MSE 3005 Mechanical Behavior of Materials

Laboratory I: Strength and Fracture Toughness of Plaster of Paris

Part I: March 31, 2016

Part II: April 02, 2016

Part III: April 05, 2016

Part IV: April 19, 2016

Shannon Parker

Section A

Submitted on April 29, 2016

Signature:

Abstract

The objective of this experiment is to determine the yield strength and fracture toughness of paleobiology plaster jackets made from Plaster of Paris. Five testing methods are used including solid beam specimens tested in three point bending, notched specimens tested in three point bending, cast specimens tested in beam bending loaded from above, cast specimens tested in beam bending loaded from below, and cast specimens tested in beam bending with fixed flanges. Experimental results show that the average yield strength for Plaster of Paris is about 4.563436061 MPa and the average fracture toughness for Plaster of Paris is about 0.14446 MPa * m1/2. These mechanical properties are vital for determining proper applications of Plaster of Paris as a protective casing for excavated fossils.

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Introduction:

Plaster of Paris is manufactured by heating gypsum (CaSO4. 2H2O) to about 1500C. When the dry plaster powder is mixed with water, hydration of the Calcium Sulphate Hemihydrate occurs as depicted in Figure 1.

Figure 1: Chemical Reaction of Plaster of Paris Powder and Water [1].

Dry plaster is a polycrystalline material that has a linear elastic behavior and undergoes permanent deformation under constant loading. Plaster of Paris is formally used by mixing its powder configuration with water and shaping the paste that forms. Over time, the plaster will cure and harden to its defined configuration. How wet or dry the cured plaster is effects the mechanical strength of the Plaster of Paris. The more water the plaster absorbs, the less strength the plaster will have [1]. Other variables that effect the strength and fracture toughness of the plaster include curing time and porosity.

Plaster Jackets are used to encase fossilized specimens for preservation purposes during transport and storage. Thus, the strength and fracture toughness of Plaster of Paris has to be to a degree that it will be able to house the fossil and protect it from applied forces that could cause damage and even fracture. The aim of this study is to determine the strength and fracture toughness of Plaster of Paris for its application purposes in designing a plaster jacket that will encapsulate the widest part of a 6-7 million year old fossilized Panamanian dolphin without further damage to the fossil.

Experimental:

Specimen Fabrication

The Plaster of Paris specimens were made by mixing two parts of plaster to one part of water. The plaster and water mixture was mixed together in a bowl and scooped from the bowl to be placed on the preparation surface for the six solid beam and seven notched specimens tested in three point bending. On the other hand, the 2:1 plaster to water mixture was mixed together in a plastic bag and then poured onto the preparation surface through a hole in the corner of the bag, much like a pastry decorating bag, for the six cast specimens tested in beam bending loaded from above and the five cast specimens tested in beam bending loaded from below as shown in Figure 2. In contrast, the five cast specimens tested in beam bending with fixed flanges were formed by mixing a 1:3 plaster to water ratio mixture in a cup that was then poured from the cup onto the preparation surface.

The preparation surface included a sheet of plastic wrap with pre-specified dimensions for the solid beam and notched specimens tested in three point bending. Whereas, the preparation surface included a sheet of plastic wrap layered on top of pre-cut sections of insulation tubing for the cast specimens tested in beam bending. The plaster and water mixture was only poured onto the preparation surface once the mixture formed a moldable substance. The ideal moldable substance reached a consistency that was of a medium viscosity so that it would be able to form

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the foundation for the specimens with minimum flowing. After pouring the initial amount of plaster onto the preparation surface, utensils were used to smooth out the plaster in an attempt to form a fairly uniform thickness as depicted in Figure 3. Once the specimens cured for two days, they were then removed from the plastic wrap and sanded down to create relatively uniform cross sections.

Figure 2: Specimen Fabrication for Beam Bending Specimens Loaded from Above and Below.

Figure 3: Specimen Fabrication by Smoothing Surfaces.

Testing Methods

Six solid beam specimens were tested in three point bending as depicted in Figure 4. The testing apparatus was designed so that the specimen was supported by textbooks on either side of the beam and suspended over a trashcan. The load applied to create a three point bending response was provided by the weight of a gallon jug suspended below the center of the specimen and connected via paperclips. The initial weight of the testing apparatus was measured using a scale, then water was added to the gallon jug until fracture. A pen was used to stabilize the gallon jug as it began to swing during loading. Once the specimen fractured, the weight of the testing apparatus combined with the amount of water added to break the specimen was measured. The difference in final and initial weight measurements provided the amount of applied load at which the specimen fractured.

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Figure 4: Solid Beam Specimen Three Point Bending Testing Apparatus.

Seven notched specimens were tested in three point bending as depicted in Figure 5. The same overall testing procedure that was used for the six solid beam specimens was applied to the notched specimens. One key difference is that the notched specimens were tested so that the load was applied opposite to the pre-formed notch. This key factor mimics the loading specifications required for a Charpy Impact test. The specimen was tested through its thickness rather than its width due to the placement of the notch. Therefore, firm yarn was used instead of paperclips to more easily alter how low the gallon jug hung from the specimen surface.

Figure 5: Single-edge Notched Specimen Loaded in Three Point Bending Testing Apparatus.

Six cast specimens were tested in beam bending loaded from above as depicted in Figure 6. The testing apparatus was designed so that the specimen was placed atop the textbooks and trashcan with a towel due to possible spilling upon fracture. The load applied to create a beam bending response was provided by the weight of a gallon jug held above the center of the specimen. The initial weight of the testing apparatus was measured using a scale, then water was

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added to the gallon jug until fracture. Upon fracture, the gallon jug was carefully held above the fractured specimen so as to avoid further damage to the fracture surfaces. Once the specimen fractured, the weight of the testing apparatus combined with the amount of water added to break the specimen was measured. The difference in final and initial weight measurements provided the amount of applied load at which the specimen fractured.

Figure 6: Apparatus for Cast Specimens Tested in Beam Bending Loaded from Above.

Five cast specimens were tested in beam bending loaded from below as depicted in Figure 7. The same exact testing procedure was used as with the six solid beam specimens tested in three point bending. The only difference is that a piece of cardboard was placed atop one of the textbooks if the height of the specimen was not consistent on either side of the applied load.

Figure 7: Apparatus for Cast Specimens Tested in Beam Bending Loaded from Below.

Five cast specimens were tested in beam bending with fixed flanges as depicted in Figure 8. The testing apparatus was designed so that the specimen was clamped at either flange to promote pure beam bending. The applied load was provided by the weight of a gallon jug suspended from one of the flanges that was connected via paperclips that were secured to the specimen through a small hole drilled into the flange. The other flange was fixed to a mechanical clamp suspended from a shower caddy. The initial weight of the testing apparatus was measured using a scale, then water was added to the gallon jug until fracture. Once the specimen fractured,

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the weight of the testing apparatus combined with the amount of water added to break the specimen was measured. The difference in final and initial weight measurements provided the amount of applied load at which the specimen fractured.

Figure 8: Apparatus for Cast Specimens Tested in Beam Bending with Fixed Flanges.

Results:

Solid beam specimens tested in three point bending

Figure 9: Formula for Calculating Strength in Solid Beam Member.

Sample l (m) b (m) h (m) F (lbf) σys (lbf/m2) Average σys (MPa)

1 0.06 0.01483 0.00289 1.4 1017264.077 5.485677214

2 0.06 0.0179 0.00331 2.4 1101399.139

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3 0.07 0.0155 0.00264 1.6 1555140.851 Standard Deviation

4 0.067 0.0169 0.00299 2.4 1596423.905 1.09701691

5 0.07085 0.0137 0.00394 2 999420.1435

6 0.065 0.0177 0.00395 3.2 1129762.451

Notched specimens tested in three point bending

Figure 10: Formulas (9.4) and (9.6) for calculating Fracture Toughness [2].

Sample

a (m) w (m) B (m) P (lbf) s (m) K1 (N/m1/2) Average Fracture Toughness

(MPa * m1/2)

1 0.00564 0.01839 0.00294 6.6 0.0503 366789.9797

0.14446

2 0.00428 0.01723 0.00444 2.2 0.03999 70443.67258

3 0.00646 0.01852 0.00203 4 0.03616 229658.6603

Standard Deviation

4 0.00427 0.01933 0.00358 7.6 0.03477 219152.9275

0.086613

5 0.00139 0.00964 0.00224 1.2 0.03691 157732.4525

6 0.00219 0.01335 0.00166 1.6 0.03956 190677.2095

7 0.00244 0.01446 0.00246 1.4 0.04126 104597.5281

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Cast specimens without fixed flanges tested in beam bending loaded from above and below

Figure 11: Formula for Calculating Strength in Plaster Cast without Fixed Flanges.

Samples Loaded from Above

R (m) h (m) b (m) F (lbf) σys (lbf/m2) Average σys (MPa)

1 0.0246 0.00115 0.03092 1.4 2526674.117 4.672413352

2 0.02502 0.00246 0.02016 1 615244.6106

3 0.02594 0.00435 0.03068 4.4 589807.151 Standard Deviation

4 0.02633 0.00243 0.02879 3 1393924.195 3.297236

5 0.02563 0.00441 0.03205 2.4 296057.3789

6 0.02714 0.0035 0.02264 3 880724.0211

Samples Loaded from Below

R (m) h (m) b (m) F (lbf) σys (lbf/m2) Average σys (MPa)

1 0.02349 0.00454 0.03649 2.6 243608.2828 1.037744764

2 0.02513 0.00409 0.02645 2.2 374855.711

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3 0.0263 0.00325 0.03294 0.6 136062.3403 Standard Deviation

4 0.02771 0.00299 0.03111 1 298892.7582 1.126183

5 0.02276 0.00353 0.02908 0.6 113057.9092

Cast specimens with fixed flanges tested in beam bending

Figure 12: Formula for Calculating Strength in Plaster Cast with Fixed Flanges.

Sample

R (m) h (m) b (m) F (lbf) σb (lbf/m2) σt (lbf/m2) Average σys

(MPa)

1 0.02475 0.00207 0.02914 0.46875

557490.532 7771.080143 3.532217618

2 0.0245 0.00208 0.03124 0.9075 987020.7283 13966.00758

3 0.024975 0.00209 0.03953 0.8825 765864.7391 10681.73043 Standard Deviation

4 0.02497 0.00313 0.034355 1.955 870237.7658 18180.77831 0.6519

5 0.02496 0.00283 0.03615 1.4025 725466.7771 13709.07438

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Fractography

Figure 13 shows the fracture surface of a plaster cast that was tested under beam bending with fixed flanges.

Figure 13: Fracture Surface of Plaster Cast.

Figure 14 depicts variations in flaw size on a fracture surface of a plaster cast specimen.

Figure 14: Fracture Surface of Plaster Cast with Multiple Flaws.

Force Estimated to Fracture the Cast

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Flaw

MirrorMist

Hackle

2.84 E -3m

2.84 E -3m

FlawFlaw Flaw

Figure 15: Formula to Calculate Estimated Force for Fracture with Fixed Flanges.

Sample

R (m) h (m) b (m) σavg from solid beam specimens tested in three point bending (lbf/m2)

Calculated F (lbf)

Average F for Fracture (lbf)

1 0.02475 0.00207 0.02914 1233235.094 1.022675055

1.719187002

2 0.0245 0.00208 0.03124 1.118057621

3 0.024975 0.00209 0.03953 1.401500121

4 0.02497 0.00313 0.034355 2.713782401

5 0.02496 0.00283 0.03615 2.339919813

Figure 16: Formula to Calculate Estimated Force for Fracture without Fixed Flanges.

Samples Loaded from

R (m) h (m) b (m) σavg from solid beam specimens tested in three point bending

Calculated F (lbf)

Average F for Fracture (lbf)

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Above (lbf/m2)

1 0.0246 0.00115 0.03092 1233235.094 0.683321 4.789997

2 0.02502 0.00246 0.02016 2.004463

3 0.02594 0.00435 0.03068 9.200015

4 0.02633 0.00243 0.02879 2.654165

5 0.02563 0.00441 0.03205 9.997266

6 0.02714 0.0035 0.02264 4.200754

Discussion:

Covering the widest part of the fossil specimen was a key component for designing the plaster jacket and as such the starting point as shown in Figure 17. Once the minimum diameter of the plaster cast was known, the dimensions of the flanges were free to vary. The flanges for each specimen were designed to be about the same length so as to limit the number of variables while determining the yield strength of Plaster of Paris. The tested plaster cast specimens were on average about 0.03 m in width due to difficulties during the fabrication of a full length plaster jacket. The properties of a section of the plaster jacket are the same as the properties of a full length plaster jacket, but the section of the plaster jacket created an easier testing surface. Also, the cast specimens created using a 1:3 ratio of plaster powder to water were much easier to shape into relatively uniform specimens than the 2:1 ratio of plaster powder to water mixture. This is perhaps due to the increased viscosity of the resulting plaster paste.

Figure 17: Plaster Jacket Encasing Fossilized Panamanian dolphin.

The fracture toughness specimen dimensions were created according to the required components necessary for a valid KIC test [2]. Therefore, the crack lengths and thickness of the single-edge notched-bend specimens loaded in three-point bending were all greater than or equal to 0.001734 m (2.5*(KIC/σys)2). Another important factor for the fracture toughness specimens is the loading conditions. The fracture toughness specimens were tested with the load applied opposite to the notch to guide the propagation of the crack so as to mimic a Charpy Impact Test.

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The single-edge notched-bend specimens loaded in three-point bending fractured due to a crack popping in during loading and then growing as more force was applied.

The key factor in creating the solid beam specimens used in determining the yield strength of the Plaster of Paris was an attempt to keep the thickness of the specimens relatively the same throughout. This was especially difficult since the Plaster of Paris kept sticking to the surfaces of the utensils used to smooth out the specimens.

The strength of the Plaster of Paris determined from the solid beam specimens loaded in three point bending was used to calculate the estimated force for fracture of the cast specimens. The estimated force for fracture of the cast specimens with fixed flanges was significantly less than the force required to fracture the cast specimens without fixed flanges. This may be due in part to the limitations of the formula applied to the cast specimens without flanges in that it ignores the height of the plaster cast and doesn’t account for deformations. Another factor that could have contributed to this difference is the increased viscosity in forming the fixed flange specimens that created more uniform specimens. Overall, the calculated values for the force for fracture of the cast specimens with fixed flanges and the cast specimens without fixed flanges loaded from above were within one standard deviation of the experimentally measured values.

Plaster of Paris is a ceramic and as such experiences a brittle failure due to crack propagation. Figure 13 depicts the fracture surface of a plaster cast specimen. The flaw (bubble) is directly surrounded by a smooth surface called the mirror region. The mirror region transitions to a region called the mist region as it becomes more irregular. The final region called the hackle region is indicated by the distinctly irregular surface [2]. Thus, the flaw that was formed during fabrication is the origin of the fracture due to its location at the area of highest stress concentration. As stated in the introduction, porosity effects the mechanical properties of the Plaster of Paris. Figure 14 depicts variations in flaw size. Flaw sizes that are greater than the grain size cause the ductility and the fracture toughness to diminish. According to Firstpallete.com, Plaster of Paris is supposed to be formed by adding the powder to the water by sifting the powder over the water so that it doesn’t coagulate in one spot while also tapping the side of the mixing container to disperse the powder into the water and remove any air bubbles [3]. Therefore, since the plaster specimens weren’t properly processed, large variations in flaw size were formed. Thus, the concentration and size of the flaws determine the strength of the Plaster of Paris.

Ceramics are characterized by having very low ductility. Since ceramics are not very ductile, no necking of the substance was observed before failure. Thus, the Plaster of Paris was unable to undergo a region of plastic deformation before failure. The low ductility and low resistance to crack propagation also caused the large difference between compressive and tensile strengths. The plaster cast specimens with fixed flanges had an average compressive strength of 3.475006043 MPa and an average tensile strength of 0.057211575 MPa. Unlike a ceramic like glass, the Plaster of Paris does not obviously display crack branching (or bifurcation).

Comparing experimental values to those exhibited in the literature give promising results. Table 1 depicts the properties of Plaster of Paris for a particular experiment in which the composition of the plaster mixture contained 62.5% water. Notice how comparable the values are for tensile strength, compressive strength, yield strength (modulus of rupture), and fracture toughness between Table 1 and Table 2. Thus, the experimental results from this study of Plaster

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of Paris should also be relatively consistent with these values. In fact they are, with an average yield strength of 4.563436061 MPa and an average fracture toughness of 0.14446 MPa * m1/2. Thus, the experiment was a success despite the inability to form fully uniform specimens.

Table 2 also includes the mechanical properties for other ceramic materials. Comparing Cement and Sandstone to Plaster of Paris shows that Plaster of Paris at a limited thickness and without fiber reinforcement is not the best material to use for structural applications. This is due to its lower strength and fracture toughness values than structural ceramics like Cement and Sandstone.

Table 1: Properties of Plaster of Paris (62.5% Water) [4].

Table 2: Mechanical Properties of Ceramics [5].

Plaster of Paris Plaster of Paris Cement Sandstone

Yield Strength (elastic limit)

0.999746-4.502 MPa 0.145-0.653 ksi 0.276- 0.435 ksi 0.58-3.19 ksi

Tensile Strength 0.999746-4.502 MPa 0.145-0.653 ksi 0.276- 0.435 ksi 0.58-3.19 ksi

Compressive Strength

13.996444-19.99492 MPa

2.03-2.9 ksi 3.48-3.92 ksi 7.25-22.5 ksi

Fracture Toughness 0.099994713-0.13955306 MPa *m1/2

0.0091-0.0127 ksi * in1/2

0.319-0.41 ksi * in1/2

0.637-1 ksi * in1/2

Conclusion:

The average yield strength and fracture toughness values for Plaster of Paris obtained from the experiment (4.563436061 MPa and 0.14446 MPa * m1/2 respectively) are directly comparable to the literature values. The restrictions on the thickness of the Plaster of Paris

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specimens and inability to use fiber reinforcements gives the Plaster of Paris less significance as a structural material than other ceramics like cement or sandstone. Thus, if the 6-7 million year old fossilized Panamanian dolphin were encased in the Plaster of Paris fabricated throughout this study, it would only be able to protect the fossil from small applied forces. Other environmental factors were not examined in this study, so there is a possibility that Plaster of Paris could be better suited under applied thermal or electrical conditions than other ceramic materials.

References:

[1] S. Meille, M. Saadaoui, P. Reynaud, and G. Fantozzi, “Mechanisms of crack propagation in dry plaster”. Sci. Direct, Cedex, France, J. of the European Ceramic Soc., Vol. 23. pp. 3105-3112. Feb. 2003. [Online]. Available: https://www.researchgate.net/publication/248454427_Mechanisms_of_crack_propagation_in_dry_plaster. [Accessed: 15-Apr-2016]

[2] M. Meyers and K. Chawla, “Fracture Testing,” in Mechanical Behavior of Materials, 2nd ed. Cambridge: Cambridge Univ. Press, 2009, ch. 9, sec. 3. Print.

[3] “Mixing Plaster of Paris,” Firstpalette.com, 2016. [Online]. Available: http://firstpalette.com/tool_box/quick_how_to/plasterofparismixture/plasterofparismixture.html. [Accessed: 07-Apr-2016]

[4] G. Vekinis, M. F. Ashby, and P. W. R. Beaumont, “Plaster of Paris as a model material for brittle porous solids”. Kluwer Academic Publishers, Cambridge, UK, J. of Materials Sci., Vol. 28 (12), pp. 3221-3227. Jun. 1993. [Online]. Available: http://link.springer.com/article/10.1007/BF00354239. [Accessed: 07-Apr-2016]

[5] Granta Inc., CES EduPack software® 2015. Cambridge, United Kingdom.

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