A set of rheological equations is developed for semiconcentrated suspensions of rigid fibers in a Newtonian fluid taking into account hydrodynamic and fiber-fiber interactions. The force generated by the fiber interactions is modeled using a linear hydrodynamic friction coefficient proportional to the relative velocity at the contact point, and weighted by the probability for contacts to occur. The equation of evolution of the second-order orientation tensor, containing advection and diffusion terms due to fiber interactions, is derived to predict fiber orientation under flow. The well known fourth-order orientation tensor, related to the hydrodynamic contribution, and a newly proposed fourth-order interaction tensor are used to evaluate the total stress in the composite. A linear and a quadratic closure approximation are proposed to describe the fourth-order interaction tensor. Results are presented using the quadratic form, which is found to be more accurate than the linear one. The model is shown to describe well simple shear data of suspensions of glass fibers in a Newtonian polybutene. Moreover, fiber orientation and the average number of contacts per fiber are predicted. The newly proposed interaction coefficient varies with fiber orientation, which appears to be realistic.

We present a numerical study of the fused deposition modeling 3D printing process of fiber-reinforced polymers by means of Smoothed Particle Hydrodynamics (SPH). For this purpose, a classical microstructure-based fiber suspension model coupled with a constitutive model for the suspending polymer is implemented within an SPH framework. The chosen model is reviewed, together with the details and specificities of its implementation in SPH. The results for several representative cases are then presented, mainly in terms of contours of fiber orientation tensor components and orientation distributions across the deposited layer thickness. The impact of the fiber concentration and its aspect ratio in a semi-concentrated regime and the effect of the ratio between extrusion and substrate velocities are investigated. Some insights into the link between the flow field and fiber orientation evolution within the printing head and as the material exits the nozzle are given. The main findings lie in the prediction of a skin/core structure in the deposited layer in which the skin regions exhibit a higher fiber alignment with respect to the core region. This effect is found to be enhanced by an increase in fiber concentration and to be sensitive to the substrate-to-extrusion velocity ratio. It is indeed enhanced in cases where the substrate velocity is low compared to the extrusion velocity and accompanied by a larger swelling of the deposit at the nozzle exit.

Laser-assisted automated fiber placement (AFP) is highly suitable for an efficient production of thermoplastic-matrix composite parts, especially for aeronautic/aerospace applications. Heat input by laser heating provides many advantages such as better temperature controls and uniform heating projections. However, this laser beam distribution can be affected by the AFP head system, mainly at the roller level. In this paper, a new optico-thermal model is established to evaluate the laser energy quantity absorbed by a poly(ether ether ketone) reinforced with carbon fibers (APC-2). During the simulation process, the illuminated radiative material properties are characterized and evaluated in terms of the roller deformation, the tilt of the robot head, and the reflection phenomenon between the substrate and the incoming tape. After computing the radiative source term using a ray-tracing method, these data are used to predict the temperature distribution on both heated surfaces of the composite during the process. The results show that both the roller deformation and the tilt of head make it possible to focus the laser beam on a small area, which considerably affects the quality of the finished part. These findings demonstrate that this optico-thermal model can be used to predict numerically the insufficient heating area and thermoplastic composites heating law.

This work is focused on shear thinning behavior of suspensions of rigid non-Brownian fibers dispersed in a Newtonian liquid. The work consists of developing a new theoretical model and conducting accurate experimental measurements. The shear thinning is expected to be caused by adhesive interactions between fibers. Experiments on polyamide (PA) fibers (present work) and carbon nanotube (CNT) suspensions [Khalkhal et al., J. Rheol. 55, 153–175 (2011)] have revealed the following features: (a) The flow curves exhibit a pronounced pseudoplastic behavior interpreted in terms of the progressive aggregate destruction at the increasing shear rate; (b) the enhancement of the shear thinning with an increasing particle volume fraction is observed and explained by an increase in the strength of effective interactions between particles, as their concentration increases; (c) a weak yield stress of the PA fiber suspensions is detected in a controlled-stress mode and explained by the liquid-solid transition as the concentration of aggregates (constituted by fibers) approaches the close packing limit; (d) the shear thinning is much stronger in CNT suspensions because the adhesive interactions play a more important role between nanosized CNT particles than between micron-sized PA fibers. A theoretical model considering the coexistence of transient aggregates with free nonaggregated fibers has been developed. The model allows viscosity calculations in terms of the aggregation parameter—the ratio of adhesive to hydrodynamic forces. It captures qualitatively the above-mentioned shear thinning behaviors and fits reasonably well to the experimental data on both PA fiber and CNT suspensions.