Showing papers on "Representative elementary volume published in 1990"

Conservation of mass and momentum for the flow of interdendritic liquid during solidification

Abstract: In this paper, mass and momentum conservation equations are derived for the flow of interdendritic liquid during solidification using the volume-averaging approach. In this approach, the mushy zone is conceived to be two interpenetrating phases; each phase is described with the usual field quantities, which are continuous in that phase but discontinuous over the entire space. On the microscopic scale, the usual conservation equations along with the appropriate interfacial boundary conditions describe the state of the system. However, the solution to these equations in the microscopic scale is not practical because of the complex interfacial geometry in the mushy zone. Instead, the scale at which the system is described is altered by averaging the microscopic equations over some representative elementary volume within the mushy zone, resulting in macroscopic equations that can be used to solve practical problems. For a fraction of liquid equal to unity, the equations reduce to the usual conservation equations for a single-phase liquid. It is also found that the resistance offered by the solid to the flow of interdendritic liquid in the mushy zone is best described by two coefficients, namely, the inverse of permeability and a second-order resistance coefficient. For the flow in columnar dendritic structures, the second-order coefficient along with the permeability should be evaluated experimentally. For the flow in equiaxial dendritic structures(i.e., isotropic media), the inverse of permeability alone is sufficient to quantify the resistance offered by the solid.

Micro-mechanics of crack initiation

Abstract: Prior to the crack initiation, damage is most often localized at a scale below the size of the classical representative volume element of the continuum mechanics. This allows the stress and strain analyses in a component to neglect the strain-damage coupling at macro-scale. At the micro-scale, this coupling plays a very important role which can be emphasized by a two scale element of an elastoplastic damaged micro-element embedded in an elastic or elastoplastic macro-element. The Lin-Taylor hypothesis of strain compatibility allows the determination of the damage at micro-scale by solving the coupled constitutive equations for a given macro-strain history. It is shown how this model may be cast in the form of a post-processor of a finite element code and how a simple damage law coupled with strain constitutive equations replicates the main features of ductile or creep crack initiation, low cycle and high cycle fatigue for the case of a three-dimensional state of stress.

Elastic Solids with Microdefects

Abstract: For a “representative volume element” (RVE) consisting of an elastic (linear or nonlinear) matrix and microdefects, relations between the overall stress and strain potentials and the corresponding local quantities are developed and discussed. Results are specialized to RVE’s with a linearly elastic matrix. Illustrations are given for micro-defects consisting of cavities, cracks, and elastic inclusions, using three averaging schemes: a scheme based on noninteracting dilute distribution of defects, the self-consistent method, and the differential scheme.

An Interlayer Model to Describe the Physical Properties of Particulate Composites

Abstract: A unified approach is presented to describe the shear modulus, bulk modulus, thermal expansivity and the dielectric constant of composites with interfacial layers. The physical properties are expressed as functions of the filler, matrix and layer properties and their respective volume fractions. The solutions for the static shear modulus and the dielectric constant are converted into dynamic solutions. The expressions for the dielectric constant and loss factor are extended by incorporating the conductivity of the constituents.

Simulating crack growth and failure in a composite: A vector model for a layered composite material

Abstract: A model has been proposed for a layered composite having an inhomogeneous microstructure. It is represented as the union of vector spaces for the mechanical characteristics of the material and the volume contents of the layers. The elastic parameters for each layer are considered as random functions of an arbitrarily defined volume. For a microscopically inhomogeneous material, one can consider a base volume such that the elastic properties of the material are retained and for which one can apply effective elastic moduli. The state of stress and strain in such a material is described by the components of the macrostress and macrostrain tensors with respect to a certain (structural) volume, which exceeds the base volume. The justification for that approach is demonstrated for a microscopically inhomogeneous orthotropic composite.

A Micromechanical Prediction of Mechanical and Thermal Properties of FRP with Interfacial Imperfections

Abstract: A theoretical model approach for the prediction of the longitudinal elastic modulus, Poisson’s Ratio and the thermal expansion coefficient in unidirectional fibre-reinforced composites was developed. The model takes into account the existence of the interphase which represents the third phase developed between the constituet phases of the composite. It was assumed that both fibre and matrix have well-defined mechanical properties while the interphase properties are varied following an exponential law of variation. Also the effect of the discontinuity of the properties at the fibre-matrix interface was investigated and interesting results have been found.

The effect of weak interface on transverse properties of a ceramic matrix composite

Abstract: Experimental studies conducted at NASA Lewis on SiC reaction-bonded Si3N4 composite system showed that transverse stiffness and strength were much lower than those predicted from existing analytical models based on good interfacial bonding. It was believed that weakened interfaces were responsible for the decrease in tranverse properties. To support this claim, a two-dimensional FEM analysis was performed for a transverse representative volume element. Specifically, the effect of fiber/matrix displacement compatibility at the interface was studied under both tensile and compressive transverse loadings. Interface debonding was represented using active gap elements connecting the fiber and matrix. The analyses show that the transverse tensile strength and stiffness are best predicted when a debonded interface is assumed for the composite. In fact, the measured properties can be predicted by simply replacing the fibers by voids. Thus, it is found that little or no interfacial bonding exists in the composite, and that an elastic analysis can predict the transverse stiffness and strength.