Subject Area

Mechanical Engineering


Extrusion-based multi-functional additive manufacturing (AM) has been a rapidly developing area in AM recently. Particulate composites are widely used in this area to provide different functionalities with different types of particulate additives. However, there is no systematic understanding of the behavior of particulate composites during extrusion (especially in small nozzles) or of their properties once deposited in the build. This work investigates the properties of the type of particulate composites usually used in additive manufacturing, composed of a polymer matrix material and particulate additives within the micrometer scale. The focus is on the material rheology in the nozzle/capillary (for the particulate suspension in the liquid phase), and its electrical resistivity (at solid phase) when the particles are electrically conductive.

A capillary rheometer with replaceable capillaries of inside diameter (ID) from 0.3302 to 4.572 mm was designed and built to quantify the rheology of materials with different particle sizes (29.9 and 41.9 ) and volume fractions (10% to 40%). Silicone based material was used as a substitute for melted thermoplastic (as would normally be used for the composite matrix material in AM applications) since both have non-Newtonian shear thinning properties, but the silicone material could be used at room temperature. The experimental measurements for the silicon-particle suspensions showed power law rheological behavior for all suspensions considered. Hence, the flow behavior ( ) and consistency ( ) indices were used on to describe the materials’ rheology. Particle volume fraction ( ) and the ratio of capillary ID to the particle mean diameter ( ) were found to be the key factors impacting the rheology. The flow behavior index was found to be only dependent on for a suspension with the same suspension fluid and it was modeled as a linear function of . The flow consistency index, , was found to follow similar trends with for different , with larger suspensions showing stronger variations with . Based on the behavior, the rheology was categorized into two regimes: the free flow condition and the particle interaction condition. The value of at the boundary between these two conditions was found to decrease with . A semi-empirical model of for the free flow condition was constructed as a function of and based on a statistical analysis of particle location coupled with the assumption that particles closer to the wall have a stronger influence on the rheology. An model of for particle interaction condition was also formulated as a function of and to capture the observed increasing with decreasing . Because of insufficient theoretical foundation and data, the model incorporated an empirical power law behavior to capture the overall trend. Jamming was observed as decreased and the when jamming occurred was also analyzed and modeled. The influence of particle size distribution was assessed by comparing results for two different particles with different distributions. Particles with a wider size distribution caused a higher and and appeared to have a higher probability of jamming, which was explained by the assumption that larger particles dominate the interactions among particles.

Electrical behavior of composites was investigated using composites made of thermoplastic matrix material and conductive particulate additives. Two matrix materials were used and micrometer-scale silver-coated nickel spheres were used as the particulate additive with particle volume fractions of 20% to 30%. The electrical resistivity of extruded filaments of these materials was investigated under stress relaxation and linear-ramp strain loading conditions. The tested materials showed stress-strain behavior typical of a Maxwell viscoelastic material. Using the quantum tunneling model to describe conductivity between adjacent particles (which dominate the material resistivity) indicated the composite resistivity was impacted by the matrix material type and the distance between adjacent particles (for a given particle type). Hence, the resistivity was analyzed and modeled by concentrating on these two factors. At a given nominal strain under the same loading conditions, the inter-particle distance was only impacted by particle volume fraction. When mechanical variable loads/strains were applied, resistivity was modeled based on the hypothesis that the change in the mean inter-particle distance was proportional to the cubic root of volume change, which is determined by the strain and Poisson's ratio for the tested material. Different matrix materials were also tested and showed that the resistivity followed the same relationship with particle volume fraction and mechanical load, but with different magnitudes, when different matrix materials were used.

Using the results of this investigation, the manufacturing process of extrusion-based AM can be improved by optimizing the extruder nozzle ID and particulate composite formulation without preliminary tests. Jamming can also be avoided. The composite formulation tuned to achieve the desired electrical behavior with few preliminary tests before utilization in AM and other possible applications.

Degree Date

Spring 5-15-2021

Document Type


Degree Name



Mechanical Engineering


Paul Krueger

Number of Pages




Creative Commons License

Creative Commons Attribution-Noncommercial 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License