laboratory module unconfined compression of …

MA300-ART01-D v1 LAB MODULE – UNCONFINED COMPRESSION OF HYDROGEL DISKS

Eff. Date: 19Sep2017 BMMT CC#2017-017

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LABORATORY MODULE UNCONFINED COMPRESSION OF HYDROGEL DISKS

The unconfined compression test is by far the most popular mechanical testing configuration

to measure the mechanical properties of cylindrical samples. Samples with non-planar

geometry can also be tested using this configuration, but data analysis requires more complex

theoretical modelling to extract the mechanical parameters. A disk is compressed between two

flat platens and is free to expand in the radial direction (slipping boundary conditions). This

test configuration is normally performed under displacement control, as in this laboratory

module. The sample's stiffness is determined by the slope of the load vs displacement curve.

By considering the geometry of the disk sample (radius and thickness), the Young's modulus

can be calculated. For purely elastic materials, the Young's modulus is independent of the

strain rate in compression, while for non-purely elastic materials (viscoelastic and poroelastic),

the Young's modulus can vary with the strain rate.

This laboratory module consists of assessing mechanical properties of both rubber and

hydrogel samples. Throughout this laboratory, each team will:

Prepare the rubber and hydrogel samples;

Rubber and hydrogel disk-shaped samples



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LABORATORY MODULE UNCONFINED COMPRESSION OF HYDROGEL DISKS

Test each sample in unconfined compression with various stain rates;

Strain Rate Compression Variation

0.1 % of �� (thickness) per second

5 % of �� (thickness) per second

20 % of �� (thickness) per second

Extract slopes from the load-displacement curves using Mach-1 Analysis software to

obtain the rubber and hydrogel samples' stiffness for various strain rates;

Calculate the corresponding Young's modulus considering the sample geometry;

Discuss the effect of stain rate on the Young's modulus for each material;

Conclude with the effect of strain rate on Young's modulus for materials with elastic

vs. non-elastic behavior.

Learning Goals 1. Become familiar with the safe operation of a mechanical tester during an

unconfined compression test.

2. Learn how to prepare disk-shaped samples for an unconfined compression

test.

3. Differentiate between stiffness and Young's modulus.

4. Measure the stiffness and Young's modulus of disk-shaped samples.

5. Understand the effect of stain rate on the measured Young's modulus for

materials used in biomedical research.

6. Understand how the structure and composition of materials determine

their behavior during compression testing.



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TABLE OF CONTENTS LEGEND ............................................................................................................................................................ 3

KEY CONCEPTS ..................................................................................................... 4

MATERIALS ..................................................................................................... 5

DEFINITIONS ..................................................................................................... 5

SAMPLE PREPARATION ..................................................................................................... 6

RUBBER ............................................................................................................................................................. 8

TESTING PROCEDURE ..................................................................................................... 8

ANALYSIS PROCEDURE .................................................................................................... 11

SAMPLE DATA ............................................................................................................ 12

HYDROGEL ..................................................................................................................................................... 13

TESTING PROCEDURE .................................................................................................... 13

ANALYSIS PROCEDURE .................................................................................................... 16

SAMPLE DATA ............................................................................................................ 17

SAMPLE DATA ............................................................................................................ 18

QUESTIONS ............................................................................................................ 19

QUESTIONS ........................................................................................................... 22

ADDITIONAL RESOURCES......................................................................................................................... 24

LEGEND

For instructors For students

This laboratory module can be used as a whole by the instructor.

The student version of the laboratory module should only include pages 1-11, 13-16, 18-21

and 24. Page 12, 17 and 22-23 should NOT be included since they contain solutions.

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KEY CONCEPTS

Rubber: A material composed of polymer chains. Rubber is an elastomer; therefore, it possesses

predominant elastic properties caused by the stretching of polymer chains under deformation or

loading.

Hydrogel: A network of hydrophilic polymeric chains that can associate with a large quantity of

water without dissolving. The polymeric chains of the gel can be engineered to give a wide spectrum

of properties to the material; mechanical and chemical, including biocompatibility. Hydrogels make

very interesting platforms for the development of various bioengineering applications: 3D scaffolds

for cell cultures, cell encapsulation, nanoparticles, etc. Hydrogels generally express a non-purely

elastic behavior due to the viscoelasticity of the polymeric chains and the poroelasticity brought on

by the presence of fluid.

Stiffness �: A structural property of a sample. By plotting force

vs. displacement during an unconfined compression and

extracting the slope, we obtain the stiffness of the sample.

In Mach-1 Analysis, the slope is in gram-force per mm (gf/mm).

The gram-force is 1 gram multiplied by the acceleration due

to gravity on Earth, exactly 9.80665 m/s².

Young's modulus �: Intrinsic mechanical property of a material

independent of its geometry. From the slope of the stress vs.

strain graph during an unconfined compression and considering

the geometry of the sample, we can calculate the Young's

modulus.

Elasticity: Property of a material to deform under load or strain and to return to its original shape

when the stress is released.

Viscoelasticity: Property of a material to exhibit both viscous and elastic characteristics when

undergoing deformation. Such material will show time-dependent mechanical behavior.

Poroelasticity: Property of an elastic or viscoelastic material with an incompressible free fluid phase.

When such a material is put under stress, fluid is released from the solid matrix. The frictional drag

generated from the movement of the fluid through the matrix affects the mechanical behavior of

such material. These materials are normally tested in a bath of fluid.

Strain rate: Change in strain or deformation of a material with respect to time.

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MATERIALS SA

MPLE

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EPA

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High-Temp. Silicone Gasket Material, 6 x 6", 1/16" thickness, McMaster-Carr:

8525T42

Miltex Dermal Biopsy Punch 8 mm, REF 33-37

Cutting board 37.5 x 27 cm

Stainless Steel Rod for Extraction of Sample, D = 1/16", L = 6", McMaster-Carr:

88915K11

DI Water

Agar powder, any brand (e.g. Telephone Brand Agar-Agar Powder)

Scale, 0.1 g minimum accuracy

200 mL beaker

100 mL graduated cylinder

Spoon or equivalent for agitating the solution

Plastic protector for sample extraction (e.g. packaging of the Biopsy Punch)

Tweezers

Petri dish, 10 cm diameter

Squirt Bottle filled with DI water

MEC

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Mechanical tester model Mach-1™ V500c (MA001) or higher models

Mach-1 Motion software (SW326)

Mach-1 Analysis software (SW186)

Single-axis load cell 250 N (MA297) or equivalent with at least 100N in

compression

o Note: All single-axis load cells use units of "gf" instead of "N". In Mach-1

Motion, ensure to use the proper units to avoid any damage to the load

cell.

Calibration holder and weight 500 g (MA327 or MA337)

Testing chamber, D = 98 mm (MA626)

Sample holder and chamber, D = 37 mm (MA740)

Flat indenter, D = 12.5 or 31.75 mm (MA262 or MA263)

DEFINITIONS

DI Deionized

RT Room Temperature

gf Gram-force: 1 gf = 0.009806650 N

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SAMPLE PREPARATION R

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1. Place the rubber sheet on a cutting board.

2. Position the 8-mm biopsy punch perpendicular to the surface of the material.

3. Push through the surface using a rotating motion to perforate the gasket material.

4. Insert the metal rod through the top end of the biopsy punch to extract the sample.

5. Repeat steps 2 to 4 twice to obtain three disk-shaped rubber samples.

SAMPLE PREPARATION

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1. Weigh 6 grams of agar and measure 100 mL of DI water.

2. Combine the DI water and agar in a 200 mL beaker and stir the solution.

3. Heat the solution in a microwave for 30 seconds and stir.

4. Heat the solution in a microwave for 10-second intervals, approximately five times,

stirring in between until complete melting of the agar and thickening of the

solution (the solution should be close to boiling but do not let it boil because air

bubbles will form).

5. Stir the mixture for 1 minute.

6. Pour into a petri dish to obtain an ideal 3 mm thickness.

7. Let cool for 15 minutes at RT.

8. Let rest at RT for 12h covered with a plastic film.

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Extraction of the rubber sample

3-mm thick hydrogel (5% agar) in petri dish



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SAMPLE PREPARATION

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9. Using tweezers, unmold the hydrogel and place it on a cutting board.

10. Using an 8-mm biopsy punch, first punch the plastic to create a disk that will

protect the hydrogel during sample extraction when using the metal rod.

11. Ensure that the plastic disk is inside the biopsy punch and then punch the

hydrogel.

12. Insert the metal rod through the top end of the biopsy punch to extract the

hydrogel disk.

13. Repeat steps 11 and 12 twice to obtain three hydrogel disk-shaped sample.

14. Store the hydrogel sample in DI water.

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Extraction of the hydrogel sample



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RUBBER TESTING PROCEDURE

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1. Turn ON the Mach-1 controller and wait until initialized.

2. Open Mach-1 Motion software.

3. Using manual controls in the software, raise the vertical stage to its maximum

height using "medium" speed.

4. Verify the load cell calibration as per Mach-1 user manual. Strongly recommended

before each test session.

5. Secure the testing chamber onto the base of the Mach-1 using four screws.

6. Screw the sample holder onto the testing chamber.

7. Gently screw the flat indenter into the thread of the load cell and lightly finger-

tighten to secure it.

8. Using manual controls, lower the stage at "medium" speed to approximately 20

mm above the sample holder. Lower the stage at "low" speed to approximately

2 mm above the sample holder.

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Test setup for unconfined compression of disk-shaped rubber samples



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TESTING PROCEDURE R

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9. Find the vertical position of the bottom platen and set it as the reference by

performing the following test sequence. Note: Since the upper flat platen indenter

and the bottom of the sample holder need to be in contact (metal-on-metal), this

step should be executed very carefully to minimize the risk of damaging the load

cell or the accessories. We suggest that this step be executed or supervised by a

qualified laboratory technician.

Functions Parameters

Zero Load No parameter

Find Contact Stage Axis: Position (z)

Load Cell Axis: Fz

Direction: Positive

Velocity: 0.01 mm/s

Contact Criteria: 3.75 gf

Stage Limit: 3 mm

Stage Repositioning: 2X Load Resolution

Zero Position Stage Axis: Position (z)

10. Using manual controls, raise the stage at least 50 mm above the sample holder.

11. Place the first 8-mm disk-shaped rubber sample in the center of the sample

holder using tweezers.


mm above the sample. Lower the stage at "low" speed to approximately 2 mm

above the sample.

13. Perform the following test sequence to measure the disk thickness L0:




Load Cell Axis: Fz

Direction: Positive

Velocity: 0.1 mm/s


Stage Limit: 3 mm


14. Report the current position of the stage axis (z) as the thickness �� of the sample

in Table 1 near the end of this document.

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TESTING PROCEDURE R

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15. Proceed with the first unconfined compression test using the following sequence.



Stress Relaxation

(Pre-Compression)

Stage Axis: Position (z)

Load Cell Axis: Fz

Ramp Amplitude: 3% of ��

Ramp Velocity: 0.4% of �� per second

Number of Ramps: 1

Stop Based On: Fixed Relaxation Time

Fixed Relaxation Time: 60 s

Save results as: 1st Test: "GrXX_TeamXX_Rubber_01.txt"

2nd Test: "GrXX_TeamXX_Rubber_5.txt"

3rd Test: "GrXX_TeamXX_Rubber_20.txt"

Stress Relaxation

(Compression)


Load Cell Axis: Fz


Ramp Velocity: 1st Test: 0.1% of �� per second

2nd Test: 5% of �� per second

3rd Test: 20% of �� per second

Number of Ramps: 1



Save results as: 1st Test: "GrXX_TeamXX_Rubber_01.txt"

2nd Test: "GrXX_TeamXX_Rubber_5.txt"

3rd Test: "GrXX_TeamXX_Rubber_20.txt"

16. Using the manual controls, raise the stage at least 50 mm above the sample

holder.

17. Repeat steps 11 to 16 with the two remaining rubber disk samples using the

parameters for the second and third unconfined compression tests.

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ANALYSIS PROCEDURE R

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1. Open Mach-1 Analysis software and open the Folder Path containing the Mach-1

results files.

2. From the File List, select the results file "GrXX_TeamXX_Rubber_01.txt".

3. Select the second "Stress Relaxation" function. The first "Stress Relaxation" being the

results from the pre-compression, it will not be analyzed.

4. Choose "Fz, N" for the Y-Axis and "Position (z), mm" for the X-Axis.

5. From the "Analysis" dropdown menu, select Slope. Use the cursors to choose

the appropriate part of the curve for analysis. Recommended range for the

extraction of the Young's modulus is the last 50% of the slope. A blue line

corresponding to the slope in the chosen range will be superimposed on the

experimental curve and the results will be computed.

6. Report the slope as the stiffness � (gf/mm) in Table 1 near the end of this document.

7. Repeat steps 2 to 6, choosing the results files

"GrXX_TeamXX_Rubber_5.txt" and "GrXX_TeamXX_Rubber_20.txt" from the "File

List".

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Structural properties will be extracted from the test result files generated during the

unconfined compression of the disk-shaped rubber samples for each strain rate.

Each sample's shape and dimensions will later be considered to obtain the

mechanical properties in terms of strain rates.

Load vs. position graph for slope analysis in Mach-1 Analysis software



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HYDROGEL TESTING PROCEDURE

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1. Open Mach-1 Motion software.

2. Using the manual controls in the software, raise the vertical stage to its maximum

height using "medium" speed.

3. Secure the transparent wall onto the sample holder (being careful not to touch

the load cell or indenter).

4. Place the first 8-mm disk-shaped hydrogel sample in the center of the sample

holder using tweezers.


mm above the sample. Lower the stage at "low" speed to approximately 2 mm

above the sample.

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Test setup for unconfined compression of disk-shaped hydrogel samples



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TESTING PROCEDURE H

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6. Perform the following test sequence to measure the disk thickness L0:




Load Cell Axis: Fz

Direction: Positive

Velocity: 0.1 mm/s


Stage Limit: 3 mm


7. Report the current position of the stage axis (z) as the thickness L0 of the sample

in Table 1 near the end of this document.

8. Fill the sample holder chamber with DI water. Pour the solution slowly to avoid

sample movement. Make sure no air bubbles get trapped under the platen and

that the solution level is at least 5 mm above the cylindrical plate portion of the

flat indenter to minimize volumetric artifacts in the load.

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Disk-shaped sample between the upper flat indenter and the bottom of the sample

holder filled with DI water



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TESTING PROCEDURE H

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9. Proceed with the unconfined compression test using the following sequence.

10. Using the manual controls, raise the stage above the sample holder.

11. Unscrew the sample holder from the testing chamber and dispose of its contents.

12. Repeat steps 4 to 11 with the two remaining hydrogel disk samples using the

parameters for the second and third unconfined compression tests.



Stress Relaxation

(Pre-Compression)


Load Cell Axis: Fz


Ramp Velocity: 0.4% of �� per second

Number of Ramps: 1



Save results as: 1st Test: "GrXX_TeamXX_Hydrogel_01.txt"

2nd Test: "GrXX_TeamXX_Hydrogel_5.txt"

3rd Test: "GrXX_TeamXX_Hydrogel_20.txt"

Stress Relaxation

(Compression)


Load Cell Axis: Fz


Ramp Velocity: 1st Test: 0.1% of �� per second

2nd Test: 5% of �� per second

3rd Test: 20% of �� per second

Number of Ramps: 1



Save results as: 1st Test: "GrXX_TeamXX_Hydrogel_01.txt"

2nd Test: "GrXX_TeamXX_Hydrogel_5.txt"

3rd Test: "GrXX_TeamXX_Hydrogel_5.txt"

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ANALYSIS PROCEDURE H

YD

RO

GEL

SA

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1. Open Mach-1 Analysis software and open the "Folder Path" containing the Mach-1

results files.

2. From the "File List", select the result file "GrXX_TeamXX_Hydrogel_01.txt".

3. Select the second "Stress Relaxation" function. The first "Stress Relaxation" being the

results from the pre-compression, it will not be analyzed.

4. Choose "Fz, N" for the Y-Axis and "Position (z), mm" for the X-Axis.

5. From the "Analysis" dropdown menu, select Slope. Use the cursors to choose

the appropriate part of the curve for analysis. Recommended range for the

extraction of the Young's modulus is the last 50% of the slope. A blue line

corresponding to the slope in the chosen range will be superimposed on the

experimental curve and the results will be computed.

6. Report the slope as the stiffness � (gf/mm) in Table 1 near the end of this document.

7. Repeat steps 2 to 6, choosing the results files "GrXX_TeamXX_Hydrogel_5.txt" and

"GrXX_TeamXX_Hydrogel_20.txt" from the "File List.

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Structural properties will be extracted from Mach-1 result files generated during the

unconfined compression of the disk-shaped hydrogel samples for each strain rate.

Each sample's shape and dimensions will later be considered to obtain the

mechanical properties in terms of strain rates.

Load vs. position graph for slope analysis in Mach-1 Analysis software



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SAMPLE DATA

Table 1: Data from the rubber and hydrogel samples

Strain rate

(% of �� per

second)

Parameter Values for

rubber samples

Values for

hydrogel samples

0.1

Sample thickness

�� (mm)

Slope (gf/mm)

5

Sample thickness

�� (mm)

Slope (gf/mm)

20

Sample thickness

�� (mm)

Slope (gf/mm)

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QUESTIONS

1. Complete the following table by extracting the Young's modulus from the stiffness of

each sample for various strain rates. Use the values in Table 1 and the space provided

below to demonstrate your calculations.

Table 2: Young's modulus of rubber and hydrogel

Strain rate

(% of �� per second)

Young's modulus

Rubber Hydrogel

0.1

5

20

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QUESTIONS

2. Compare the Young's modulus obtained for both materials in terms of strain rates.

Comment on the materials' behaviors.

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3. Explain how the structure and composition of poroelastic materials (like hydrogels)

affect their mechanical properties under varying stain rates.

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QUESTIONS

4. Discuss what could be expected if the hydrogel had been tested in air instead of

water.

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5. Determine two error sources that you think could have been significant during

experimental manipulations and data analysis.

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ADDITIONAL RESOURCES

Biomomentum's website (www.biomomentum.com) contains more information on

unconfined compression test and the Mach-1 mechanical tester. There, you can find case

studies as well as literature related to this laboratory module.

laboratory module unconfined compression of …

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