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Material extrusion (ME), sometimes called Fused Deposition Modeling® or Fused Filament Fabrication, is an additive manufacturing technique that places order 300 μm diameter molten polymer filaments sequentially onto a moving substrate to build an object. The feed material is a solid fiber that acts like a continuous piston in a heated barrel, which plasticates itself to push molten material through a nozzle. The barrel pressure is substantial, of order 30 MPa ( ≈4000 psi), and similar to that developed in contemporary polymer processing. The similarity does not end here with all the non-Newtonian and viscoelastic effects and heat transfer limitations that challenge extrusion operations coming to bear in the ME. These will be discussed in this review with suggestions of areas of study.

The fused filament fabrication (FFF) process is similar to classic extrusion operations; solid polymer is melted, pressurized, and extruded to produce an object. At this level of investigation, it appears no new science or engineering is required. However, FFF has heat transfer limitations that are unique to it, due to its small throughput, not encountered in contemporary polymer processing, negating the use of present-day correlations or heuristics. Here, we quantify heat transfer by rheological modeling of the pressure drop data in the process to generate a general Nusselt number–Graetz number correlation. This is the first time the pressure has been measured in the die (nozzle) during normal printing that we accomplished by monitoring the power used to drive the hot end. Ultimately, we find that fouling within the region used to melt/soften the polymer significantly reduces the heat transfer rate.

The failure (maximum) feed velocity in a LulzBot Taz 4 3D printer at various temperatures is determined for three polymers: Acrylonitrile butadiene styrene, poly(lactic acid) (PLA), and a PLA polyhydroxybutyrate copolymer. Through an approximate solution of the energy balance, we develop a model to correlate the dimensionless fiber feed velocity (represented by a Peclet number) with a dimensionless temperature. Using these dimensionless parameters, all polymers fall onto the same curve. However, when molten polymer is forced through a small nozzle to enable 3D printing, this curve also depends on another parameter: Nozzle diameter. Our model does not account for this parameter because it does not consider hydrodynamics due to the complexity of the coupled energy and momentum balances. Thus, we modify the Peclet number to account for hydrodynamics and produce a satisfactory master curve for all diameters and polymers. Our dimensionless numbers require determining the polymer thermal and rheological propert...

The elongation viscosity of kaolin pigment suspensions (71 wt %–49 vol %) was measured with a technique developed in our laboratory. Elongation thickening became apparent at rates of 103 s−1 while shear thickening occurred at a shear rate an order of magnitude larger. It is not entirely clear if elongation thickening was in fact due to shear within the elongation flow geometry, however, possible parasitic effects have been considered and it is believed the observed elongation thickening is close to a true material property. Torsional rheometer stress measurements at lower shear rates allowed the total stress to be deconvoluted into the viscous (hydrodynamic) and elastic (thermodynamic or structural) components using the stress jump technique. The total stress was equal to that obtained with the capillary rheometer lending some confidence in the experimental technique. Furthermore, it was found that the stress (or viscosity) at higher shear rates was dominated by the viscous component. Thus, particle hydro...

We present an approximate theoretical treatment of pressure and viscous heating effects on the flow of a power law fluid through a slit die. It is assumed that the flow remains one dimensional, and the accuracy of this approximation is checked via finite element simulations of the complete momentum and energy equations. For pressures typically achieved in the laboratory it is seen that the one dimensional approximation compares well with the simulations. The model therefore offers a method of including pressure and viscous heating effects in the analysis of experiments and is used to rationalize experimentally obtained pressure profiles for the flow of polymer melts through a slit die. Data for the flow of a linear low density polyethylene and a polystyrene melt in a slit die show these two effects are significant under normal laboratory conditions. Thus, the shear stress–shear rate curves will be affected to the point of being inaccurate at high shear rates. In addition, it is found that the typical technique to correct for a pressure dependent viscosity is also inaccurate being affected by the viscous heating and heat transfer from the melt to the die.

The use of hyperbranched polymers (HBPs) as a processing aid for linear low density polyethylene (LLDPE) was investigated. Various generation (or pseudo-generation) HBPs were used which had either 16 carbon atom alkanes or a mixture of 20/22 carbon atom alkanes on the end groups. In addition, the degree of end group substitution was studied. Blends of up to 10% HBP content were mixed via extrusion at 170 °C to produce 1 mm diameter fibers. Processability, surface appearance and the rheological properties of the blends were evaluated. It was found the power requirement for extrusion was significantly decreased as a result of reduced blend viscosity, and also, the mass flow rate for a given extruder speed was greater than virgin LLDPE for all HBP blends. Melt fracture and sharkskin of the blends was successfully eliminated, and minimal preprocessing time was required for the effect to take place. Surface analysis using x-ray photoelectron spectroscopy and transmission electron microscope techniques were performed with both showing that the HBP had a preference to accumulate at the fiber surface. Rheological experiments were similarly affected, therefore, the blend viscosity is really a composite of a HBP rich phase and a neat LLDPE phase. It is hypothesized that the HBP rich phase acted as a lubricating layer at the polymer/die wall interface. The HBP with a greater degree of end group substitution acted better as a processing/rheological property aid. Blends of LLDPE and paraffin wax were also studied. The surface appearance of HBPs/LLDPE blends was superior to those blends mixed with paraffin wax, as was the extruder performance. The results suggest that HBPs, at trace levels (≈500 ppm), may offer a number of advantages when used as a processing aid for LLDPE.

The slip of monodisperse polystyrene melts next to a solid, inhomogeneous, metal substrate (stainless steel) is measured at small stress levels for a variety of temperatures. A critical stress, below which no slip occurs, is not seen and the polystyrene melts used here slip at all stress levels. The slip velocity is quantified by the slip length (b, equal to the slip velocity divided by the shear rate) and friction coefficient (k, equal to the slip velocity divided by the shear stress). The slip length shows complicated dependence with both the molecular mass and temperature, however, when converted to the friction coefficient a master curve with molecular mass results for temperatures above 170 °C. The data are compared to contemporary theories for slip. It is concluded that none of the present theories accurately represent the data and that the number of adsorbed molecules are in a dynamic equilibrium which affects the slip behavior. Analysis of the force on the adsorbed molecules during shear demonstrates this may cause adhesive failure which contributes to the slip.

In this work we thoroughly explore the meanings of dissipation (sometimes referred to as viscous dissipation) and stress power. To do this we utilize the Cauchy momentum equations and the first and second laws of thermodynamics. First, the generalized engineering Bernoulli equation (GEBE) is derived from the Cauchy momentum equations and it is clearly shown to have nothing to do with a balance of energy. Next, the first law of thermodynamics or energy balance is discussed and a combined equation by subtracting the two is derived which we refer to as the mechanoenergy balance (sometimes referred to as the ‘‘equation of thermal energy’’). The fact that a difference exists further reinforces that the GEBE is not related to a balance of energy. Finally, the second law of thermodynamics is presented and the concept of dissipation introduced. An example is presented to demonstrate the utility of these equations which will hopefully eliminate some confusion in the literature.

A mock truncated cone was manufactured and sent to 12 participants throughout the world for measurement of appropriate dimensions. The results indicated that the error in measuring the cone diameter was trivial while the cone angle and truncation height had errors of ±4.79% and ±12.4%, respectively, based on the standard deviation of all measurements. Two groups had reported values of the cone angle which were statistically high and when these values were ignored the error in the cone angle was reduced to ±1.38%. These errors are lower than previously quoted accuracies in the literature. Since the measurement techniques used for the five most accurate measurements are not new, it is concluded that care of the person performing the measurement is critical. The effect of errors on the geometric variables’ values on the shear rate, shear stress, and first normal stress difference are discussed.

In this work it is shown that the amount of stress retained at the instant of shear cessation, denoted as the elastic stress by Doi, and not the total shear stress is proportional to the shear equivalent of the optic birefringence even in the nonlinear shear stress–shear rate region. The system studied was xanthan gum in a viscous solvent, fructose dissolved in water, and may be considered as a system with rigid constraints. Coaxiality of the elastic stress and refractive index ellipsoids has been predicted theoretically for these systems; however, previous studies have only compared the total stress to the birefringence which generally leads to invalidation of the stress‐optic relation. The results of this work have three consequences; it reinforces the fact that stress jumps are present, the stress‐optic relation is only true when the elastic and not the total stress is used, and two unique types of stress constitute the total stress as predicted by theory for systems with rigid constraints.

The low shear rate slip behavior of monodisperse polystyrene melts was characterized with the parallel plate geometry in a torsional rheometer. It was found that all melts studied exhibited some slip behavior. Tool material of construction showed no appreciable effect. Results were analyzed according to deGennes’ theory of slip, and values of the characteristic slip dimension, b, were calculated for each molecular weight. The slip dimension was found essentially proportional to the molecular weight to the first power. A slider block and spring model is proposed in an attempt to explain slip phenomena in the low shear rate limit.

The rheological properties of polymeric liquid crystals are quite complicated and theories over the last decade and a half have made great progress in explaining this seemingly unique behavior. Most theories have considered only the elastic stress and neglected the viscous stress which can be measured by determining the amount of stress instantaneously lost on cessation of shear. The elastic stress is the stress that is left which subsequently decays with time after cessation. Data is presented that shows the viscous stress contribution determined from shear cessation experiments is present for both the biphasic and liquid‐crystalline mesophase of hydroxypropylcellulose‐water solutions. This system shows the three regions for the shear viscosity at higher concentrations. The viscous stress is the dominant contribution at high shear rates, well within region III, and is caused by viscous drag on the molecules. The viscous stress contribution is still present in the intermediate region II although to a lesser extent (approximately 20% of the total); however, as region I is approached it becomes more prominent. We explain this behavior as due to a phenomenon similar to superplasticity by viscous dissipation between domains or within defects.

The effect of surfaces on the rheology and processing of polymers is a newly developing area of research. In this work, a stainless steel slit die was used with a variety of inserts of other metals, at the exit. The viscosity measured with the slit die was well predicted by the generalized Maxwell model containing a damping function with parameters determined from separate shear experiments. The viscosity was not affected by different metal type at the die exit. However, there was a marked increase in exit pressures for flow over brass inserts at the die exit. This effect coincided with the production of a porous, copper‐rich brass surface and it was shown that this was the result of surface dezincification. This was postulated to cause increased adhesion between the LLDPE and the brass via physical interlocking at the porous surface which subsequently increased the exit pressure.