Axisymmetric wrinkling of snug-fit lined pipe

An analytical bifurcation solution is presented for axisymmetric wrinkling on a lined pipe under axial compression without internal pressure. The internal liner consists of corrosion-resistant alloy (CRA), it is not metallurgically bonded to the carbon steel backing pipe, and it is assumed to be in a snug fit condition: i.e. there is no gap between the liner and the backing pipe, but also no prestress that would lead to a positive contact or gripping pressure between the liner and the backing. The backing is assumed to be much thicker than the liner, so that wrinkling-related deformations of the backing pipe can be neglected.The solution indicates that the incipient wrinkling strain for the snug-fit pipe without any imperfections is the same as the incipient wrinkling strain for a single pipe with (5/3) times the wall thickness of the liner, and the same midsurface diameter, as determined by the solution of Batterman (1965) for the case of small strains, or Peek (2000a) for the case of finite strains. For the case when the liner-pipe friction is included the factor (5/3) increases slightly.A positive contact pressure due to prestress or internal pressure raises the wrinkling strain, whereas imperfections (e.g. at seam or girth welds) reduces it. The snug-fit solution accounts for neither, but nevertheless provides a useful reference wrinkling strain, and can be used to validate numerical solutions, and it gives a bifurcation modeshape and wrinkle length that can be used in numerical models to investigate post-bifurcation behaviour.