Y - MIT

Plastic Deformation of Polycrystalline and Sodium Borate Glass
Julia Rubin, Annie Dunn, Tanner Guerra, Anna Jungbluth, Amma Okwara, Tiffany Yeh
3.014 Lab Group 4
Department of Materials Science and Engineering
Massachusetts Institute of Technology
Abstract
Results and Discussion
Stress vs. Strain: Unannealed Brass Rod
Stress vs. Strain: Annealed Brass Rod
140
600
120
500
100
400
80
Stress (MPa)
y = 46707x - 17.82
60
40
20
200
100
0
0
•  Applying a force to a material results in elastic deformation: a
temporary displacement along the direction of the force. When the
force is removed, the material returns to its original size and shape.
•  At a certain yield stress, σy, plastic deformation occurs, where the
material retains a permanent deformation after the force is removed.
o  σy is characterized by a point discontinuity in the stress-strain
curve, followed by a decrease in the slope.
o  Below the glass transition temperature, glasses are brittle and
do not undergo plastic deformation. [2]
•  Deformation and yield stress are defined by Young’s Modulus.
σ stress
force per unit area
Y= =
=
Fig. 1 Deformation along the axis
ε strain displacement per length
of applied force resulting in a slip
plane [1]
Materials
0.01
0.015
0.02
0.025
0.03
0.035
0
0.04
0.005
0.01
0.015
0.02
0.025
0.03
Strain (mm/mm)
Strain (mm/mm)
Fig. 5 Stress versus strain curve for the annealed brass rod
Fig. 6 Stress versus strain curve for unannealed brass rod
Annealed Rod
Young’s Modulus: 46.707 Gpa
Yield Stress: ~85 Mpa
Unnnealed Rod
Young’s Modulus: 74.622Gpa
Yield Stress: ~400 Mpa
2
s
Y =v ρ
Fig. 9 SEM image for annealed brass rod
Vs is the sound velocity, Y is the Young’s Modulus and ρ is the density of the rod.
FL
Y=
3
12δπ a b
3
y = 4532.4x - 3.2435
R² = 0.9828
2
F = force applied
L = two po int distance
δ = slope of Force vs. Displacement curve
1.5
1
a = major diameter
b = min or diameter
0.5
0
Slip Trace Observations in SEM
•  Mount sections on SEM specimen stub, insert into SEM. Image
secondary electron emission signal and observe slip traces.
0
Fig. 3 Scanning Electron
Microscope. Courtesy of
Tiffany Yeh
0.0005
0.001
0.0015
0.002
Displacement [m]
0.0025
Y = 71.00 GPa
Fig. 7 The linear relationship between force and displacement
confirms elastic behavior
Data lacks a clear trend. We would expect that as
mole fraction of sodium oxide increases, Young’s
Modulus would increase up to a certain maximum
and then decrease, as the boron anomaly predicts
the initial conversion of BO3 triangles to BO4
tetrahedra.
Young's Modulus of Sodium Borate Glass
vs. Composition
60.0
50.0
40.0
30.0
20.0
10.0
0.0
0.00
0.10
0.20
0.30
Mole fraction of Na2O
Fig. 11 The linear relationship between force and
displacement confirms elastic behavior
0.40
Error may be due to calibration issues with the
apparatus or incorrect measurement of rod length.
Y of brass rod: 104.5 GPa
Expected value: 115 GPa [3]
Error: 9.13%
Conclusion
3
2.5
Line 1: 6/10 µm
Line 2: 5/10 µm
Areal density = 0.6± 0.1µm-1
Sound Velocity
•  Yield stress occurs at a significantly higher stress for the unannealed brass rod (400 MPa)
=
than for the annealed brass rod (80 MPa)
•  This is expected; annealing removes impurities and dislocations that can lock together and
make a material resist the formation of slip planes and plastic deformation.
•  The slope of the curve past the yield stress is the work hardening rate.
•  The Young’s Modulus should be the same in both tests, given that the Young’s Modulus is a
material characteristics, and both brass rods have the same composition. The difference
could be due to human and machine error, as discussed in the conclusion.
Fig. 2 Instron 4505 Tensile
Testing Machine. Courtesy of
Tiffany Yeh
Fig. 10 SEM image for annealed brass rod
Grain size ≈ 56.1 µm * 52.1 µm =
2922.81 µm2 = 2.92281 mm2
Force vs. Displacement for.35 Molar Fraction Sodium
Borate Glass
Tensile Test
•  Measure diameter of brass rods. Load annealed rod into tensile grips. Zero force and
displacement. Measure gauge distance between grips.
•  Repeat for unannealed rod.
Sound Velocity
•  Load borate glass fiber under microscope. Measure major and minor
diameter at several points with slide caliper rule. Mark position of the
edge of the fiber.
•  Obtain 10g of force on the balance. Record force and displacement,
mark the edge and measure displacement. Increase load by 20g
intervals until fiber breaks and measure displacement.
0.005
Three Point Bend Test
Methods
3 Point Bend Test
•  Load borate glass fiber under microscope. Measure major and minor
diameter at several points with slide caliper rule. Mark position of the
edge of the fiber.
•  Obtain 10g of force on the balance. Record force and displacement,
mark the edge and measure displacement. Increase load by 20g
intervals until fiber breaks and measure displacement.
0
Force [N]
Materials
•  2 Cu-30wt%Zn brass rods (3.18mm diameter, 200mm long)
o  1 annealed 600°C, 10 hours
o  1 unannealed
o  Borate glass fibers with variable Na2O mole fractions (6cm long)
Equipment
•  Instron 4505 with Tensile Testing Machine Grips
•  Scanning Electron Microscope
•  Slide caliper rule
y = 74622x - 241.17
300
Young's Modulus (GPa)
Introduction
Tensile Test
Stress (MPa)
The objective of this experiment was to investigate plastic deformation as a result of dislocation
on slip planes. Young’s Moduli was tested in sodium borate glass and annealed and unannealed
brass rods. Tensile testing revealed a Young’s Modulus of 48 GPa for the annealed rod and 75
GPa for the unannealed rod. The non-identical Young’s Moduli for these rods indicates
experimental error, given that one can expect identical moduli for materials of identical
compositions. Three point bend testing on a .35 molar sodium borate glass rod revealed a
modulus of 71 GPa, while sound velocity testing yielded a modulus of 104.5 GPa.
Results and Discussion Continued
• 
Data indicates different Young’s Moduli for annealed and unannealed brass rods. Based on
their identical composition, this is unexpected and may be due to error.
•  The annealed rod has a higher yield stress (400 MPa) than the unannealed rod (80 MPa).
Annealing removes impurities and dislocations, making the formation of slip planes easier.
•  Based on the Sound Velocity and Three Point Bend Tests, the Young’s Modulus of .35 molar
sodium borate glass is between 42.4 and 71.00 GPa.
•  There was a great deal of error in this experiment. Possible sources include faulty machine
grips, incorrect length measurements, rod slippage.
Future directions
•  Testing rods of different compositions to determine how composition affects Young’s Modulus.
•  Determining a most accurate method for Young’s Modulus analysis.
•  Run multiple tests to compare data points and eliminate error.
•  Stiffness is a crucial material property and can help engineers develop more durable
materials.
Scanning Electron Microscopy
References
•  Slip traces look like stairs.
•  Slip planes have the highest density
of atoms. They are angled about 45°
from the deformation axis.
•  In FCC crystals, slip occurs along
the close packed plane: {111} with
slip direction <110> .
Fig. 4 Schematic of the 3
point bend test. Distance
between the two points is L.
The third force is applied at
L/2 [1]
Fig. 8 SEM image for annealed brass rod
[1] L.C. Kimerling, Module D: Mechanical Properties of Crystals and Glasses
[2] L.C. Kimerling and F. Hobbs, Structure and Mechanical Properties of Borate Glasses
[3] Diehl Metal: Brass. <http://www.diehl.com/fileadmin/diehl-metall/dlc/Beispielordner/
Diehl_Metall_Strips_MB30_V2_M-SM.pdf>
Acknowledgements
I would like to acknowledge Professor Kimerling and Mr. Hobbs for their guidance with this
experiment. I would like to thank the members of lab group 4 for their assistance in
conducting the experiment and analysis as well as lab groups 3, 7, and 8 for sharing their
data with us. I would also like to thank the WRAP instructors and 3.014 staff for their support.
rubinjg

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