Residual strength analysis of structures in aluminium alloy and fibre metal laminates

In aircraft structures made of Fiber-Metal Laminates (FML), sufficient residual strength is required when the structure is damaged by fatigue or by impact damage. For FML fuselages, large impact damage from engine disintegration seems to be the most likely cause of large through cracks. Fatigue cracks, either starting from rivet holes, small impact damage or other stress concentrations, are only part-through cracks because the fibres remain intact across the crack in the aluminium layers. These intact fibres can increase the residual strength in case of fatigue damage, compared to that of a structure with through cracks from impact damage. The present study addresses the residual strength analysis of FML fuselages with through cracks, such as caused by large impact damage from uncontained engine disintegration. The study focuses on the crown of a wide-body fuselage with a circumferential crack. A finite element method is presented for predicting the residual strength of FML and aluminium alloy structures. The validity of the method is demonstrated in a comparison with experimental work performed stiffened panels. These panels were on 800 mm wide and were equipped with five stringers. To model a crack from an accidental damage, a two-bay saw-cut was used. Also the central stringer in each panel was cut. Both a FML design and a conventional design in monolithic aluminium alloy were tested. In the analysis method, both the failure of the skin and the stringer are modelled. The failure of the skin is predicted by computing the energy release rate and comparing this to the crack growth resistance expressed in an effective R-curve. The effective R-curve is derived with a modified version of Irwin's model of the plastic zone at the crack tip. The modification compensates for the interaction of the plastic zone and the edge of the skin sheet. The energy release rate is computed with a finite element version of the crack closure method. A refinement of the mesh around the crack tip in the finite element mesh is shown to be unnecessary. The failure of the stringers is predicted by computing the plastic deformations in the stringer flanges. In the experiments, the stringers failed in the net-section beside the first rivet hole near the crack. This failure mode is modelled by attributing effective material properties to the riveted flange of the stringers. The effective properties link the average stress in the undisturbed part of the flange to the average strain over one rivet pitch, without modelling the actual deformations. Only uniaxial deformations are modelled and in the finite element model the stringer can be represented with beam elements. From the comparison of the analysis and the experiments, the proposed analysis method is shown to provide accurate predictions of the residual strength of the structure and of the deformations in the various parts. Modelling of the geometrical non-linear bending in the stringer is shown to be essential. The large size of the plastic zone around crack tips in damage tolerant aircraft materials is expected to be an important source of errors in the predictions. Besides the finite element analysis, also a computer code based on the displacement compatibility method is presented. This code also employs the effective properties for the riveted flange of the stringers. The energy release rate in the skin is derived from closed-form solutions. The reduction in computation time that is obtained by using the closed-form solutions instead of a flnite element mesh, can be an advantage in parametric studies. In order to be able to include the plasticity effects and the geometrical non-linear deformations in the stringer, the governing equations of the displacement compatibility method are modifled. The deformations of the stiffening elements are described with a finite element representation, instead of with a flexibility matrix as in the original version. The validity of the computer code is limited to cases where buckling of cracks and bending of broken stringers do not have a decisive influence on the residual strength of the structure. The buckling of cracks cannot be taken into account because the method uses superposition of various solutions to describe the skin deformations. The bending of a broken stringer cannot be represented accurately when this bending is not limited to a neighbourhood around the crack. When these effects have a decisive influence on the residual strength, the errors in the predictions obtained from the displacement compatibility method are larger than the errors observed in the flnite element analysis.