A method for bonding a composite multi-layer shell having complex curvature by the delta-alpha high temperature bonding process uses a novel tool. The tool includes a plurality of segments that combine to form a mandrel assembly having a substantially continuous outer surface. The outer surface has a substantially axisymmetric shape including a complex curvature. When the segments are combined to form the mandrel assembly, at least one of the segments is configured to be movable in a substantially inward direction without substantial obstruction by any other segment. The segments are constructed of a first material have a first coefficient of thermal expansion that is greater than a second coefficient of thermal expansion of a second material of a composite multi-layer shell to be bonded together using the tool.