Prediction Of Elastic Modulus Research Articles

Prediction of elastic moduli via crack density in pressurized and thermally stressed rock

The elastic moduli of crystalline rocks show marked reductions when heated to high temperatures (T), even when subjected to confining pressure (P). This degradation of moduli has been attributed to the creation of new microcracks or opening of preexisting microcracks from thermal stresses due to differential thermal expansion between mineral grains. A similar lowering of moduli is observed on depressurization of crystalline rock and is also thought to be due to microcrack opening. A spherical inclusion model has been used to predict whether a given change in T or P will introduce a tensile crack between a mineral constituent and the rock matrix. By using the principal thermal expansions and compressibilities of individual minerals, and simplifying assumptions, we are able to predict crack densities as a model rock is subjected to changes of P and T. Experimental crack densities for three granitic rocks, a gabbro, and two basalts are calculated from high temperature, high pressure Young's modulus data. The predicted and inferred crack densities are then compared for these six rocks. The results are dependent upon the P,T path to which the rock is subjected, and comparisons are for the case in which the rocks are heated only at maximum P, and then decompressed isothermally. Considering the simplicity of the model, we believe the comparisons are quite close for the three granitic rocks. The model underestimates the crack densities of the quartz‐free gabbro and basalts.

Prediction of elastic moduli of solids with oriented porosity

There have been no simple equations available to predict the effects of arbitrarily shaped voids over the entire range of porosity encountered in real materials. Empirical expressions have been proposed, but they agree neither with appropriate theoretical analyses nor with extensive experimental data. Theoretical predictions have been linear in porosity and thus predict an insufficient reduction. Only a few analyses account for void shapes other than spherical. The present work represents a semi-empirical approach to fill these information deficiences.

Theoretical predictions of the elastic moduli of polymer‐impregnated hardened cement paste and mortars

AbstractHardened coment pastes with water‐to‐cement (w/c) ratios of 0.4 and 0.6 and hydration times of one, three, seven, and 28 days were oven dried and subsequently impregnated with an epoxy resin formulation which was then polymerized in situ at 75°C. Portland cement mortars containing Ottawa sand and asbestos fibers as filler were also subjected to this impregnation process. Dynamic elastic moduli (E′) were measured at audio frequencies over a range of temperatures (100–400°K). Experimental values were compared with moduli calculated using various theoretical approaches based on two‐phase composite materials theory. Best agreement between experimental and calculated results occurs when Wu's theory for spherical polymer inclusions was applied to a cement‐based matrix. In the case of polymer‐impregnated mortars, experimental and theoretical results are in closest agreement at low temperatures and at low volume fraction of filler.

Stresses and displacements in lamellar composites. II

For pt.I see ibid., vol.8, p.34 (1975). The two-dimensional problem in infinitesimal elasticity of a series of rectangular blocks of two different materials interleaved in a stack of infinite extent, loaded along its axis is solved by two complementary techniques. These are (i) a Fourier series solution of the Airy stress function and (ii) a finite element calculation. Tables and graphs of representative calculations are given. The shape of the distorted layers is of barrel and pincushion type and the positions of the maximum stresses differ from the predictions of more elementary calculations. The analysis is applied to the prediction of elastic moduli and failure mechanisms in real lamellar polymers modelled by long strips, such as oriented linear polyethylene, oriented polychloroprene, and cis-polyisoprene and 'elastic-hard' fibres.

Relationship between single-crystal and polycrystal elastic constants

A new method is given for computing effective polycrystalline elastic constants from single-crystal elastic coefficients. Agreement with observation is good. The method is based on the assumed equivalence of the lattice-vibrational properties of single crystals and polycrystals of the same material; single-crystal and polycrystal Debye temperatures are equated. Present predictions of polycrystal elastic moduli differ significantly from those of most other averaging methods by being lower than the familiar Voigt-Reuss-Hill results.

Elastoplastic Transverse Properties of a Unidirectional Fibre Reinforced Composite

An approximate theoretical study is made to predict the overall trans verse elastoplastic properties of a unidirectional fibre reinforced composite. Based on the simplest deformation theory of plasticity, the overall trans verse polyaxial elastoplastic constitutive equations for an incompressible composite are obtained. A simple formula is suggested to evaluate the average stress in the fibres. Furthermore, with the prediction of the overall transverse elastic moduli of a compressible composite, the overall trans verse uniaxial stress-strain curve for a compressible composite in the entire elastic-plastic range is obtained. A detailed example is given for a Boron- Aluminum composite. Comparison is made with the experimental and theoretical work done by General Dynamics and Adams respectively.

Influence of the Shape of Dispersed Particles on the Elastic Behavior of Composite Materials

Young's modulus was measured on a series of composites of magnesium oxide which contained low concentrations of graphite as flakes, fibers, and nearly spherical particles. The measured modulus was in excellent agreement with predictions of elastic behavior based on particle shape. Not only do the results indicate that accurate predictions of elastic moduli are possible, but also that the shape of dispersed particles has a dominating influence on the elastic properties of composite materials at low concentrations of an included phase.