A thermo-viscoelastic analytical model for residual stresses and spring-in angles of multilayered thin-walled curved composite parts

The thermo-viscoelastic effects play an important role in the development of residual stresses and deformations of fiber-reinforced polymer composite parts during curing. In this paper, an analytical model is proposed to consider thermo-viscoelastic effects on residual stresses and spring-in angles of thin-walled curved composite parts during curing. The proposed model is first established to describe the viscoelastic mechanical behavior of an unidirectional curved composite layer based on the viscoelastic constitutive model with N+1 Maxwell elements. The explicit closed-form solution is obtained by a new iterative solution strategy. Then, the analytical model is extended to investigate the cure-behavior of multilayer curved composite parts. The viscoelastic effects on the residual stresses and spring-in due to tangential and radial thermal-chemical expansion are separately considered to aid in understanding of their individual influence. The analytical results show good agreements with experimental data in literature and numerically predicted results by viscoelastic FEA for the curved composite parts with symmetrical ply layup cured on a wound carbon-epoxy tube tool. Further numerical investigation on the composite parts with unsymmetrical ply layups shows that the viscoelastic effects on the spring-in angles are closely related to the ply layups and the thickness of composite parts and have different responses for those due to tangential and radial effects.