A previously developed linear elastic crack-tip element analysis is reviewed briefly, and then extended and refined for practical applications. The element provides analytical expressions for total energy release rate and mode mix in terms of plate theory force and moment resultants near the crack tip. The element may be used for cracks within or between homogeneous isotropic or orthotropic layers, as well as for delamination of laminated composites. Classical plate theory is used to derive the equations for total energy release rate and mode mix; a “mode mix parameter,” Ω, as obtained from a separate continuum analysis is necessary to complete the mode mix decomposition. This parameter depends upon the elastic and geometrical properties of the materials above and below the crack plane, but not on the loading. A relatively simple finite element technique for determining the mode-mix parameter is presented and convergence in terms of mesh refinement is studied. Specific values of Ω are also presented for a large number of cases. For those interfaces where a linear elastic solution predicts an oscillatory singularity, an approach is described which allows a unique, physically meaningful value of fracture mode ratio to be defined. This approach is shown to provide predictions of crack growth between dissimilar homogeneous materials that are equivalent to those obtained from the oscillatory field solution. Application of the approach to delamination in fiber-reinforced laminated composites is also discussed.
This paper discusses the analytical and numerical results for the impact responses of two types of plates with equal areal weights: hybrid laminated composite plates and homogeneous metallic plates. The loadings and the boundary conditions for the two types of plates are the same, and an impact load was applied at the center of each plate. An analytical solution based on Fourier expansion was developed to obtain the impact responses of the plates. The finite element method (FEM) was used to perform numerical analyses to verify the analytical solutions. The response patterns from the results were compared and a preliminary conclusion made on the impact resistance ratio between the hybrid laminates with proper interfacial bonding and that of equivalent homogeneous metallic plates. The effect of different shapes of pulse on the laminated composites was also examined. Three loading cases were considered, each being a function of time. The effect of different pulse shapes on the impact response was evaluated. Finally, a solution based on shear deformation theory was developed, and the comparison between classical plate theory results and shear deformation theory results indicates that for the problem examined classical plate theory predicts relatively accurate results.
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