1. • Annealing a material eliminates the work hardening in the
crystal, resulting in larger grain sizes and a smaller number of
dislocations. This in turn results in a lower dislocation density
and yield strength.
• There are two data sets that indicate error.
• The first would be the speed of sound tests for the Borate
Glass rods. Composition for max Y came out to be xNa2CO3 = .
28. We can’t be sure because of the lack of a trend in the
graph, especially in comparison to other groups.
• The second would be the tensile tests for the brass rods. Trial
1 prematurely ended, which I believe, weakened the material
for the second trial. Then for the poor annealed Y value, in the
lab it seemed the Instron wasn’t pulling directly vertical.
• Between the 3 methods for calculating Y, it seems that speed
of Sound and Tensile do the best job. But, speed of sound
testing is more versatile because a uniform specimen is not
required.
Strength and stiffness of a material are determined by its stress-strain
relationship. This relationship is described as:
σ = Yε
σ is the stress (pressure [GPa]), ε the strain (displacement [m/m]), and Y
the Young’s modulus [GPa]. Y is the stiffness of the material. When
straining a material, deformation is initially elastic and is described by a
constant σ/ε slope. Elastic deformation exists up to critical stress,
known as the yield stress, σy. At this point the material plastically
deforms along slip planes.
If a material is too brittle, it will not plastically deform, rather it will fail by
fracture, a propagation of a crack in the material.
In theory, plastic deformation is slowed by “obstacles”. These obstacles are
edge dislocations and screw dislocations. Edge dislocations are defined
when a new plane is inserted into the system. Screw dislocations arise from
shearing planes relative to each other. The number of dislocations per
volume or area is the dislocation density. By increasing dislocation density,
“obstacles” increase, changing, the point of plastic deformation, or yield
stress of the material. These dislocations define grain boundaries.
Work hardening decreases grain size (adding dislocations), thus the
likelihood that dislocations interact increases. Annealing a material will heal
dislocations in a material by heating it up.
Surface slip traces can be visualized using a scanning electron microscope
(SEM). Slip planes are normally along the planes with the highest density of
atoms. These surface slip traces reveal grain boundaries, therefore grain size
and slip density.
Glasses are amorphous solids that lack long range periodicity. They are solid
below their glass transition temperature (Tg) and flow above it. Adding
network modifiers changes the viscosity of the glass, and typically lower it.
Disloca(on
Based
Plas(city
in
Metals
&
Network
Modified
Glasses
Tanner
Guerra
3.014
Materials
Laboratory
Introduc(on
Conclusion
Discussion
References
Modern life depends on material performance; material properties dictate
efficacy. Mechanical properties express how a material will react to physical
forces. Situations often arise where a material with a certain strength and
stiffness is needed. These properties can be adjusted, for example, by
altering processing techniques and adding network modifiers.
Theore(cal
Background
Materials
and
Methods
Results
The experiment confirmed that annealing a material affects
some, but not all, of its mechanical properties. Annealed
materials will have a lower yield strength compared to if it was
unannealed, and work hardened, due to larger grain sizes and a
lower dislocation density. Although, the annealed and
unannealed material should have the same Young’s Modulus,
our results presented the contrary (explained above). The
Borate glass was very brittle because it was below its Tg causing
it to fracture around 2.75 N of force. If strength is required
unannealed/work hardened materials are useful, while
annealing is useful if a material needs further processing.
1. Kimerling,
L.;
Hobbs,
F.
3.014
Module
D
Handout,
2014.
2. Hull,
D.;
Bacon,
D.
J.
In
Introduc(on
to
Disloca(ons
(FiEh
Edi(on);
Hull,
D.;
Bacon,
D.
J.,
Eds.;
BuCerworth-­‐Heinemann:
Oxford,
2011;
pp.
85–107.
3. "Brass
(Copper-­‐Zinc):
MB30."
RolledDiehl.
Diehl
Metal,
n.d.
Web.
I would like to mention Franklin Hobbs as a mentor throughout the experiment as well as Professor Lionel
Kimerling for guiding me. In addition, I would like to acknowledge my group members: Anna Jungbluth, Annie
Dunn, Tiffany Yeh, Chimdimma Okwara, and Julia Rubin. I would also like to think Brian Xiao for this template.
Acknowledgements
Edge Dislocation Grain Boundaries
F
δ
bonds
stretch
return to
initial
Elastic Deformation Plastic Deformation
1. The diameter of an unannealed and an annealed Cu-30wt%Zn
(Brass) rod was measured.
2. The rods were placed into the Instron 2505
machine grips, the distance between the grips
was measured.
3. Force and displacement were zeroed on the
machine, then a tension force was applied to
the rod, straining it at a rate of 3mm/min.
Obtaining Young’s Modulus.
4. Once the measurements were completed, the
rods were placed in a Scanning Electron
Microscope (SEM), to magnify the surface.
5. The magnified slip traces were analyzed to
calculate the grain size and slip density for
the brass rods.
6. In the SEM, Energy-Dispersive X-ray spectroscopy (EDS) was
performed on the rods to calculate composition.
7. Young’s Modulus was confirmed with Sound Velocity (below).
SEM Analysis
Tensile Test
Young’s Modulus of Sodium Borate Glass
0
100
200
300
400
500
600
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
Strain
(MPa)
Strain
(mm/mm)
E1 P1
P2E2
Annealed
Stress vs. Strain: Unannealed & Annealed Rods (Tensile)
E = Elastic Region
P = Plastic Region
Unannealed (Trial 2)
Unannealed (Trial 1)
σy,2
σy,A
* Values effected by trial 1 which was a mis-trial.
Continuing with glasses, reducing viscosity in turn reduces the Tg of
the glass, because the resultant structure is less connected. For
Borate glasses, the reverse is true. At small concentrations of an
alkali modifier (Na2O3 in this experiment) the glass will become more
viscous, thus stiffer and with a higher Y. This is known as the Boron
Anomaly. Essentially, rather than leaving non-bridging oxygens
(NBOs), it creates a stronger network. This continues until it
reverses because the modifier oversaturates the network, letting
NBOs return.
Young’s Modulus of the Brass Rod using Speed of Sound
Density
(kg/m^3)
Speed of Sound
in Rod (m/s)
Young’s
Modulus
8500 3506 104.5 GPa
!
0
0.5
1
1.5
2
2.5
3
0
0.0005
0.001
0.0015
0.002
Force
[N]
Displacement
[m]
Force vs. Displacement:
3 pt. bend of a .35 mol fraction of Na2CO3 borate glass rod
Using the equation: displacement = Force L3 / (12 Y π a3 b)
The trendline of the above graph can be related to Force = slope *
dis. According to the equation, the slope can be set to a constant that
contains young's modulus. So, the slope = (12 Y π a3 b)/L3
Young’s Modulus: Glass (xNa2CO3 = .35): 71 GPa
tguerra@mit.edu
Intersecting slip systems : slip planes are angled
about 45° from the deformation axis, which
is what we expected.
Grain Size: ≈ 56.1 µm * 52.1 µm = 2922.81
µm2 = 2.92281 mm2
Slip density: Slip lines through lines were
counted. (1) = 6/10 µm, (2) 5/10 µm
Density approximately 0.6±0.1 µm-1
Grain Size = 2.92 mm2
Slip Density = 0.6 ± 0.1 µm-1
Brass Rod Composition (EDS):
• 1.85 ± 0.02 wt % O
• 67.2 wt % Cu
• 30.95 ± 0.02 wt % Zn
Composition: About 1-3% deviation from the
manufacturer‘s specifications. About 2%
oxidation on the surface
Young’s Modulus of the Glass Rods using Speed of Sound
0.0
10.0
20.0
30.0
40.0
50.0
60.0
0.00 0.10 0.20 0.30 0.40
Young'sModulus(GPa)
Mole fraction of Na2O3
Young's Modulus of Sodium Borate
Glass vs. Composition
1. Sodium borate glasses of varying alkali concentrations were
produced from H3BO3 and Na2CO3.
2. For 3 point bend, the major and minor axis of xalkali = .35 fiber
were measured, along with length, L, and cut to fit in the apparatus
(below). Then force vs. displacement was recorded to find Young’s
Modulus.
3. For sound velocity, lengths of straight fibers of different
compositions were measured.
4. The speed of sound (vs) of the material was measured by timing
a compression pulse that was propagated through the rod/fiber.
Enabling the calculation of Young’s Modulus (Y).
vs = √ (Y/density)