Abstract
In this work, we consider the effect of modeling details on the potential initiation of failure within a laminated composite in the classical free edge problem. The work follows the demonstration by Pagano and Rybicki (1974) that the artificial singularities introduced by the effective modulus (EM) approach may lead to inconsistencies in the physical/mechanical behavior, such as failure, of the body. The present authors (1998) have recently revisited this issue by solving the same boundary value problem using modern finite element technology (ANSYS) in a micro mechanical model (MM) and have shown stresses that were in very good agreement with the earlier work. Unfortunately, the transverse stresses developed in the composite studied were very small, so that experimental confirmation based on failure initiation is not feasible. Therefore, we now consider a similar laminate under a transverse loading (loading normal to the fiber direction) to accentuate these stresses, as well as the fiber-matrix interfacial stresses.
The MM considered treats the generalized plane strain problem consisting of symmetrical rows of parallel silicon carbide fibers embedded in an epoxy matrix. Thus, a 2D boundary value problem is solved in the absence of stress singularities, although practical test specimens may encounter micromechanical singularities at the intersection of the fiber ends with the free edges. Remarkably, in this configuration, free edge effects are nearly negligible, at least at moderate values of the local fiber volume fraction. In addition to the fiber-matrix interfacial shear and radial tensile tractions, a tensile hoop stress acts in the matrix at the interfaces. Thus, fiber-matrix interfacial debonding and matrix cracking in response to the matrix principal stresses are the most probable modes of initial damage, depending on the strength / fracture properties of the constituents, including possible coatings or interphase regions.
In contrast, the EM solution predicts the presence of singularities in the stress field at the “interfaces” between the homogenized fiber row moduli and the “layers” of matrix material. Delamination initiating at the free edge is the predicted failure mode in this modeling. Under low magnification, the EM delamination and MM debonding may appear quite similar, although these failure mechanisms are completely different. It will be interesting to compare the potential consequences of the same stress component in the two problems by use of various failure theories, although no well established fracture mechanics technology is available to assess the effect of the non-square root singularity in the EM solution. It will also be interesting to compare the appearance of the expected failure modes in the two models. Finally, examination of the local disturbances in the strain field and an assessment of the capability to detect such features is important. In conducting such analyses, however, we must be aware of the fact that EM may represent nothing more than a gross approximation of the elasticity problem, which will be quite sensitive to the scale and arrangement of the microstructure. By coupling these considerations with detailed experiments expected to be presented in this conference, we can determine the need to explore more advanced theories of elasticity.
