Showing papers on "Micromechanics published in 2016"

Matrix design of strain hardening fiber reinforced engineered geopolymer composite

Abstract: The feasibility of developing a fiber reinforced engineered geopolymer composite (EGC) exhibiting strain hardening behavior under uni-axial tension has been recently demonstrated. The effect of different alkaline activators on the matrix and composite behavior of such EGC has also been evaluated to enhance its compressive and tensile strengths with relatively low concentration activator combinations. The focus of this study, as a follow up investigation, is to evaluate the quantitative influence of geopolymer matrix properties on the strain hardening behavior of the recently developed fly ash-based EGC with the aim of selecting the appropriate type of geopolymer matrix to manufacture the strain hardening EGC with enhanced elastic modulus while maintaining the tensile ductility behavior of the composite. The effects of water to geopolymer solids ratio, sand size and sand content, as the most significant matrix-related parameters, on the matrix properties including workability, compressive strength, elastic modulus, fracture toughness and crack tip toughness, and the uni-axial tensile performance of the composite were evaluated. Experimental results revealed that lowering the water to geopolymer solids ratio and the addition of sand enhanced the elastic modulus of the geopolymer matrix and composite in all cases. However, the excessive use of fine sand and the use of coarse sand adversely affected the strain hardening behavior of the developed EGC due to the increase of the matrix fracture toughness and the first-crack strength of the composite. Only geopolymer matrices with suitable fracture toughness, as defined by the micromechanics design model, maintained the desirable tensile ductility of the developed fly ash-based EGC.

Granular micromechanics based micromorphic model predicts frequency band gaps

Abstract: Granular materials are typically characterized by complex structure and composition. Continuum modeling, therefore, remains the mainstay for describing properties of these material systems. In this paper, we extend the granular micromechanics approach by considering enhanced kinematic analysis. In this analysis, a decomposition of the relative movements of interacting grain pairs into parts arising from macro-scale strain as well as micro-scale strain measures is introduced. The decomposition is then used to formulate grain-scale deformation energy functions and derive inter-granular constitutive laws. The macro-scale deformation energy density is defined as a summation of micro-scale deformation energy defined for each interacting grain pair. As a result, a micromorphic continuum model for elasticity of granular media is derived and applied to investigate the wave propagation behavior. Dispersion graphs for different cases and different ratios between the microscopic stiffness parameters have been presented. It is seen that the model has the capability to present band gaps over a large range of wave numbers.

Finite element simulation of residual stress and failure mechanism in plasma sprayed thermal barrier coatings using actual microstructure as the representative volume

Abstract: The residual stress and failure mode of thermal barrier coating (TBC) containing metallic bond coat (BC) and ceramic top coat (TC) with and without thermally grown oxide (TGO) were predicted using a micromechanical-based finite element method (FEM). Actual microstructures of the TBC taken by a scanning electron microscope (SEM) were utilized as the representative volume elements (RVEs) in the computational model. Failure mode of the representative volume was numerically simulated as thermal stress localization during thermal cycle. Computations were done on the representative volume to quantitatively assess the effects of thermal and mechanical properties of the TBC constituents as well as the presence of TGO on the macroscopic mechanical response of the TBC. Comparisons of computed results with experiments verified that, the computational method can successfully predict residual stress and crack initiation mode of the studied thermal barrier coatings. Moreover, based on the computed results, both shear and normal failure mode occur in the thermal barrier coating which is in good agreement with experimental findings.

Computational micromechanics evaluation of the effect of fibre shape on the transverse strength of unidirectional composites: An approach to virtual materials design

Abstract: Computational micromechanics of composites is an emerging tool required for virtual materials design (VMD) to address the effect of different variables involved before materials are manufactured. This strategy will avoid unnecessary costs, reducing trial-and-error campaigns leading to fast material developments for tailored properties. In this work, the effect of the fibre cross section on the transverse behaviour of unidirectional fibre composites has been evaluated by means of computational micromechanics. To this end, periodic representative volume elements containing uniform and random dispersions of 50% of parallel non-circular fibres with lobular, polygonal and elliptical shapes were generated. Fibre/matrix interface failure as well as matrix plasticity/damage were considered as the fundamental failure mechanisms operating at the microscale under transverse loading. Circular fibres showed the best averaged behaviour although lobular fibres exhibited superior performance in transverse compression mainly due to the higher tensile thermal residual stresses generated during cooling at the fibre/matrix interface.

Micromechanical modelling of deformation and fracture of hydrating cement paste using X-ray computed tomography characterisation

Abstract: Cement paste is the basic but most complex component in cement composites, which are the dominant construction material in the world. Understanding and predicting elastic properties and fracture of hydrating cement paste are challenging tasks due to its complex microstructure, but important for durability assessments and life extension decisions. A recently proposed microstructure-informed site-bond model with elastic-brittle spring bundles is developed further to predict the evolution of elastic properties and fracture behaviour of cement paste. It is based on microstructural characteristics of hydrating cement paste obtained from X-ray computed microtomography (micro-CT) with a spatial resolution of 0.5 μm/voxel. Volume fraction and size distribution of anhydrous cement grains are used to determine the model length scale and pore-less elasticity. Porosity and pore size distribution are used for tuning elastic and failure properties of individual bonds. The fracture process is simulated by consecutive removal of bonds subjected to surface energy based failure criterion. The stress–strain response and elastic properties of hardened cement pastes with curing ages of 1, 7 and 28 days are obtained. The simulated Young's modulus and deformation response prior to peak stress agree very well with the experimental data. The proposed model provides an effective tool to evaluate time evolution of elastic properties and to simulate the initiation, propagation, coalescence and localisation of micro-cracks.

Micromechanics-based viscoelastic analysis of carbon nanotube-reinforced composites subjected to uniaxial and biaxial loading

Abstract: Viscoelastic response of carbon nanotubes (CNTs) reinforced polyimide nanocomposites subjected to the action of uniaxial and biaxial loads is studied using a micromechanical model based on the unit-cell method. The developed micromechanical model is simple and efficient, and provides closed-form expressions for the effective viscoelastic response of nanocomposites. The representative volume element (RVE) of nanocomposites consists of three phases including continuous CNTs, polyimide matrix and interphase. The state of dispersion of CNTs into the polymer matrix is considered to be random. The obtained elastic and viscoelastic responses are found to be in good agreement with those predicted through other methods and experimental data. The model is then used to study the effects of interphase materials (elastic and viscoelastic) on the creep behavior of nanocomposites. Also, the effects of stress level, CNT radius and interphase on the viscoelastic response of nanocomposites under uniaxial and equi-biaxial including transverse/transverse and longitudinal/transverse loading conditions are examined.

The Eshelby, Hill, Moment and Concentration Tensors for Ellipsoidal Inhomogeneities in the Newtonian Potential Problem and Linear Elastostatics

Abstract: One of the most cited papers in Applied Mechanics is the work of Eshelby from 1957 who showed that a homogeneous isotropic ellipsoidal inhomogeneity embedded in an unbounded (in all directions) homogeneous isotropic host would feel uniform strains and stresses when uniform strains or tractions are applied in the far-field. Of specific importance is the uniformity of Eshelby’s tensor $\mathbf{S}$ . Following Eshelby’s seminal work, a vast literature has been generated using and developing Eshelby’s result and ideas, leading to some beautiful mathematics and extremely useful results in a wide range of application areas. In 1961 Eshelby conjectured that for anisotropic materials only ellipsoidal inhomogeneities would lead to such uniform interior fields. Although much progress has been made since then, the quest to prove this conjecture is still not complete; numerous important problems remain open. Following a different approach to that considered by Eshelby, a closely related tensor $\mathbf{P}=\mathbf{S}\mathbf{D}^{0}$ arises, where $\mathbf{D}^{0}$ is the host medium compliance tensor. The tensor $\mathbf{P}$ is associated with Hill and is of course also uniform when ellipsoidal inhomogeneities are embedded in a homogeneous host phase. Two of the most fundamental and useful areas of applications of these tensors are in Newtonian potential problems such as heat conduction, electrostatics, etc. and in the vector problems of elastostatics. Knowledge of the Hill and Eshelby tensors permit a number of interesting aspects to be studied associated with inhomogeneity problems and more generally for inhomogeneous media. Micromechanical methods established mainly over the last half-century have enabled bounds on and predictions of the effective properties of composite media. In many cases such predictions can be explicitly written down in terms of the Hill tensor, or equivalently the Eshelby tensor and can be shown to provide excellent predictions in many cases. Of specific interest is that a number of important limits of the ellipsoidal inhomogeneity can be taken in order to be employed in predictions of the effective properties of, for example, layered media and fibre reinforced composites and also to the cases when voids and cracks are present. In the main, results for the Hill and Eshelby tensors are distributed over a wide range of articles and books, using different notation and terminology and so it is often difficult to extract the necessary information for the tensor that one requires. The case of an anisotropic host phase is also frequently non-trivial due to the requirement of the associated Green’s tensor. Here this classical problem is revisited and a large number of results for problems that are felt to be of great utility in a wide range of disciplines are derived or recalled. A scaling argument leads to the derivation of the Eshelby tensor for potential problems where the host phase is at most orthotropic, without the requirement of using the anisotropic Green’s function. The Concentration tensor $\boldsymbol{\mathcal{A}}$ linking interior fields to those imposed in the far-field is derived for a wide variety of problems. These results can therefore be used in the various micromechanical schemes. Directly related to the tensors of Eshelby and Hill is the so-called Moment tensor $\mathbf{M}$ . As well as arising in the literature on micromechanics, this tensor is important in the vast area of research associated with inverse problems and specifically with the problem of identifying an object inside some domain given the application of a specific set of boundary conditions. Due to its fundamental importance and direct link to the Eshelby and Hill tensors, here we state the connection between $\mathbf{M}, \mathbf{P}$ and $\mathbf{S}$ in an effort to ensure that the work is of use to as wide a community as possible. Both tensor and matrix formulations are considered and contrasted throughout. Appendices give various details that illustrate the implementation of both approaches.

Multi-scale defect interactions in high-rate brittle material failure. Part I: Model formulation and application to ALON

Abstract: Within this two part series we develop a new material model for ceramic protection materials to provide an interface between microstructural parameters and bulk continuum behavior to provide guidance for materials design activities. Part I of this series focuses on the model formulation that captures the strength variability and strain rate sensitivity of brittle materials and presents a statistical approach to assigning the local flaw distribution within a specimen. The material model incorporates a Mie–Gruneisen equation of state, micromechanics based damage growth, granular flow and dilatation of the highly damaged material, and pore compaction for the porosity introduced by granular flow. To provide initial qualitative validation and illustrate the usefulness of the model, we use the model to investigate Edge on Impact experiments ( Strassburger, 2004 ) on Aluminum Oxynitride (AlON), and discuss the interactions of multiple mechanisms during such an impact event. Part II of this series is focused on additional qualitative validation and using the model to suggest material design directions for boron carbide.

A simplified multiscale damage model for the transversely isotropic shale rocks under tensile loading

Abstract: A simplified multiscale damage model is proposed for the transversely isotropic shale rocks under tensile loading. In this framework, the multiscale representations for the shale rocks are presente...

The Master SN curve approach – A hybrid multi-scale fatigue simulation of short fiber reinforced composites

Abstract: Typical short fiber reinforced composites (SFRCs) components have a different statistical distribution of orientation of fibers at different points leading to different static and fatigue behavior at different locations across the component. To link component-scale calculations with this variability of fiber orientations, each element in the FE model is modeled as a Representative Volume Element (RVE); the static and fatigue properties must be calculated for each of these elements. While there are established methods to estimate the static properties, there are none for the fatigue properties. A hybrid (combination of micromechanics and tests) and multi-scale (damage in micro-scale linked to macroscale fatigue properties) method of predicting the SN curve for every point in a short fiber composite has been developed. This proposed method is based not only on tests but on a combination of manufacturing simulation, tests and multi-scale mechanics. An extensive test program was undertaken to study the fatigue behavior of short fiber composites and validate the concept of the Master SN curve (MSNC) approach. The MSNC approach is compared with two prevalent approaches – strength based scaling and test based interpolation. The MSNC approach was found to be in a good agreement with the experimental results and was confirmed to be more accurate than the prevalent methods.

Homogenization of elastic properties of short-fiber reinforced composites based on measured microstructure data

Abstract: Mechanical properties of short-fiber reinforced composites are crucially influenced by their microstructure. The microstructure itself is mainly governed by the manufacturing process like injection...

Micromechanics-based progressive failure analysis of carbon fiber/epoxy composite vessel under combined internal pressure and thermomechanical loading

Abstract: A progressive failure analysis algorithm based on micromechanics of failure (MMF) theory and material property degradation method (MPDM) is developed, wherein the MMF is used to predict the failure initiation at constituent level and the MPDM is employed to account for the post failure behavior of the damaged materials. The progress of damage is controlled by a linear damage evolution law, which is based on the fracture energy dissipating during the process. This micromechanics-based approach is implemented by a user-material subroutine (UMAT) in ABAQUS, which is sufficiently general to predict the ultimate strength and complex failure behaviors of the composite vessel subject to both high pressure and thermal loading. In addition, the predictions of the model are also compared with those by experiment and traditional finite element analysis.

Shear response of carbon fiber composite octet-truss lattice structures

Abstract: Ultralight three dimensional space filling octet-truss lattice structures have been fabricated from carbon fiber reinforced polymer (CFRP) laminates using a mechanical snap-fitting and adhesive bonding technique. The lattice structures moduli and strengths have been measured during (0 0 1) in-plane shear as a function of the lattice relative density ( ρ ¯ ). Their strength was determined by the activation of two strut failure modes: elastic buckling of the struts governed the response when ρ ¯ 5 % , while delamination failure controlled the strength for 16 % > ρ ¯ > 5 % . The measured shear strengths are shown to be well predicted by micromechanics models based on the elastic buckling and delamination failure of the struts. Snap-fit CFRP octet-truss lattice structures with densities of 24–230 kg m −3 are found to have mechanical properties superior to polymer and metal foams, and are competitive with Balsa wood and recently reported Ti–6Al–4V octet-truss lattices. They provide new opportunities for ultra-lightweight multi-axially loaded structures.