Mechanism of warpage orientation rotation due to viscoelastic polymer substrates during thermal processing

The warpage orientation, which refers to the direction of maximum and minimum curvatures in a cylindrical warpage, was observed to have changed by flipping from a concave to a convex shape during thermal processing. In this paper, the mechanism of the warpage orientation rotation is demonstrated through analyzing the stress state and curvatures of the specimens using finite element method (FEM) simulations and experiments. It is revealed that the warpage transition temperature, where the curvature changes to other shapes, corresponds to the stationary point of the stress-temperature curve and the curvature change of the minimum direction precedes the curvature change of the maximum direction during the warpage orientation rotation. This precedence results from the stress relaxation of the fiber reinforced polymer (FRP) substrate. Because the curvature of minimum direction flips backward in advance of maximum direction, the cylindrical warpage shape converts to a saddle shape and it induces the rotation of the warpage orientation. The simulation without the viscoelastic properties of the FRP substrate is conducted and used for comparison in order to verify the stress relaxation effect of the warpage orientation rotation phenomenon. In conclusion, it is demonstrated that the viscoelastic properties of the FRP substrate are a critical factor in analyzing the warpage orientation rotation and its behavior.