Ceramic-matrix Composite Materials and Their Bending Properties

1. Making one plain plaster sample

1. Obtain a blue rubber mold from the instructor. Each mold can make 3 bar-shaped samples, the size of the each bar is roughly about 26 mm in the width, 43 mm in the length, and 10 mm in the thickness.
2. Weigh 40 grams of dry plaster powder into a paper cup. Slowly add 20 ml of deionized water, and stir the slurry with a wooden stick, until a smooth consistency is achieved. Proceed immediately to step 3! The plaster starts to harden in ~5 minutes.
3. Pour the resulting slurry into one of the compartments of the mold. Fill the mold completely, and smooth it over with the wooden stick. Throw away the cup and any excess plaster; keep the stick for future use.

2. Making two composite samples

1. Prepare the sample made with chopped fiber reinforcement:
   a.) Weigh 4 grams of chopped glass fibers into a paper cup.
   b.) Weigh 40 grams of plaster powder into the same cup.
   c.) Slowly add 20 ml of deionized water, and stir the slurry with the wooden stick, until the fibers are thoroughly mixed in, and a smooth consistency is achieved.
   d.) Pour the slurry into one of the mold compartments. Fill the mold completely, and smooth it over with the wooden stick.
2. Prepare the sample made with fiberglass tape:
   a.) Cut 2 strips of fiberglass tape, about 5 inches long. Weigh the strips.
   b.) Weigh 40 grams of dry plaster powder into a paper cup. Slowly add 20 ml of deionized water, and stir the slurry until a smooth consistency is achieved.
   c.) Pour about one third of the plaster into the mold. Place one strip of fiberglass tape on top of the plaster, and press it down with the wooden stick. Make sure that the plaster thoroughly wets the fiberglass tape.
   d.) Pour about half of the remaining plaster on top of the fiberglass tape. Place the second strip of tape on top of the plaster, and press it down with the wooden stick.
   e.) Pour the rest of the plaster on top of the second strip, and press it down with the wooden stick. Make sure that the plaster thoroughly wets the fiberglass tape, and squeeze out any air bubbles.

3. Performing experiments

1. Measure the average length, thickness and width of each bar Measure L (span length in the figure below) on the 3-point test fixture, use calibrated calipers for the measurement.
2. Use a displacement speed of 5 mm/min for all tests. (The UTM then should be zeroed and initiated at a displacement speed of 5mm/min). For the plain plaster and chopped fiber sample, run the test until the sample fails. For the fiberglass tape sample, run the test until the deflection is 6 mm.
3. Use the LabVIEW program on the computer to collect the data from each test into a text file.

4. MATLAB Program

1. Create a MATLAB program that will do the following:
2. Read a single column text file and separate the readings into force and deflection data. Convert the raw data into force and deflection using the following conversion factors:
   Force = (Load Cell Maximum Value / 30000) * Number generated by UTM (2)
   Deflection = 0.001mm * Number generated by UTM (3)
3. Calculate the flexural strength and flexural strain of each sample:
   Flexural strength σ_f = (3FL)/(2wt²)   (4)
   Flexural strain ε_f = (6Dt)/(L²)   (5)
4. Plot a stress-strain curve for each sample. Let ε_f be the horizontal axis and σ_f be the vertical axis.
5. Find the maximum σ_f and ε_f values for each sample. For the composite samples, select the ε_f value that corresponds to the maximum σ_f value.
6. Find the flexural modulus E_f by calculating the slope of the curve in the elastic region.
7. Find the area under each stress-strain curve.

5. Data Analysis

1. Comparison of the flexural strength and modulus of the composite samples to that of the plain plaster sample
   Since the UTM generates a single column text file, for both force and deflection, MATLAB interface has to sort the corresponding values into different arrays. Thus, to determine both the force and deflection needed for Equations 4 and 5, Equations 2 and 3 should be implemented into MATLAB.
   Using a Load Cell Maximum of 1000, the determination of flexural strength and strain is the combination of all equations. Since MATLAB also generates the stress-strain curve of each sample, the flexural modulus was ascertained by calculating the slope of the elastic region. Using Equation 6, the flexural modulus will be calculated with respect to the two selected points on the stress-strain plot:
     (6)
   Examining a sample data, we will see that as different forms of reinforcement are added, the strength of the samples will be increased, with fiberglass tape providing the greatest additional strength. In the terms of ductility, (which can be considered as the "most plastically deformable") the fiberglass tape reinforced specimen will be the greatest as well.
   Also, fiber length and orientation drastically affect the properties of composite samples. For example, maximum reinforcement can only be achieved when the fiberglass tape is set parallel to the surfaces of the specimen. In doing so, this spatial orientation allows the fiberglass tape to withstand additional forces as the plaster matrix fails. In addition, it can also be concluded that longer strips of fiberglass tape would prove to provide more strength than shorter strips. Longer pieces would allow for maximum traction under the conditions of a 3-point bending test, as there is more plaster surrounding the fiberglass reinforcement.
2. Energy absorption during bond test
   The area under the stress-strain curve represents the energy a material absorbs before failure. According to the results we will achieve, it will be shown that the fiberglass reinforced specimen absorbs the greatest amount of energy. In addition, since toughness corresponds to the ability of a material to absorb energy and plastically deform without fracturing and the fiberglass sample proved to be the most ductile by absorbing the greatest amount of energy; the fiberglass specimen is inherently the toughest amongst the three. Hence, toughness is the balance between strength and ductility, and the fiberglass sample had the largest area beneath its stress strain curve.
3. Calculation of the theoretical strength of the chopped fiber and fiberglass tape composites using the "rule of mixtures" formula (the relevant material properties are listed in Table 1).
   The theoretical strength of the composite can be calculated through Equation 1, where:
   V_F = volume fraction of fiber = (volume of fiber)/(total volume of the sample)
   Volume of fiber = (mass of fiber)/(density of fiber)
   Volume fraction of plaster = V_P = 1- V_F .

	Density, g/ml	Flexural strength, MPa
Chopped glass fibers	2.5	35
Fiberglass tape	0.45	35
Plaster	NA	NA

Table 1. Material properties.