Design, Strength and Failure of Paleobiology Plaster Jackets

Keshav Swarup MSE 3005: Mechanical Behavior of Materials
4/28/2016 Final Project
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MSE 3005: Mechanical Behavior of Materials
Final Project
Design, Strength, and Failure of Paleobiology Plaster Jackets
Name: Keshav Swarup
Group Members: Tim Widing, Mari Nguyen, Ryan Dwyer
This lab report being submitted was completed on my own and is consistent with Georgia Tech’s
Academic Honor Code and Student Code of Conduct. Any collaboration and/or references will be
explicitly stated.
Signature: ______________________
Date: 4/29/2016
Abstract
This investigation studies the effectiveness of a plaster of Paris paleobiology jacket in protecting
a given jaw bone fossil model. The plaster’s strength and fracture toughness was initially evaluated
and found to be 5.178 ± 1.488 MPa and 0.304 ± 0.097 MPa√m, respectively. These results were
used to estimate the strength of the jacket test specimen and tested to evaluate the accuracy of our
predictions. Our prediction was that the measured strength would be lower but the jacket strength
proved to be slightly higher in the case of the bending test (5.232 ± 2.428 MPa) and significantly
lower for the compression test (3.372 ± 1.056 MPa). Comparisons to the predicted values and
literature values indicated differences attributed to geometric variability, differences in stress
distribution, fabrication conditions as well as varied testing methods.

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1. Introduction
Plaster of Paris, also known as Gypsum plaster or Calcium Sulphate hemihydrate (CaSO4½H2O),
is made by heating gypsum between 120°C and 160°C with the following reaction:
CaSO4 H2O  CaSO4½H2O + 1½ H2O
When mixed with water, the reverse reaction takes place as water is reabsorbed with the formation
of gypsum. The reaction is exothermic, releasing heat, and results in a coherent mass of
interlocking needle-shaped gypsum crystals. [1]
DAP Plaster of Paris was used for the purpose of the experiments in this project, made up of Plaster
of Paris (75 – 100 wt.%), Limestone (10 – 25 wt.%) and Quartz (1.0 – 2.5 wt.%) [1]. The setting
of unmodified plaster is known to start in about 10 min after mixing and be complete in about 45
minutes; but not fully set for 72 hours [2]. A shorter time was selected for the purpose of our
experiment (24 hours) due to time constraint and observed completion of the drying process. These
processing conditions specifically affect strength and fracture toughness, especially the water to
plaster mixing ratio, as well as the amount of time the plaster is allowed to set. We built a plaster
paleobiology jacket in order to protect the given jaw bone fossil model. The structure was designed
to completely cover the specimen’s widest portion with a single, circular arc-shape that has a flange
on either side, as illustrated by Figure 1.
Figure 1: Cross-sectional depiction of the plaster jacket’s geometry (arc and flange dimensions)
We tested and characterized the jacket’s strength and fracture toughness by first by evaluating the
strength and fracture toughness of the plaster, before proceeding to estimate the strength of our
idealized plaster jacket test specimen. We then finally tested the idealized plaster jacket specimen
to evaluate the accuracy of our estimate.

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2. Experimental
Cylindrical specimen were fabricated using a 2:1 plaster to water mixing ratio. A mass scale was
utilized for a precise method to weigh out the exact amounts. A spoon with a cylindrical handle
was used. The spoon’s handle was wrapped in aluminum foil, and carefully removed foil to create
and maintain shape of the foil. Filled foil with plaster-water mix and allowed it to set for
approximately 24 hours. Specimen were approximately 1cm in diameter and 8cm in length. Five
were left un-notched for strength tests and five had a 2cm notch cut in them with a kitchen knife,
for the fracture toughness tests, as shown in Figures 2.1 and 2.2 below, respectively.
Figure 2.1: Un-notched cylindrical specimen Figure 2.2: Notched cylindrical specimen
Full jacket specimen were fabricated using a machined stainless steel mold, as seen in Figure 3.
The flange length (F) was designed to be greater than the radius of the circular arc-shape (R).
Figure 3: (a) Stainless steel machining process for fabrication of (b) final plaster jacket mold
A similar 2:1 mixing ratio was used with 1.5 cups of plaster of Paris powder and 0.75 cups of
water. This mix was gently poured over a sheet of wax paper that was laid on the mold to facilitate
ease of removal upon drying. After 15 minutes, a butter knife was used to laterally cut the total
cast into three separate pieces. A spoon was used to shape out the mold and even out the thickness.
(a)
(b)

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It was allowed to set for approximately 3 hours, before separating the jacket off the mold and
removing the wax paper. It was then left to dry for approximately another 20-21 hours. The
cylindrical specimen were tested for strength and fracture toughness in order to estimate the
performance of our plaster jacket specimen, with five trials for each test.
For the strength test, we conducted a 3-point bending test on five samples, while keeping all factors
constant (geometry, cure time, water/powder ratio, etc.). The setup was created with the cylindrical
specimen resting on two inverted glasses as supports, and were taped down after being placed on
a mass balance, as shown in Figure 4.
Figure 4: Experimental setup for 3-point bending strength test of cylindrical specimen
A thread was used to apply a downward force at the center of the cylindrical specimen, and the
mass balance was used to quantify the force based on the mass change. A slow-motion video was
used to capture the exact mass change at the precise moment of fracture.
A similar setup was used for the fracture toughness test. Five cylindrical specimen were tested in
the same manner, with a 0.2 cm thick notch cut in each specimen.
The strength of the plaster jackets was measured using two loading modes, i.e. compression with
a single load applied at the top (center) of the arc while the flanges rest on a flat surface, and
bending (flexure), when the specimen is held (gripped) at the flanges.
The compression test was conducted on five plaster jackets by resting the jacket on a sheet of
cardboard and placing it on a mass balance and a downward force was applied by pressing the
center of the circular arc surface. The mass balance was used to measure the mass change and
thereby quantify the force upon fracture.

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The setup is illustrated in Figure 5 below:
Figure 5: Experimental setup for compression strength test of plaster jacket
The bending (flexure) test was conducted on five plaster jackets by holding down one flange of
the jacket to a flat surface using duct tape, which acted as a grip. A force was applied on the other
flange using a cup, with a known mass, while gradually pouring small increments of water into the
cup until a force large enough was generated to fracture the jacket. The experimental setup is
illustrated in Figure 6 below:
Figure 6: Experimental setup for bending strength test of plaster jacket

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The strength of the cylindrical specimen was measured using Equation 4, which was derived from
a series of equations (1-4) based on a 3-point bending free body diagram, described below:
σ =
My
I
(1)
where M is the moment (Nm), y is the distance from neutral axis (m) and I is the moment of
sections. I and M were determined using equations 2 and 3, respectively.
I =
πr4
4
(2)
where r (m) is the radius of the cylindrical specimen
M =
F
2
×
l
2
(3)
where F is the downward force applied at the center of the arc (N) and l is the length of the
specimen (m). Inserting equations 2 and 3 into 1, and simplifying, the strength of the specimen
can be calculated using equation 4:
σ =
F l
πr3 (4)
The fracture toughness of the cylindrical notched specimen was calculated based on the fracture
stress equation 5, as described below:
KIC = 1.22σ√πa (5)
The above stress intensity equation and geometry factor (1.22) was chosen based on the loading
configuration and the fact that the crack tip was at the surface and not internal to the specimen.
The strength of the plaster jacket was calculated by making an assumption that the jacket behaves
like a beam in both compression and bending tests. Although this assumption fails to account for
the geometrical differences and would thus not be accurate, it was done to simplify the calculation.

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The following free body diagrams illustrate the calculation method in Figure 7:
Figure 7: Free body diagrams for calculation of jacket strength for (a) Compression test (b)
Compression test with beam assumption (c) Bending test (d) Bending test with beam assumption
For the compression test, strength was calculated from a series of equations (6-9) based on a 3-
point bending diagram, described below:
σ =
My
I
(6)
where M is the moment (Nm), y is the half the thickness of the arc (m), and I is the moment of
I =
bh3
12
(7)
where b (m) is the width of the arc and h (m) is the thickness of the arc
M =
P
2
× L =
∆mgL
2
(8)
where P is the downward force applied at the center of the arc (N) measured by the mass change
(Δm) using the scale (kg), L is the length illustrated in Figures 6 (a) and (b). Inserting equations 7
and 8 into 6, and simplifying, the strength of the specimen can be calculated using equation 9:
σ =
3∆mgL
bh2 (9)
(d)
(a)
(b)
(c)

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For the bending test, strength was calculated from a series of equations (10-13) based on a 3-point
bending diagram, described below:
σ =
My
I
(10)
where M is the moment (Nm), y is the half the thickness (h) in metres, and I is the moment of
I =
bh3
12
(11)
where b (m) is the width of the arc and h (m) is the thickness of the arc
M = P × L = ∆mgL (12)
where P is the downward force applied at the non-fixed flange (N) measured by the mass change
(Δm) using the scale (kg), L is the length illustrated in Figures 6 (c) and (d). Inserting equations
11 and 12 into 10, and simplifying, the strength of the specimen can be calculated using equation
13:
σ =
6∆mgL
bh2
(13)
The dimensions of the cylindrical samples and their corresponding mass change for the 3-point
bending strength and fracture toughness tests, are described in Tables 1.1 and 1.2, respectively.
Table 1.1: Raw data for 3-point bending strength test on cylindrical specimen
Specimen Diameter (cm) Length (cm) Mass Change (kg)
1 1.2 8.3 4.750
2 1.1 8.3 4.607
3 1.2 8.2 4.739
4 1.3 8.4 3.951
5 1.2 8.2 3.055
Table 1.2: Raw data for 3-point bending fracture toughness test on cylindrical specimen
Specimen Diameter (cm) Length (cm) Mass Change (kg)
1 1.1 8.1 2.430
2 1.3 8.0 2.940
3 1.2 8.2 4.249
4 1.3 8.2 2.352
5 1.2 8.1 2.990
Note: Notch thickness was 0.2cm for all five specimen

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The dimensions of the plaster jacket samples and their corresponding mass change for the
compression and bending strength tests, are described in Tables 2.1 and 2.2, respectively.
Table 2.1: Raw data for compression strength test on plaster jacket specimen
Specimen
Flange
Thickness (cm)
Arc Thickness
(cm)
Flange
Length (cm)
Arc Width
(cm)
Arc Radius
(cm)
Mass
change (kg)
1 0.35 0.30 7.40 7.20 6.60 0.629
2 0.30 0.35 8.10 8.40 7.05 1.288
3 0.40 0.40 8.20 6.80 6.40 0.706
4 0.40 0.30 8.40 8.60 7.25 0.713
5 0.25 0.20 7.10 8.10 7.10 0.488
Table 2.2: Raw data for bending strength test on plaster jacket specimen
Specimen
Flange
Thickness (cm)
Arc Thickness
(cm)
Flange
Length (cm)
Arc Width
(cm)
Arc Radius
(cm)
Mass
change (kg)
1 0.40 0.30 7.40 8.10 7.10 0.222
2 0.20 0.25 7.20 8.10 7.00 0.170
3 0.45 0.30 7.40 8.00 6.90 0.272
4 0.30 0.20 7.50 8.10 6.75 0.101
5 0.30 0.20 7.50 8.00 7.00 0.241
Results from the 3-point bending strength and fracture toughness tests conducted on the cylindrical
specimen are summarized in Tables 3.1 and 3.2, respectively.
Table 3.1: Calculated fracture stress for strength test on cylindrical specimen
Specimen Fracture Stress (MPa)
1 5.700
2 7.177
3 5.618
4 3.774
5 3.622

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Table 3.2: Calculated fracture stress and fracture toughness for fracture toughness test on notched
cylindrical specimen
Specimen Fracture Stress (MPa) Fracture Toughness
1 3.694 0.328
2 2.674 0.237
3 5.037 0.447
4 2.193 0.195
5 3.501 0.311
Results from the compression and bending strength tests conducted on the plaster jacket are
summarized in Table 4 below.
Table 4: Calculated values for strength test on plaster jacket
Specimen
Compression Test
Fracture Stress (MPa)
Bending Test
Fracture Stress (MPa)
1 2.942 3.872
2 4.089 4.190
3 2.005 4.714
4 3.104 3.853
5 4.721 9.531
Statistical analysis of the results from strength test and fracture toughness tests conducted on the
cylindrical specimen are summarized in Table 5.
Table 5: Statistics for strength and fracture toughness tests for cylindrical specimen
Specimen Statistic Fracture Stress (MPa) Fracture Toughness (MPa√m)
Un-notched
Mean 5.178 -
Std. Dev. 1.488 -
Notched
Mean 3.420 0.304
Std. Dev. 1.091 0.097

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Statistical analysis of the results from compression and bending strength tests conducted on the
plaster jacket are summarized in Table 6.
Table 6: Statistics for compression and bending strength tests for plaster jacket
Strength Test Mean Fracture Stress (MPa) Fracture Stress Std. Dev. (MPa)
Compression 3.372 1.056
Bending 5.232 2.428
Fracture surface analysis was done using visual interpretation with the help of photos taken from
a camera. A combination of brittle and ductile fracture was observed, with the former being the
predominant type. Fracture dimensions and surfaces for strength tests conducted on un-notched
and notched cylindrical specimen are illustrated in Figures 8 and 9, respectively.
Figure 8: Un-notched cylindrical specimen (a) Fracture dimensions and (b) fracture surfaces
Figure 9: Notched cylindrical specimen (a) Fracture dimensions and (b) fracture surfaces
(a) (b)
(a) (b)

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Fracture surfaces for strength tests conducted on the jacket specimen are illustrated in Figure 10
below.
Figure 10: Fracture surfaces of plaster jacket for (a) Compression test and (b) Bending test
As seen in the above figures, it can be gathered that there are significant cracks present in the
fracture surface, indicating that brittle fracture occurred during the strength tests. This applies to
both the cylindrical specimen, as well as the jacket specimen. These cracks could have been created
during the fabrication process of the specimen or during fracture in itself.
With regards to the origin of the fracture, it is most likely to be associated with the part of the
specimen that is in tension at the location of the applied force. This is because ceramics tend to
fracture at smaller loads under tension. For the cylindrical specimen tests, it would be under tension
at the bottom surface at the location where the downward force was applied for both notched and
un-notched specimen. For the jacket specimen, the origin of the fracture varied between the
compression and bending strength tests. For the former, the origin of the fracture would be at the
bottom surface at the center of the arc. This is the portion of the jacket that is under tension.
However, for the latter test, the jacket would be under tension at the top surface of the center of
the arc when one flange was pinned and the downward force was at the other non-fixed flange.
3. Discussion
We decided to use cylindrical specimens for our strength and fracture toughness tests for the sake
of easy geometry. As described in the earlier sections, it was fabricated using an aluminum foil-
wrapped cylindrical spoon handle as a mold. This specimen geometry allowed for simplified
calculations in the process of calculating fracture stress.
For the jacket design, the mold was machined using sheet metal, as illustrated in Figure 3 earlier,
in the Invention Studio. The placement of a sheet of wax paper over the sheet metal aided in the
process of removal and separation of the plaster from the mold. The ratio of mixing plaster of Paris
with water was decided to be 2:1 based on the directions on the box of plaster. The dimensions of
(a) (b)

Page 13 of 15
the jacket were calculated based on the size of the fossil and the dimensional requirements for the
flange and arc, as explained by Figure 1.
Plaster of Paris fails under tension and exhibits brittle fracture. This is very common as with almost
all or most ceramics because of the unavoidable presence of microscopic flaws such as micro-
cracks, internal pores, and atmospheric contaminants. These are formed during cooling from the
melt. This leads to crack formation and propagation orthogonal to the applied stress, and is usually
transgranular along cleavage planes. The flaws cannot be closely controlled in the manufacturing
process and hence leads to large variations in the fracture strength of plaster of Paris, and ceramics
in general. [3]
The mean fracture strength was 5.178 ± 1.488 MPa for the un-notched cylindrical specimen. This
was fairly accurate with a 10.7% error when compared to the literature value for the modulus of
rupture of plaster of Paris (5.8 ± 0.6 MPa). [4] The mean fracture toughness was 0.304 ± 0.097
MPa√m for the notched cylindrical specimen. This was relatively inaccurate with a 117% error
when compared to the theoretical value for the single-edge notched bend (SENB) fracture
toughness of plaster of Paris (0.14 ± 0.015 MPa√m). [4]
The strength results for un-notched specimen are relatively comparable (10.7% error) due to the
same geometry used as Vekinis et. al., i.e. choice of cylindrical specimen, and this would play a
role in the calculations done using the 3-point bending test free body diagram, as described in
equations 1 – 4 earlier. The variation between experimental and theoretical values for fracture
toughness (117% error) could be due to several reasons. Firstly, the processing conditions quoted
in the literature indicate a mixing ratio of 100:62.5, whereas our procedure involved a 2:1 ratio.
Secondly, the geometrical differences of the samples also need to be considered as some of the
literature experiments were conducted on rectangular specimen. Lastly, Vekinis et. al. reports a
cure time of 7 days while our procedure only allowed the plaster to set for a minimum required
duration of 24 hours on average, due to our time constraint. In addition to specific deviations in
the processing conditions, there is also the equipment limitation that needs to be accounted for as
our experiment was conducted using basic apparatus and a simplified setup based on available
materials. Sophisticated lab testing machinery was used by Vekinis et. al. and hence led to the
accuracy of their results.
The calculation of strength and fracture toughness required several assumptions to be made for
various reasons. For all specimen, including cylindrical as well as the plaster jacket, we assumed
that they are symmetrical, uniform and homogenous throughout. This ignores the porosity and
non-uniformity of the samples due to the limitations of our fabrication process. Based on the same
assumption we applied simple beam statics to the 3-point bending test, as well as the
compressive/bending strength tests on the jacket as illustrated earlier in Figure 7. This assumption
that the U-shape jacket can be taken as a beam, is a limitation as it does not account for the
geometrical complexity of the jacket, with the semi-circular arc as well as the flanges and hence
limits the accuracy of our strength/fracture toughness results. We also simplified the beam statics

Page 14 of 15
by calculating the moments under the assumption that all forces were applied at a fixed location
instead of being distributed. Specifically for the compression test, we took the force applied by our
finger at the center of the arc to be a point force and the reactionary support force from the
cardboard sheet to be at the center of the flanges, as seen in Figure 7 (a) and (b). For the bending
test, we took the flange fixed by the duct tape clamp as a pin support, illustrated in Figure (c) and
(d). Also, the cross-section of the jacket was taken to be rectangular for the purpose of the moment
of inertia.
The above assumptions and their consequent limitations can thus be attributed to variation in
fabrication and testing methods/conditions. Strength results would definitely be lower than
expected if the time allowed for the plaster to dry was less than the optimum duration (24 hours),
which was the case for some samples. Odd fracture toughness results can thus be predicted to
deviate from the literature because of the geometry variability and stress distribution since the
stress intensity factor equation and the geometry factor is challenging to predict accurately.
A secondary limitation that also needs to be factored in would be the fractography of the specimen
in terms of fracture surface analysis. The lack of suitable imaging equipment or software such as
an electron microscope prevented us from making accurate topographical observations such as the
determination of crack growth or origin.
We used the 3-point bending test results for the un-notched cylindrical specimen’s mean fracture
stress to predict the jacket strength, i.e. 5.178 ± 1.488 MPa. However, we anticipated a slightly
lower strength value due to the U-shape which could prove to allow brittle fracture for smaller
loads at the circular arc portion. For the compression strength test, the mean experimental strength
of our plaster jacket was found to be 3.372 ± 1.056 MPa. This implied a relatively inaccurate value
with a 34.87% error when compared to our predicted value based on the cylindrical specimen
(5.178 ± 1.488 MPa). The jacket strength is lower than the cylindrical specimen which is as
expected and thus justifies the error. This discrepancy can be attributed to the differences in
fabrication and testing methods/conditions for our jacket as compared to our cylindrical specimen.
This would also be attributed to the previously described geometry variability between the
cylindrical specimen and the U-shaped jacket. There is also the factor of the loading conditions
that affect the stress distribution between the cylindrical specimen and the jacket. For the bending
strength test, the mean experimental strength of the plaster jacket obtained was 5.232 ± 2.428 MPa.
This is a slightly higher value with 1.04% error when compared to our predicted value based on
the cylindrical specimen (5.178 ± 1.488 MPa). The reason for this similarity could be the testing
conditions as the use of duct tape as a clamp proved to be a very effective method for fixing one
of the two flanges, resulting in a practical flexure test setup. Also, the circular arc-shape might
have compensated for the lower threshold of the jacket’s fracture stress by providing added
flexibility when subject to flexure.

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4. Conclusions
This investigation was able to successfully prove the effectiveness of the paleobiology jacket we
built, in protecting the given jaw bone fossil model. This was achieved by initially evaluating
cylindrical specimen fabricated to test the strength and fracture toughness of the plaster of Paris
used to make the jacket. These proved to be 5.178 ± 1.488 MPa and 0.304 ± 0.097 MPa√m,
respectively. The above results were used to estimate the strength of our jacket test specimen and
then later tested to evaluate the accuracy of our predictions. Despite our prediction that the
measured values might be lower, the measured jacket strength proved to be highly accurate in the
case of the bending test (1.04% error) but relatively inaccurate for the compression test (34.87%).
The accuracy for the former was attributed to the setup and the U-shape’s added flexibility that
compensated for the lower strength of the jacket. In the case of the latter, the jacket’s significantly
lower fracture stress was due to the vulnerability of the circular arc, geometric variability,
differences in stress distribution, fabrication conditions as well as testing methods between the
cylindrical specimen and the jacket. In summary, the overall predictions made were highly
effective in allowing us to reach the conclusion that the jacket is able to successfully protect the
fossil, and specifically more so in bending than under compression.
References
[1] DAP, Plaster of Paris Safety Data Sheet, Baltimore, Maryland, 2015.
[2] Parmar et. al., "Assessment of the physical and mechanical properties of plaster of Paris,"
Veterinary World, pp. 1123-1126, 2014.
[3] U. o. Virginia, "Chapter 13. Ceramics - Structures and Properties," [Online]. Available:
http://www.virginia.edu/bohr/mse209/chapter13.htm.
[4] Vekinis et. al., "Plaster of Paris as a model material for brittle," Journal of Materials Science,
vol. 28, pp. 3221-3227, 1993.

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