomb cores. Herein, a global model, in which the complete structure is discretized with standard shell elements, is coupled with multiple local models, describing the microstructure of the sandwich throughout the full thickness coordinate and using shell elements for discretization as well. The local formulation is implemented by means of a constitutive law for the global model, so that one local boundary value problem is evaluated in each integration point of the global structure. By reevaluating the local models in every iteration step in a nonlinear simulation, physical and geometrical nonlinearity can be described. For instance, it will be shown in numerical examples that elasto-plastic material behavior and pre- and postcritical buckling behavior can be described, contrary to most classical homogenization methods. Next to the derivation of theoretical fundamentals and the introduction of the coupled method as well as several numerical examples, additional chapters are detailing some issues concerning mesh generation and the implementation of a high-bandwidth data interface between global and local models

Homogenization of composites with extended general interfaces: comprehensive review and unified modeling

Abstract Interphase regions that form in heterogeneous materials through various underlying mechanisms such as poor mechanical or chemical adherence, roughness, and coating, play a crucial role in the response of the medium. A well- established strategy to capture a finite-thickness interphase behavior is to replace it with a zero-thickness interface model characterized by its own displacement and/or traction jumps, resulting in different interface models. The contributions to date dealing with interfaces commonly assume that the interface is located in the middle of its corresponding interphase. We revisit this assumption and introduce a universal interface model, wherein a unifying approach to the homogenization of heterogeneous materials embedding interfaces between their constituents is developed. The proposed novel interface model is universal in the sense that it can recover any of the classical interface models. Next, via incorporating this universal interface model into homogenization, we develop bounds and estimates for the overall moduli of fiber-reinforced and particle-reinforced composites as functions of the interface position and properties. Furthermore, we elaborate on the computational implications of this interface model. Finally, we carry out a comprehensive numerical study to highlight the influence of interface position, stiffness ratio and interface parameters on the overall properties of composites, where an excellent agreement between the analytical and computational results is observed. The developed interface-enhanced homogenization framework also successfully captures size effects, which are immediately relevant to emerging applications of nano-composites due their pronounced interface effects at small scales

Microstructure generation and micromechanical modeling of sheet molding compound composites

We introduce an algorithm that allows for a fast generation of SMC composite microstructures. An exact closure approximation and a quasi-random orientation sampling ensure high fidelity. Furthermore, we present a modular framework for anisotropic damage evolution. Our concept of extraction tensors and damage-hardening functions enables the description of complex damage-degradation. In addition, we propose a holistic multiscale approach for constructing anisotropic failure criteria

Experimental and Numerical Investigation of the Damage Response of Ceramic Matrix Composites.

Ceramic matrix composites (CMCs) are of interest in the aerospace industry due to their ability to retain high stiffness at elevated temperatures. CMC materials are slated to replace metal alloys currently used in the combustion section of aerospace jet engines, leading to weight savings due to the lower density. In this work monotonic tensile tests at room and high temperature are conducted. Three different composite layups are investigated. Mechanics based numerical models based on finite element analyses are developed to predict the damage behavior of CMCs. The energy based crack band model implemented in Abaqus' user subroutines is used to enforce mesh objectivity. Crack densities are predicted with microstructural FEM models including hundreds of fibers. Geometrical inhomogeneities are included in the model in order to represent the microstructure accurately. Crack-paths and stress-strain responses are compared to experimental results. Component level numerical predictions are developed using a multiscale approach referred to as the integrated finite element method (IFEM). In the IFEM, a representative volume element, which includes nonlinear response due to constituent level damage, is embedded within Abaqus user subroutine UMAT. This allows the user to capture the influence of constituent stress-strain relation at the RVE level. Energy based fracture mechanics models are implemented in the constitutive relations of the RVE model. Damage of each constituent within the RVE is predicted. Macroscopic crack paths are predicted and compared to experimental results. In support of IFEM, micromechanics based models are developed to study the effect of fiber packing and other geometrical features on the transverse response of CMC plies. Experiments on CMCs at elevated temperature revealed the existence of fiber debonding and subsequent sliding and pullout of the fibers. A numerical model is developed to predict the fiber debonding using discrete cohesive zone elements (DCZM).PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111477/1/pasmey_1.pd

Microstructure generation and micromechanical modeling of sheet molding compound composites

We introduce an algorithm that allows for a fast generation of SMC composite microstructures. An exact closure approximation and a quasi-random orientation sampling ensure high fidelity. Furthermore, we present a modular framework for anisotropic damage evolution. Our concept of extraction tensors and damage-hardening functions enables the description of complex damage-degradation. In addition, we propose a holistic multiscale approach for constructing anisotropic failure criteria

Progressive Damage and Failure Analysis of 3D Textile Composites Subjected to Flexural Loading.

3D textile composites (3DTCs) are becoming increasingly attractive as light-weight materials for a variety of structural load bearing applications, including those in the aerospace, marine, automotive, and energy generation sectors. The focus of this research is to investigate the deformation response of 3DTCs through flexural tests. The experimental results are subsequently used as a basis for the development of a multiscale mechanics based model for the deformation, damage and failure response of 3DTCs, predominantly under flexural loading. Quasi-static flexural tests were performed either on a screw-driven loading device or on a hydraulically activated loading machine. To achieve higher loading rates, tests were carried out using a drop tower facility, which can provide different impact velocities by varying the height of the weight that is dropped onto the specimen. Fiber tow kinking, which developed on the compressive side of the specimen was found to be a strength limiting mechanism for this class of materials. Distributed matrix cracking was observed in regions of predominant tension. A mechanics based multiscale computational model was developed for 3DTCs based upon a global-local modeling strategy, in which the influence of textile architecture is incorporated in a mesoscale finite element model, while the composite is homogenized at the macroscale. The fiber tow pre-peak nonlinear response is computed using a novel, two-scale model, in which the subscale micromechanical analysis is carried out in closed form based upon on a unit cell of a fiber-matrix concentric cylinder. Therefore, the influence of matrix microdamage at the microscale manifests as the progressive degradation of the fiber tow stiffness at the mesoscale. The post-peak strain softening responses of the fiber tows and matrix are modeled through the smeared crack approach, which is designed to be mesh objective. The load-deflection response, along with the progressive damage and failure events, including matrix cracking, tow kinking, and tow tensile breakage, are successfully predicted through the proposed multiscale model. Since all the inputs are from the constituent level, the model is useful in understanding how the 3DTC macroscopic response is influenced by the geometry of textile architecture and the constitutive response of the constituents.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/107292/1/dianyun_1.pd

Quasi-static and fatigue delamination characterisation for carbon fibre reinforced woven laminates: investigation into the nesting effect between layers

Low weight is one of the most important design criteria to be considered during the selection of the material for different applications. Weight saving is necessary in the applications where the components are in motion. Materials for transportation systems such as high-speed trains, automobiles, aircraft, or mobile components like wind turbine blades need to fulfil the strength requirement without increasing the component’s thickness and, consequently, weight. Accordingly, composite materials offer the advantage of providing a lightweight structure because of their low density but with a considerable increase in strength-to-weight ratio. Under different load conditions, static and/or dynamic, the layers of the composite material may try to debound. This phenomenon is called delamination and it is a common damage mechanism that ends up in a loss of stiffness and strength. This is the reason why in order to prevent delamination damage in composite materials, the correct characterisation and modelling of the interlaminar fracture behaviour can play an important role in the design of composite parts. The initiation of a delamination does not mean that there is a catastrophic failure in the material. The delamination may not grow any further for the rest of its service life if the loading condition does not exceed a specified crack propagation limit. The design procedure must not only cover the static interlaminar strength calculation of the component, but also the dynamic interlaminar strength calculation, and be able to support maximum load levels and fatigue dynamic loads without total failure. Good knowledge of interlaminar fracture behaviour can facilitate reliable and efficient design criteria to prevent the final failure of the component. Carbon fibre reinforced woven textile laminates are widely used in aeronautics, automotive or sport equipment applications due to their excellent performance and low weight. One of the reasons is that as the drapability of these textiles is high compared to unidirectional laminates, curved shapes can be manufactured easily. Due to the yarn alignment in orthotropic directions, woven structures show good in-plane mechanical behaviour, but low delamination resistance because of poor through-thickness properties. Many authors have seen in their experimental tests that fracture toughness and surface geometry can be affected because of textile structure geometry characteristics; the inner structure of the woven material has an impact on the delamination damage evolution in the laminate. The nesting effect, for example, which is the interaction between neighbouring layers of a textile composite laminate, can be strongly linked to the fracture surface geometry and the delamination behaviour. In this work the internal structure geometry is linked to the static and dynamic fracture toughness values. The analysed properties are the nesting and the unit cell size effect. The most suitable test methods are proposed for measuring the static and fatigue fracture toughness values for the selected textile composite material. The conclusions show that fracture behaviour of the woven textile composite material changes depending on the internal structure