Shear-Lag Analysis of the Effect of Thickness on Spring-in of Curved Composites

A new analytical solution is presented for spring-in of curved thermoset matrix composites taking into account the low shear stiffness of the material in the rubbery state before it is fully cured. It is shown that shear-lag through the thickness can have a significant effect in reducing spring-in arising from thermal stresses and chemical shrinkage between gelation and vitrification. Results are presented in a nondimensional form that shows the influences of subtended angle, through-thickness shrinkage, the ratio of curved arc length to part thickness, and the ratio of in-plane modulus to rubbery interlaminar shear modulus, providing greater physical insight into the spring-in mechanism. The analysis predicts a significant effect of thickness on spring-in angle. This is verified by experimental measurements on cross-ply carbon-epoxy C-sections cured on a carbon fiber tool, confirming the validity of the new solution.