Sample Formal Lab Report
LABORATORY “0”
THE FRACTURE OF GLASS
John Doe
Jane Roe
Joe Sixpack
John Q. Public
MatE 453
Lab Section 1
August 27, 2013
1
ABSTRACT
The behavior of brittle materials was studied by performing 3-point bend tests on
laboratory glass slides. Both as-received and chemically etched specimens were tested to
failure. The Young’s modulus of the glass was determined from the load–deflection data.
The results demonstrated that the deformation of the glass slides remained elastic up to
the moment of fracture. The fracture strength of the glass was greatly improved by the
chemical etching process; the etched specimens had nearly twice the fracture strength of
the untreated specimens.
1. INTRODUCTION
1.1 Brittle Fracture
Rock, glass and concrete are brittle materials in that they exhibit no plastic deformation
prior to fracture. Since the strain to fracture of brittle materials is entirely elastic, their
strain at fracture and the energy they absorb are undesirably (and sometimes dangerously)
small. Moreover, the fracture strength of brittle materials is controlled by the size of the
largest flaw. Thus brittle materials and structural components made from them have a
very low tolerance for stress-concentrating defects, particularly for those located at the
outer surface, where the highest stresses usually occur.
1.2 Historical Background
The theory of brittle fracture was established by Griffith [1], who used energy arguments
to derive an expression for the conditions that lead to instability, that is, to rapid
propagation of cracks in brittle materials such as glass:
f 
2 E
,
c
(1)
2
where
 f = remote stress at the moment of fracture,
E = Young’s modulus,
 = surface energy of the glass,
c = major axis of an elliptical crack (half crack length).
This equation may be used to compute the stress required to propagate an existing crack
or to compute the size of surface flaw (crack) that will grow rapidly at a given level of
applied stress, leading to failure. Griffith’s work on the fracture of glass is one of the
cornerstones of modern fracture science, and Eqn. (1), as proposed in 1924, is still the
relationship used to describe the behavior of brittle materials, such as glass.
1.3 Laboratory on the Fracture of Glass
In this laboratory session, small specimens of a soda-lime-silica glass were tested to
failure in 3-point bending to determine their fracture stress in the as-received condition
and after a chemical etch that removed many of the larger surface flaws. Both modulus
and fracture data were obtained.
2. EXPERIMENTAL PROCEDURES
2.1 Materials
Several standard laboratory glass slides with nominal dimensions of 0.93 x 25.5 x
63.5 mm were provided. These dimensions were confirmed by measurement with a
micrometer. The glass slides were handled only at their edges so as to avoid introducing
additional surface damage (flaws).
3
2.2 Specimen Preparation
Eight slides were selected for testing; of these, four were tested in the as-received
(untreated) condition and four were given a chemical etch treatment to remove surface
flaws prior to testing. The etched specimens were immersed in a 5% hydrofluoric (HF)
acid solution for 10 minutes, after which they were washed successively in tap water, in
absolute ethyl alcohol, and finally in petroleum ether.
2.3 Testing Procedures
Each of the four laboratory groups tested two specimens—one untreated and one etched.
The slides were mounted in a 3-point bending test fixture (see Fig. 1). Mass was added
as shown, and the resulting mid-span deflection (indicated by a dial gage) was recorded.
Since the growth of cracks may initially be quite slow, at least 30 seconds were allowed
to elapse before an additional mass was added. Mass was added in large increments
(500 g) until a total of 1500 g was applied, after which mass was added in smaller
increments (50 g). Mass was added until the specimen failed, and the time delay between
the application of the last mass and the failure event was recorded.
3. RESULTS
3.1 Load–Deflection Results
The measured values of mass and resulting mid-span deflection for the untreated and
etched specimens are listed in Tables 1 and 2, respectively, and are plotted in Figs. 2
and 3. It is evident from the linear relationships between load and deformation observed
in the two graphs that the deformation of both the untreated and the etched slides
remained elastic until fracture occurred. A regression analysis was performed for the
data in both Figs. 2 and 3, the results of which are shown in each figure. The average
4
slope of the two mass–deformation experiments was 2.22 kg/mm. The Young’s modulus
of the glass slides was then calculated from the deflection relation for a beam loaded in
3-point bending:
y
FL3
,
48EI
(2)
where
y = mid-span deflection for 3-point bending,
F = applied force,
L = span between beam supports,
E = Young’s modulus,
I = moment of inertia.
Note that I  bh 3 /12 , where b = beam width and h = beam depth (thickness). For b =
25.5 mm and a measured value of h = 0.922 mm, I = 1.666 mm4. Equation (2) may be
rearranged to give
 F  L3 
 ,
E   
 y  48I 
(3)
where
F
= the slope of the load–deflection plot.
y
For the data in Figs. 2 and 3,
F m
kg
m
N
 g  2.22
 9.81 2  21.8
,
y
y
mm
s
mm
N  (63.5mm)3
N

E   21.8
 69,800
 69.8GPa .

4
mm  (48)(1.666 mm )
mm2

The experimental value of 69.8 GPa compares favorably with a textbook value for
E-glass of 72.3 GPa [2].
5
3.2 Fracture Stress Calculation
The fracture loads observed for all the untreated and etched specimens tested are listed in
Table 2. The fracture strength was calculated using the relationship for elastic stresses in
a beam loaded in 3-point bending:
f 
3FL
.
2bh 2
(4)
An example calculation for an untreated specimen is as follows:
f 
(3)(1814.5g) (9.81 m/s2 )(63.5mm)
 78.2 MPa .
(2)(25.5mm)(0.922 mm)2
The average and standard deviation values were calculated for the pooled fracture
strength data (Table 3). The number of observations is really too small to consider these
statistics to be accurate, but is sufficient to illustrate certain general tendencies in the
fracture behavior: compared with the untreated specimens, the etched specimens had
much higher fracture strengths and proportionately much greater standard deviation of
fracture strengths, indicating more variability in the etched results.
4. DISCUSSION
4.1 Load–Deformation Behavior
The load–deformation behavior of the two glass slides tested in 3-point bending remained
linear up to the point of fracture. Thus no mechanism of deformation other than the
elastic stretching of atomic bonds is evident. While the specimens were not unloaded, it
would be expected that the induced strains (deflections) would be totally recovered on
unloading.
6
The calculated value of Young’s modulus agreed well with a published value. Thus it
seems that the simple experiment performed in this laboratory provided an adequate
method of determining that quantity. Only a small difference in slope (and hence
Young’s modulus) was observed between the untreated and etched slides. This
observation was expected because Young’s modulus is a bulk property and is therefore
not affected much by the presence of surface flaws.
4.2 Effect of Surface Treatment
The etched specimens had a substantially greater fracture strength and a more than
proportionately greater variability in fracture strength. The average strength of the etched
specimens was roughly double that of the untreated specimens. From this observation it
must be concluded that the etching treatment greatly reduced the number and size of
surface flaws present. This phenomenon was first described by Joffé, and indeed the
increase of the fracture stress of specimens tested in solution as a consequence of the
dissolution of the outer surface is known as the Joffé effect [3].
5. CONCLUSIONS
The conclusion can be written in paragraph form, bullets or a combination of both
(preferred).
1. The deformation of the glass slides remained elastic until the moment of fracture.
2. The calculated value of Young’s modulus agreed with a textbook value.
3. Removing surface flaws by chemical etching greatly increased the level and
variability of fracture strength.
4. The technique proved valuable in analyzing etched glass under this type of
deformation. The technique may also be applied to other similar investigations.
7
6. ACKNOWLEDGMENTS
This simulated laboratory report utilized data from an actual laboratory performed by
Prof. N. R. Sottos while a student at the University of Delaware.
7. REFERENCES
1. Dieter, G. E., Mechanical Metallurgy, McGraw-Hill, 2nd Edition, 1961, p. 253.
2. Askeland, D. R., The Science and Engineering of Materials, PWS-Kent Publishing
Company, 1989, p. 591.
3. Cottrel, A. H., The Mechanical Properties of Matter, Wiley, 1964, p. 346.
8
Table 1. Added mass and measured mid-span deflections for untreated glass slide
Mass added (g)
Total mass, m (g)
Deflection, y (mm)
190.1
190.1
0.0
302.0
492.1
0.13
197.7
689.8
0.25
100.6
790.4
0.29
165.0
955.4
0.37
200.0
1155.4
0.46
297.2
1452.6
0.60
58.1
1510.7
0.61
45.8
1556.5
0.63
51.5
1608.0
0.65
51.4
1659.4
0.68
53.5
1712.9
0.70
55.3
1768.2
0.74
46.3
1814.5
0.75
Time to fracture = 60 s.
9
Table 2. Added mass and measured mid-span deflections for etched glass slide
Mass added (g)
Total mass, m (g)
Deflection, y (mm)
190.1
302.0
288.0
280.2
297.2
165.0
45.8
46.3
47.6
48.5
58.1
53.5
56.6
53.5
54.9
60.7
40.0
41.1
66.7
36.1
49.6
81.9
47.2
29.4
57.9
190.1
492.1
780.1
1070.3
1367.5
1532.5
1578.3
1624.6
1672.2
1720.7
1778.8
1832.3
1888.9
1942.4
1997.3
2058.0
2098.0
2139.1
2205.8
2241.9
2291.5
2373.4
2420.6
2450.0
2507.9
0.0
0.12
0.25
0.38
0.51
0.59
0.61
0.63
0.65
0.67
0.69
0.72
0.74
0.77
0.79
0.82
0.83
0.85
0.88
0.89
0.91
0.95
0.97
0.98
1.02
Time to fracture = 10 s.
10
Table 3. Fracture stress for the untreated and etched glass slides
Condition
(group)
Fracture stress
(MPa)
Delay time
(sec)
Untreated 1
62
65
Untreated 2
74
25
Untreated 3
72
60
Untreated 4
59
15
Etched 1
79
14
Etched 2
137
30
Etched 3
103
10
Etched 4
131
40
Mean fracture
stress (MPa)
Standard
deviation (MPa)
67
7
112
27
Fig. 1. Schematic diagram of the experiment.
11
Fig. 2. Added mass versus measured mid-span deflection for the untreated glass slide.
12
Fig. 3. Added mass versus measured mid-span deflection for the etched glass slide.
13
Sample Letter Report
ACE GLASS TESTING, INC.
“Serving your glass testing needs since 1958”
Aug. 21, 2012
Mr. C. Threw
DontThrowStones Glass Co.
836 Brittle Blvd.
Clearview, CO 75232
RE: Load bearing ability of etched glass
Dear Mr. Threw,
I am pleased to report that we have completed testing of your standard laboratory glass
slides. Several tables, charts, and sample calculations are attached to summarize our
findings. A full laboratory report that includes experimental procedures and analysis is
available upon request. You are free to publish these results as part of the qualityassurance documentation for your company’s finished glass products.
Eight slides were tested. Four were tested in the as-received condition and four were
chemically etched in a 5% HF solution for 10 minutes. The Young’s modulus and
strength of the glass slides were tested by three-point bend tests, as shown in Fig. 1. The
results are summarized in Table 1. As shown in Figs. 2 and 3, deformation of the glass
slides remained elastic up to the moment of fracture. The Young’s modulus of the glass
for both types of specimen was determined from the load–deflection data to be
approximately 69.8 GPa, a value that compares favorably with a textbook value of
72.3 GPa for E-glass.
The tests showed that the fracture strength of brittle materials is extraordinarily sensitive
to flaws introduced at their surface during manufacture and subsequent usage. The
fracture strength of the glass slides was greatly improved by the chemical etching
process. The chemical etch reduced the size of the larger flaws and resulted in a doubling
of fracture strength. This phenomenon is known in the literature as the Joffé effect. Note
that there was proportionately more scatter in the results for the etched specimens.
Sample calculations for modulus and strength are appended to this report.
Please call me at (515) 555-1234 if you have any questions regarding the results. We
look forward to assisting you with glass testing in the future.
Sincerely,
John Doe, Jane Roe, Joe Sixpack, and John Q. Public
Materials Engineering Students, Iowa State University
Enclosure
cc: Professor of MatE 453/MSE 553
15
16
Table 1. Fracture stress for the untreated and etched glass slides
Condition
(group)
Fracture stress
(MPa)
Delay time
(sec)
Untreated 1
62
65
Untreated 2
74
25
Untreated 3
72
60
Untreated 4
59
15
Etched 1
79
14
Etched 2
137
30
Etched 3
103
10
Etched 4
131
40
Mean fracture
stress (MPa)
Standard
deviation (MPa)
67
7
112
27
Fig. 1. Schematic diagram of the experiment.
17
Fig. 2. Added mass versus measured mid-span deflection for the untreated glass slide.
18
Fig. 3. Added mass versus measured mid-span deflection for the etched glass slide.
19
Sample calculations
Modulus of elasticity
The Young’s modulus of the glass slides was calculated from the deflection relation for a
beam loaded in 3-point bending:
y
FL3
,
48EI
(1)
where
y = mid-span deflection for 3-point bending,
F = applied force,
L = span between beam supports,
E = Young’s modulus,
I = moment of inertia.
Note that I  bh 3 /12 , where b = beam width and h = beam depth (thickness). For b =
25.5 mm and a measured value of h = 0.922 mm, I = 1.666 mm4. Equation (1) may be
rearranged to give
 F  L3 
 ,
E   
 y  48I 
(2)
where
F
= the slope of the load–deflection plot.
y
For the data in Figs. 2 and 3,
F m
kg
m
N
 g  2.22
 9.81 2  21.8
,
y
y
mm
s
mm
N  (63.5mm)3
N

E   21.8
 69,800
 69.8GPa .

4
mm  (48)(1.666 mm )
mm2

20
The experimental value of 69.8 GPa compares favorably with the value for E-glass of
72.3 GPa given Askeland’s textbook, The Science and Engineering of Materials,
PWS-Kent Publishing Company, 1989, p. 591.
Fracture strength
The fracture strength was calculated using the relationship for elastic stresses in a beam
loaded in 3-point bending:
f 
3FL
.
2bh 2
(3)
An example calculation for an untreated specimen is as follows:
f 
(3)(1814.5g) (9.81 m/s2 )(63.5mm)
 78.2 MPa .
(2)(25.5mm)(0.922 mm)2
Complete data are given in Table 1.
21
Sample Presentation Report
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23
Purpose
• Explore behavior of brittle materials
• Determine Young’s modulus and
fracture strength of glass slides
• Investigate effect of chemical etch on
properties of glass
24
Theoretical Background
• Glass is brittle
• Brittle fracture is described by Griffith’s
equation,
2 E
c
f 
where  f is remote fracture stress and
c is half crack length
Brittle materials exhibit little or no plastic deformation prior to failure, so the amount of
energy a brittle material can absorb is small.
In 1924, Griffith proposed an equation to relate remote fracture stress, Young’s modulus,
surface energy, and half crack length in brittle materials (see Dieter, G. E., Mechanical
Metallurgy, 2nd ed., McGraw-Hill, 1961, p. 253). Notice that as crack length is
increased by a factor of four, the remote fracture stress is reduced by one-half. We
therefore expect the amount of load that our glass specimens can sustain to be highly
dependent on the presence and size of small cracks, or flaws.
25
Specimen Preparation
•
•
•
•
Standard laboratory glass slides
Dimensions: 0.93 x 25.5 x 63.5 mm
Four tested in “as-received” condition
Four tested after chemical etch
– Immersion in 5% HF solution for 10 min.
– Washed in tap water
– Rinsed in ethyl alcohol and petroleum
ether
A micrometer was used to confirm slide dimensions.
The specimens were handled by the edges at all times to reduce the introduction of
additional surface flaws.
26
Mass was added to the weight bucket. Deflection was measured by a dial gage at the
center of the slide. The masses were added in 30 s intervals to allow for slow crack
growth. Large masses (500 g) were added until a total of 1500 g was applied; then small
masses (50 g) were added until fracture.
27
Load Deflection Results
To tal A dded M ass (g)
3 00 0
Etc hed
y = 2 2 8 0 .2 x + 1 9 9.5 8
2 50 0
2
R = 1 .0 0 0
U ntreated
2 00 0
Linear
(Etc hed)
Linear
(U ntreated)
1 50 0
1 00 0
y = 21 7 3 .5 x + 1 7 4.7 2
2
R = 0 .99 9
50 0
0
0.0
0 .2
0 .4
0 .6
0 .8
1.0
1 .2
Mid -s p a n D e fle c tio n (m m )
This graph shows the relationship between load and deflection for an untreated and an
etched glass slide. Both curves remain linear until specimen fracture, indicating that both
the untreated and etched glass slides undergo only elastic deformation. The Young’s
moduli for the samples were nearly identical since the slopes of the load–deflection
curves were similar. Using linear beam theory, we can calculate the Young’s modulus of
the untreated slide from the formula
FL3
y
48EI
where y = mid-span deflection, F = applied force, L = beam length, E = Young’s
modulus, and I = moment of inertia.
Rearranging, and noting that F/y is the slope of the load–deflection plot, we find
F m
kg
m
N
 g  2.22
 9.81 2  21.8
,
y
y
mm
s
mm
N  (63.5mm)3
N

E   21.8
 69,800
 69.8GPa .

4
mm  (48)(1.666 mm )
mm2

This value is close to the published value of Young’s modulus for glass, 72.3 GPa (see
Askeland, D. R., The Science and Engineering of Materials, PWS-Kent, Boston, 1989,
p. 591).
28
Fracture Stress for the Untreated
and Etched Glass Slides
Condition
(group)
Untreated
Untreated
Untreated
Untreated
Etched
Etched
Etched
Etched
(1)
(2)
(3)
(4)
(1)
(2)
(3)
(4)
Fracture
stress
(MPa)
Delay
time
(sec)
62.07
74.33
72.09
59.10
65
25
60
15
78.50
136.82
103.00
130.64
14
30
10
40
Mean fracture Standard
stress
deviation
(MPa)
(MPa)
66.9
7.4
112.5
26.8
Fracture stress calculation
Using elastic beam theory, we have
f 
3FL
2bh 2
where f = fracture stress, F = applied force, L = beam length, b = beam width, and h =
beam depth.
Substituting in values for untreated slide 3 gives
f 
(3)(1814.5g) (9.81 m/s2 )(63.5mm)
 78.2 MPa .
(2)(25.5mm)(0.922 mm)2
The etched specimens were roughly twice as strong as the untreated specimens.
Referring to the Griffith equation, it can be concluded that etching the glass reduced the
size of the flaws present. The phenomenon was first described by Joffé (see Cottrel,
A. H., The Mechanical Properties of Matter, Wiley, 1964, p. 346).
29
Conclusions
• Deformation of glass remained elastic
until moment of fracture
• Calculated Young’s modulus agreed
with published values for glass
• Etched specimens gave much higher
fracture strengths due to Joffé Effect
30