Recovery of microfields in fiber-reinforced composite materials: Principles and limitations

Andrew J Ritchey, Purdue University

Abstract

A detailed investigation of the limitations and errors induced by modeling a composite layer composed of straight carbon fibers embedded in an epoxy matrix as an homogenous layer with Cauchy effective moduli is performed. Specifically, the material system studied has IM7 carbon fibers arranged in a square array and bonded together with 8552 epoxy resin (IM7/8552). The finite element method is used to study the effect of free surfaces on the local elastic fields in 0°, 45° and 90° laminae, in which as many as 256 individual fibers are modeled. Through these analyses, it is shown that a micro-boundary layer, analogous to the macro-boundary layer observed in composite laminates, is developed at the microlevel. Additionally, [0/90]s and [90/0]s laminates are studied to investigate the joint action of the macro- and micro-boundary layers. Unless otherwise noted, fiber volume fractions of Vƒ=0.20 and Vƒ=0.65 are selected and the domains are subjected to uniform axial extension. Although this study is done for a highly idealized geometry (i.e. with a single material system and under a simple loading condition) the principles of periodicity, symmetry and antisymmetry used to efficiently perform a direct numerical simulation with a large number of fiber inclusions is general, and can be applied to more complicated geometries and boundary conditions. The purpose of the current work is to be the first step in a building block approach to understanding the interaction of multiple scales in fiber-reinforced composites through direct numerical simulations. The main part of the current manuscript focuses on the characterization of a micro-boundary layer that develops in fiber reinforced composite layers. This phenomena results from the changing constraints on the constituent phases as a result of discontinuities, such as free surfaces or ply interfaces. The effect is most pronounced in laminae that have a fiber termination intersecting a free surface, and appears to be maximized in a 90° lamina. In an individual lamina, under uniform extension, the micro-boundary layer emanating from a free surface intersected by a fiber termination is analogous to the macro-boundary layer described by Pipes and Pagano. One consequence of the micro-boundary layer is a variation of apparent moduli in this region. The use of homogeneous effective moduli, whether they are based on Cauchy elasticity, micropolar elasticity, or some other higher order theory, cannot capture the effect in composite laminae. Methods based on the use of modified effective modulus theory (e.g. GOALS or Voroni cell finite elements) are capable of capturing this effect. This is because these types of methods place a realistic representation of the microstructure in critical locations. Accuracy results when correct microstructure overlaps correct boundary conditions. The methods used to perform direct numerical simulations on individual laminae are extended to cross-ply laminates (i.e. [0/90]s and [90/0]s). In this final study of the current manuscript, many interesting results are observed because of the joint action of the micro- and macro-boundary layers. First, more error is observed in the 0° plies than in the individual 0° laminae under uniform extension. This result is expected because of the differences in loading applied to the layers in the different configurations. In agreement with other studies, the largest amount of error in a 0° ply is observed at the free-surface ply interface with a 90° ply. In addition, a stacking sequence effect is observed in the 0° plies. Compared to the individual laminae results, there is an increased error in the effective modulus stiffness observed in the interior of the individual plies of the cross-ply laminates. However, the largest errors in the entire laminate are observed at the free surface intersected by fiber terminations in the 90° plies. Rather unexpectedly, the overall maximum error in the 90° plies is removed from the interface with the 0° plies for both stacking sequences. For the current laminate and loading configuration, the errors in the 90° plies are bounded by the errors observed in the individual 90° laminae under uniform extension. This result indicates that for fiber-reinforced polymer-matrix composites, it might be possible to estimate the overall maximum error in a multiscale analysis from a relatively simple direct numerical simulation of a 90° layer. (Abstract shortened by UMI.)

Degree

Ph.D.

Advisors

Pipes, Purdue University.

Subject Area

Aerospace engineering|Materials science

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