Benrabah, Z., Mir, H., and Zhang, Y., "Thermo-Viscoelastic Model for Shrinkage and Warpage Prediction During Cooling and Solidification of Automotive Blow Molded Parts," SAE Int. J. Mater. Manf. 6(2):349-364, 2013, doi:10.4271/2013-01-1397.
Blow moulding is one of the most important polymer processing methods for producing complex thermoplastic automotive parts. Contrary to injection molding, little attention has focused on process control and simulation of blow molding processes. Yet, there are still several problems that affect the overall success of forming these parts. Among them are thermally induced stresses, relevant shrinkage and part warpage deformations caused by inappropriate mold design and/or processing conditions. Tolerance issues are critical in automotive applications and therefore part deformation due to solidification needs to be controlled and optimized accordingly. The accurate prediction tool of part deformation due to solidification, under different cooling conditions in automotive formed parts, is important and highly suited for part designers to help achieve an efficient production.This paper describes in detail the three dimensional membrane element in large displacement formulation with an integration and implementation of the KBKZ constitutive equation to model the blowing phase of forming processes. Thereafter, we focus on the development of a linear thermo-viscoelastic constitutive equation based on a Zener model for modeling shrinkage and warpage of molten-solidified polymeric material during the cooling and solidification. The derivation of the governing equations as well as the implementation in our BlowView software is discussed and presented. The finite element method (FEM) will be used to numerically solve the derived governing equations and the shell theory, presented as an assemblage of flat elements formed by combining the Constant Strain Triangle element (CST) and Discrete Kirchhoff plate theory (DKT element), is applied. This shell theory is well suited for thin complex blow molded automotive parts. The numerical implementation and integration in BlowView is presented in detail.Finally, finite element warpage simulation results in terms of displacements and deformations, obtained with this formulation are presented for a simple and complex automotive part. The simulation results are compared to experimental and literature results to determine the accuracy and the limitations of the proposed model.