Theoretical analysis of fiber motion and loads during flow

Abstract

A pseudo‐analytical model for the forces exerted on fibers during flow that lead to fiber damage is proposed and solved. The fundamental derivations for the forces on fibers moving in suspensions developed by Burgers (1938) were used as a comparison. The cases of the motion of a fiber along its axis and perpendicular to its axis and in shear flow at a −45 degree‐angle were investigated for aspect ratios between 10 and 300. The values for the overall forces on the fiber were in good agreement with the results found earlier by Burgers and others. However, the force distribution along the fiber was found to be significantly different from the constant distribution assumed by Burgers. Because of the higher forces on the fiber from the exact solution, the criterion for the onset of buckling in shear flow was revised. The pseudo‐analytical solution was also compared to numerical results done with the boundary element method (BEM); the results were in good agreement.

Simultaneous measurement of temperature and strain in glass fiber/epoxy composites by embedded fiber optic sensors: I. Cure monitoring

“…The experimental results reveal instead the occurrence of different slopes due to the fact that, as the resin state evolves from liquid to gel, its thermal expansion coefficient α s changes. In addition, as confirmed by recent experiments [23], resin flow phenomena occurring during the early stage of the cure reaction can generate a not negligible tensional state of stress within the matrix. This effect is clearly shown in figure 9 by the greater slope of the segment AB: by introducing the term ε flux accounting for the additional expansion of the matrix due to resin flow, equation ( 2) can be modified as…”

A model for the carbon fiber breakage along the twin‐screw extruder

“…Since the lignocellulose fibers also separate into individual fibers, a similar equation is established for the diameter. [7] Hernandez et al [8] developed a pseudo-analytical model which describes the forces leading to fiber damage during flow. Investigations were carried out for l/d ratios between 50 and 300, fiber motions along its axis, perpendicular to its axis and in a shear flow at a − 45 degreeangle.…”

“…Furthermore, the solutions were compared to numerical results performed with the boundary element method (BEM). [8] One of the most extensive research projects on the twin-screw extruder was carried out by Durin et al [9] In this model, a fiber position in the flow using a Jeffery equation is used. After determining the buckling parameter for each position, the breaking potential is calculated.…”

“…The buckling criterion was modified by a factor of 2 to correct the maximum force at the center of the fiber. Furthermore, the solutions were compared to numerical results performed with the boundary element method (BEM) [8] …”