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The equation for prediction of the spring-in angle of a cylindrically orthotropic segment is shown to be independent of all material properties except for the anisotropic coefficients of thermal expansion and a stress-free state is insured for the corresponding unconstrained deformation. In contrast, the complete cylindrical geometry is shown to provide constraint to thermal deformation and thereby induce thermal residual stresses in the form of a moment. The method of superposition is demonstrated whereby traction-free conditions yield stress-free cylindrical elements with corresponding angular displacements at the element free boundaries. The first derivation of the spring-in equation is attributed to Radford, in contrast to the widely accepted view that the equation was first developed by Spencer et al. Finite-element methods, combined with the superposition approach, further validate the accuracy of the Radford equation for cylindrically orthotropic segments and explore its limitations for multiaxial composite laminates. [ABSTRACT FROM AUTHOR]

Stamp forming with thermoplastic composites provides high-rate production of structural components. A series of physical phenomena develops concurrently as a blank of fiber reinforced thermoplastic is consolidated, reheated, stamp formed, cooled within the tool, and released from the tool in the stamp forming process. Transient phenomena contributing to the residual deformation of continuous fiber-reinforced thermoplastics processed by stamp forming were described and characterized in this work. The transient phenomena considered included anisotropic heat transfer, anisotropic shrinkage, thermoviscoelastic behavior, and semi-crystalline polymer melting and crystallization kinetics. A comprehensive experimental characterization of the material properties required to model the phenomena involved in shape change is summarized in this work. The digital twin of this process, termed FORM3D and based on the finite element solvers ABAQUS and ANIFORM, has been constructed with the goal of describing the important phenomena in thermoplastic stamp forming, particularly to predict shape change. Shape change predictions made with FORM3D were validated against experimental measurements for a double curvature geometry made with a quasi-isotropic stacking sequence. The double curvature geometry developed both spring-in and spring-out deformations in the minor and major radii of curvature, respectively. FORM3D predictions were in excellent agreement with the experiments in both magnitude and distribution of the deformation. The same correlation was observed for three repetitions of the stamp formed experiment carried out in this work. [ABSTRACT FROM AUTHOR]

Shape compensation of tooling for stamp forming of carbon fiber thermoplastic laminated composites is described as a process wherein the virtual twin, FORM3D is utilized to determine the tooling geometry required to produce the desired part geometry in a single step process. FORM3D is a physics-based virtual twin that incorporates anisotropic phenomena including transient heat transfer, thermoviscoelasticity, thermoelastic and crystallization shrinkage, and polymer crystallization and melting kinetics. This procedure for determining the compensated tool geometry is illustrated for a composite laminate constructed of AS4/PEKK prepreg, supplied by Solvay Thermoplastic Composites, for a quasi-isotropic layup of variable thickness and double curvature: major radius of curvature of 1556.7 mm and minor radius of curvature of 75.7 mm. The resulting, compensated shape was shown to agree with the desired geometry within ±0.25 mm. [Display omitted] • Shape compensation for stamp forming • Compensated tool geometry • Tool compensation validated within 0.25 mm. [ABSTRACT FROM AUTHOR]