Spring-in Angle Prediction for Thermal Shrinkage in Cross-Ply Laminate

Thermal shrinkage in advanced composite manufacturing causes residual stress in a cylindrical anisotropic segment. The residual stress later induces a spring-in angle when the temperature change is negative. The superposition method in the finite element method (FEM) by ABAQUS© proves that only the residual stress in the circumferential direction controlsthe springin angle and induces the radial residual stress. To predict the angle change, the residual stress is firstly determined by using the closed-loop geometry in FEM and then implemented into the cylindrical cross-ply symmetric laminate segment. Consequently, the geometry creates the springin angle under the traction-free surface. The angle change is in good agreement with the Radford equation and is found to depend on the coefficient of thermal expansion (CTE) in the circumferential and radial directions rather than other material properties and geometry dimensions. The study found a new limitation of the Radford equation, in that it is accurate when the part is anisotropic symmetric laminate, but not when it is unsymmetric. The accuracy of the Radford equation is further explored with the double curve geometry. Using the superposition method, the circumferential residual stress along the major curve is found to have an influence on the angle change not only of the major curve, but also of the minor curve. The negative temperature change produces the spring-in angle on the major curve, and both spring-in and -off angles on the minor curve, which rely on the radius ratio. In addition, the spring-in angle on the major curve is coincident with the Radford equation. In sum, knowing the spring-in angle is very helpful in designing a tool in advanced composite manufacturing, and the superposition method and the Radford equation are applicable to predict the spring-in angle