A correlation between fluid-induced damage and anomalous fluid sorption in polymeric composites

Abstract

A mechanism is presented to explain the experimental observations that, under exposure to ambient fluid or humidity, desorption and resorption behaviors of polymeric composite samples do not replicate the initial absorption process. It is shown that the above disparities can be attributed to damage, in the form of distributed fiber/matrix interfacial microcracks, which is caused by residual hygrothermal and mechanically induced stresses. Such damage occurs in the interior of composite samples during the early stages of initial fluid absorption, and subsequently in regions adjacent to exterior boundaries during the early stages of desorption. The extents of the foregoing damage regions can be assessed by stress analysis. A certain portion of the fluid remains entrapped within the damaged regions, or attached by adsorption to the faces of the microcracks, which act like capillary channels. Analytical diffusion models, which account in part for the presence of the abovementioned damage and based upon equivalent diffusivity and capillary action, respectively, are presented and shown to yield results that exhibit all the experimentally recorded characteristics.

Introduction

The process of fluid sorption in polymeric composites is usually monitored by weight-gain data. Since these data, which record the integrated amount of fluid concentration c(x,t) over the entire material volume, do not suffice to determine the spatial and temporal variation of c(x,t), it was necessary to recover the latter quantity with the aid of theoretical models. In as much as the classical Fickian diffusion model is inadequate in predicting weight gain data in many circumstances [1], [2], several additional models were proposed. Among these is the “two-phase diffusion” model [3], [4], [5] which assumes that while overall diffusion follows Fick's law, a certain portion of the diffusing matter becomes permanently entrapped within the composite. Another model [6], [7] attempts to account for the time dependent response of the composite material by incorporating the coupling between the viscoelastic behavior of the polymeric resin and the temporal aspect of the diffusion process, both of which occur on similar time-scales [7].¹ The above models can explain deviations between recorded weight-gain data during first exposure to ambient fluid and predictions based upon Fick's law [4, Section 14.4, [5], [9]. A variety of other causes for departures from Fickian diffusions can be found in the extensive literature on the subject, some of which are listed in references [1] and [2].²

It is worth noting that while some of the above models can explain various features of weight-gain sorption data, they fail, with few exceptions, to account for rather consistently recorded characteristics noted in desorption data of fully saturated samples and none seems capable of explaining the distinctive behavior of resorption data of re-dried samples, as shown in Fig. 1, Fig. 2, and reported elsewhere [2], [10].

In addition to the aforementioned weight-gain data, it was also reported in the literature (e.g. [1], [2] and references listed therein) that fluids may cause damage within polymeric composites, mainly in the form of interfacial fiber/matrix micro-cracks as shown in Fig. 3. During the absorption stage, such damage was observed to occur mostly in the interior of the composite, while more intense microcracking was observed near the outer boundaries during desorption. Increasing amounts of damage were observed under cyclic wet/dry exposures [11]. While the above observations are qualitatively consistent, the microcracking phenomenon is highly random and difficult to quantify. Typically, the microcracks are dispersed non-uniformly within the composite and meander along tortuous paths. Overall, these paths tend to incline perpendicularly to the outer boundaries in interior regions and parallel to the above boundaries in outer regions of the composite. Consequently, the analysis presented in the sequel employs several simplifying assumptions regarding aspects of diffusion and damage, while striving to provide a rational account for observed behavior.

This work models a diffusion process that accounts for the sequential presence of interior, followed by exterior (i.e. in the vicinities of the outer boundary), micro-cracks within a polymeric composite, as they occur during the absorption and desorption stages, respectively. Both sets of cracks are considered to exist during the re-sorption process with interior and exterior damaged regions being, in general, disjoint.

The modeling employs two distinct approaches. The first approach is based on the concept of equivalent diffusivity. It was assumed that sorption within the damaged regions proceeds by diffusion only, but with enhanced diffusivity coefficients D₁ and D₃, and equilibrium saturation levels α₁c_∞ and α₃c_∞, for the interior and exterior damaged regions, respectively.

The second approach is based on the concept of capillary action where diffusion is assumed to proceed throughout the composite with a common diffusion coefficient D and capillary motion is considered to arise within the fiber/matrix interfacial micro-cracks that occur in the damaged regions. Note that the observed width of these micro-cracks is approximately 1 μm, which is three to four orders of magnitude larger than the dimension of water molecules. Since capillary motion was noted to proceed at an exceedingly faster rate (7 mm/min) than diffusion [12], fluid motion by capillary action was taken to occur instantaneously. Though the diffusion process with damage is in fact three-dimensional due to the varied orientations of the micro-cracks, the model employs a one-dimensional approximation. This simplification, which assumes that all capillary motion within the damaged zones proceeds in a direction normal to the boundaries, is necessitated by the highly irregular shape and distribution of the internal micro-cracks which renders a three-dimensional approach intractable. Thereby, while the interior micro-cracks are considered to draw a portion of the diffusing fluid into the capillary channels, the exterior ones have the additional effect of desorbing a portion of the fluid into capillary channels that connect to the exterior boundaries.

It was shown that both approaches can lead to very similar results.

It is worth noting that an alternate model for the coupling between damage and diffusion was proposed recently [13]. In that approach the effect of damage was incorporated within a “reduced time” factor. Although such an interpretation is seemingly equivalent to a corresponding enhancement of the diffusion coefficient D (in view of the fact that the diffusion process depends on the non-dimensional time $\text{t}{}^{\mathrm{\ast }}\text{=}\text{Dt}\text{l}{}^2$), it nevertheless does not lend itself to a methodical approach to diffusion in the presence of non-uniformly distributed damage, as observed experimentally.