Showing papers on "Micromechanics published in 2013"

Finite Element Analysis of Composite Materials using Abaqus

Abstract: Mechanics of Orthotropic Materials Lamina Coordinate System Displacements Strain Stress Contracted Notation Equilibrium and Virtual Work Boundary Conditions Continuity Conditions Compatibility Coordinate Transformations Transformation of Constitutive Equations 3D Constitutive Equations Engineering Constants From 3D to Plane Stress Equations Apparent Laminate Properties Introduction to Finite Element Analysis Basic FEM Procedure General Finite Element Procedure Solid Modeling, Analysis, and Visualization Elasticity and Strength of Laminates Kinematic of Shells Finite Element Analysis of Laminates Failure Criteria Predefined Fields Buckling Eigenvalue Buckling Analysis Continuation Methods Free Edge Stresses Poisson's Mismatch Coefficient of Mutual Influence Computational Micromechanics Analytical Homogenization Numerical Homogenization Local-Global Analysis Laminated RVE Viscoelasticity Viscoelastic Models Boltzmann Superposition Correspondence Principle Frequency Domain Spectrum Representation Micromechanics of Viscoelastic Composites Macromechanics of Viscoelastic Composites FEA of Viscoelastic Composites Continuum Damage Mechanics One-Dimensional Damage Mechanics Multidimensional Damage and Effective Spaces Thermodynamics Formulation Kinetic Law in Three-Dimensional Space Damage and Plasticity Discrete Damage Mechanics Overview Approximations Lamina Constitutive Equation Displacement Field Degraded Laminate Stiffness and CTE Degraded Lamina Stiffness Fracture Energy Solution Algorithm Delaminations Cohesive Zone Method Virtual Crack Closure Technique Appendix A: Tensor Algebra Appendix B: Second-Order Diagonal Damage Models Appendix C: Software Used Index Problems appear at the end of each chapter.

Finite Element Analysis of Composite Materials Using ANSYS

Abstract: Mechanics of Orthotropic Materials Material Coordinate System Displacements Strain Stress Contracted Notation Equilibrium and Virtual Work Boundary Conditions Continuity Conditions Compatibility Coordinate Transformations Transformation of Constitutive Equations 3D Constitutive Equations Engineering Constants From 3D to Plane Stress Equations Apparent Laminate Properties Suggested Problems References Introduction to Finite Element Analysis Basic FEM Procedure General FEM Procedure FE Analysis with CAE Systems Suggested Problems References Elasticity and Strength of Laminates Kinematics of Shells FE Analysis of Laminates Failure Criteria Suggested Problems References Buckling Bifurcation Methods Continuation Methods Suggested Problems References Free Edge Stresses Poisson's Mismatch Coefficient of Mutual Influence Suggested Problems References Computational Micromechanics Analytical Homogenization Numerical Homogenization Local-Global Analysis Laminated RVE Suggested Problems References Viscoelasticity Viscoelastic Models Boltzmann Superposition Correspondence Principle Frequency Domain Spectrum Representation Micromechanics of Viscoelastic Composites Macro-Mechanics of Viscoelastic Composites FEA of Viscoelastic Composites Suggested Problems References Continuum Damage Mechanics One-Dimensional Damage Mechanics Multi-Dimensional Damage and Effective Spaces Thermodynamics Formulation Kinetic Law in Three-Dimensional Space Damage and Plasticity Suggested Problems References Discrete Damage Mechanics Theoretical Formulation Numerical Implementation Model Identification Laminate Damage References Bibliography Delaminations Two-Dimensional Delamination Delamination in Composite Plates Suggested Problems References Appendices ANSYS BMI3 References Index

Rheology, fiber dispersion, and robust properties of Engineered Cementitious Composites

Abstract: The capability of processing robust Engineered Cementitious Composites (ECC) materials with consistent mechanical properties is crucial for gaining acceptance of this new construction material in various structural applications. ECC’s tensile strain-hardening behavior and magnitude of tensile strain capacity are closely associated with fiber dispersion uniformity, which determines the fiber bridging strength, complementary energy, critical flaw size and degree of multiple-crack saturation. This study investigates the correlation between the rheological parameters of ECC mortar before adding PVA fibers, dispersion of PVA fibers, and ECC composite tensile properties. The correlation between Marsh cone flow rate and plastic viscosity was established for ECC mortar, justifying the use of the Marsh cone as a simple rheology measurement and control method before fibers are added. An optimal range of Marsh cone flow rate was found that led to improved fiber dispersion uniformity and more consistent tensile strain capacity in the composite. When coupled with the micromechanics based ingredient-tailoring methodology, this rheological control approach serves as an effective ECC fresh property design guide for achieving robust ECC composite hardening properties.

Molecular modeling of crosslinked graphene–epoxy nanocomposites for characterization of elastic constants and interfacial properties

Abstract: The mechanical properties of crosslinked graphene/epoxy nanocomposites have been investigated using molecular mechanics (MM) and molecular dynamics simulations (MD). The influence of graphene nanoplatelet concentrations, aspect ratios and dispersion on elastic constants and stress–strain responses are studied. The cohesive and pullout forces at the interface of G–Ep nanocomposites are also investigated. The simulated MD models were further analyzed through radial distribution function, molecular energy and atom density. The results show significant improvement in Young’s modulus and shear modulus for the G–Ep system in comparison to neat epoxy resin. The graphene concentrations in the range of 1–3% and graphene with low aspect ratio are seen to improve Young’s modulus. The dispersed graphene system is seen to enhance in-plane elastic modulus than the agglomerated graphene system. The cohesive and pullout forces versus displacements data were plotted under normal and shear modes in order to characterize interfacial properties. The cohesive force is significantly improved by attaching chemical bonding at the graphene–epoxy interface. It appears that elastic constants determined by molecular modeling and nanoindentation test methods are comparatively higher than the micromechanics based predicted value and coupon test data. This is possibly due to scaling effect.

The Theory of Materials Failure

Abstract: 1 The perspective on failure and direction of approach 2 History, conditions, and requirements 3 Isotropic baselines 4 The failure theory for isotropic materials 5 Isotropic materials failure behavior 6 Experimental and theoretical evaluation 7 Isotropic materials failure examples 8 The ductile/brittle transition for isotropic materials 9 Defining yield stress and failure stress (strength) 10 Fracture mechanics 11 Anisotropic, unidirectional fiber composites failure 12 Anisotropic, fiber composite laminates failure 13 Micromechanics failure analysis 14 Nanomechanics failure analysis 15 Damage, cumulative damage, creep, and fatigue failure 16 Probabilistic failure and probabilistic life prediction

Micromechanical analysis of heterogeneous structural materials

Abstract: This paper shows an efficient methodology based on micromechanical framework and grid nanoindentation for the assessment of effective elastic properties on several types of microscopically heterogeneous structural materials. Such task is a prerequisite for successful nano- and micro-structural material characterization, development and optimization. The grid nanoindentation and statistical deconvolution methods previously described in the literature e.g. for cementitious materials [1] , [2] , alkali activated materials [3] or high-performance concretes [4] have been employed. In this paper we demonstrate their utilization also for other types of structural composites with crystalline nature and we validate the results by using enhanced numerical method based on fast Fourier transform (FFT). The direct procedure of using grid nanoindentation data in the FFT method simplifies the evaluation of effective composite properties and leads to the assemblage of the full stiffness matrix compared to simple analytical approaches. The paper deals namely with cement paste, gypsum and aluminum alloy. Nanoindentation is used for the determination of phase properties in grid points at the scale below one micrometer. Statistical approach and deconvolution methods are applied to assess intrinsic phase properties. Elastic properties obtained by nanoindentation are homogenized in the frame of the representative volume element (RVE) by means of analytical and numerical FFT-based schemes. Good correlation of the results from all methods was found for the tested materials due to the close-to-isotropic nature of the composites in the RVE having dimensions ∼100–200 μm. Results were also verified against macroscopic experimental results. The proposed and validated numerical approach can be successively used for the material modeling in finite element software or for optimization of materials with inhomogeneous microstructures.

Effect of the matrix behavior on the damage of ethylene–propylene glass fiber reinforced composite subjected to high strain rate tension

Abstract: This study investigates the origin of the strain rate effect on the mechanical behavior of a discontinuous glass fiber reinforced ethylene–propylene copolymer (EPC) matrix composite. This kind of composite materials are commonly used for automotive functional and structural applications. To this aim, a multi-scale experimental approach is developed. The deformation processes and the damage mechanisms observed at the microscopic scale are related to the material mechanical properties at the macroscopic scale. Tensile tests up to failure and specific interrupted tensile tests have been optimized and performed for high strain rates up to 200 s−1 to quantify the strain rate effect at different scales. High speed tensile tests have also been performed on the pure copolymer matrix. The threshold and the kinetic of damage have been quantified at both microscopic and macroscopic scales. Experimental results show that the composite behavior is strongly strain-rate dependent. The multi-scale analysis leads to the conclusion that the strain rate effect on the damage behavior of the EPC matrix composite is mainly due to the viscous behavior of the EPC matrix. SEM observations and analysis show that a localized deformation in the interface zone around fibers occurs at high strain rates and directly affects the visco-damage behavior. It is established that when the strain rate increases, the local deformation zone around the fibers behaves like a dissipation zone. Consequently, the damage initiation is delayed and the related kinetic is reduced with respect to the quasi-static loading case.

Micromechanics-based progressive failure analysis prediction for WWFE-III composite coupon test cases

Abstract: As a part of a world-wide study, a commercial code (General Optimization Analyzer), based on multi-scale (micro–macro) progressive failure analysis (PFA), is used to provide theoretical predictions...

Micromechanical model for viscoelastic materials undergoing damage

Abstract: We have derived a stress–strain relationship for viscoelastic materials undergoing damage using a granular micromechanics approach. This approach assumes the material to possess a granular meso-structure such that the material is treated as a discrete or a particulate system. By considering the particle kinematics in terms of Taylor series expansion, a continuum model of the discrete system is obtained. The material rate-dependence and damage are modeled by assuming appropriate inter-granular force–displacement relationships that satisfy thermodynamic constraints. The advantage of this micromechanical approach is that the resultant continuum model retains the discrete nature by incorporating the effect of nearest neighbor grain interactions through the inter-granular force–displacement relationship and orientation vector. As a result, the derived model has the ability to predict a number of material phenomena, such as loading-induced anisotropy, dilation or pressure sensitivity, and secondary creep, which often manifest due to material granularity.

Micromechanics of High-Strength, High-Ductility Concrete

Abstract: This paper reports the microscale investigation of a new fiber-reinforced cementitious composite, high-strength, high-ductility concrete (HSHDC), which possesses a rare combination of very high compressive strength (166 MPa [241 ksi]) and very high tensile ductility (34% strain capacity) The investigation involved experimental determination of fiber/matrix interaction properties using single-fiber pullout tests A new mechanism of inclination-dependent hardening in fiber pullout—unique for a high-strength cementitious matrix—is discovered The existing fiber-pullout analytical model for strain-hardening cementitious composites (SHCCs) is modified to incorporate the new mechanism The modeled fiber-pullout behavior is used in a scale-linking model to compute the crack bridging (σ-δ) relation of HSHDC, which is also empirically verified through single-crack tests The σ-δ relation of HSHDC satisfies the micromechanics-based necessary strength and energy conditions of steady-state flat crack propagation that prevent localized fracture The microscale investigation of HSHDC in this research thus demonstrates the rational basis for its design combining both high compressive strength and high tensile ductility

Estimation of the interfacial shears strength, orientation factor and mean equivalent intrinsic tensile strength in old newspaper fiber/polypropylene composites

Abstract: The present paper investigates the suitability of old newspapers (ONPs) as a source of reinforcing fibers for composite materials. Different percentages of ONP fibers were compounded with polypropylene (PP). A coupling agent was added to the compound to improve the interface between matrix and reinforcing fibers. Tensile test were performed to obtain the mechanical properties of the composite materials. Micromechanics of the fibers were obtained using Hirsch model, Bowyer–Bader methodology and Kelly–Tyson equations. Due to the presence of a percentage of calcium carbonate in the obtained fibers (10%), the computed intrinsic characteristics were addressed as equivalent. The most important results were the mean equivalent intrinsic tensile strength of the ONP fibers, the mean orientation angle and the mean interfacial shear strength. The contributions of the matrix, the subcritical and the supercritical fibers to the tensile strength of the composite material were also computed.

Effects of CNT waviness on the effective elastic responses of CNT-reinforced polymer composites

Abstract: In this study, the effects of fiber waviness on the effective elastic responses of CNT–polymer composites are investigated based on the framework of micromechanics and homogenization. By taking advantage of an ad hoc Eshelby tensor, the load-transfer capability of wavy carbon nanotube (CNT) embedded in the polymer matrix is accounted for. Further, the effective elastic responses of composites are simulated by using the multi-phase Mori–Tanaka method to study the influence of randomly oriented wavy CNT. It is demonstrated that the proposed micromechanics-based closed form solution is effective to tackle the underlying problem. The present predictions and the comparisons with the available experimental data indicate that the CNT waviness leads to the degradation of effective responses of composites. Finally, in addition to the effect of CNT waviness, the significance of CNT interface is briefly discussed based on the experimental observations.

On the contribution of carbon nanotube deformation to piezoresistivity of carbon nanotube/polymer composites

Abstract: The change in electrical resistance due to mechanical deformation of carbon nanotube (CNT)/polymer composites can be rationalized in terms of two effects: (i) changes in the composite electrical resistivity due to changes in the CNT network configuration and (ii) deformation of the CNTs themselves. The contribution of CNT dimensional changes (ii) to the piezoresistivity of CNT/polymer composites is investigated here. An analytical model based exclusively on dimensional changes which describes the CNT change of electrical resistance in terms of its mechanical deformation is proposed. A micromechanics approach and finite element analysis are performed to correlate the macroscale composite strain to the individual CNT strain. The CNT change of electrical resistance is quantified for different matrix elastic moduli and CNT weight fractions. The CNT/polymer composite is also modeled as an effective continuum material in terms of both its electrical and mechanical responses so that the effect of dimensional changes on the global piezoresistivity can be investigated. Based on the modeling predictions and previous experimental results, it is estimated that the CNT change of resistance due to the macroscale composite strain is marginal (∼5%) compared to the total composite change of resistance commonly measured in the laboratory, suggesting that the dominant effect in the piezoresistivity of CNT/polymer composites is the change in the CNT network configuration.

An anisotropic elastic-viscoplastic damage model for bone tissue

Abstract: A new anisotropic elastic-viscoplastic damage constitutive model for bone is proposed using an eccentric elliptical yield criterion and nonlinear isotropic hardening. A micromechanics-based multiscale homogenization scheme proposed by Reisinger et al. is used to obtain the effective elastic properties of lamellar bone. The dissipative process in bone is modeled as viscoplastic deformation coupled to damage. The model is based on an orthotropic ecuntric elliptical criterion in stress space. In order to simplify material identification, an eccentric elliptical isotropic yield surface was defined in strain space, which is transformed to a stress-based criterion by means of the damaged compliance tensor. Viscoplasticity is implemented by means of the continuous Perzyna formulation. Damage is modeled by a scalar function of the accumulated plastic strain \({D(\kappa)}\) , reducing all element s of the stiffness matrix. A polynomial flow rule is proposed in order to capture the rate-dependent post-yield behavior of lamellar bone. A numerical algorithm to perform the back projection on the rate-dependent yield surface has been developed and implemented in the commercial finite element solver Abaqus/Standard as a user subroutine UMAT. A consistent tangent operator has been derived and implemented in order to ensure quadratic convergence. Correct implementation of the algorithm, convergence, and accuracy of the tangent operator was tested by means of strain- and stress-based single element tests. A finite element simulation of nano- indentation in lamellar bone was finally performed in order to show the abilities of the newly developed constitutive model.

Multi-Inclusion modeling of multiphase piezoelectric composites

Abstract: Recent work on multifunctional materials has shown that a functionally graded interface between the fiber and matrix of a composite material can lead to improved strength and stiffness while simultaneously affording piezoelectric properties to the composite. However the modeling of this functional gradient is difficult through micromechanics models without discretizing the gradient into numerous layers of varying properties. In order to facilitate the design of these multiphase piezoelectric composites, accurate models are required. In this work, Multi-Inclusion models are extended to predict the effective electroelastic properties of multiphase piezoelectric composites. To evaluate the micromechanics modeling results, a three dimensional finite element model of a four-phase piezoelectric composite was created in the commercial finite element software ABAQUS with different volume fractions and aspect ratios. The simulations showed excellent agreement for multiphase piezoelectric composites, and thus the modeling approach has been applied to study the overall electroelastic properties of a composite with zinc oxide nanowires grown on carbon fibers embedded in the polymer. The results of this case study demonstrate the importance of the approach and show the system cannot be accurately modeled with a homogenized interphase.