Meaning
Empirical constitutive equations describe the non-Newtonian flow behavior and temperature dependence of molten thermoplastics across wide ranges of shear rate and processing pressure. The cross-wlf viscosity model combines the Cross shear-thinning formulation with the Williams-Landel-Ferry temperature and pressure shift function to calculate melt viscosity throughout injection and packing phases. Mold filling software uses this formulation to predict injection pressure requirements, melt front advancement, and viscous dissipation inside the cavity.
The model ceases to describe material response accurately once the polymer solidifies below its glass transition or crystallization temperature, where solid mechanics replace fluid rheology.
Rheological Equation
Six distinct material constants characterize the rate-dependent thinning and thermal response of a specific resin grade under dynamic flow. At zero shear rate, the formulation establishes a Newtonian plateau viscosity that depends on temperature according to free-volume theory. As injection velocity forces the polymer chains through tight gates, the cross-wlf viscosity model tracks the dramatic drop in viscosity caused by shear alignment and molecular disentanglement.
The mathematical expression captures the transition region between Newtonian zero-shear flow and power-law thinning behavior with high numerical stability. Polymer characterization laboratories determine these parameters using high-pressure capillary rheometers operating under controlled isothermal conditions.
Simulation Input
Finite element solvers integrate these rheological coefficients to resolve velocity and pressure fields within runner systems and complex wall geometries. Accurate curve fitting prevents underestimating peak injection pressures during fast filling of thin-walled electronic housings. When a compounder switches from virgin resin to a recycled grade with a broader molecular weight distribution, new laboratory test data must be fitted to update the simulation parameters.
Processing errors multiply rapidly if simulation teams rely on generic database curves instead of batch-specific resin characterization data.
Viscosity Shift
Rising hydrostatic pressure compresses the free volume between macromolecules, driving the zero-shear viscosity upward during the high-pressure packing phase. The pressure dependence coefficient within the cross-wlf viscosity model quantifies this shift, which proves decisive when sizing gating for thick-walled structural components. High packing pressures can raise the effective glass transition temperature of amorphous polymers like polycarbonate by several degrees.
This thermodynamic coupling determines whether hold pressure can successfully transfer through the gate before freeze-off halts volumetric compensation.
