2017 Volume 58 Issue 3 Pages 499-504
Experimental viscosity measurements (50 to 100 Pas at mold walls, T = 273 to 373 K) of an injection-molded highly-filled glass fiber reinforced polyester bulk molding compound (GFRP-BMC) whose fiber length (lfiber = 0.44 mm) was optimized for tensile mechanical strength agreed well with that previously calculated by Navier-Stokes equation from fiber orientation mapping. The mapping was from 0.44 mm fiber formulation molded sample exhibiting ～60, ～40 and 20% higher tensile strength, strain, and modulus, respectively than commercially used (lfiber = 6.4 mm). Based on the viscosity measurements a new “mold filling” model is constructed with physical meaning to predict needed injection molding parameters pressure (dP), shot time (ts) and shot weight (ms) for various size dog-bone specimens varying length (Ltot), gauge length (LB), width (w) and thickness (th) for the optimized formulation. Moreover, the Mooney-Rabinowitsch calculation is found to be a decent predictor for shear rates across specimen thickness and at mold walls measured from the mapping. This was without buying new equipment, using the existing injection molding machine to save cost.
Glass fiber reinforced polymer (GFRP) bulk molded compounds (BMCs) have had a wide market for aerospace, automotive parts, housing for electrical wiring, corrosion-resistant needs, and day-to-day articles. BMCs offer precise dimensional control, flame and tack resistance, high dielectric strength, corrosion and stain resistance, and color stability. Short glass fiber BMCs are lower cost than steel, Al and Mg when making parts in high quantity. They are lighter and have a higher strength/density ratio than steel and Al. For mass production, BMCs are lower production cost than GFRP long fiber layup possessing easier production than prepreg long fiber production methods. BMCs have excellent flow characteristics that make them well suited for parts requiring precise dimensions and detail. Injection molding is commonly used for BMC as it can be easily produced with high productivity for mass production of large and small components with a smooth and attractive surface finish. GFRP-BMCs are 3-phase composite systems typically composed of short glass fiber, polymer, and contain a high mass% of powder filler such as CaCO3. Glass fiber reinforcement usually ranges from 5 to 30 mass% with nominal lengths of 3.2 to 12.7 mm (1/8 to 1/2 in),1) and nominal diameters ～14 μm.2) CaCO3 filler particles' long axes in molded specimen measure from <1 to 7 μm.3)
However, it was recently reported shortening E-glass fibers in an injection molded BMC from commercial 6.4 to sub-millimeter 0.44 mm, below the critical fiber length, lc of ～1.0 mm,4,5) yields substantially superior tensile strength and strain increased 58 and 43%, respectively6) with tensile modulus increased 5–25%.3) This was a new finding for FRPs:6,7) up to that time shortening fibers to below 1.0 mm was reported to decrease mechanical properties4,5,8–10) but research was limited to 2-phase FRPs without filler.
In this study, we determine viscosity measurements of BMC paste by parallel-plate rheometer accurately predict viscosity calculated by fiber orientation mapping2) of the enhanced reduced fiber length BMC (lfiber,avg = 0.44 mm: mean aspect ratio l/d = 39.0). Figure 1 shows the specimen where mapping was taken across center section ‘B’. The mapping resulted in velocity profile and parabolic fit in Fig. 2. From the mapping, required effective viscosity at mold walls, ηeff to push the ultra-high viscosity BMC paste through the mold as a function of injection pressure, δP (MPa) was calculated by derivation from the Navier-Stokes equation:2)
| \[ \begin{split} \eta_{\rm eff} = {}& (\delta P/\delta z)_{\rm tot}/8 \{2U_{\rm c,A} [(1/th_{\rm A})^2 + (1/w_{\rm A})^2] \\ & + U_{\rm c,B} [(1/th_{\rm B})^2 + (1/w_{\rm B})^2] \} \end{split} \] | (1) |
Mold flow through dog-bone specimen sections ‘A’ and gauge length section ‘B’.2)
Velocity profiles of injection molded GFRP-BMC, vmap and vP from fiber orientation mapping and its parabolic fit through gauge length (B) section [2]. Uc,P(B) is centerline velocity for parabolic fit (arrow).
Research shows viscosity of FRP is influenced by fiber length. In fiber-filled liquid polymer, viscosity is reported to increase with fiber length, particularly at low shear rates, while at higher shear rates the fiber length effect is less significant.8) Likewise, for injection-molded short glass fiber reinforced thermoplastics it is reported at low shear rates and glass fiber concentration viscosity increased with fiber length, but at high shear rates the dependency was reversed.11) During injection molding, fiber length is generally reduced by shear forces during compounding and molding. In polypropylene containing 10 mass% glass fibers, measured mean fiber length was reduced from 0.71 mm in pellets to 0.274 mm in a molded plaque,8) which would probably lower viscosity at low shear rates. Empirical models have been suggested relating relative viscosity of polymer melt, polyethylene (PE) or polypropylene (PP) filled with glass or carbon fiber, talc, or CaCO3 powder to volume fractions for particle aspect ratios from 6 to 27;12) while numerical simulation has been used extensively to obtain rheological properties of injection molded resin and their GFRPs.13,14) Since there are no studies found of effect of fiber length on viscosity for GFRP-BMCs, this study pinpoints an optimum fiber length (0.44 mm) for tensile mechanical strength and utilizes its viscosity in a “mold-filling” model to predict needed injection molding parameters of required pressure (δP), shot time (ts) and shot weight (ms) for various size dog-bone specimens varying length (Ltot), width (w) and thickness (th) for the optimum formulation to be useful in mold design. This is using the existing injection molding machine to save cost.
Two BMC formulations of [paste] and [paste+fibers+filler] provided by Citadel Plastics of Conneaut, Ohio 44030 were analyzed by viscosity measurements as shown in Table 1. The [paste] formulation consisted of polymers, black pigment and mixing agents prepared without the normally added E-glass fibers and CaCO3 filler. To obtain reliable viscosity measurements cross-linking and thickening agents were omitted from the [paste] formulation of which are proprietary. Thus, volume fraction, Vf of the [paste] formulation of polymers plus remaining mixing agents was 1.000.
| Polymer mixture mass% | glass fiber mass% | CaCO3 filler mass% | |
|---|---|---|---|
| [paste] | 100.0 | 0 | 0 |
| [paste+fibers+filler] | 32.9 | 20.0 | 47.1 |
The [paste+fibers+filler] was prepared consisting of: 13.95 mass% propylene glycol maleate polyester (33 mass% styrene solution), 13.95 mass% styrene butadiene copolymer (70 mass% styrene solution), 20.00 mass% glass fibers, 47.10 mass% calcium carbonate filler (CaCO3), 0.35 mass% t-butyl perbenzoate, 0.10 mass% t-butyl peroctoate, 0.25 mass% carbon black pigment, 1.20 mass% calcium stearate, 3.00 mass% aluminum silicate, and 0.10 mass% magnesium oxide. The [paste+fibers+filler] formulation is used commercially and had calculated volume fractions Vf for polymers, E-glass fibers, and CaCO3 filler of 0.578, 0.132 and 0.290, respectively.
2.2 Samples preparationFiber orientation mapping was previously carried out on the [paste+fibers+filler] molded specimen in Fig. 1 across the 3.3 mm thickness.2) The [paste+fibers+filler] formulation with lfiber of 3.2 mm was mixed in a double-arm sigma blade mixer for a total of 50 min at room temperature to shorten them to the superior submillimeter. The mixture was allowed to stand for several hours and then injected molded into an ASTM D-638 family mold for dog-bone shaped specimens15) (Fig. 1) with a 3.03 × 105 N (75 ton) New Britain with the following processing parameters: mold temperature 436 K (163℃), barrel temperature RT, injection pressure 3.50–6.90 MPa, shot time, ts = ～2.0 s, hold time 15 s, and cure time 1.5–2.0 min. Average glass fiber length, lfiber of about 1,000 fibers was measured to be 0.44 mm with a standard deviation of 0.203 mm by SEM.1,2) In general, two standard deviations comprise approximately 95% of the population, which is 0.04 mm < lfiber < 0.85 mm. Although nominal fiber diameter, d was 14 μm, measurement by SEM mapping showed average d = 11.4 μm with standard deviation of +/−1.15 μm, thus 95% of the population was 9.1 < d < 13.7 μm.3) Therefore aspect ratio is 2.91 < [lfiber/d] < 93.4, with a mean of 39.0.
2.3 Viscosity measurementsTable 2 shows viscosity measurements on the BMC formulations in Table 1 of [paste] and [paste+fibers+filler] by a HAAKE MARS Modular Advanced Rheometer System parallel-plate rheometer, Model Number 3 at EKO Instruments Trading Company, Ltd. in (Shibuya) Tokyo, Japan. The top parallel plate had a 1–4 deg incline angle while the bottom plate was flat. The rheometer had a CTC temperature control flow chamber, and a 150 W heater on the outer perimeter with 100 W radiation heater coils close to the specimen. The cooler was by water flow. The CTC controlled the test temperatures according to Table 2 accurately all within +/− 0.06 K, with experimental means of 20.463℃ (293.463 K) +/− 0.057℃, 59.999℃ (332.999 K) +/− 0.023℃ and 100.006℃ (373.006 K) +/− 0.041℃ for [paste], and 170.000℃ (443.000 K) +/− 0.035℃ and 20.368℃ (293.368 K) +/− 0.030℃ for [paste+fibers+filler] formulations. For each temperature one specimen was tested ramping the shear rate up then down. Subscripts ‘p’ and ‘pff’ will refer to the [paste] and [paste+fibers+filler] formulations, respectively. For the [paste+fiber+filler] formulation at 293 K the shear rate was only ramped up due to slip occurring between the sample and metal disc. Figure 3 shows the parallel plate viscometer with the black pigmented BMC [paste] without the E-glass fibers or CaCO3 filler.
| [paste] without fibers or filler T = 20℃, 60℃, 100℃ (293, 333, 373 K) $\dot{\gamma}_{\rm p}$ = 1 → 2 → 5 → 10 → 20 → 50 → 100 → 200 → 100 → 50 → 20 → 10 → 5 → 2 → 1 s−1 |
| [paste+fibers+filler] T = 20℃ (293 K) $\dot{\gamma}_{\rm pff}$ = 1 → 2 → 3 → 5 → 10 → 20 → 30 → 50 → 100 s−1 T = 170℃ (443 K) $\dot{\gamma}_{\rm pff}$ = 3 × 10−5 → 7.5 × 10−5 → 1 × 10−3 → 8 × 10−2 → 0.1 → 0.2 → 0.3 → 0.5 → 1 → 2 → 3 → 5 → 10 → 20 → 30 → 50 → 100 → 200 → 100 → 50 → 30 → 20 → 10 → 5 → 2 → 1 → 0.5 → 0.3 → 0.2 → 0.1 → 6 × 10−5 → 2.5 × 10−5 → 3 × 10−5 s−1 |
| Each temperature was a separate specimen. |
Photo of BMC [paste] without the E-glass fibers or CaCO3 filler in parallel plate viscometer holder.
Viscosity measurements of paste without fibers or filler [paste] were made to determine if they agree with effective viscosity at mold walls, ηeff by Navier-Stokes calculation in eq. (1) from velocity profile by fiber orientation mapping.
Results in Fig. 4 show the measured viscosity values by parallel plate rheometer of the [paste], designated ηp are a good predictor of the ηeff. The experimental hysteresis curves of the [paste] without fibers or filler at temperatures of 20℃ (293 K), 60℃ (333 K) and 100℃ (373 K) all fall within the ηeff range of 50 to 100 Pas (box). The [paste] displayed non-Newtonian shear-thinning behavior as a decrease in its viscosity, ηp with increasing shear rate, $\dot{\gamma}$ probably due to reduction in carbon black pigment particle size by continued friction between disc and specimen, and within the specimen itself. Then, during the ramp-down cycle from 200/s to 1/s thixotropic behavior is observed as a decrease in viscosity from the ramp-up by the reduced size carbon black pigment particles that are further reduced in the viscometer.
Experimental viscosity, ηp (Pas) vs. shear rate, $\dot{\gamma}$ (s−1) curves of the BMC [paste] without fibers or filler as a function of test temperature compared with calculation of effective viscosity range of melt at mold walls, ηeff by fiber orientation mapping with Navier-Stokes equation2) (between solid lines).
Shear stress τp (Pa) vs. shear rate $\dot{\gamma}$ (/s) curves are typically used as an indicator of good contact between rotating metal disc and specimen in viscosity measurements as shown in Fig. 5 corresponding with the Fig. 4 data. The 20 and 60℃ (293 and 333 K) curves show good contact between the parallel plates and [paste] as shown by the increase in τp with $\dot{\gamma}$. However, at 100℃ (373 K) slip between the metal plates and [paste] was initiated when the shear stress, τp began to decrease at shear rates above $\dot{\gamma}$ = 30/s. Specimen observation showed solidification occurred; probably from crosslinking at the higher temperature, hence tests were not conducted at 140° and 170℃ (413 and 443 K). Although the slip occurred in the 100℃ (373 K) sample, its viscosities fell within the ηeff range predicted by eq. (1) at low shear rates as shown in Fig. 4.
Experimental shear stress, τp (Pa) vs. shear rate, $\dot{\gamma}$ (s−1) curves of the BMC [paste] without fibers or filler of the data in Fig. 4. Yield stress region is slip initiation by resin solidification.
Figure 6 shows as expected experimental viscosity curves of the commercial [paste+fibers+filler] formulation designated ηpff (Pas) are higher than those of the [paste], ηp (Pas) included from Fig. 4. As expected, the ηpff curves showed slightly higher viscosity values at 20° (293 K) than at 170℃ (443 K).
However, shear stress-shear rate curves in Fig. 7 from data in Fig. 6 show shear stress, τpff reductions an indicator that slip occurred with increasing shear rate between metal plate and specimen. Samples were observed to be solidified with a hardened buffed surface from the movement between the flat rheometer disc and specimen as the rotational force of the disc exceeded the frictional force on the specimen from hard particles of fibers and filler. Also, the Citadel data of [paste+fibers+filler] at 20℃ (293 K) was 2 orders of magnitude higher than the ηpff at 293 K.
Experimental shear stress, τpff (Pa) vs. shear rate, $\dot{\gamma}$ (s−1) curves of the commercial BMC-GFRP [paste+fibers+filler] of the data in Fig. 6. Yield stress region is slip initiation observed from hard components fibers and filler, and resin solidification.
A serrated fixture for the [paste+fibers+filler] formulation would be recommended, but may need a correction factor to be compared with the flat disc used for the [paste] formulation since serrations would put stress normal to fiber surfaces in rotation direction.
3.3 Mooney-Rabinowitsch as predictor for shear rate, $\dot{\gamma}$ in the specimenTo determine if the Mooney-Rabinowitsch equation, eq. (2) is a good predictor of shear rates across specimen thickness in gauge length section Fig. 8 shows comparison with shear rates calculated by velocity profile by fiber orientation mapping. The Mooney-Rabinowitsch equation is.16)
| \[\dot{\gamma}_{\text{M-R}} = 4Q/\pi R^3 = 8U_{\rm b}/D_{\rm H}\] | (2) |
Comparison of shear rates (s−1) from: 1) velocity profile estimated from fiber orientation across specimen thickness, $\dot{\gamma}_{\rm map}$; 2) its parabolic fit for Navier-Stokes equation, $\dot{\gamma}_{\rm P}$; and 3) the Mooney-Rabinowitsch equation $\dot{\gamma}_{\text{M-R}}$ along with experimental shear rate range for the [paste+fibers+filler]. Note for $\dot{\gamma}_{\rm P}$ data, slope = 0 at centerline.
When velocity profile data points, vk,i are measured across specimen thickness where ‘k’ is: “map” from fiber orientation mapping or “P” for parabolic fit (see Fig. 2). Separated into 24 sections, i where 1 < i < 24 as in other studies,2,18) the $\dot{\gamma}_{\rm k,i}$ are obtained:
| \[\dot{\gamma}_{\rm k.i} = |\delta {\rm v}_{\rm k,i}|/\delta x\] | (3) |
| \[\dot{\gamma}_{\rm k.i} = |{\rm v}_{\rm i} - {\rm v}_{{\rm i}-1}|/(x_{\rm i} - x_{{\rm i}-1})\] | (4) |
A “mold filling” model is constructed in Figs. 9 to 11 to predict needed injection molding pressure (dP), shot time (ts) and shot weight (ms) for various size dog-bone specimens to overcome the ηeff (50 to 100 Pas) to push the highly viscous core through the mold. The dP, ts and ms are plotted against total specimen length, Ltot. Solving eq. (1) for dP in terms of total specimen length, Ltot, thickness, and width of ‘A’ and ‘B’ sections, thA, thB, wA, and wB we obtain:
| \[ \begin{split} dP_{\rm tot} = {}& 8L_{\rm tot} \eta_{\rm eff} \{ U_{\rm c,P(B)} [(1/th_{\rm B})^2 + (1/w_{\rm B})^2] \\ & + 2U_{\rm c,P(A)}[(1/th_{\rm A})^2 + (1/w_{\rm A})^2]\} \end{split} \] | (5) |
| \[ \begin{split} dP_{\rm tot} = {}& 8L_{\rm tot} \eta_{\rm eff} \{ U_{\rm c,P(B)} [(1/Xth_{\rm B})^2 + (1/Xw_{\rm B})^2] \\ & + 2U_{\rm c,P(A)} [(1/Xth_{\rm A})^2 + (1/Xw_{\rm A})^2] \} \end{split} \] | (6) |
| \[ \begin{split} dP_{\rm tot} = {}& 8X^{-2} L_{\rm tot} \eta_{\rm eff} \{ U_{\rm c,P(B)} [(1/th_{\rm B})^2 + (1/w_{\rm B})^2] \\ & + 2U_{\rm c,P(A)} [(1/th_{\rm A})^2 + (1/w_{\rm A})^2]\} \end{split} \] | (7) |
Predicted required injection pressure, dP (MPa) range [high (hi), low (lo)] to push the [paste+fibers+filler] through the mold as a function of total specimen length, Ltot (m) and gauge length LB = 0.476Ltot for various normalized thickness/width factors, X.
Figure 9 shows eq. (7) the required injection pressure, dP plotted against Ltot for various practical size specimens where X = 0.25, 0.50, 0.75, 1.00, 1.25, 1.50, 1.75 and 2.00; for Ltot from 10 to 700 mm. Pressure range (hi) and low (lo) are depicted. For example, the experimental values, when X = 1.00 and Ltot = 0.21 m, required dP range is from 3.5 to 6.9 MPa. In addition, Fig. 9 shows dP as a function of at constant gauge length to total length ratio (RL = LB/Ltot = 0.476) in the bottom x-axis
Therefore, required pressure ranges, dP for many practical size dog-bone specimens can be approximated keeping with standard specimen geometry ratios Rc and RL.
Moreover, required shot time ts (s) can be approximated as a function of total specimen length, Ltot as shown in Fig. 10 and calculated by the following equation:
| \[t_{\rm s} = V_{\rm tot}/Q\] | (8) |
| \[V_{\rm tot} = V_{\rm B} + 2V_{\rm A}\] | (9) |
| \[V_{\rm tot} = R_{\rm B} L_{\rm tot} w_{\rm B} th_{\rm B} + (1 - R_{\rm B}) L_{\rm tot} w_{\rm A} th_{\rm A}\] | (10) |
| \[V_{\rm tot} = R_{\rm B} L_{\rm tot} Xw_{\rm B} Xth_{\rm B} + (1 - R_{\rm B}) L_{\rm tot} Xw_{\rm A} Xth_{\rm A}\] | (11) |
| \[t_{\rm s} = L_{\rm tot} thX^2 [R_{\rm B} w_{\rm B} + (1 - R_{\rm B}) w_{\rm A}]/Q\] | (12) |
| \[t_{\rm s} = L_{\rm tot} thX^2 [0.476w_{\rm B} + 0.524w_{\rm A}]/Q\] | (13) |
Predicted shot time, ts (s) needed vs. dog-bone specimen length, Ltot (m) and gauge length LB = 0.476Ltot for various normalized thickness/width factors, X.
In addition, required shot weight ms can be calculated by eq. (14):
| \[m_{\rm s} = \rho Qt_{\rm s}\] | (14) |
| \[m_{\rm s} = \rho L_{\rm tot} thX^2 [0.476w_{\rm B} + 0.524w_{\rm A}]\] | (15) |
Predicted shot weight, ms (g) needed vs. dog-bone specimen length, Ltot (m) and gauge length LB = 0.476Ltot for various normalized thickness/width factors, X.
To confirm smooth laminar flow type for the normalized thickness/width factors, X in the “mold filling” model, the dimensionless Reynolds number, Re is employed. The Re is useful to characterize the flow pattern in relation to other fluids, pipe sizes and geometries:
| \[Re = \rho U_{\rm b} D_{\rm H}/\eta_{\rm b}\] | (16) |
| \[Re = [2U_{\rm b} \rho wth/\eta_{\rm b}(w + th)]X\] | (17) |
We are grateful to Citadel Plastics in Conneaut, Ohio for providing the pastes, EKO Instruments Trading Company, Ltd., Tokyo (Shibuya), Japan for assisting with viscosity measurements, and Shigehito Inui, Takumi Okada, and Juanha Quan of Tokai University for help with sample preparation.
