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STRESS FIELDS NEAR HOLES OR CUT-OUTS IN A UNIDIRECTIONAL FIBER REINFORCED COMPOSITE LAMINA
Using shear-lag theory we analyze fiber tensile and matrix shear stresses near elliptical holes and diamond shaped cut-outs in a unidirectional composite lamina under a remote tensile stress applied in the fiber direction. Such holes and cut-outs are traditionally treated by modeling the material as a homogeneous orthotropic continuum, where the details of the fiber and matrix length-scale are lost. In this thesis, we extend the shear-lag framework (Hedgepeth, 1961) to build a computational model that can treat not only the removed material, viewed as a group of removed fiber segments, but also groups of fiber breaks adjacent to the hole as would occur as the remote load is increased. In the shear-lag setting, the response to the hole ideally can be viewed as equivalent in effect to the superposition of the stress field responses of a sufficiently large number of isolated fiber breaks, which have a distribution of weights chosen to satisfy the stress free boundary condition around the hole. By appropriate modeling of the weight distribution of the isolated fiber break solutions, we apply the break influence superposition technique (BIS), developed in the context of the shear-lag model by Sastry, Beyerlein and Phoenix (1996), to calculate the stress field in the composite. Stress fields for three different hole shapes have been studied and compared to elastic continuum-based solutions. This technique is more efficient than other numerical techniques as the computation time is tied only to the damaged area and the weight distributions can be approximated well using linear, and occasionally quadratic, polynomial functions. Once all the influence functions are computed, a priori, and stored as reusable quantities, subsequent simulations take only a few minutes. The biggest advantage of this technique is that we can let the holes propagate in any fashion and calculate the stress field in a few minutes simply by adding the influence functions from the new fiber break to the initial ones and re-computing the weights. The same task would take a much longer time for finite element or finite difference methods since every single change demands a new mesh and remodeling the whole lamina.
Fiber; Shear-lag Theory; Composite; Fracture
dissertation or thesis