Thermal buckling of thin injection-molded FRP plates

The occurrence of buckling during cooling of an injection-molded fiber-reinforced plastic (FRP) object is a complex phenomenon which can result in unacceptably large deformations. The present work focuses on the thermal buckling of injection-molded thin disks, as they are representative for the local behavior in parts of a more complex object. An analytical approach based on the Föppl-von Kármán theory for thin elastic plates is presented and used to analyze its buckling stability and initial post-buckling behavior. The system of equations is formulated in a coordinate-free approach for a thin anisotropic linear thermo-elastic body with residual thermal stresses. Large out-of-plane displacements are assumed. The particular case of a free disk with cylindrical orthotropy and uniform thermo-elastic properties through its thickness is considered. A general technique to study the bifurcation in the solutions (i.e., buckling) based on a perturbation approach and the Fourier-Galerkin method to determine post-buckling deflections is proposed. Experimental and numerical results available in the literature are used as validation cases. The results of the present model show qualitative agreement with the experimental data. It is found that the periodicity of the first buckling mode for orthotropic disks is fully determined by the ratio between the elastic moduli in the tangential and radial directions. The predictions are also in excellent quantitative agreement with the numerical results of FEM models for the same cases. The effect of the disk thickness on the buckling temperature and warpage magnitude is correctly captured.