Propagation of delamination in layered anisotropic cylinders
The propagation of delamination in a layered anisotropic cylinder is studied under different loading conditions. Initially, a closed-form solution is obtained for an infinitely long cylinder by treating it as a thin shell, with an axisymmetric crack in the adhesive layer between two laminae, and an axisymmetric loading acting as the driving force. The axial and shear strains of the reference plane are considered negligible compared to its circumferential strain. The cylinder, after delamination, is modelled as three shell elements joined at the crack tip. A sharp, flat crack tip is assumed, and the slopes of the three shell elements at the crack tip are set to zero. The radial displacements of the three regions, obtained through the imposition of the proper boundary and matching conditions, are substituted into Clapeyron's theorem to obtain the total strain energy in the cylinder. The change in this strain energy for a unit change in the crack length is used in the Griffith energy balance criterion to evaluate the critical loading at which the delamination propagates. The critical loading is studied as a function of the half crack length. Due to the assumption of a flat crack tip, only the moment continuity across the crack tip is imposed. Normal shear continuity is not enforced and this leads to interesting results in a few cylinders. "Crack arrest" regions, or ranges of crack length within which no real value of the loading could make the delamination propagate, are observed in some cases. Two different loading conditions are treated: one with a pressure acting on the crack surface, and the other with a loading on the inner cylindrical surface. "Crack arrest" phenomenon occurs in the latter problem for certain layer thickness ratios.
As the next step, a more general crack tip geometry is assumed and shear force continuity across the crack tip is enforced. This model establishes the fact that the abnormal delamination behaviour in the previous model, like the "crack arrest", is due to the absence of normal shear continuity across the crack tip. It also shows that the crack tip assumption made in the previous formulation - a flat, sharp crack - is valid. When the crack tip geometry is generalized the radial displacements in the cylinder are obtained numerically. Four different crack tip geometries are assumed.
The axial and shear strains in the reference plane are included in a subsequent model to determine their effect on the delamination behaviour. A general observation is that the critical value of the loading is lowered for any initial crack length. The magnitude of the drop depends on the geometric and material properties of the plies that constitute the layered cylinder. When the loading is applied on the inner cylindrical surface, the effect is predominant for very small crack lengths. On the contrary, the decrease in the critical value of the pressure acting on the crack surface is considerable for large crack lengths.