Biaxial Extensional Deformation Dynamics of Semi Crystalline Polymer Sheets
Biaxial extensional strain hardening controls sheet thinning, requiring precise melt strength, tool friction, and temperature tuning to set uniform container wall thickness.
Velocity Gradient Tensor
Meaning
Mathematical representations describe the spatial variation of fluid velocity during polymer melt processing. In injection molding and extrusion, the velocity gradient tensor captures the deformation rate and flow type experienced by the polymer melt. This tensor is used in computational fluid dynamics to simulate the shear and elongational forces that act on the polymer chains.
It stops applying to solid-state polymer processes where the material is not flowing, or to purely static melt conditions.
Flow Modeling
The tensor is decomposed into symmetric and asymmetric parts to separate the rate of deformation from the rate of rotation. This decomposition is critical for predicting the orientation of polymer chains and fillers during molding. In high-shear regions near the gate, the deformation rate is high, which leads to highly oriented skin layers in the molded part.
By simulating these flow dynamics, molders can predict and prevent problems such as warpage and anisotropic shrinkage. This simulation is particularly useful when designing complex multi-cavity molds where balanced filling is required to ensure consistent part quality across all cavities.
Rheological Feedback
Applying this tensor to non-Newtonian polymer flows allows for the calculation of the local viscosity and shear stress. High shear rates can reduce the melt viscosity, which improves flow into thin sections but can also cause thermal degradation if the shear heat is too high. This mathematical tool enables the design of runner systems and gates that minimize shear degradation while maintaining uniform fill rates.
Simulation Performance
Modern mold-filling software relies on this tensor to calculate the distribution of fiber orientation in reinforced composites. The orientation of short glass fibers is determined by the history of the velocity gradients as the melt flows through the cavity. Accurate predictions allow engineers to locate weld lines in areas of low stress and to design parts that can withstand the expected mechanical loads.
By adjusting the gate location and processing parameters in the simulation, the developer can optimize the fiber alignment to maximize the stiffness of the final molded component.