Effect of the interphase on the thermo-mechanical response of unidirectional fiber-reinforced epoxies: modeling, analyses and experiments
The complexity of the fiber-matrix interphase in a composite is largely due to the myriad of variables (material, processing, and design) that affect its formation. The interphase, thus formed, has to be characterized at several levels (micro-structural, chemical, and mechanical) in order for one to fully understand the nature of the bond between the fiber and matrix and in order to perform a stress analysis of the fiber-interphase-matrix assemblage.
A thorough thermo-mechanical characterization of the interphase is difficult, at present, due to the necessity of studying the interphase in situ, its small dimension (usually on the order of a micrometer), and its general complexity. However, a cursory glance at the literature shows that great progress has been made in all of the three levels of characterization mentioned above for various composite systems. Several recent attempts have focused on the physical characterization (evaluation of volume fraction, thickness, Young's modulus, shear modulus and coefficient of thermal expansion) of the interphase.
Models of physical properties (thickness, Young's modulus, Poisson's ratio and coefficient of thermal expansion) of the interphase have been considered by several researchers in an effort to study the influence of the interphase on overall composite properties and behavior. Hypotheses on interphase formation and properties have been proposed and tested by some researchers. Both experimental characterization as well as modeling studies are necessary to achieve a more profound understanding of the interphase and its behavior.
The interphase, in a composite, is usually modeled as a homogeneous region, despite the fact that it may have spatial property variations.However, it is important to the understanding of composite behavior to incorporate a realistic interphasial region into the analysis and testing of composite material systems. A new thermo-elastic model for the interphase properties in fiber-reinforced thermosets is proposed. The Young’s modulus and coefficient of thermal expansion of the interphase are assumed to be functions of distance from the fiber in this model. The Poisson’s ratio of the interphase is assumed to be the same as that of the matrix.
The new model is used in a concentric cylinder assemblage analysis for the determination of the residual thermal stresses in unidirectional fiber-reinforced epoxies. The governing field equations in terms of displacements are solved in “closed form”. It is found that, although the solution is dilute, the property variations in the interphase have a distinct effect on the residual thermal stresses. This is significant, considering the fact that residual thermal stresses play an important role in controlling the structural performance of a composite.
The new model is used in Mori-Tanaka analyses for the determination of non-dilute local stress fields in unidirectional fiber-reinforced epoxies under thermo-mechanical loading situations. The governing field equations in terms of displacements are solved in “closed form”. It is found that property variations in the interphase have a distinct effect on the local stresses. This is also significant, considering the fact that local stresses play an important role in controlling the structural performance of a composite.
A model composite system consisting of a coated glass rod embedded in Epon 828 is considered; coatings are applied to the glass rod in succession to simulate two different interphase types. The model composite specimens are loaded in transverse compression and transverse shear, and the resulting in-plane displacements are measured by the use of the Moire interferometry technique. Differences in displacement fields between the various specimens, due to the presence of interphasial regions, are found to be minimal. More sensitive measurements are needed to measure pointwise displacements in the interphasial (coatings) region.