Resumen de Study of the unfolding failure of curved composite laminates
The use of composite materials in structural applications has been considerably increased in the last years. This increment has introduced the use of composite laminates in complex components including highly curved zones. Highly curved laminates are prone to unfolding failure, a delamination caused by a bending moment which tries to atten the curvature.
Unfolding failure is classically associated to the Interlaminar Normal Stress (INS), which is characterized by the InterLaminar Tensile Strength (ILTS). The ILTS is typically obtained by a four-point bending test applied to an L-shaped specimen with all the plies oriented at 0o. If this test procedure is applied to composite laminates with di erently oriented plies an apparent ILTS is obtained. The apparent ILTS exhibits a thicknessdependence which has not been physically explained yet.
INS may be obtained by using FEM. Notwithstanding, analytical models are desirable for obtaining lower modelling and calculation times. Nowadays, analytical models have shown high errors in the calculation of the INS for some kinds of geometries and loading states. These errors are due to a free-edge e ect associated with the curvature changes, e.g., in the joint of a curved part with a straight arm. Di erences in INS values due to a change of curvature may be even of a 100% with respect to the actual value.
The PhD project has studied, in a rst stage, the four-point bending test, which is the one typically employed for ILTS determination, obtaining a non-linear model for the calculation of the load-displacement and loadbending moment distributions. The model has been successfully correlated with experimental results.
The second stage of the PhD has been focused to the INS calculation, developing two di erent bi-dimensional models based on a series expansion of the displacement and a higher-order moments de nition in the stresses.
The rst model is based in monomials, with very low computational times and a good accuracy, and the second model is based in Legendre polynomials, with still low computational times and a very high accuracy. Both models have allowed the change-of-curvature problem to be solved and to analyse in detail the di erent parameters involving the stresses distribution near to free-edges.
The third stage of the PhD has been focused on the expansion of the bidimensional models to obtain a three-dimensional model in order to consider also the e ect of the torsion and the anticlastic e ect combined with the curvature, as well as the e ect of the nite width of the specimens. This model let us also to calculate accurately the out-of-plane stress state.
Finally, in the fourth stage of the PhD, the stress calculation methodologies developed have been used for the data reduction of an existing test campaign. Results suggest that in laminates with a low apparent ILTS, intralaminar failures in the matrix direction may have taken place before delamination. Comparing the load causing the failure with the predictions made for the rst intralaminar/interlaminar failure, and observing the crack locations in tested coupons, a feasible explanation for the thickness dependence has been found. This explanation consists in distinguishing two kinds of unfolding failures: rst, the traditional unfolding initiated by the INS and, second, the newly de ned induced unfolding, which is initiated by a failure associated to intralaminar stresses that propagates as a delamination due to the presence of the high INS.
Based in the previous results, some optimization guidelines have been de ned for the design and sizing of curved composite laminates based in the unfolding failure.
