I: (a)What are precursor materials used to manufacture composites?
(b) Please search the literature including the web to identify and list, along with a schematic or a illustration, different types of precursor materials.

II. What are fiber sizings. Give a few examples of fiber sizings

IIIa: Injection Molding

1. What is ``fountain flow'' in injection molding? What process and material parameters determine its significance? What is the result of this flow?
2. What are ``skin'' and ``core'' layers in injection molding?
3. Does the length of the fibers change during the flow of suspension in injection molding? Explain why.
4. Give some examples of common products that are injection molded.
 

IIIb: Extrusion
1. What are the two phenomena that help to soften and then melt the solid polymer pellets in an extrusion machine before it is pushed by the screw? Which one creates more heat?
2. What is ``die swelling?'' What causes it?
3. What are the similarities and differences between the extrusion and injection molding processes?
4. Give some examples of common products that are manufactured with the extrusion process.

IIIc: Compression Molding

1. What is ``initial charge'' in the compression molding process? Why is it crucial to properly place it inside the mold?
2. The tensile strength and elastic modulus of compression molded parts might exhibit significant variations from one molding to another. What are the two main reasons?

IV: Advanced Thermoplastic Manufacturing

List the advanced composite thermoplastic manufacturing methods. What are the advantages and disadvantages of these manufacturing processes?

V: Advanced Thermoset Composites

List important transport issues in thermoset filament winding, autoclave processing and liquid composite molding. Name at least two issues that are common to all the thermoset processes listed above, and name two issues that are specific to each individual process.

VI: Process Selection

You have been chosen to select a composite manufacturing process due to your familiarity with the processes as a result of the course you took at the University of Delaware. Your company is looking at making the following five components and would like you to recommend which process should be considered with a single sentence explanation as to why you selected that process.
1.) Short fiber reinforced dashboards for the new Acura car.
2.) Telephone poles for the city of Newark
3.) I-beams for Ford Passenger Vans
4.) Axi-symmetric casing for the rocket motor
5.) Recycleable door panels for the Mercedes Benz
6.) A composite spring for a helicopter.

VII: Manufacturing Process and Part Geometry

Please submit a hard copy and e.mail me (advani@udel.edu) your answers in a word file.

I.  Consider unidirectional stretching of a cylinder as shown in the figure below. At any time, t, assume that R(t) is independent of z.

(a) Using only the conservation of mass show that the velocity field is given by
   u_z  =  U *z/L(t)        and u_r = - U *r/2*L(t)

b)   find the components of the strain rate tensor

c) Neglecting surface tension and inertia, calculate the force F required to pull the Newtonian Viscous cylinder.

II. Radial Flow between Porous Cylinders

An incompressible fluid is made to flow radially (in the negative -r direction in cylindrical coordinates) from a porous cylinder of radius R to another porous cylinder of radius kR, where k <1.

a. Write down the equation of continuity and motion for the postulates that vr and P are functions of r only
b. Integrate the equation of continuity to get vr as a function of r. Determine the constant of integration by writing it in terms of the constant volume flow rate Q through the length L of the cylinders
c. Integrate the equation of motion to get the pressure difference required to maintain a flow rate Q. Express the pressure difference in terms of r,Q,k,R and L. How come there is no dependence on m?

 III. A layer of fluid with thickness d (delta)  flow down  a vertical wall as shown below. Gravity acts to pull the fluid down the wall.

 a.Find and sketch the velocity distribution for a Viscous Newtonian fluid of viscosity m (mu).
b. If you can measure the flow rate, what will be its thickness d (delta) in terms of viscosity and the flow rate Q
 

Due Date: After Lecture15 (Oct. 21st)

Consider a glass-polypropylene composite1.25 cm thick  at room temperature of 25C to be heated by conduction by  aluminum platens  held at 200C.

1.  How long will it take for the midplane of the glass-polypropylene composite containing 50% glass fibers to reach 175C?.
2. If the composite contained 50% carbon fibers instead of glass fibers, how long would you wait until the center reaches 175C?.
3. If these composites were placed in an oven at 200C, estimate the time  it would take to heat the composite to 175C. Assume the heat transfer coefficient between the air and the composite is 10 W/mK

2. Viscosity Measurements:
Below you are given some of the measurements made using a cone and plate viscometer of the torque and angular velocities. The radius of the plate is 1 cm and the angle of the cone is 9 degrees (pi/20)

         Torque (N-m)             angular Speed (rad/s)
         2.08E-05 0                    .015707963
         2.08E-04                        0.157079633
         6.53E-04                         1.570796327
         2.12E-03                         15.70796327
         6.47E-03                         157.0796327

1. Find the parameters of this material if one were to use a three parameter Carreau fluid (the fourth parameter viscosity at very high shear rates is zero)
2. Find the two parameters if one were to use a two parameter power-law model
3. Using the power-law model determine the pressure drop required to pump this material at a flow rate of 100 cc/s through a circular tube of radius 1 cm that is one meter long.

3.Circulating slow flow of a viscous resin

A thin plate (thickness 2kH) moves with constant velocity V through a wide and long container (thickness 2H, where H<< length (L) and the width (W)) filled with an incompressible viscous liquid. The fluid circulates in the container, moving to the right along the central core and moving to the left close to the fixed wall of the container.

1. It is desired to find the velocity distribution in the container, away from the end disturbances. k is just slightly less than unity.
2. Also calculate the force, required to move the plate if we ignore the end disturbances in terms of the V, L,W,k,H and viscosity, m of the viscous fluid.
3. If you modify this set-up such that the plate was a circular fiber tow and the container was cylindrical, would any fluid impregate inside the fiber tow? Do you expect the most impregnation downstream or upstream ? Why ?

 

 
 












Assignment no:4

                                            Due Date: After Lecture18 (Nov 4th)


    I. PERMEABILITY CHARACTERIZATION EXPERIMENT
    The goal is to find the permeability of a glass fabric in one of its principal directions. The permeability characterization experiment will be performed for a selected fiber volume fraction with the fluid being injected under constant injection pressure.  A video camera will record the visible flow front progression through the transparent mold lid. A scale may be placed along the mold length to later extract the information of location of the flow front as a function of time

    Steps in the procedure

     Partially assemble the mold
    Carefully cut the fabric layers
    Stack the fabric layer in the mold cavity
    Close the mold
    Prepare the corn syrup and water mixture and measure its viscosity ( in the range of 50 to 500 cp) ( one cp is the viscosity of water)
    Place the fluid in the container and pressurize it.
    Inject the fluid into the mold with constant pressure at the inlet
    Record the motion of the flow front with the camera
    Stop the experiment when the fluid reaches the vent
    Dismantle the setup
    Clean-up the mold and the area
    Process the data to find the permeability

     The estimated duration of the experiment and clean up is 2.5 hours.

    Injection pressure to be obtained during the experiment: 15-20 psi (Please DO NOT exceed)

     Conduct the experiment in a group of 2 or 3 and find the permeability of the preform for the fiber volume fraction you used. Show all your calculations on how you obtained the permeability value. List possible errors in your experiments and recommend how you would improve the experiment. The group can share the experimental data but the report should be written individually.
 

    II. Dimensionless Analysis
The goal here is to non-dimensionalize the governing equation stated below which describe the flow through a dual scale fabric media.



     The resin impregnates from the left from a constant injection pressure, Pin. It will saturate the regions in between the fiber tows as shown in the figure below much faster than the resin in between the fiber tows. The permeability of the media in between the fiber tows is K_xx and the permeability inside the fiber tows is K_TOW. The length of the fluid domain is L and the radius of the fiber tows is R_TOW. The viscosity of the resin is  and S is the saturation of a fiber tow. S=1 implies complete saturation of the fiber tow and zero means it is still empty. Hence S is already dimensionless. Vi is the initial fiber volume fraction and vf is the final fiber volume fraction. vf tow is the fiber volume fraction in the fiber tow.

    1) Chose characteristic values for all variables, (that is for pressure,P, distance in the fluid domain,x, fiber volume fraction, vf  and time t) such that the dimensionless variables are of order one. For time, use tc as there is no obvious choice for tc

    2) Write the dimensionless form of the equation

    3) From the dimensionless form find what value should be used for tc?  What does this value physically signify?

    4) Group one important dimensionless parameter and comment on its significance in modeling the flow as dual scale porous media
 
 


 
 





Assignment no:5

                                            Due Date: After Lecture18 (Nov 20th)

For Distant Students:

I. Heat Generation in planar Poiseuille flow

 Consider planar Poiseuille flow of a very viscous material bewteen two parallel plates separated by distance h as shown below. Both plates are held at temperature To and the initial temperature of the material entering the parallel plates is also To. Find and sketch the temperature profile in the equilibrium, adiabatic and the transition regime. What is the maximum temperature difference and in which regime does it occur if


II. Pressure build up

  One way to create partially impregnated thermoplastic tape is to continuously pull the fiber preform through a step die that is filled with the thermoplastic melt of Newtonian viscosity, m, as shown below. By having a step change, the melt can be pressurized which will help partially impregnate the fiber tows. Find the relationship between maximum pressure, dimensions of the die and the pulling speed. Assume that the polymer impregnating the preform is negligible as compared to the amount in the die. Express your solution in non-dimensional form.


 
 

For in-class students

 

Problem-1 Example of Resin Transfer Molding (RTM) Process 

The first case involves infiltration of stationary fibrous porous media placed into a closed mold. The resin is injected under a positive constant pressure from one of the mold faces. The fill-time for this one dimensional filling can also be found analytically.

First, find the analytical solution for the case shown in Figure 1. Next, use the first model (Model1.dmp) to simulate the mold filling in LIMS. Use all the nodes on the left side of the mesh to model the injection gate. The material properties and the process parameters for this model are given in Table 1. See Figure 4 - Figure 9 for help in applying all of these properties. Compare the numerical fill-time with the analytical fill-time. Comment on your results.

Problem-2 Example of SCRIMP Process 

This case involves applying a vacuum to pull the resin at atmospheric pressure into the mold. To reduce the fill-time, a highly permeable porous media, also called as a distribution media, is usually placed on top of the preform (Figure 2).

Numerical modeling:

To model such scenario, use the second and the third models (Model2.dmp, Model3.dmp) as input geometry files for the LIMS simulation. These files contain mesh information only for preform. To model the distribution media, first add one-dimensional elements on top of the preform as follows in LIMS UI to create the distribution media:

1.click the select elements icon

2.click the select edge icon

3.click the create surface cover icon

4.click on any element along the top edge of the mesh – this will create a row of 1D elements over the 2-D mesh to simulate the distribution media

Next, assign the appropriate properties to the distribution media material:

1.click the filter select until it says 1-D

2.select all elements

3.adjust the permeability and volume fraction of distribution media as specified in Table 2

4.click the filter select until it says 2-D

5.select all elements

6.adjust permeability and volume fraction of preform as specified in Table 2

7.Save the altered file

Inject the resin from top-left corner of the model (i.e. use the node at the top-left corner of the model as injection gate).Find the fill-time for the complete filling of the part.

Crude analytical model:

Using the analytical solution developed in the first problem, find the time to completely fill the distribution media (Assuming that there is no resin flowing into the preform from the distribution media).Then using the average pressure in the distribution media, find the time to completely fill the preform in the thickness direction assuming 1D flow in the thickness direction.Add the times to fill the distribution media and the preform and compare the total with the numerical results.Comment on your results.

Approximate analytical model:

The analytical solution for the fill-time is developed by Hsiao et. al (2000)(Hsiao, K. T., Mathur, R., Gillespie, J. W., Fink, B. K., Advani, S. G., " A Closed Form Solution for the vacuum Assisted Resin Transfer Molding Process", Journal of Manufacturing Science, 122,pp. 463-472 (2000)). which will be supplied to you in the Excel file. The form of the model is as follows:



The abovementioned variables are explained in Figure 3. The important material properties are listed in Table-2, while the values of T₀ and D₀ can be assumed zero (assuming the flow develops instantaneously). Compare the analytical and numerical solutions for fill-times from all the cases and comment on the results.

Problem 3: Effect of distribution media on fill time

Change the distribution media permeability values to the following values and repeat problem 2 above.

• 5e-09 m²
• 1e-08 m²

List the numerical and analytical results for all the cases and comment on the ability of the distribution media to lower the fill time.

What else could you suggest to reduce fill time for this mold?





Figure 1
Schematic of the model for RTM process simulation




Figure 2 Schematic of the model for SCRIMP process simulations

Vf	K	Pinj	m
	M2	Pa	Pa s
0.5	1.00E-09	100000	1

Table 1 Material properties for the RTM process simulations.

	Preform		Distribution Media
Vf	Kxx	Kyy	Vf	K	Pinj	m
	m2	m2		m2	Pa	Pa s
0.55	1.00E-10	1.00E-12	0.1	1e-09	95000	0.1

Table 2 Material properties for SCRIMP process simulations.



Figure 3: Analytical model formulation

:

Figure 4: The LimsUI menu system with relevant commands



Figure 5: The node menu with resultant window



Figure 6: The element menu with resultant window



Figure 7: The resin menu with resultant window



Figure 8: The simulation window – make sure to set output file type to “Dump Results” and give a new filename



Figure 9: The results menu with resultant window
 
 


Assignment no:6

                                            Due Date: After Lecture23 (Dec 4th)

I A screw extruder is 50 mm in diameter, 1 m long, has a 50mm lead, a channel 5 mm deep and a flight 3 mm wide. It is used to pump a fluid with m = 5 x 105 poise and operates at a screw speed of 50 rpm.

a. What is the maximum possible flow rate of the extruder under the circumstances ? What is the maximum possible pressure ?

b. A die is attached to the end of the extruder, for which flow rate, is given as

Q = KDP/m,

where K=8.5 x 10-5 cm2. What flow rate and pressure result ?

c. Does the  flow rate and pressure  in Part  (b) change if the viscosity increases ?


 

2. Consider injection molding of a plaque 1 meter long, 50 centimeters wide and  0.25 centimeters thick. The injection is at one end of the plaque all along the width as shown in the figure below.



 

Two different plaques are to be manufactured. First one will contain polypropylene with 25% glass fibers which has an effective viscosity of 100 Poise and the second one contains nylon with 30% carbon fibers which has an effective viscosity of 1000 Poise. The mold wall is held at 25C. The polypropylene melt temperature is 175C and that of Nylon is 250C. The effective thermal conductivity of polypropylene with 25% glass is k= 1W/mC and that of Nylon with 30% carbon fibers is 10 W/mK. The injection rate is held constant at 100 cc/sec.

a. Find the approximate frozen layer thickness assuming fully developed flow away from the injection gate and the flow front for both, polypropylene and nylon

b. Find the maximum pressure that will be required approximately to fill the both the polypropylene and the nylon plaque.

c. If your marketing dept. wants to reduce the thickness of the plaque by half, how much pressure will the injection molding machine have to generate to fill the plaque under the same flow rate conditions?