Mechanical behavior of glass-filled epoxy resins: experiments, homogenization methods for syntactic foams, and applications

This thesis is mainly concerned with the investigation of the mechanical behavior of heterogeneous materials made up of glassy hollow spheres dispersed into an epoxy resin matrix.
This peculiar composite morphology characterizes the so-called syntactic foams, whose phases can in general be constituted by any homogeneous material which meets proper technological specifications. However, the use of both glassy fillers and epoxy binders is the most common because this choice allows one to both obtain good properties for the
final composite and best satisfy the technological requirements in the manufacturing stage.

The key goal of this research consists of providing analytical tools able to predict the mechanical behavior of such composites, which are being increasingly employed in the engineering practice, but still designed by means of rules of thumb. A micromechanical approach based on the homogenization theory has been followed, in order
to obtain constitutive laws based on both geometrical and mechanical data of the phases.

Since the homogenization approach requires the knowledge of the constitutive laws of all the phases, the mechanical behavior of epoxy resins, interesting engineering materials in themselves and apparently not much studied in their glassy state, has been investigated as well.

The research herein reported involves the following steps:
1) performing experimental tests on both epoxy resins and syntactic foams in order to both get an insight into their mechanical behaviors and make results available
to validate the analytical models;
2) the development of a linear elastic homogenization procedure able to accurately estimate the elastic moduli of syntactic foams for a wide range of constituent parameters;
3) the verification of the capability of such a homogenization method to design syntactic foams in the linear elastic range;
4) the development of a constitutive law for epoxy resins;
5) the micromechanical analysis of the syntactic foams behavior beyond the linear elastic range.

The first point is embodied in the first part of the thesis which also includes the description of the production modalities of both the epoxy resins and the syntactic foams tested for this research. Both the second and third points are treated in the
second part of this dissertation, concerned with the homogenization methods in the linear elastic range.
Finally, the third part of this thesis deals with the last two points and, in general, with the analysis of nonlinear and inelastic effects on the studied materials.

The linear elastic homogenization procedure has been developed to be suitable for syntactic foams (i) made up of isotropic phases, (ii) whose filler can be constituted by graded hollow spheres, possibly of different (isotropic) materials, and (iii) in which the imperfect vacuum manufacturing has left adventitious air bubbles entrapped in the matrix.

As an engineering application example, this model has been employed for the optimum elastic design of syntactic foamed sandwich panels used in the naval industry.

The constitutive law for epoxy resins has been developed in order to describe their behavior before the material strength is reached, which has been shown, through the experimental tests, to be mainly nonlinear viscoelastic. Such a constitutive model is needed to investigate the nonlinear and inelastic behavior of syntactic foams constituted by glassy fillers into epoxy matrixes, by means of a numerical homogenization based on Finite Element analyses.

The analytical homogenization of the syntactic foam behavior beyond the linear elastic range has been based on both the here developed linear elastic homogenization procedure and
a simplified constitutive law for epoxy resins. The nonlinea