Design, Strength, and Failure of Paleontology Plaster Jackets

Georgia Institute of Technology

School of Material Science and Engineering

771 Ferst Drive

J. Erskine Love Building

Atlanta, GA 30332-0245

MSE 3005 Mechanical Behavior of Materials

Final Group Project

April 2, 2016

Through

April 2-20, 2016

Tyler Rice

Group Members: Kinsey Canova, Jarad Heimer, Shannon Parker

Submitted on April 29, 2016

Abstract

In this experiment, the fracture toughness and strength of plaster were found by using

compression and three-point bending. These values were found using plaster bar samples with

and without notches, and the strength of plaster jackets used for protecting fossils was found.

The fracture toughness was found to be 0.0256 MPa m1/2, the strength of the plaster bars was

found to be 151 MPa, the strength of the jackets put under compression was found to be 4.35

MPa, and the first and second bending strength of the jackets were found to be 1.33 MPa and

3.47 MPa, respectively. The results found from the experiments were not exactly the same as

what was found in the literature, and are accounted for later in this report.

Introduction:

Plaster of Paris consist of Calcium Sulfate Hemihydrate, 𝐶𝑎𝑆𝑂4 ∙1

2𝐻2𝑂. This is formed

by heating gypsum to a temperature between 120°C and 160°C. The reaction is as follows:

𝐶𝑎𝑆𝑂4 ∙ 2𝐻2𝑂 ↔ 𝐶𝑎𝑆𝑂4 ∙1

2𝐻2𝑂 + 1

1

2𝐻2𝑂

When in reverse, this reaction is exothermic and allows for the interlocking needle-shaped

gypsum crystals that are seen in Plaster of Paris. Plaster of Paris is a brittle solid, and has fracture

properties similar to cement, sandstone, and many other porous ceramics [1]. Plaster of Paris is

the ideal ceramic to use when forming casts to protect and transport fossils.

Plaster molds are commonly used to produce nonferrous castings because it has a

smoother as-cast surface, better dimensional accuracy, and thinner sections than what can be

produced by other sand casting techniques [2]. Plaster of Paris is very easy to make. It just takes

two parts of plaster to one part of water to rehydrate it. It is then easily poured into molds and

begins to cure within ten minutes, but takes around 72 hours to fully cure [3].

In this experiment, the strength and fracture toughness of the Plaster of Paris was found

using various techniques. Flat slabs of the plaster were used to find the data in a three-point bend

and under compression. Small scale jackets that could possibly be used to protect a fossil were

then put under three-point bend and compression as well to find the data needed to calculate the

strength and fracture toughness of the specimens.

Procedure:

The plaster used in this experiment was made using the following instructions. Mix a ¼

cup of plaster with a 1/8 cup of water to get the consistency needed to form the strength, fracture

toughness, and jacket specimens. The mixture was mixed until there were no more clumps or

powder left. Then the mixture was used to form the specimens needed for the various test.

In order to form the specimens for the strength test, the plaster mixture was poured onto

cardboard wrapped in aluminum foil that was cut to fit five specimens on it. After the mixture

was poured, a fork was used to divide the plaster into five samples needed for the testing. The

plaster was then allowed to cure for three days. The following measurements were taken on the

third day for all samples using a digital caliber: length of specimen, width of specimen, and

thickness of specimen. After these measurements were taken, each sample had a gallon jug hung

from it, and water was poured into the jug until the sample broke. The weight of the setup was

measured before and after testing each sample, with the scale being tared before each test.

Figure 1 Set up for Strength Specimens

To form the specimens for the fracture toughness test, the plaster was poured onto

cardboard wrapped in aluminum foil that was cut to fit five specimens on it. After the mixture

was poured, a fork was used to divide the plaster into five samples, and add the notches needed

for the testing. The plaster was then allowed to cure for four days. The following measurements

were taken on the fourth day for all samples using a digital caliber: length of specimen, width of

specimen, notch length, and thickness of specimen.

Figure 2 Measuring Length of Notched Specimen

After these measurements were taken, each sample was then held upright by a team

member and a gallon jug was hung from it. Water was then poured into the jug until the sample

broke. The weight of the setup was taken before and after the testing for each sample, and the

scale was tared before each test.

Figure 3 Set Up for Notched Specimen

To form the specimens for the compression and bending of the plaster jackets,a plumbing

cover was first cut in half and then cut into pieces big enough to be tested. Then these pieces

were covered in saran wrap and had plaster was poured onto them. The plaster was then spread

out using forks and butter knives to get the desired thickness and length of the flanges.

Figure 4 Making of the Jacket Specimens

These samples were then allowed to cure for three days. The following measurements

were taken on the third day for all samples using a digital caliber: length of each flange, radius of

curvature, width, and thickness of specimen.

For the compression of the plaster jackets, the jacket was laid on a flat surface while a

team member held a gallon jug in place on top of the arc of the jacket. Then, another team

member poured water into the gallon jug until the jacket broke. The weight of the set up was

taken before and after for each sample, and the scale was tared before each test.

Figure 5 Set Up for Compression of Jacket Specimens

For the first bending experiment, each sample had a gallon jug hung from it, and water

was poured into the jug until the sample broke. The weight of the set up was taken before and

after for each sample, and the scale was tared before each test.

Figure 6 Set Up for First Bending of Jacket Specimens

To form the specimens for the second bending experiment of the plaster jackets, a

plumbing cover was first cut in half and then cut into pieces big enough to be tested. Then these

pieces were covered in saran wrap. Plaster was made with three to one ratio of plaster to water,

and then poured onto the saran wrapped models. The plaster was then spread out using forks and

butter knives to get the desired thickness and length of the flanges. These samples were allowed

to cure for 48 hours. The samples were then sanded, and the following measurements were taken

for all samples using a digital caliber: length of each flange, radius of curvature, width, and

thickness of specimen. Then one of the flanges of each sample was hung after being clamped by

a wremch, while the other flange had a gallon jug hung from it. Water was then added to the jug

until fracture occurred. The gallon jug was weighed before and after each experiment, and the

scale was tared before each test.

Figure 7 Second Bending Experiment

Results:

Table 1. Raw Data for Strength Test (Three Point Bend)

Sample Length (m) Width (m) Thickness(m) Load(lbs)

1 0.06 0.01483 0.00289 1.14

2 0.06 0.0179 0.00331 2.4

3 0.07 0.0155 .00264 1.6

4 0.067 0.0169 0.00399 2.3

5 0.07085 0.0137 0.00394 2

6 0.065 0.0177 0.00395 3.2

Table 2. Raw Data for Fracture Toughness (Compression)

Sample Length (m) Thickness (m) Notch (m) Width (m) Load (lbs)

1 0.0503 0.00294 0.00564 0.01839 6.6

2 0.03999 0.00444 0.00428 0.01723 2.2

3 0.03616 0.00203 0.00646 0.01852 4

4 0.03477 0.00358 0.00427 0.01933 7.6

6 0.03691 0.00224 0.00139 0.00964 1.2

7 0.03956 0.00166 0.00219 0.01335 1.6

8 0.04126 0.00246 0.00244 0.01446 1.4

Table 3. Raw Data for Compression of Plaster Jackets

Sample Radius (m) Thickness

(m)

Right

Flange (m)

Left Flange

(m)

Load (lbs) Width (m)

1 0.0246 0.00115 0.02852 0.02871 1.4 0.03092

2 0.02502 0.00246 0.02838 0.04914 1 0.02016

3 0.02594 0.00435 0.03125 0.02866 4.4 0.03068

4 0.02633 0.00243 0.03139 0.02933 3 0.02879

5 0.02563 0.00441 0.03037 0.03463 2.4 0.03205

11 0.02714 0.00454 0.03511 0.06499 2.6 0.02264

Table 4. Raw Data for First Bending of Plaster Jackets


(m)

Right

Flange (m)

Left Flange

(m)


6 0.02349 0.00409 0.04039 0.0244 2.2 0.03649

7 0.02513 0.00325 0.03542 0.03069 0.6 0.02645

8 0.0263 0.00299 0.02387 0.03596 1 0.03294

9 0.02771 0.00353 0.03307 0.04603 0.6 0.03111

10 0.02776 0.0035 0.02645 0.02682 3 0.02964

Table 5. Raw Data for Second Bending of Plaster Jackets


(m)

Right

Flange (m)

Left Flange

(m)


1 0.02475 0.00207 0.02595 0.04162 0.46875 0.02914

2 0.0245 0.00208 0.03226 0.0281 0.9075 0.03124

3 0.024975 0.00209 0.03332 0.0385 0.8825 0.03953

4 0.02497 0.00313 0.0281 0.03831 1.955 0.03435

5 0.02496 0.00283 0.0312 0.0343 1.4025 0.03615

The following equations were used to find the Stress of the Plaster Bars [4].

𝜎 =𝑀𝑌

𝐼 (1)

Where

𝑀 =𝐹

2=

𝐿𝑜𝑎𝑑∗0.45359237

2 (2)

𝑌 = 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠

2 (3)

𝐼 =𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠∗𝑊𝑖𝑑𝑡ℎ3

13 (4)

Table 6. Strength of Three Point Bend Plaster Bars

Sample Number Stress (Pa)

1 1.51E+08

2 1.63E+08

3 1.98E+08

4 1.14E+08

5 1.25E+08

6 1.55E+08

Average 1.51E+08

Standard Deviation 26920863.13

The following equations were used to find the Fracture Toughness of the Plaster Bars [4].

𝐾𝐼𝐶 = 𝑓(𝑎

𝑊)

𝑃

𝐵√𝑊 (5)

Where:

𝑓 (𝑎

𝑊) =

3𝑆

𝑊√

𝑎

𝑊

2(1+2𝑎

𝑊)(1−

𝑎

𝑊)

32

[1.99 −𝑎

𝑊(1 −

𝑎

𝑊) ∗ {2.15 − 3.93 (

𝑎

𝑊) + 2.7 (

𝑎

𝑊)2}] (6)

Table 7. Fracture Toughness of Plaster Bars

Sample KIC (Pa m1/2)

1 58593.55652

2 9184.685291

3 42298.25288

4 25922.06963

6 14192.86712

7 18416.26292

8 10273.15159

Average 25554.40656


The following equations were used to find the stress of Compression of the Plaster

Jackets [4].

𝜎 =𝑀𝑌

𝐼 (7)

Where:

𝑀 =𝐹𝑜𝑟𝑐𝑒

2∗ 𝑅𝑎𝑑𝑖𝑢𝑠 (8)


2 (9)

𝐼 = 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠∗𝑊𝑖𝑑𝑡ℎ3

12 (10)

Table 8. Stress found from Compression of the Plaster Jackets

Sample Stress (Pa)

1 11231585

2 2734889

3 2621814

4 6196279

5 1316036

11 2016546

Average 4352858.051


The following equations were used to find the stress of the plaster jackets under a three

point bend [4].

𝜎 =𝑀𝑌

𝐼 (11)

Where:

𝑀 = 𝐹𝑜𝑟𝑐𝑒 ∗ 𝑅𝑎𝑑𝑖𝑢𝑠 (12)


2 (13)

𝐼 =𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠∗𝑊𝑖𝑑𝑡ℎ3

12 (14)

Table 9. First Set of Plaster Jackets Under Three Point Bend

Sample Stress (Pa)

6 1129011

7 719721.4

8 1190976

9 571941.3

10 3058718

Average 1334073.587


Table 10. Second Set of Plaster Jackets Under Three Point Bend

Sample Stress (Pa)

1 2478160

2 4387510

3 3404426

4 3868385

5 3224849

Average 3472665.928


Figure 8 Fracture Surface for Bending of Plaster Bar

Figure 9 Fracture Surface for Compression of Plaster Bar

Figure 10 Fracture Surface for Compression of Plaster Jacket

Figure 11 Fracture Surface for First Bending of Plaster Jackets

Figure 12 Fracture Surface of Second Bending of Plaster Jacket

Discussion:

As seen in Figures 8-12, all the fractures are brittle fractures. This can be determined

because all of the fractures appear caused by a pore, or a pre-notch. It is also seen in the figures

that they are brittle fractures because no necking occurs. If any necking had occurred, then it

would have been a ductile fracture. The fracture surfaces are also rough, which is a sign of brittle

fracture.

In the literature, it was found that the fracture toughness of the plaster is 0.14±0.015 MPa

m1/2 [1]. From the experiments, it was found that the average fracture toughness of the plaster is

0.0256 MPa m1/2. It was also found in the literature that the tensile strength of Plaster of Paris is

3.2±0.6 MPa [1]. From the experiments performed, the average strength for the plaster bars was

found to be 151 MPa, the average stress due to the compression of the plaster jackets was found

to be 4.35 MPa, the average stress due to the first bending done on the plaster jackets was found

to be 1.33 MPa, and the average stress due to the second bending done on the plaster jackets was

found to be 3.47 MPa.

There are many possible reasons that the fracture toughness experiment was considerably

low compared to the literature. One of them is that the viscosity of the plaster mix between

different samples could different. This could be caused by different plaster to water ratios being

used when mixing the plaster. The ratio being inconsistent would have casued the viscosity to be

different. Along with that, there caould have been pores in the samples, allowing for a brittle

break. Pores would have made it easier for the samples to break. Pores could have formed as

water evaporated out of the samples as they cured.

On average, the strength of the plaster jackets ended up being close to what was found in

the literature. The strength of the plaster bars is very high compared to what the literature says.

The difference between the experimental and literature strengths could be caused by one of the

errors from calculating fracture toughness: either viscosity differences between samples, or the

formation of pores during the curing process. Another error that could have occurred is human

error when calculating the strength. It is possible that the wrong equations were used, wrong

assumptions were made, or errors when calculating occurred.

The assumptions made in all of the calculations were that the samples had a uniform

thickness throughout, along with the width and radius of the jackets. This is not true for any of

the samples with the thickness, width, and radius of the jackets being inconsistent throughout due

to the way the plaster samples were molded. Also, when calculating the strength of the plaster

jackets, it was assumed that the area affected the most was rectangular in shape to make

calculating Equations 4, 10, 14 easier. It is a good assumption, but it is not accurate. It does not

take into consideration that the samples are semi-circles with flanges.

The strength of the jacket specimens was predicted to be around the same strength as the

plaster bars that were first tested. This was not the case. As seen in the literature mentioned

earlier, the jackets were close to it, but the plaster bars were far from what was in the literature.

They are different because of the possible errors discussed earlier about the viscosity, pores, and

human error in math calculations.

Conclusion:

In conclusion, all of the specimens broke as they were expected to break, with a brittle

fracture that starts from either a pre-notch, or from a pore in the material. The stress that it took

for the specimens to break was not as expected. This could be caused by different viscosities

among the samples, different amount of pores present in each sample, and human error in the

calculating the stress. Plaster of Paris is known to be a porous material, which is why it makes it

ideal for the protection of fossils. It is easy to make on site, and is strong enough to protect the

fossils as seen in the experiments. It can withstand the stresses due to the transportation of the

fossils, and if it was dropped it would possibly protect the fossil by either absorbing all the force

and breaking or by absorbing the force and not breaking.

References:

1. G. Vekinis, M.F. Ashby, P.W.R. Beaumont, Plaster of Paris as a Model Material for

Brittle Porous Solids, Journal of Materials Science, Cambridge University Engineering

Department, Cambridge, 1993.

2. Thomas S. Piwonka, Plaster Casting, Molding Methods, ASM Handbooks Online, The

University of Alabama, 2002. Retrieved from:

http://products.asminternational.org/hbk/do/section/content/MH/D26/A03/S0079547.htm

l?anchor=_top&highlight=true&start=0.

3. A. J. Parmar, S. K. Tyagi, V. S. Dabas, J. N. Mistry, S. K. Jhala, D. N Suthar, R. H.

Bhatt, D. V. Pansuria, I. M. Bhatti, Assessment of the Physical and Mechanical

Properties of Plaster of Paris Bandage Cast Used as a Splinting and Casting Materials,

Veterinary World, December 2014.

4. Marc Meyers, Krishan Chawla, Mechanical Behaviors of Materials, Cambridge, MA:

Cambridge Univeristy Press, 2008.

http://products.asminternational.org/hbk/do/section/content/MH/D26/A03/S0079547.html?anchor=_top&highlight=true&start=0

http://products.asminternational.org/hbk/do/section/content/MH/D26/A03/S0079547.html?anchor=_top&highlight=true&start=0