Showing papers on "Micromechanics published in 1991"

Mechanics of Composite Materials: A Unified Micromechanical Approach

Abstract: 1. Fundamentals of the Mechanics of Composites. Representative volume element. Volumetric averaging. Homogeneous boundary conditions. Average strain theorem. Average stress theorem. Effective elastic moduli. Relations between averages-direct approach. Relations between averages - energy approach. 2. Basic Models in the Mechanics of Composites. The Voigt approximation. The Reuss approximation. Hill's theorem. The dilute approximation. The composite spheres model. The self-consistent scheme. The generalized self-consistent scheme. The differential scheme. The mori-tanaka theory. Exhelby equivalent inclusion method. 3. The Micromechanical Method of Cells. The method of cells for fiber reinforced materials. Coefficients of thermal expansion. Hill's relations. Thermal conductivities. Specific heats. The method of cells for short-fiber composites. Randomly reinforced materials. Periodically billlminated materials. 4. Strength and Fatigue Failure. Micromechanics prediction of composite failure. 5. Viscoelastic Behaviour of Composites. Linearly viscoelastic composites. Thermoviscoelastic behaviour of composites. Nonlinear viscoelastic behaviour of composites. 6. Nonlinear Behaviour of Resin Matrix Composites. Macromechanical analysis. Micromechanical analysis. 7. Initial Yield Surfaces of Metal Matrix Composites. The initiation of yielding in isotropic materials. Initial yielding of metal matrix composites. Investigation of the convexity of initial yield surfaces. 8. Inelastic Behaviour of Metal Matrix Composites. Constitutive equations of plasticity. Unified theories of viscoplasticity. Bodner-partom viscoplastic equations. Inelastic behaviour of laminated media. Inelastic behaviour of fibrous composites. Matrix mean-field and local-field. Subsequent yield surfaces prediction of metal matrix composites. Metal matrix composite laminates. Short-fiber metal-matrix composites. 9. Imperfect Bonding in Composites. General considerations. The flexible interface imperfect bonding model. Periodically billaminated materials. Fiber-reinforced materials. Short-fiber and particulate composites. The Coulomb frictional law for the modeling of interfacial damage in composites. Index.

Why Continuum Damage is Nonlocal: Micromechanics Arguments

Abstract: The paper presents two micromechanics arguments showing that continuum damage caused by microcracking ought to be nonlocal, defined by a spatial integral. Argument I is an analysis of a simplified model in which the microcracks are of such size, density, and arrangement that that they do not interact. The release of stored energy caused by the formation of one microcrack is calculated as a function of the associated relative displacement across the cell, which corresponds to the average strain of the macroscopic continuum. After imposing two homogenizing conditions, it is shown that damage is a nonlocal variable that is a function of the averaged (nonlocal) strain from a certain neighborhood of the given point. Argument II is an analysis of a body with arbitrary interacting cracks. The local damage is proportional to the forces applied on the cracks to replace the stresses before cracking. Crack formation changes the openings of the neighboring cracks, which represents an interaction described by crack in...

Experimental Micro Mechanics Methods for Conventional and Negative Poisson’s Ratio Cellular Solids as Cosserat Continua

Abstract: Continuum representations of micromechanical phenomena in structured materials are described, with emphasis on cellular solids. These phenomena are interpreted in light of Cosserat elasticity, a generalized continuum theory which admits degrees of freedom not present in classical elasticity. These are the rotation of points in the material, and a couple per unit area or couple stress. Experimental work in this area is reviewed, and other interpretation schemes are discussed. The applicability of Cosserat elasticity to cellular solids and fibrous composite materials is considered as is the application of related generalized continuum theories. New experimental results are presented for foam materials with negative Poisson's ratios.

Experimental micro mechanics methods for conventional and negative Poisson's ratio cellular solids as Cosserat continua

Abstract: Continuum representations of micromechanical phenomena in structured materials are described, with emphasis on cellular solids. These phenomena are interpreted in light of Cosserat elasticity, a generalized continuum theory which admits degrees of freedom not present in classical elasticity. These are the rotation of points in the material, and a couple per unit area or couple stress. Experimental work in this area is reviewed, and other interpretation schemes are discussed. The applicability of Cosserat elasticity to cellular solids and fibrous composite materials is considered as is the application of related generalized continuum theories. New experimental results are presented for foam materials with negative Poisson's ratios.

Mean-field micromechanics model and its application to the analysis of thermomechanical behaviour of composite materials

Abstract: This overview article is concerned with the mean-field micromechanics model that has been developed by several investigators as a powerful modification of Eshelby's theory for the study of the macro-mechanical behaviour of composite materials. First, a general framework of the model is reformulated with emphasis on clarification of the key approximation involved. The model is then applied to the prediction of overall thermoelastic properties of some specific composites of practical interest. For the system with randomly oriented spheroidal particles in particular, the overall bulk and shear moduli, computed as functions of the particle aspect ratio, are shown to vary systematically within the margins which coincide with those bounded by Hashin and Shtrikman. The remainder of this article is devoted to the analysis of anisotropic elastic-plastic responses of metal matrix composites to multiaxial thermomechanical loads. The energy approach that has been proposed is generalized and its applications to specific problems are presented and discussed in comparison with experimental data.

A micromechanics constitutive model of transformation plasticity with shear and dilatation effect

Abstract: B ased on micromechanics, thermodynamics and microscale t → m transformation mechanism considerations a micromechanics constitutive model which takes into account both the dilatation and shear effects of the transformation is proposed to describe the plastic, pseudoelastic and shape memory behaviors of structural ceramics during transformation under different temperatures. In the derivation, a constitutive element (representative material sample) was used which contains many of the transformed m-ZrO2 grains or precipitates as the second phase inclusions embedded in an elastic matrix. Under some basic assumptions, analytic expressions for the Helmholtz and complementary free energy of the constitutive element are derived in a self-consistent manner by using the Mori-Tanaka method which takes into account the interaction between the transformed inclusions. The derived free energy is a function of externally applied macroscopic stress (or strain), temperature, volume fraction of transformed phase and the averaged stressfree transformation strain (eigenstrain) of all the transformed inclusions in the constitutive element, the latter two quantities being considered to be the internal variables describing the micro-structural rearrangement in the constitutive element. In the framework of the Hill-Rice internal variable constitutive theory, the transformation yield function and incremental stress strain relations, in analogy to the theory of metal plasticity, for proportional and non-proportional loading histories are derived, respectively. The theoretical predictions are compared with the available experimental data of Mg-PSZ and Ce-TZP polycrystalline toughening ceramics.

Micromechanical Damage Models for Brittle Solids. Part I: Tensile Loadings

Abstract: Threedimensional micromechanical anisotropic damage models for microcrackweakened brittle solids are presented. The selfconsistent method is employed together with analytical solutions for weakly i...

Micromechanical Damage Models for Brittle Solids. Part II: Compressive Loadings

Abstract: In this sequel, threedimensional selfconsistent damage models for brittle solids under compressive triaxial loadings are developed based on micromechanics and microcrack geometry within a represent...

Differential continuum damage mechanics models for creep and fatigue of unidirectional metal matrix composites

Abstract: Three multiaxial isothermal continuum damage mechanics models for creep, fatigue, and creep/fatigue interaction of a unidirectional metal matrix composite volume element are presented, only one of which will be discussed in depth. Each model is phenomenological and stress based, with varying degrees of complexity to accurately predict the initiation and propagation of intergranular and transgranular defects over a wide range of loading conditions. The development of these models is founded on the definition of an initially transversely isotropic fatigue limit surface, static fracture surface, normalized stress amplitude function and isochronous creep damage failure surface, from which both fatigue and creep damage evolutionary laws can be obtained. The anisotropy of each model is defined through physically meaningful invariants reflecting the local stress and material orientation. All three transversely isotropic models have been shown, when taken to their isotropic limit, to directly simplify to previously developed and validated creep and fatigue continuum damage theories. Results of a nondimensional parametric study illustrate (1) the flexibility of the present formulation when attempting to characterize a large class of composite materials, and (2) its ability to predict anticipated qualitative trends in the fatigue behavior of unidirectional metal matrix composites. Additionally, the potential for the inclusion of various micromechanical effects (e.g., fiber/matrix bond strength, fiber volume fraction, etc.), into the phenomenological anisotropic parameters is noted, as well as a detailed discussion regarding the necessary exploratory and characterization experiments needed to utilize the featured damage theories.

The Adiabatic Thermoelastic Effect in Laminated Fiber Composites

Abstract: The influence of material inhomogeneity and anisotropy on the reversible, adiabatic thermoelastic effect in laminated, continuous-fiber composites is investigated analytically and experimentally. The plane-stress solution for strains in a uniform laminate is combined with a simple micromechanics description of a fiber-reinforced lamina to approximate the nonhomogeneous strains in the fibers and matrix. The equations of anisotropic, linear thermoelasticity are then used to evaluate the temperature change in each of the microconstituents during an adiabatic deformation. The average temperature change of the surface plies of several carbon/epoxy laminates are computed and compared with experimental data obtained via differential infrared thermography. Results indicate that material parameters such as the volume fraction and thermoelastic properties of the microconstituent materials, the orientations of the laminae within the laminate, and the orientation of the lamina on the surface of observation affect the...

Computational simulation of damping in composite structures

Abstract: A computational methodology is developed for the prediction of passive damping in composite structures. The method involves multiple levels of damping modeling by integrating micromechanics, laminate, and structural damping theories. The effects of temperature and moisture on structural damping are included. The simulation of damping in the structural level is accomplished with finite-element discretization. Applications are performed on graphite/epoxy composite beams, plates, and shells to illustrate the methodology. Additional parametric studies demonstrate the variation of structural modal damping with respect to ply angles, fiber volume ratio, and temperature.

Thermal fatigue behavior of a unidirectional SCS6/Ti-15-3 metal matrix composite

Abstract: Damage mechanisms in a unidirectional titanium matrix composite with silicon carbide fibers (SCS6/Ti-15-3) subjected to thermal cycling from 149°C to 427°C and 149°C to 649°C were investigated. The degradation of the reaction zone was the first sign of damage due to thermal cycling. It initiated at 500 cycles and continued to grow with increase of thermal cycles. The Young's modulus, Poisson's ratio and residual tensile strength did not change due to thermal cycling up to 15,000 cycles for both temperature ranges. However, the observed internal damage as the degradation of the reaction zone manifested in the form of linear stress-strain response during residual tensile test. A simplified micromechanics analysis was also conducted to assess the state of stress to interpret the experimentally observed response of the tested metal matrix composite.

Analysis of Thermomechanical Fatigue of Unidirectional Titanium Metal Matrix Composites

Abstract: Thermomechanical fatigue (TMF) data was generated for a Ti-15V-3Cr-3Al-3Sn (Ti-15-3) material reinforced with SCS-6 silicon carbide fibers for both in-phase and out-of-phase thermomechanical cycling. Significant differences in failure mechanisms and fatigue life were noted for in-phase and out-of-phase testing. The purpose of the research is to apply a micromechanical model to the analysis of the data. The analysis predicts the stresses in the fiber and the matrix during the thermal and mechanical cycling by calculating both the thermal and mechanical stresses and their rate-dependent behavior. The rate-dependent behavior of the matrix was characterized and was used to calculate the constituent stresses in the composite. The predicted 0 degree fiber stress range was used to explain the composite failure. It was found that for a given condition, temperature, loading frequency, and time at temperature, the 0 degree fiber stress range may control the fatigue life of the unidirectional composite.

Mechanical identification of composites

Abstract: General Lectures.- Identification of the Rigidities of Composite Systems by Mixed Numerical/Experimental Methods.- Measurement of Complex Moduli of Composite Materials and Discussion of some Results.- Moire Interferometry for Composites.- A Damage Approach for Composite Structures: Theory and Identification.- Contributions.- Identification.- Identification of Temperature Dependence for Orthotropic Material Moduli.- Experimental Identification of Complex Stiffnesses of Composite Materials by Ultrasonic Wave Propagation.- A Hybrid Method to Determine Material Parameters of Composites.- Non Determined Tests as a Way to Identify Wood Elastic Parameters: the Finite Element Approach.- Measurement of Laminate bending Elastic Parameters from Non-Uniform Strain Fields.- Identification of the Shear Properties of the Lamina in the Framework of Plasticity.- Parametric Identification of Mechanical Structures: General Aspects of the Methods used at the LMA.- Static and Dynamic Characterization.- Material Parameters in Anisotropic Plates.- Evaluation of Global Composite Laminate Stiffnesses by Structural Wave Propagation Experiments.- Dynamic Measurements of Elastic Properties of Filament-Wound Cylindrical Shells.- Torsion Response Analysis of T300/914 and T800/914 Unidirectional Specimens.- A Computerized Test Setup for the Determination of the In-Plane and Out-of-Plane Shear Modulus in Orthotropic Specimens.- Some Experience from the Application of the Iosipescu Shear Test.- Constitutive Prediction for a Non-linear Orthotropic Media.- Creep and Relaxation of Coated Fabrics under Biaxial Loading.- Joints and Assemblies of Composite Material Structural Elements: Characterization of adhesives in bulk form and in composite structures.- Static and Dynamic Characterization of Composites using a Fourth Generation Programming Language on a Macintosh.- Impact Behaviour and Damage Characterization.- Use of the Shadow Moire Technique for the Investigation of the Impact Behaviour of Composite laminates.- Delamination Detection via Holographic Interferometry Techniques.- Dynamic Failure Processes in Fibre-Reinforced Composites.- Effect of Strain Rate on the Compressive Strength of Woven Glass-Reinforced/Epoxy Laminates.- Characterization of Highly Anisotropically Reinforced Solids in High Velocity Tension.- Micromechanics and Interfaces.- Determination of the Effective Mechanical Response of Polymer Matrix Composites via Microstructural Data.- A microstructural Method for Predicting the Damping of Lamina.- Theoretical and Experimental Study Technique of the Mechanical Properties of Fiber-Reinforced Laminates and of the Strain Features of Structural Elements.- Dynamic Properties of Layer Reinforced by Two Families of Fibres.- Micromechanical Modelling of Unidirectional Glassfiber Reinforced Polyester: Effect of Matrix Shrinkage.- Plastic Failure of Unidirectional Fibrous Composite Materials with Metal Matrix in Compression.- Analytical Model of Fibre Pull-Out Mechanism.- Nonlinear Viscoelastic Behavior of the Fibre-Matrix Interphase: Theory and Experiment.- Empirical Model Building and Surface Response Methodology Applied to Sclerometrical Investigation for Refractories Concrete.- Fracture and Fatigue Damage Mechanics.- Development of Fatigue Damage Mechanics for Application to the Design of Structural Composite Components.- Influence of Fibre Orientation on the Cracking and Fracture Energy in Brittle Matrix Composites.- Application of the Method of Caustics to Fibre-Reinforced Materials.- Modelling of Orthotropic Layered Structures Containing Cracks in the Interfaces.- A Criterion of Mixed Mode Delamination Propagation in Composite Material.- Fracture and Fatigue Damage in a CSM Composite.- Damage Modelling and Non-Destructive Testing.- Non linear Behaviour of Ceramic Matrix Composites.- Notched Strength and Damage Mechanism of Laminated Composites with Circular Holes.- Damage Modeling and Experimental Tools for 3D Composites.- Increasing Energy Absorption by 'Rope Effect' in Brittle Matrix Composites.- Specific Damping of a Carbon/Epoxy Laminate under Cyclic Loading.- The Application of automated Ultrasonic Inspection for Damage Detection and Evaluation in Composite Materials.- The Use of Vibrothermography for Monitoring Damage Evolution in Composite Materials.- Acoustic Emission Source Location in Anisotropic Plates.- List of Participants.- Index of Contributors.

Micromechanics of Crack Initiation in High-Cycle Fatigue

Abstract: Publisher Summary This chapter discusses micromechanics of crack initiation in high-cycle fatigue. Fatigue failures occur under loadings substantially lower than the yield strength of the material. Fatigue cracks occur in two stages that include crack initiation and crack propagation. A crystal subject to shearing stress deforms elastically until gliding starts in some region of the crystal. Part of the crystal slides with respect to the rest by unit atomic spacing. This slip can occur in a portion of a plane separating two parts of a crystal. The displacement gradient of an elastic-plastic body can be considered to consist of the elastic distortion and plastic slip. During plastic deformation, dislocation lines not only increase in number but also move within the crystal. The positive and negative dislocations move in opposite directions on the slip plane. The concentration of the positive dislocation on one side of the crystal and negative dislocations on the other side, referred to as the polarization of dislocations, facilitates the development of long-range internal stresses. The chapter also elaborates the analogy between inelastic strain and applied force.

Modeling the Viscoplastic Behavior of Fiber-Reinforced Thermoplastic Matrix Composites at Elevated Temperatures

Abstract: An investigation was performed to study the mechanical response of fiber-reinforced thermoplastic matrix composites at elevated temperatures. The primary concern of the study was the effect of temperature on the viscoplastic behavior of the composites. During the investigation, an analytical model was developed for analyzing the response of both unidirectional and multidirectional composites at elevated temperatures. The model considers that the fibers have a linearly elastic behavior but the matrix responds viscoplastically with temperature. Micromechanics theories were adopted and developed to integrate fibers and matrix properties for predicting the response of unidirectional composites. Numerical algorithms were developed based on the lamination theory for evaluating the response of the laminated composites. Based on the model, a computer code was also developed for calculating the mechanical response of thermoplastic matrix composites subjected to both thermal and mechanical loading. In order to veri...

Cracks Interacting with Particles or Fibers in Composite Materials

Abstract: Micromechanics analysis of damage in heterogeneous media and composites cannot ignore the interactions among cracks as well as between cracks and inclusions or voids. Previous investigators can to this conclusion upon finding that states of distributed (diffuse) cracking (damage) cannot be mathematically represented merely as crack systems in a homogeneous medium, even though stable states with distributed damage have been experimentally observed in heterogeneous materials such as concrete. This paper presents a method for modeling interactions between a crack and many inclusions. Based on the Duhamel‐Neuman analogy, the effect of the inclusions is equivalent to unbalanced forces acting on the contour of each inclusion in an infinite homogeneous solid. The problem is solved by superposition; it is decomposed into several standard problems of elasticity for which well‐known solutions are available. The problem is finally reduced to a system of linear algebraic equations similar to those obtained by Kachano...

Probabilistic micromechanics and macromechanics of polymer matrix composites

Abstract: A probabilistic evaluation of an eight ply graphite-epoxy quasi-isotropic laminate was completed using the Integrated Composite Analyzer (ICAN) in conjunction with Monte Carlo simulation and Fast Probability Integration (FPI) techniques. Probabilistic input included fiber and matrix properties, fiber misalignment, fiber volume ratio, void volume ratio, ply thickness and ply layup angle. Cumulative distribution functions (CDFs) for select laminate properties are given. To reduce the number of simulations, a Fast Probability Integration (FPI) technique was used to generate CDFs for the select properties in the absence of fiber misalignment. These CDFs were compared to a second Monte Carlo simulation done without fiber misalignment effects. It was found that FPI requires fewer simulations to obtain the cumulative distribution functions as opposed to Monte Carlo simulation techniques. Furthermore, FPI provides valuable information regarding the sensitivities of composite properties to the constituent properties, fiber volume ratio and void volume ratio.

Micromechanics Analysis of Space Simulated Thermal Stresses in Composites. Part I: Theory and Unidirectional Laminates:

Abstract: A micromechanics analysis is used to study the effects of constituent properties on thermally induced stresses in continuous fiber reinforced composites. A finite element formulation is described, and results are presented for unidirectional carbon/epoxy laminates. It is shown that significant stresses develop in composites exposed to thermal excursions typical of spacecraft operating environments and that the fiber thermoelastic properties have a minimal effect on the magnitude of these stresses. The finite element micromechanics analysis is then extended to the study of multidirectional laminates using a simple global/local formulation. Damage initiation predictions are compared with experimental data, and factors controlling the initiation of damage are identified. Ways of improving the durability of composites are discussed.

Micromechanics Analysis of Space Simulated Thermal Stresses in Composites. Part II: Multidirectional Laminates and Failure Predictions

Abstract: A finite element micromechanics approach was used to predict thermally induced stresses in fiber reinforced polymer matrix composites at temperatures typical of spacecraft operating environments The influence of laminate orientation was investigated with a simple global/local formulation Thermal stress calculations were used to predict probable damage initiation locations, and the results were compared to experimentally observed damage in several epoxy matrix composites Multidirectional (O±t) s laminates had larger predicted matrix stresses than unidirectional (0) laminates The stresses in- creased with increasing lamination angle t, and resulted in large tensile radial stresses at the fiber/matrix interface, that were not present in unidirectional laminates Thermally in- duced matrix failure predictions, using a failure criterion based on the maximum radial in- terfacial stress and the ultimate radial interfacial strength, were in excellent agreement with experimental data This criterion was able to accurately account for the influence of both laminate configuration and constituent properties Predictions based on the bulk matrix tensile strength or on lamina stresses (computed from laminated plate theory) and strengths were in poor agreement with experimental data

A Unified Formulation of Micromechanics Models of Fiber-Reinforced Composites

Abstract: In a micromechanics constitutive model the overall instantaneous properties of fibrous composites are defined by relations between overall stress and strain averages Such averaging techniques are also known as ‘homogenization’ The models may account for fiber, matrix and fiber-matrix interface properties and their interactions (see [1–5]) Various micromechanics approaches are used to calculate overall stress and strain fields using different representative micro-geometries (ie unit cells); see, for example, the self-consistent method of Hill [1], the variational formulation of Hashin [2], the vanishing fiber diameter model of Dvorak and Bahei-El-Din [3], periodic rectangular array of Aboudi [4], and the periodic hexagonal array (PHA) model of Teply and Dvorak [5] Although various models use different representative geometries of the unit cell and different approximations of the displacements and/or stresses to obtain the overall properties, they all share certain common basis The present paper has the objectives of finding the common basis so that the models can be related to each other

Thermal stress analysis of a silicon carbide/aluminum composite

Abstract: Thermal deformations and stresses were studied in a silicon-carbide/aluminum filamentary composite at temperatures up to 370 C (700 F) Longitudinal and transverse thermal strains were measured with strain gages and a dilatometer An elastoplastic micromechanical analysis based on a one-dimensional rule-of-mixtures model and an axisymmetric two-material composite cylinder model was performed It was established that beyond a critical temperature thermal strains become nonlinear with decreasing longitudinal and increasing transverse thermal-expansion coefficients This behavior was attributed to the plastic stresses in the aluminum matrix above the critical temperature An elastoplastic analysis of both micromechanical models was performed to determine the stress distributions and thermal deformation in the fiber and matrix of the composite While only axial stresses can be determined by the rule-of-mixtures model, the complete triaxial state of stress is established by the composite cylinder model Theoretical predictions for the two thermal-expansion coefficients were in satisfactory agreement with experimental results

Compressive and Flexural Creep Behavior of Carbon Fiber/PEEK Composites

Abstract: The present study deals with the compressive and flexural creep properties of polyetheretherketone (PEEK), a high temperature semicrystalline thermoplastic. The compressive and flexural modes are important from a practical viewpoint, and yet rather limited viscoelastic data exist presently for testing in the two modes. The creep compli ance results of the unreinforced PEEK and the carbon fiber/PEEK composites are reported for temperatures ranging from 120°C to 160°C. Transverse compressive and cross-ply [±45°]s flexural compliances, the matrix dominated properties, displayed a significant viscoelastic behavior. The unidirectional 0° samples, on the other hand, displayed only a very limited time dependent response since the composite properties in the longitudinal direction are controlled by the almost elastic response of the fibers. The time-dependent experimental compliance values for the composites are compared to the results predicted from a micromechanics model and the classical lamination theory in c...

Microfracture in high temperature metal matrix laminates

Abstract: Computational simulation procedures are described to evaluate the composite microfracture behavior, establish the hierarchy/sequence of fracture modes, and the influence of compliant layers and partial debonding on composite properties and microfracture initiation. These procedures are based upon three-dimensional finite element analysis and composite micromechanics equations. Typical results for the effects of compliant layers and partial debonding, microfracture initiation, and propagation and the thermomechanical cyclic loading on a SiC/Ti15 composite system are presented and discussed. The results show that interfacial debonding follows fiber or matrix fracture, and the thermomechanical cyclic loading severely degrades the composite integrity.