Constitutive modeling of woven-fabric composites for concurrent design.

摘要

In this study, new analytical models are developed to predict effective constitutive properties of woven-fabric composite laminates as functions of the properties of the constituent materials, the micro-architecture of the reinforcement and fiber volume fraction. Numerical simulations of the developed microscale boundary value problems are conducted for mechanistic understanding of three-dimensional interactions and for validity checks of the analytical models. Experiments are conducted for validation of the results obtained. The effective orthotropic properties investigated are thermal conductivity, dielectric constant, dielectric loss tangent and coefficient of thermal expansion.;Effective properties are defined analogous to the microscale properties in terms of state variables such as temperature, electric potential stress and strain. Relations among the macroscale and microscale properties are obtained by a new application of a two-scale asymptotic homogenization technique. Steady state thermal, electrostatic and static thermo-mechanical boundary value problems (BVPs) are formulated at the microscale of woven-fabric reinforced composite laminates for their effective orthotropic thermal conductivity, dielectric permittivity and coefficient of thermal expansion, respectively. A representative microscale domain called the unit-cell, enclosing the characteristic periodic repeat pattern in the fabric weave, is isolated and modeled.;The steady state thermal and electrostatic BVPs are solved analytically using the series-parallel network models for thermal conductivity and dielectric constant. Coefficients of thermal expansion (CTEs) of woven-fabric reinforced laminates are derived based on Rayleigh-Ritz energy principles. The dielectric constant is determined analogous to thermal conductivity, by neglecting the contribution from the constituent materials' loss tangents which are order(s) of magnitude lower than the respective dielectric constants. The effective loss tangent is obtained analogous to mechanical viscoelastic problems as a weighted linear combination of the constituent loss tangents. Laminate effective orthotropic thermal conductivity, dielectric constant and CTEs are also obtained numerically using finite element simulations. The analytically predicted values of effective properties are compared with numerical finite element predictions, with existing models in the literature and with experimentally obtained values.;Parametric studies are conducted to quantify the effect of fiber and resin properties and fiber volume fraction on the effective thermal conductivity, dielectric permittivity and CTE of the laminate. Influence of the orthotropic thermal conductivity and dielectric permittivity on effective thermal conductivity and dielectric permittivity of the laminate is also investigated. Effect of fiber stiffness, CTE, Poisson's ratio and orthotropy of the fiber on the effective CTE of the laminate is also quantified. Relationships among the components of effective orthotropic properties is obtained for various laminate material systems.;A method for utilizing the prediction models in a design environment is suggested and its use is demonstrated with an example problem.