On the detachment of step-tapered doublers: Part 1 - Foundations

One-dimensional edge debonding of layerwise step-tapered patches from both flat and cylindrical structures is examined. The problems are approach from a unified point of view, as propagating boundary problems in the calculus of variations, with the models for both flat and curved structures being formulated simultaneously. The effects of a contact zone adjacent to the bonded region are incorporated as is the phenomenon of edge-point contact. The formulation results in a selfconsistent representation of the various intact and debonded segments of the composite structure comprised of a multilayer patch and a base structure. It concurrently yields the conditions which establish the locations of the propagating boundary of the bonded (intact) region, and the propagating boundary of the contact zone. The former condition yields the selfconsistent and physically interpretable expressions for the corresponding energy release rates for debonding. The conditions governing edge-point contact are likewise established. Three types of loading conditions are considered : (i) in-plane/circumferential tension, (ii) three-point transverse loading, and (iii) applied transverse (internal ) pressure. It is shown analytically, within the context of the mathematical models employed for both flat and curved structures, that of the loading types considered the third admits a contact zone for certain common conditions of the supports. Results of numerical simulations, based on analytical solutions, pertaining to the test configurations of flat structures subjected to applied in-plane tension and three-point transverse loading are presented for various taper angles and compared.