MATS 402 Materials Lab (I)
Lab Manual
German University in Cairo
Faculty of Engineering and Materials Science
Materials Engineering Department
\Faculties\Engineering Design\MATS\Materials Lab I
Laboratory Manual
MATS 402
Materials Lab I
2013
1
MATS 402 Materials Lab (I)
Lab Manual
Content
I. Laboratory Policies for student
.2
II. Laboratory Safety Rules
.5
III. Lab a
IV. Lab a
e
...7
e
8
V. Experimental
Group 1: Macro/Microstructure
1. (A) Metallograph
.9
2. (B) X- a
...20
Group 2: Heat treatment
3. (E) CCT d a a
..52
4. (J) P a e d a a
.60
5. (F) J
e d
e c
e
...71
6. (G) Ca b
78
Group 3: Mechanical test
7. (H) Hardness
8. (D) Te
..80
e
89
9. (C) Impact
..
10. (I) Strain gauge
97
.101
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I. Laboratory Policies for Students
Introduction
The information presented herein is intended for all students working within the
equipment-related laboratories of the Materials Engineering Department. The policies
outline the laboratory access, working, machines handling and safety practices to be
followed to ensure the health and safety of all students, as well as to avoid any machine
machines damage.
Responsibilities
The Material's engineering equipment-related laboratory policies are written to make you
aware of your surroundings so that you will be less likely to be injured as you work.
Remember that you are responsible for:
Your own health and safety.
The health and safety of those around you.
The security and the safe use of equipment and facilities that you have been
authorized to use.
Understanding and complying with all laboratory policies.
General Laboratory Policies
In order to manage risks, it is necessary to limit access to equipment, laboratories, and
certain storage facilities. The following general policies apply to ALL equipment-related
laboratories within department. Policy pertaining to laboratories identified and posted as
"machinery laboratory" is also to be followed in addition to the general polices outlined
below.
Access, Equipment Use, Safety and Rules
A faculty or staff member must be present in the lab in order for you to
operate any foundry equipments.
You are allowed to access to the laboratory during the time of your
scheduled laboratory and not at any time during open lab hours
assigned for other groups.
If you miss to attend the laboratory with your scheduled group and you
want to make up the experiment with another group which you are not
normally scheduled, you MUST have accepted reason for the absence
and you MUST get the approval from the lab Coordinator. However,
as per the GUC policy announced to the students If a
den
attends other than his/ her scheduled classes, the attendance,
assignments and quizzes will not be counted.
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Lab Manual
You are not permitted to enter the lab if you are 15 minutes late than
your schedule time.
You should read your experiments before coming to the lab, you will
be pre-tested and graded before starting the experiment (10% from the
total lab weight)
Your behaviour during the lab time (the work with Materials, Machine
and Computer) will be recognized and will be graded (20% from the
total lab weight). Keep the work area clean and tidy. When you have
finished for the day, make sure all tools, equipment, and supplies are
returned to their proper storage (including electronic components back
to drawers), and the equipment is shut down.
You should not attempt to operate equipment or apparatus unless you
are specifically authorized to use that equipment, or you must ask one
of the lab supervisors. The cost of any damage will be directly
charged to you.
Do not attempt to modify or repair any equipment or apparatus unless
you inform one of the lab supervisors.
You should locate posted information regarding emergency contact
information and identify the location of fire extinguishers and eye
washes (if appropriate) within the laboratory.
You should review and understand all additional posted access, safety
warnings, and safety policies for the laboratory.
All injuries that occur in the laboratory must be reported immediately
to Police and Safety Services and one of the lab supervisors.
If you create a hazard you must control it. It is important to notify and
involve a faculty member or technician where the hazard is located.
Consumption of food and drink is prohibited in those laboratories
where such restrictions are posted.
Suitable clothing and footwear as determined by the Materials Eng. Department must be
worn in the laboratory. Additionally, please read carefully the following laboratory
safety Rules
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II. Laboratory Safety rules
In case of a fire:
Notify your lab supervisor. If the fire cannot be contained, sound the alarm. Exit
using the procedure below (when the fire alarm sounds).
If the fire alarm sounds:
Exit out the main door of the laboratory to the end of the hall. Move a safe distance
away from the building.
In case of a spill:
Notify one of the supervisors immediately.
If skin or eyes are affected, move immediately to the eye-wash station and flush with
water.
In case of burn:
Notify one of the supervisors immediately.
Move immediately to the sink and flush the affected area with water.
In case of an injury:
Notify one of the supervisors immediately.
In case of mechanical malfunction:
Notify one of the supervisors immediately.
Emergency numbers:
Fire:
Ambulance:
Public Safety:
Health Protection Office:
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Safety Rules:
You must wear impact resistant safety glasses with permanent plastic fixtures on the
side. You also must have shoes that are non-porous in nature. During laboratory
periods when experiments are being conducted, you must also wear
pants/jeans/slacks. Depending on other experiments, further precautions may be
needed. If this is the case, your teaching assistant will give you guidance.
ABSOLUTELY NO EATING, DRINKING, OR SMOKING IN THE MATERIALS
SCIENCE LAB. Please do not discard food or beverage containers in the lab waste
cans. They must be discarded before entering the lab.
Violation of the safety rules will result in you being asked to leave the lab. If you are
asked to leave, you will take a zero for the lab report.
Feedback is always welcome for suggestions for improvement of the lab and/or
about safety concerns.
Materials Engineering Department
Prof. Dr. rer. nat. Ahmed Abd El-Aziz
Aziz
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MATS 402 Materials Lab (I)
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III. Laboratory weight
Quiz (theoretical)
20%
Class work (Practical)
40%
Report (theoretical)
40%
Total
100%
Practical (experiment and report)
Received at:
___________________________
Report:
- 5 points
ID
Pre-test
: ________ ________
________
: _____/ 20% _____/
_____/
: _____/ 40% _____/
_____/
Behaviour (Class work,
Preparation, Measurements,
Cleaning)
Report (Introduction,
Procedure, Results, Discussion,
Figures, Conclusion)
: _____/ 40% _____/
Total
:
/ 100%
_____/
/
/
____________
Signature
Very important: Please submit your report within one week from the experiment
time.
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IV. Laboratory report
What should be in the report
1. Write precisely your report, introduction, experimental procedure, results and
discussion. Do not include more than very brief necessary details of the
experimental procedure.
3. As a result, explain and analyze the diagrams of the figures what you will draw
or get from the experiment.
4. As discussion describe and discuss your obtained results
5. Write some sentences as a summery about your results.
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V. Experimental
{Group 1}: Macro/Microstructure
Exp. (A): Metallography
1. Introduction
Metallography can be defined as the visual study of the constitution and structure of
materials. Metallographic examinations can be broadly classified into two types namely,
macroscopic examinations and microscopic examinations. Macroscopic examinations
refer to the observations carried out at a magnification of x10 of less. Microscopic
examinations, on the other hand, refer to the examination of the structure at a
magnification greater than x10. Microscopic examinations, depending on the nature of
information to be extracted, can be accomplished using an Optical Microscope (up to
x2000) or Scanning Electron Microscope (up to x 50000) or a Transmission Electron
Microscope (up to x500000). For most of the routine purposes in optical microscope is
used to obtain first hand information on the geometric arrangement of the grains and
phases in a material. In order to retain the information visualized using the microscope,
microstructural details are often recorded on a 35 mm film or a Polaroid film or by
digital camera.
The study of microstructaral details is important due to its correlation with the ensuing
mechanical properties of the material. As an example, if material A exhibits a more
homogeneous and refined microstructure than material B , it may very well be anticipated
that material A will exhibit better room temperature properties when compared to
material B.
In order to metallographically examine a specimen, it is essential to learn about the
various steps that are required to prepare it. The following section briefly describes the
various steps involved in the metallographic preparation of the samples.
Ferrite
Ferrite -perrlite
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Hypo-Eutectoid
Eutectoid
Hyper-Eutectoid
Martensite
Grey iron
Nodular (ductile) iron
Fig. 1: Examples of grain structures of carbon steel and cast iron.
The basic operation outlining the metallographic preparation
of the specimens is as follows:
1. 2.1 Selection of the Size of the Specimen:
The selection of the size of the specimen is dependent on the nature of material and the
information to be gathered. Normally, the linear dimensions may vary from 5 mm to 30
mm while the thickness is kept lower than the linear dimensions.
2.2
Mounting the Specimen:
The primary purpose of mounting specimens is for convenience in handling specimens
of difficult shapes or sizes during the subsequent steps of preparation and examination.
A secondary purpose is to protect and preserve extreme edges or surfaces defects during
preparation. Specimens also may require mounting to accommodate various types of
automatic devices used in laboratories or to facilitate placement on the microscope stage.
An added benefit of mounting is the ease with which a mounted specimen can be
identified by name, alloy number, or laboratory code number for storage by scribing the
surface of the mount without damage to the specimen.
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Mount Size and Shape
As the size of the specimen increases, so does the difficulty of keeping the specimen
surface area flat during grinding and polishing. A saving in the time required for the
preparation of one large metallographic specimen may be realized by sectioning the
specimen into two or more smaller specimens. A specimen having an area of
approximately 1/4 sq in. is perhaps the most suitable; the maximum area should be
limited to about 4 sq in. if possible. Thickness of the mount should be sufficient to
enable the operator to hold the mount firmly during grinding and polishing and thereby
to pervent a rocking motion and to maintain a flat surface. Circular mounts are
commonly 1 to 2 in. in diameter and are the most easily handled. The length-to-width
ratio of rectangular mounts should be limited to approximately 2 to 1 to facilitate
handling (See Figure 1).
Figure (2) A mounted specimen (shows typical dimensions)
Mounting Methods
The method of mounting should in no way be injurious the microstructure of the
specimen. Mechanical deformation and the heat are the most likely sources of injurious
effects. The mounting medium and the specimen should be compatible with respect to
hardness and abrasion resistance. A great difference in hardness or abrasion resistance
between mounting media and specimen promotes differential polishing characteristics,
relief, and poor edge preservation. The mounting medium should be chemically resistant
to the polishing and etching solutions required for the development of the microstructure
of the specimen.
Mounting Methods:
Clamp Mounting
Compression Mounting
Cold Mounting
Conductive Mounting
Compression mounting
Compression mounting, the most common mounting method, involves molding around
the specimen by heat and pressure such molding materials as bakelite diallyl phthalate
resins, and acrylic resins. Bakelite and diallylic resins are thermosetting, and acrlyic
resins are thermoplastic. Both thermosetting and thermoplastic materials require heat and
pressure during the molding cycle, but after curing, mounts made of thermosetting
materials may be ejected from the mold at maximum temperature. Thermoplastic
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materials remain molten at the maximum molding temperature and must cool under
pressure before ejection.
Mounting presses equipped with molding tools and heater, are necessary for
compression mounting. Readily available molding tools for mounts having diameters of
25, 30, 40, 50 mm. It consists of a hollow cylinder of hardened steel, a base plug, and a
plunger (See Figure 3).
A specimen to be mounted is placed on the base plug, which is inserted in one end of the
cylinder. The cylinder is filled with appropriate amount of molding material in powder
form, and the plunger is inserted into open end of the cylinder. A cylindrical heater is
placed around the mold assembly, which has been positioned between the platens of the
mounting press. After the prescribed pressure has been exerted and maintained on the
plunger to compress the molding material until it and the mold assembly have been
heated to the proper temperature (see Table 1, the finished mount may be ejected from
the mould by forcing the plunger entirely through the mold cylinder.
Not all materials or specimens can be mounted in thermosetting or thermoplastic
mounting mediums. The heating cycle may cause changes in the microstructure, or the
pressure may cause delicate specimens to collapse or deform. The size of selected
specimen may be to large to be accepted by the available mold sizes. These difficulties
are usually overcome by cold mounting.
Fig(3) Struer LabosPress-1 machine
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Table (1) embedding order of Struers LaboPress-1 machine.
2.3
Grinding
Grinding is a most important operation in specimen preparation. During grinding the
operator has the opportunity of minimizing mechanical surface damage that must be
removed by subsequent polishing operations. Even if sectioning is done in a careless
manner, resulting is severe surface damage; the damage can be eliminated by prolonged
grinding. However, prolonged polishing will do little toward eliminating severe surface
damage
introduced
by
grinding.
The grinding procedure involves several stages, using a finer paper (higher number) each
time. Each grinding stage removes the scratches from the previous coarser paper.
Between each grade the specimen is washed thoroughly with water to prevent
contamination from coarser grit present on the specimen surface.
Rough Grinding: Rough grinding is carried out on the emery belt surface in order to
round off the corners, if necessary and to remove deep scratches from the surface.
Fine Grinding:
Fine grinding involves rubbing of the specimen surface against the silicon carbide
powders bonded onto specially prepared papers. There are various grit sizes of silicon
carbide papers and. the ones normally used are 400 grit, 600 grit and 1000 grit papers.
These papers are normally mounted on a flat surface. Grinding involves holding the
specimens face downwards on the abrasive paper followed by rubbing in forward and
backward directions until the surface is covered with an even pattern of fine scratches.
The process is repeated with successively finer grade papers (increase in grit number).
With each change of paper, the specimen should be turned through 90 to facilitate the
observation of the disappearance of the previous scratch marks. In addition, at every
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MATS 402 Materials Lab (I)
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new stage the specimen and equipment should be washed of grit and dirt from the
preceding grinding.
All grinding should be done wet, provided water has no adverse effects on any
constituents of the microstructure. Wet grinding minimizes loading of the abrasive with
metal removed from the specimen being prepared. Water flushes away most of the
surface removal products before they become embedded between adjacent abrasive
particles. Thus the sharp edges of the abrasive particle remain exposed to the surface of
the specimen throughout the operation.
Another advantage of the wet grinding is the cooling effect of the water. Considerable
frictional heat can develop at the surface of a specimen during grinding and can cause
alterations of the true microstructure - for example, tempering of martensite in steel that cannot be removed during polishing. Wet grinding provides effective control of
overheating.
2.4
Polishing:
Polishing discs are covered with soft cloth impregnated with abrasive diamond particles
and an oily lubricant. Particles of two different grades are used : a coarser polish typically with diamond particles 6 microns in diameter which should remove the
scratches produced from the finest grinding stage, and a finer polish typically with
diamond particles 1 micron in diameter, to produce a smooth surface. Before using a finer
polishing wheel the specimen should be washed thoroughly with warm water followed by
alcohol to prevent contamination of the disc.
Rough Polishing:
This stage involves the polishing of the specimen surface on a rotating wheel using
alumina or diamond abrasive with a particle size of about 3 microns. Polishing aids
include diamond particle suspension or alumina powder suspension. In the polishing
stage, the specimen is moved around the wheel in the direction opposite to the wheel
itself.
Fine Polishing:
This stage involves the removal of very fine scratches and the thin distorted layer
remaining from the rough polishing stages. Fine polishing is usually carried on a
polishing wheel using fine alumina particles with an average size of less than 1 micron
(normally 0.5 micron size is used). Fine polishing, if properly carried out, yields a
scratch free surface ready for etching.
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MATS 402 Materials Lab (I)
Fig(3)
2.5
Lab Manual
Struers LaboPol 5 Sample Polishing, Grinding device
Etching:
Etching is carried out on the properly dried specimen obtained from fine polishing step.
Etching involves chemically treating the specimen surface using a mild acidic or alkaline
solution. The etching differentially attacks various microstructural features as a result of
their different chemical affinities. This differential attack leads to a non-similar
reflection of light into the objective lens leading to the generation of contrast between
the various microstructural features.
For each type of material, there is appropriate etching solution, See Table (2)
After etching is successfully carried out, the specimen can be taken to the optical
microscope for microstructural examination.
Etching Solution
Nital or Picral
Ferric Chloride
Cds
Material
Cast Iron
Stainless steel
Cast iron, Steel
Ferritic & Martensitic
-
Copper & alloys
Stainless steels
Table (2) Etching solutions
2.6
Cleanliness
Cleanliness is an important requirement for successful sample preparation. Specimens
must be cleaned after each step, all grains from one grinding and polishing step must be
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MATS 402 Materials Lab (I)
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completely removed from the specimen to avoid contamination, which would reduce the
efficiency of the next preparation step.
2.7
Sample Storage
When polished and etched specimens are to be stored for long periods of time, they must
be protected from atmospheric corrosion. Desiccators and vacuum desiccators are the
most common means of specimen storage, althrough plastic coatings and cellophane tape
are sometimes used.
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SCOPE
In accordance with the subject matter covered in the present manual, the scope of this
laboratory exercise will be twofold:
1. To obtain experience in the metallographic preparation of metallic specimens, and
2. To observe the various microstructures in Steel sample
Equipment:
Struers LaboPol 5 sample Polishing device.
Zeiss microscope with digital Camera.
PROCEDURE
Steel samples have codes .
1.
2.
3.
4.
5.
Mount the specimen using Struers LaboPress-1 device using the table (1) to find
the correct temperature, pressure, time and number of spoons of molding
granules.
Grind the specimen using the coarser grade MD120 disc laid on the grinding disc.
Hold the specimen face downwards on the MD 120. Turn on Struers LaboPol 5
for 6 min with 300 rpm. Lubricant is water.
Wash the specimen and repeat step 1 using the finer grade MD Allergo disc and
the belonging abrasive liquid (9-15µm). Turn on Struers LaboPol 5 for 5 min with
150 rpm.
Wash the specimen when only fine scratch marks are obtained.
Polish the specimen using a cloth-covered rotating MD Mol disc with diamond
liquid ( 3µm) and lubricant RED. as the polishing agent until a flat and scratchfree mirror -like finish is obtained ( 10min, 150 rpm)
(see Table 3).
Grinding/Pol
Lubricant
Grain size
Disc
(µm)
MD120
Water
MD Allergo
Green
15-9
MD Mol
Red
3
MDNap
Red
1
Table (3) Grinding and polishing routine
6.
7.
Time(Min)
Speed
6
5
10
3
300
150
150
150
Wash first with water and immediately with alcohol and dry.
Have a look at the surface by using the microscope.
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MATS 402 Materials Lab (I)
8.
9.
10.
11.
12.
13.
14.
15.
Lab Manual
Etch the surface of the specimen with 3% alcoholic Nitric (3 parts of concentrated
nitric acid and 97 parts of ethyl alcohol by volume) for a few seconds till you see
any change at the sample.
Rinsing is most frequently used and consists of holding specimen under a stream
of running water and wiping the surface with a soft brush or cotton swab.
After cleaning, specimens may be dried rapidly by rinsing in alcohol, benzene, or
other low-boiling-point liquids, then placed und a hot-air drier for sufficient time
to vaporize liquids remaining in cracks and pores.
The specimen is now ready for observation (compare with examples of Fig. 1).
Observe the specimen under an optical microscope (See the procedure in the next
page).
Ask the experiment supervisor to have a look and if he is satisfied that your
preparation has produced clearly observable microstructures then proceed to step I
1. If not, repolish and re-etch the specimen until the microstructures are
observable.
Sketch the general microstructural arrangement of the various distinguishable
zones stating the magnification used.
Your sketches are to be of high quality. Label all important features neatly.
Guide for 12. Microscope Procedure
Fig(4) Zeiss Microscope Imager MAT
1.
Turn the microscope on.
2.
Push in the light path selector.
3.
Place the specimen on the stage plate.
4.
Move the 5x objective lens into place to focus on the specimen.
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MATS 402 Materials Lab (I)
5.
6.
7.
8.
Lab Manual
Adjust the brightness.
Adjust the coarse and fine adjustment knob until object is focused.
Observe object by using the x-y-table.
Change the magnification step by step till 500x or 1000x and compare it with the
photos presented in the manual.
REFERENCES
1.
W.D. Callister, Jr.,in "Material Science and Engineering, An Introduction," (John
Wiley And Sons (SEA) Pte Ltd, Singapore, 1994).
2.
R.E. Reed - Hill and R. Abbaschian, in "Physical Metallurgy Principles,"(PWSKent Publishing Co., Boston, USA, 1992).
3.
Metals Handbook, ASM Desk Edition, Eds: H.E. Boyer and T.L. Gall, ASM,
Metals Park, OH, USA, Vol. 2, 1985.
4.
Metals Handbook: Metallography and Microstructure, Vol. 9, 9th Edition, ASM,
Metals Park, OH, USA, 1985.
5.
M.N.A. Hawlader, Metallography Laboratory Manual, 1984.
6.
D.S. Clark and W.R. Varne, in "Physical Metallurgy for Engineers", (Van
Nostrand, 1962).
7.
G.L. Kehl, in "The Principles of Metallographic Laboratory Practice", (McGrawHill, 1949).
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{Group 1}: Macro/Microstructure
Exp. (B): X-ray
Bragg Reflection
Determining the Lattice constants of Monocrystals
Objects of the experiment
Investigating and comparing Bragg reflection at an LiF and an NaCl monocrystal.
Determining the lattice constant a0 of NaCl and LiF.
Introduction
X-rays
To generate x-rays we need a source of electrons, a means of accelerating the
electrons to high speeds, and a target for the accelerated electron to interact with.
X-rays are produced when the free electrons cause energy to be released as they
interact with the atomic particles in the target.
Nature of X Rays
X rays are electromagnetic radiation ranging in wavelength from about 100 Å to 0.01 Å.
The shorter the wavelength of the X ray, the greater is its energy and its penetrating
power. Longer wavelengths, near the ultraviolet-ray band of the electromagnetic
spectrum, are known as soft X rays Spectrum. The shorter wavelengths, closer to and
overlapping the gamma-ray range are called hard X rays Radioactivity. A mixture of
a d ee
a ee
a
e X a ,a
ed
c
a c
X rays, which represent only a single wavelength. Both light and X rays are produced by
transitions of electrons that orbit atoms, light by the transitions of outer electrons and X
rays by the transitions of inner electrons. In the case of bremsstrahlung radiation, X rays
are produced by the retardation or deflection of free electrons passing through a strong
electrical field.
X rays are produced whenever high-velocity electrons strike a material object. Much of
the energy of the electrons is lost in heat; the remainder produces X rays by causing
changes in the target's atoms as a result of the impact. The X rays emitted can have no
more energy than the kinetic energy of the electrons that produce them Energy.
Moreover,
the emitted radiation is not monochromatic but is composed of a wide range of
wavelengths with a sharp, lower wavelength limit corresponding to the maximum
energy of the bombarding electrons. This continuous spectrum is referred to by
the German name bremsstrahlung,
c
ea
ba
,
d
,
radiation, and is independent of the nature of the target.
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In addition to the continuous spectrum there are lines, known as the characteristic
X rays, which represent wavelengths that depend only on the structure of the
target atoms. In other words, a fast-moving electron striking the target can do two
things:
It can excite X rays of any energy up to its own energy;
Or it can excite X rays of particular energies, dependent on the nature of the
target atom.
David R. Lide CRC Handbook of Chemistry and Physics 75th edition, 10-227, CRC
Press. ISBN 0-8493-0475-X.
X-ray K-series spectral line wavelengths (nm)
for some common target materials
Target
K
1
K
2
K
1
K
2
Fe
0.17566 0.17442 0.193604 0.193998
Ni
0.15001 0.14886 0.165791 0.166175
Cu
0.139222 0.138109 0.154056 0.154439
Zr
0.070173 0.068993 0.078593 0.079015
Mo
0.063229 0.062099 0.070930 0.071359
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Principles
Bragg Law1
We study crystal structure through the diffraction of photons, neutrons, and electrons.
When the wavelength of the radiation is comparable or smaller than the lattice constant,
we may find diffracted beams in directions quite different from the incident direction.
W. L. Bragg presented a simple explanation of the diffracted beams from a crystal.
Suppose that the incident waves are reflected from parallel planes of atoms in the crystal,
with each plane reflecting only a very small fraction of the radiation, like a slightly
silvered mirror.
In mirror like reflection the angle of incidence is equal to the angle of reflection. The
diffracted beams are found when the reflections from parallel planes of atoms interfere
constructively as in Fig. 1
d
dsin
We treat elastic scattering, in which the energy of the x-ray is not changed on reflection.
Consider parallel lattice planes spaced d apart. The radiation is incident in the plane of
the paper. The path difference for rays reflected from adjacent planes is 2d sin
planes occurs when the path difference is an integral number n of wavelengths , so that
n
2 d sin
This is Bragg law. Bragg reflection can occur only for wavelength
2d. T
parallel planes add up in phase to give a strong reflected beam. If each plane were
perfectly reflecting, only the first plane of a parallel set would see the radiation, and any
wavelength would be reflected. But each plane reflects 10-3 to 10-5 of the incident
radiation, so that 103 to 105 planes may contribute to the formation of the Bragg-reflected
beam in a perfect crystal.
1
See Charles Kittel: Introduction to Solid State Physics
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MATS 402 Materials Lab (I)
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Ba
a
e ec
de c be e d ac
a e a e a a
c a a e
selective reflection of the waves at a set of lattice planes within the crystal. Due to the
periodicity of the crystal, the lattice planes of a set have a fixed spacing d. An incident
wave with the wavelength is reflected with maximum intensity when the Bragg
condition
n = 2 d sin
(I)
n: diffraction order
: wavelength
d: spacing of lattice planes
is fulfilled
Three-dimensional representation of the structure of NaCl
d: Spacing of lattice planes in [100]-direction
a0: lattice constant
The angle shows the direction of the incident and reflected wave with respect to the set
of lattice planes and is often referred to as the glancing angle.
Fig. 2
In a cubic crystal with NaCl structure, the lattice planes run parallel to the surfaces of the
c a
ce
e
e ca e. Their spacing d corresponds to one half the lattice
constant:
d = a0/2
(II)
This lets us use (I) as an equation for determining the lattice constant a0:
n × = a0 × sin
(III)
In other words, to determine a0 we need to measure the glancing angle q for a known
wavelength l and diffraction order n. This method is more precise when the glancing
angles are also measured in higher diffraction orders. In this experiment, the
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molybdenum x-rays are used as radiation of a known wavelength. Table 1 shows its
Table 1: Wavelengths of the characteristic x-ray radiation of Molybdenum.
Line
k
K
/pm
71.08
63.09
24
A Geiger-Müller counter tube is used to detect the x-rays; this instrument and the crystal
are both pivoted with respect to the incident x-ray beam in 2 coupling the counter tube
is turned by twice the angle of the crystal (cf. Fig. 3). The zero point = 0° is
characterized by the fact that the lattice planes and the axis of the counter tube are
parallel to the incident x-ray beam. As the lattice planes are seldom precisely parallel to
the surface of the crystal, the zero point of each crystal must be calibrated individually.
Fig. 3 Schematic diagram of diffraction of x-rays at a monocrystal and 2q coupling
between counter-tube angle and scattering angle (glancing angle) 1 collimator, 2
monocrystal, 3 counter tube
Setup
Setup in Bragg configuration:
Fig. 4 shows some important details of the experiment setup.
Fig. 4 Experiment setup in Bragg configuration
MATS 402 Materials Lab (I)
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Carrying out the experiment2
You will carry out the experiment for NaCl crystal and you will find data for LiF crystal
in next page to calculate its lattice parameter.
Notes:
NaCl and LiF crystals are hygroscopic and extremely fragile. ; avoid mechanical stresses
on the crystals; handle the crystals by the short faces only. If the counting rate is too low,
you can reduce the distance s2 between the target and the sensor somewhat. However, the
distance should not be too small, as otherwise the angular resolution of the goniometer is
no longer sufficient to separate the characteristic K and K lines.
a) Bragg reflection at an NaCl monocrystal:
Fig. 5 Front panel of the X ray Apparatus.
Recording the diffraction spectrum:
2
For more details see attached PDF file [ the manual of the machine]
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Get yourself familiar with the X ray apparatus [see the attached the manual of the
machine and ask your instructor]
Using b3 [Parameter selecting key] adjust the High Voltage to 35 kV and the current
filament to 1 mA.
Press the COUPLED key to activate 2q coupling of target and sensor and set the lower
limit of the target angle to 4° and the upper limit to 24°.
Sa
e
a e X- a A a a
c ea a e
ea e e da a
e
button or the F4 key.
Start measurement and data transfer to the PC by pressing the SCAN key.
When you have finished measuring, save the measurement series under an appropriate
name by pressing the button or the F2 key.
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Fig. 6 Diffraction spectrum of x-rays in Bragg reflection to the third diffraction order at
an LiF monocrystal with logarithmic display of counting rate R.
Parameters of x-ray tube: U = 35 kV, I = 1 mA
Evaluation
In each diagram3, click the right mouse button to access the evaluation functions of the
a e X- a A a a
a d e ec e c
a d Ca c a e Pea Ce e
e a ae
the diffraction spectra.
U
e e
eb
, a
e
d
eac ea a d
ed
e
center values in a table as the glancing angle.
For each glancing angle , calculate the values sin and plot these value pairs in a
diagram. In each case, the results lie along a straight line through the origin; in
accordance with (III), its slope corresponds to the lattice constant a0.
Questions
Which of these is not involved in the diffraction of X-rays through a crystal?
a) Electron transitions
b) Crystallographic planes
c) Nuclear interactions
Constructive interference
2
What is the largest wavelength of radiation that will be diffracted by a lattice
plane of the interplanar spacing d?
a. 0.5d
b. d
c. 2d
d. No limit
3
A crystal has a primitive lattice with a spacing between (100) planes is
0.420 nm. What will the value of the Bragg angle ( ) be for the 100 reflection
of X-rays of wavelength 0.154 nm?
a. 5.3°
b. 10.6°
c. 21.2°
d. 42.4°
4
How could X-ray diffraction be used to determine the phase diagram of an
alloy?
To what voltage would you have to go in order to see the characteristic spectral lines
K and K for tungsten? Would both lines appear simultaneously or would one appear
5
and then the other only after the voltage had been further raised?
3
For LiF crystal you will get the data from the instructor.
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{Group 2}: Heat Treatment
Exp. (E): CCT Diagram by using Dilatometer
1. General Description of a Dilatometer
Dilatometers serve the measurement of a thermal change in length. This change can be a
reversible change or a sum of reversible and irreversible
Fig. 1 General view of Dilatometer DIL801
Change in length,
Phase transformation,
Mass transfer,
Crystallization,
Change in modification and sintering.
Principally, samples (solids, liquids, powders, bulk materials, foils, and fibers) lying in a
sample holder are linearly heated as the case may be cooled. The sample temperature is
recorded by a thermocouple (up to 1550 oC).
The change of length is transmitted by means of a push rod from furnace on linear
variable differential transducer (LVDT).
Measurements can also be carried out under vacuum or inert gas.
The record change in length is strictly a measure a difference. The single push rod
Dilatometer DIL 801 measure the difference between the sample and the sample holder
(See Fig 2).
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Fig(2) the measuring head for Dilatometer
1.1 Dilatometer system components
2. Definitions
2.1 Linear Thermal Expansion:
The change in length of a material resulting from a temperature change. Linear thermal
expansion is symbolically represented by L/L0, where L is the observed change in
length ( L = L1 - LO), and LO and L1 are the lengths of the specimen at reference
temperature T0 and test temperatures T1. Linear thermal expansion is dimensionless, it is
often expressed as a percentage, or in parts per million (such as mm/m) units.
2.2 Mean Coefficient of Linear Thermal Expansion:
The linear thermal expansion per change in temperature. The mean coefficient of linear
thermal expansion, a, is defined as:
= 1/L0 [(L1 - L0) / (T1 - T0)] = [1/L0 ( L/ T)]
(It is customary to designate the coefficient of thermal expansion with the greek letter
alpha ( ). For the mean coefficient, a bar is placed over it, and is referred to as alphabar. In industry, frequently the whole process is referred to as "CTE testing".)
The value of the mean coefficient must be accompanied by the values of the two
temperatures.
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2.3 Instantaneous Coefficient of Linear Thermal Expansion:
The slope of the linear thermal expansion curve at temperature T. Instantaneous
coefficient of linear thermal expansion represented by:
T
= (1/L0) L/dT
The value of the instantaneous coefficient must be accompanied by the temperature at
which it is determined.
There are two main types of transformation diagram that are helpful in selecting the
optimum steel and processing route to achieve a given set of properties. These are
time-temperature transformation (TTT) and continuous cooling transformation (CCT)
diagrams.
CCT diagrams are generally more appropriate for engineering applications as
components are cooled (air cooled, furnace cooled, quenched etc.) from a processing
temperature as this is more economic than transferring to a separate furnace for an
isothermal treatment.
2.4Time-temperature transformation (TTT) diagrams
T (Time) T(Temperature) T(Transformation) diagram is a plot of temperature
versus the logarithm of time for a steel alloy of definite composition.
It is used to determine when transformations begin and end for an isothermal
(constant temperature) heat treatment of a previously austenitized alloy.
In other words a sample is austenitised and then cooled rapidly to a lower
temperature and held at that temperature whilst the rate of transformation is
measured, for example by dilatometry. Obviously a large number of experiments
is required to build up a complete TTT diagram.
2.5 Continuous cooling transformation (CCT) diagrams
It is a plot of temperature versus the logarithm of time for a steel alloy of definite
composition. It measures the extent of transformation as a function of time for a
continuously decreasing temperature. For example a sample is austenitised and
then cooled at a predetermined rate and the degree of transformation to another
phase is measured. Obviously a large number of controlled cooling experiments
are needed to build up a complete CCT diagram.
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3. Scope
The dilatometric technique is used to build the Continuous Cooling Transformation
(CCT) diagram for 42CrMo4 Steel
4. Material and Experimental Procedures
1-The material used in this work is a commercial 42CrMo4steel with the chemical
composition given in Table 1.
C
0.41
Si
0.30
Mn
0.70
Cr
1.10
Mo
0.20
2- To construct the CCT diagrams, dilatometric tests are carried out using 8 mm
diameter, 50 mm long samples (check the length and dimension using vernier caliper).
3- The sample is placed into a holder, usually called the dilatometer tube. The sample,
when it expands, pushes the tube and the push-rod in opposite directions. This movement
is sensed by a transducer. The tube and the transducer are fixed to the same reference
surface with the moving member of the transducer coupled to the push-rod.
Mounting and demounting of the sample will be done by the assistant only!!!
4- Temperature Control and Measurement:
Usually a thermocouple (RtRh10Pt-Pt) is used. It is imperative to measure the
temperature of the sample region (somewhat away from the sample (why??)) precisely,
and to control the furnace to provide uniform sample temperature (see Fig. 3).
Fig. 3 Structure of measuring system
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5- Temperature program:
The sample is heated continuously to 850 oC with heating rate 100K/min, annealed at 850
o
C 10 min, and then cooled at different cooling rates (why?)
Do not start the experiment without the OK of the assistant! The assistant must be
present for starting.
6- Evaluation of data:
2. Use the evaluation software installed on the control computer.
Make a plot of the length change (y-axis) versus temperature (x-axis).
Determine the phase transition temperature (see fig. 4).
Determine a in the rang from 820 oC -790 oC.
Make a plot of the length change (y-axis) versus time (x-axis).
Determine the time at which the phase transformations begine
Make a plot of the temperature (y-axis) versus the time (x-axis linear or log
scale).
Mark the phase transition temperature, and time which is determined
before (see fig. 4).Calculate the personal error
Insert the results into the respective CCT diagram!
Compare experimental data with theoretical data
References:
1. William D. Callister, Introduction of Material science, Ch.10.
2. http://www.matter.org.uk/steelmatter/metallurgy.
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Appendix (CCT diagram)
Fig. 4 Example of such a measurement evaluation
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Fig 5 example of CCT diagram
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{Group 2}: Heat Treatment
Exp. (J): Tin-lead phase diagrams
NOTE: Read the Safety and Procedure sections completely
before starting the lab. Lead is a poison, wear gloves or use
forceps when handling, and do not breathe fumes.
N.B. Report any problems or breakage. You will not be penalized for problems,
even if you helped to create them. We want only to fix problems, not to fix blame.
1. Objectives
To make 4 different alloys of lead and tin (5, 20, 60 and 90% by weight tin).
To melt samples of 100% lead and 100% tin.
To determine a rough phase diagram of the Pb-Sn alloy system.
To observe and record the microstructure of each alloy.
To report on the relative mechanical properties of these alloys.
2. Materials and equipment
Ring stand with ring and clamp, wire triangle, two-jaw clamp to hold thermocouple.
K-type thermocouple
Propane torch with flint lighter/lighter
Crucible, Crucible tongs
Dish, aluminum, weighing
Spatula, stainless, large
Spatula, stainless, small
Digital balance
Forceps, metal, coarse
Tin, bulk stock cut up
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Lead, c
c
e c
Lab Manual
ead
Plastic beaker
Metallurgical microscope
Stereo microscope
Paper towel
Sn-Pb
3. Safety
1. Read the Material Safety Data Sheets (MSDS) provided for lead and tin, before
starting work.
2. Note position of nearest fire extinguisher.
3. Note position of nearest telephone. It has emergency numbers marked on it.
4. Turn on fume hood fan and light switches (switches on either side of fume hood glass).
Check that Magnehelic gauge indicates acceptable flow rate/pressure differential (see
sign on fume hood for acceptable reading).
5. All team members must wear goggles or face shields at all times.
6. Keep fume hood glass about half way down and keep the glass between your face and
the experiment.
7. Remember that crucibles and samples are hot. Carefully use tongs to handle crucibles.
When pouring molten material, grip edge of crucible firmly and carefully with point of
tongs. Trying to cradle crucible does not work.
8. Apply only enough heat to the crucible to liquefy the sample. DO NOT continue to
heat indefinitely after melting is complete; you may be able to turn down torch and still
maintain melt.
9. Melt should not become red hot. If it does, it is probably covered in excess dross. In
any event, do not plunge thermocouple into it until it has taken on the liquid silver
appearance of mercury. Otherwise the thermocouple may break.
10. Turn off torch firmly but gently -- gas control is by way of a delicate needle valve
which is easily damaged by overtightening.
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11. LIGHT AND USE TORCH ONLY WHEN ACTUALLY HEATING SAMPLES
DO NOT LEAVE IT ON OTHERWISE THIS IS WASTEFUL AND DANGEROUS
4. Procedure
N.B. Start your work with the high % tin alloys. These melt at lower temperatures and
will give you a feel for temperature, melt time, use of thermocouple, etc.
N.B. Please read each numbered section of this procedure completely before starting to
perform the operations called for by that section.
N.B. You should not have to adjust the position of the crucible
assembly to one side for lighting or to remove it as a heat source.
just slide whole torch
1. Use an aluminum weighing dish and weigh out the correct proportion of lead and tin.
Record the weights of your metals. Use larger pieces of material to get close to the
desired weights and then use progressively smaller pieces to reach the actual final weight.
Your sample mixtures need only be within ~ +/- 1% of the stated sample proportions, but
be sure to record exactly what the final figures are.
Use the coarse metal tweezers and/or spatulas to handle the tin and lead.
A total weight of about 50 grams for each sample should suffice --this will provide the
needed depth-of-melt of approximately 5-10 mm. The 90% tin mixture will require about
40-45 grams of tin, and the 5% tin mixture will require about 45-50 grams of lead.
Be sure that the balance is at zero with nothing on either pan. Your sample goes on the
right pan of the balance.
2. Mix the weighed samples in a small crucible. Place the crucible in the ring stand
triangle.
3. Make sure the thermocouple is raised well away from the propane torch so that the
torch flame will not affect it. Move the torch to a convenient spot for lighting and
adjustment of the controls. Light it with the flint striker/lighter and adjust the flame so
that its flared blue cones extend about 1. -1.5 cm beyond the end of the torch. Adjust the
position of the torch so that the end of the highest flame is just about 3- 5 cm. from the
bottom of the crucible. It does not have to be pointing directly up at the crucible; pointing
at the bottom of the crucible from below and to one side is fine. DO NOT TURN UP
THE FLAME OR MOVE THE TORCH CLOSER IN ORDER TO TRY TO SPEED
THINGS UP. Ensure that the flame heats the crucible evenly.
4. While waiting for the melting to occur, fill the plastic beaker at least 3/4 full of cold
water.
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5. Melt should take about 5-10 minutes, depending on mix and flame intensity. Your
sample will melt a little faster if you have small pieces on the bottom to melt first -- once
there is a liquid present, heat transfer to the other pieces will be a bit quicker.
As material melts, stir the melt carefully with the stainless steel spatula. Do not splash
melt out of crucible or hit thermocouple, which should be clamped with the tip well out
of the crucible at this point.
Use the small spatula to remove any excessive dross or scum (the granular junk floating
on the surface), and place this in a weighing dish to cool, then in the designated waste
container. Lab staff will dispose of this waste correctly later. Most dross will be dark
coloured and may even look like lead that refuses to melt. If you see a lot of coloured
dross (yellow, white or red), turn heat down slightly.
Failed samples may also be placed in this waste container.
6. When material has melted, is reasonably free of dross and has a silvery appearance,
carefully turn propane torch flame down, but not off, and gently lower the thermocouple
into the melt, while watching the temperature reading to ensure that thermocouple does
not go off scale (remove it if it does and cool sample). Clamp thermocouple gently but
firmly so that it is suspended in the middle of the crucible and does not touch the crucible
bottom. About 2-3 mm off bottom of crucible is good.
7. Record liquid temperature. Turn off the propane torch carefully to avoid spilling the
c c b e. Be e a e
a d
,b d
e
e . Be
e e
e
temperature measurements and observations. Cooling time will be about 1-2 minutes; if
cooling happens too quickly, try turning the torch flame down but not off. It is suggested
that temperature readings and observations of the melt be made about every 5 seconds.
MAKE YOUR DATA CHART UP AHEAD OF TIME, LEAVING ROOM FOR PLOTS
OF TEMPERATURE/TIME MEASUREMENTS, AND SOME ROOM FOR
COMMENTS ON THE VISCOSITY OF THE MELT. Stir gently with the small spatula
during cooling. Describe viscosity in terms of butter, margarine, putty, plasticine, glue,
syrup, etc., whatever comes to mind.
8. Remelt sample a d ec d e e a e a d b e a
,b
e a
a d
during cooling again. Remelt time may differ from the original melt time, because you
are now melting the alloy, not its components.
9. Remelt sample one last time (recording data on the wa
) a d e
e
thermocouple well out of crucible. Grasping the edge of the crucible firmly with the
tongs, VERY CAREFULLY pour half of the melt into the water in the plastic beaker and
the other half into one of the aluminum weighing dishes have this sitting on the square
of wire screening to speed the cooling process and to prevent damage to the counter top.
10. When the samples have cooled, identify them (i.e. by marking them) to avoid
confusion later.
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11. Repeat procedure for other tin/lead proportions and for the 100% lead and 100% tin
samples.
12. Using the microscopes, observe any crystal structure on the surface of the alloy
specimens.
13. Carefully scrape crucible clean with spatula when finished and deposit scrapings in
the designated a e c a e e
ed ab e. T e c c b e
e e ,b
should not have a thick film of metal in it.
14. Turn off light and fan in fume hood. MAKE SURE TORCH IS TURNED OFF.
15. Plot temp/time observations and comment (4 data sets plotted on one graph for each
sample).
16. Save all samples and return to Gary in an envelope with your group name on it.
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Appendix (phase diagram)
Cooling curves
Cooling curves for pure substances
Suppose you have some pure molten lead and allow it to cool down until it has all
solidified, plotting the temperature of the lead against time as you go. You would end up
with a typical cooling curve for a pure substance.
Throughout the whole experiment, heat is being lost to the surroundings - and yet the
temperature doesn't fall at all while the lead is freezing. This is because the freezing
process liberates heat at exactly the same rate that it is being lost to the surroundings.
Energy is released when new bonds form - in this case, the strong metallic bonds in the
solid lead.
If you repeated this process for pure liquid tin, the shape of the graph would be exactly
the same, except that the freezing point would now be at 232°C. (The graph for this is
further down the page.)
Cooling curves for tin-lead mixtures
A sample curve
If you add some tin to the lead, the shape of the cooling curve changes. The next graph
shows what happens if you cool a liquid mixture containing about 67% lead and 33% tin
by mass.
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There are lots of things to look at:
Notice that nothing happens at all at the normal freezing point of the lead. Adding
the tin to it lowers its freezing point.
Freezing starts for this mixture at about 250°C. You would start to get some solid
lead formed - but no tin. At that point the rate of cooling slows down - the curve
gets less steep.
However, the graph doesn't go horizontal yet. Although energy is being given off
as the lead turns to a solid, there isn't anything similar happening to the tin. That
means that there isn't enough energy released to keep the temperature constant.
The temperature does stop falling at 183°C. Now both tin and lead are freezing.
Once everything has solidified, the temperature continues to fall.
Changing the proportions of tin and lead
If you had less tin in the mixture, the overall shape of the curve stays much the same, but
the point at which the lead first starts to freeze changes.
The less tin there is, the smaller the drop in the freezing point of the lead.
For a mixture containing only 20% of tin, the freezing point of the lead is about 275°C.
That's where the graph would suddenly become less steep.
BUT . . . you will still get the graph going horizontal (showing the freezing of both the tin
and lead) at exactly the same temperature: 183°C.
As you increase the proportion of tin, the first signs of solid lead appear at lower and
lower temperatures, but the final freezing of the whole mixture still happens at 183°C.
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That continues until you have added enough tin that the mixture contains 62% tin and
38% lead. At that point, the graph changes.
This particular mixture of lead and tin has a cooling curve which looks exactly like that
of a pure substance rather than a mixture. There is just the single horizontal part of the
graph where everything is freezing.
However, it is still a mixture. If you use a microscope to look at the solid formed after
freezing, you can see the individual crystals of tin and lead.
This particular mixture is known as a eutectic mixture. The word "eutectic" comes from
Greek and means "easily melted".
The eutectic mixture has the lowest melting point (which is, of course, the same as the
freezing point) of any mixture of lead and tin. The temperature at which the eutectic
mixture freezes or melts is known as the eutectic temperature.
What happens if there is more than 62% of tin in the mixture?
You can trace it through in exactly the same way, by imagining starting with pure tin and
then adding lead to it.
The cooling curve for pure liquid tin looks like this:
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It's just like the pure lead cooling curve except that tin's freezing point is lower.
If you add small amounts of lead to the tin, so that you have perhaps 80% tin and 20%
lead, you will get a curve like this:
Notice the lowered freezing point of the tin. Notice also the final freezing of the whole
mixture again takes place at 183°C.
As you increase the amount of lead (or decrease the amount of tin - same thing!) until
there is 62% of tin and 38% of lead, you will again get the eutectic mixture with the curve
we've already looked at.
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The phase diagram
Constructing the phase diagram
You start from data obtained from the cooling curves. You draw a graph of the
temperature at which freezing first starts against the proportion of tin and lead in the
mixture. The only unusual thing is that you draw the temperature scale at each end of the
diagram instead of only at the left-hand side.
Notice that at the left-hand side and right-hand sides of the curves you have the freezing
points (melting points) of the pure lead and tin.
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Note: The two lines meeting at the eutectic point have been simplified slightly so that they are drawn as
straight lines rather than slight curves. It doesn't affect the argument in any way. I haven't been able to find
the actual data to plot them accurately, so the simplification is to avoid giving the impression that I actually
know exactly what the curves look like!
To finish off the phase diagram, all you have to do is draw a single horizontal line across
at the eutectic temperature. Then you label each area of the diagram with what you would
find under the various different conditions.
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{Group 2}: Heat Treatment
Exp. (F): Jominy End Quench Test
Objectives
Student will learn about:
How to harden the steel alloy by carrying out the Jominy End Quench Test.
The hardness
Effect of alloying element on the microstructure
Phase transformation of steel
1. Introduction
The Jominy end-quench test is the standard method for measuring the
hardenability of steels. This describes the ability of the steel to be hardened in depth by
quenching. Knowledge about the hardenability of steels is necessary to select the
appropriate combination of alloy steel and heat treatment to minimize thermal stresses
and distortion in manufacturing components of different sizes. Hardenability depends on
the chemical composition of the steel and also be can affected by prior processing
conditions, such as the austenitizing temperature. It is not only necessary to understand
the basic information provided from the test, but also to understand how the information
obtained from the Jominy test can be used to understand the effects of alloying in steels
and the steel microstructure.
Hardening of steels can be understood by considering that on cooling from high
temperature, the austenite phase of the steel can transform to either martensite (Fig. 1a) or
a mixture of ferrite and pearlite (Fig. 1b). The ferrite/pearlite reaction involves diffusion,
which takes time. However, the martensite transformation does not involve diffusion and
essentially is instantaneous. These two reactions are competitive, and martensite is
obtained if the cooling rate is fast enough to avoid the slower formation of ferrite and
pearlite. In alloyed steels, the ferrite/ pearlite reaction is further slowed down, which
allows martensite to be obtained using slower cooling rates. Transformation to another
possible phase (bainite) can be understood in a similar way.
Steels having high hardenability are required to make large high-strength
components, such as large extruder screws for injection molding of polymers, pistons for
rock breakers, mine-shaft supports, aircraft undercarriages, as well as for small, highprecision components, such as die-casting molds, drills and presses for stamping coins.
Steels having low hardenability may be used for smaller components, such as chisels and
shears, or for surface-hardened components, such as gears, where there is a desire to
maintain a ferrite/pearlite microstructure at the core to improve toughness. The Jominy
end-quench test is the standard method to measure the hardenability of steels [DIN EN
ISO 642].
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High hardness occurs where high volume fractions of martensite develop. Lower
hardness indicates transformation to bainite or ferrite/pearlite microstructures.
Fig 1 Microstructures observed in the Jominy end-quench test of a 0.4wt% carbon steel:
(a) untempered martensite; (b) ferrite and pearlite. Pearlite, the darker constituent, is a
eutectoid mixture of ferrite and iron carbide.
Effects of alloying and microstructure
The Jominy end-quench test measures the effects of microstructure, such as grain size,
and alloying on the hardenability of steels. The main alloying elements that affect
hardenability are carbon, a group of elements including Cr, Mn, Mo, Si and Ni, and
boron.
Carbon
Carbon controls the hardness of the martensite; increasing carbon content increases the
hardness of steels up to about 0.6wt% carbon. However, at higher carbon levels, the
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critical temperature for the formation of martensite is depressed to lower temperatures.
The transformation from austenite to martensite may then be incomplete when the steel is
quenched to room temperature, which leads to retained austenite.
Fig 2 Schematic of typical hardness profile in a Jominy specimen.
The hardenability is described by a hardness curve for the steel (Fig. 2), or more
commonly by reference to the hardness value at a particular distance from the quenched
end.
Carbon also increases the hardenability of steels by retarding the formation of pearlite
and ferrite. Slowing down this reaction encourages the formation of martensite at slower
cooling rates. However, the effect is too small to be commonly used for control of
hardenability. Furthermore, high-carbon steels are prone to distortion and cracking during
heat treatment and can be difficult to machine in the annealed condition before heat
treatment. It is more common to control hardenability using other elements and to use
carbon levels of less than 0.4wt%.
Other alloying elements
Cr, Mo, Mn, Si, Ni and V retard the phase transformation from austenite to ferrite and
pearlite. The most commonly used elements are Cr, Mo and Mn. The retardation is due to
the need for redistribution of the alloying elements during the diffusional phase
transfromation from austenite to ferrite and pearlite. The solubility of the elements varies
between the different phases, and the interface between the new growing phase cannot
move without diffusion of the slowly moving elements. There are quite complex
interactions between the different elements, which also affect the temperatures of the
phase transformation and the resultant microstructure. Alloy steel compositions are,
therefore, sometimes described in terms of a carbon equivalent, which describes the
magnitude of the effect of all of the elements on hardenability. Steels of the same carbon
equivalent have similar hardenability.
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Boron
Boron is a very potent alloying element, typically requiring 0.002 to 0.003wt% to have an
equivalent effect as 0.5wt% Mo. The effect of boron is independent of the amount of
boron, provided a sufficient amount is added. The effect of boron is greatest at lower
carbon contents and it typically is used with lower carbon steels.
Boron has a very strong affinity for oxygen and nitrogen, with which it forms
compounds. Boron can, therefore, only affect the hardenability of steels if it is in
solution. This requires the addition of "gettering" elements such as aluminum and
titanium to react preferentially with the oxygen and nitrogen in the steel.
Grain size
Increasing the austenite grain size increases the hardenability of steels. The nucleation of
ferrite and pearlite occurs at heterogeneous sites such as the austenite grain boundaries.
Increasing the austenite grain size therefore decreases the available nucleation sites,
which retards the rate of the ferrite/pearlite phase transformation (Fig. 6). This method of
increasing the hardenability is rarely used because substantial increases in hardenability
require large austenite grain size, obtained through high austenitizing temperatures. The
resultant microstructure is quite coarse, with reduced toughness and ductility. However,
the austenite grain size can be affected by other stages in the processing of steel, and,
therefore, the hardenability of a steel also depends on the previous stages used in its
production.
Vickers Hardness
The Vickers hardness test uses a square pyramidal diamond indentor. The recorded
hardness depends on the indentation load and the width of the square indentation made by
the diamond. The indentation load is typically between 10 and 30 kg. The hardness
number is usually denoted by HV20 for Hardness Vickers 20 kg, for example.
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2. Experimental procedure
In this test the hardenability of a low-alloy steel is compared to that of a plain carbon
steel.
The experimental procedure is as follows:
3. position a Jominy specimen (See Fig.7) on the tray and push the tray into the
furnace set at 950°C using tongs and heat resisting gloves.
Fig. 7 Jominy Specimen
4. Adjust the water column height in the Jominy end quenching tank to 65 mm
above the orifice with faceplate valve wide open. Close the faceplate without
changing the water column height adjustment so that when the faceplate is opened
later on the water column will rise immediately to 65mm.
5. After 30 minutes in the furnace transfer the Jominy specimen to the specimen
holder of the Jominy end quenching tank. Then after the Jominy specimen is in
place, turn on the water and quench the bottom end of the specimen (See Fig. 2).
Transfer from furnace to quench should be rapid (in minor than 5 seconds). You
are advised to practice the motions in advance. The first student with heat
resisting gloves open the furnace and a second student with tongs or large pliers
transfers the Jominy specimen to water bath. while the other one operates the
quick opening valve. Care should be taken to position the specimen so that it
hangs straight down and a uniform umbrella pattern of water rebounds from the
specimen bottom (See Fig.8).
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Fig.8 schematic diagram of appliance of quenching
6. Leave the specimen in place with the water flowing for at least 10 minutes.
7. Remove the specimen from the holder and cool it in water.
8. Grind a flat on the side of the specimen at least 0.4mm deep. use 120 Grit paper..
Grind gently with coolant water flowing on the surface of the grinding paper.
9. Mark a scale on the flat as follows (See Fig. 3). Divide the first 16 from the
quenched end into 2 mm increments. Divide the next 65 mm into 5mm
increments.
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10. Measure the Vickers hardness HV30. Start at the quenched and work towards the
other side. Thereafter, record the hardness at each increment that you have
marked off. It is important to keep the indentations in the center of the flat, since
errors will arise if they are at the edges of the flat.
3. Analysis
11. Make a plot of the hardness (y-axis) versus the distance from the quenched end
(x-axis).
4. References
1. D. R. Askeland, The Science and Engineering of Materials, Alt. Ed., PWS
Engineering, 1984, pp. 288-303, 351-376.
2. L. H. Van Vlack, Elements of Materials Science and Engineering, 5th ed., 1985,
pp. 402 - 415, 431-435,439-445, 455-463, 469-478.
3. G. L. Kehl, Principles of Metallographic Laboratory Practice, McGraw-Hill,
1949, pp. 303-310, 229-240.
4. J. Wulff, et. al., Structure and Properties of Materials, Vol. 1, pp. 184-197; Vol. 2,
pp. 123-128.
5. G. Guy, Physical Metallurgy for Engineers, 1962, Addison-Wesley, 1962, pp.
122-124, 294-298, 301-311.
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{Group 2}: Heat Treatment
Exp. (G): Carburizing
Carburization is a technique used to harden the surface of steels by diffusing into the
crystal lattice. The carbon enters the interstitial spaces between the iron atoms. It
strengthens the metal by distorting the crystal lattice, thus making it difficult for
dislocations to move. Carburization is a surface technique because, even at high
temperatures, diffusion is a slow process. The source of carbon can either be a gas or
solid carbon.
1. Objectives
The practical aims to familiarize you with a solution of Fick's Second Law of diffusion
by studying the diffusion of carbon into iron.
You will gain experience of heat treatment in furnaces, preparation of metallographic
sections and etching, The microscopy will require interpretation of more complicated
microstructures.
2. Safety
Care is needed in handling hot materials; use proper tongs, wear suitable protection
(gloves and visor) and don't leave hot materials on the bench without a notice that they
are hot . Normal safety precautions are adequate for the etches used here, i.e. lab coat,
gloves and eye protection.
3. Procedure
You are provided with two small pieces of Mild steel, this has a low C content.
One will be as blank (for comparison) and the other is required for carburizing at
950 ºC.
Heat the samples in the oven at 950 oC for one hour. At the end turn off the oven,
and let the samples cool in air to room temperature. This process is caused
normalization, and can be done several days or weeks before the experiment;
however the sample should be at room temperature for at least 24 hours before
proceeding to the next step.
To carburize your sample:
Clean the surface of the specimen by polishing up to 9 m.
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The samples is packed in a ceramic crucible in a mixture of powdered charcoal
and sodium carbonate activator (10 % w/w). The carbonate releases carbon dioxide
that reacts with C to give carbon monoxide and form a carburizing gas. A lid is
needed to exclude air.
Place your crucible in the furnace for 2 hours at 1000°C.
Remove from the oven and quench the sample (hot) in water.
Perform a Vickers hardness test, and examine the surface under the optical
microscopy.
Compare the data before and after carburizing and describe the microstructure.
Note: after carburizing the sample need to be polished; in particular it is important that
the rusted (oxide) surface is removed to expose a bulk cross-section. After grinding and
polishing, the specimens need to be etched, in 2% Nital. Check that the etch time is
sufficient to show the structure clearly across the whole carbon profile.
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{Group 3}: Mechanical tests
Exp. (H): Hardness
Scope
To study the effect of heat treatment of steel (Jominy-end quench test) and the
case hardening (carburizing) on the surface of the metals.
Introduction
The hardness test measures the resistance of a material to an indentor or cutting
tool. The indentor is usually a ball, pyramid or cone made of a material much harder than
that being tested. In most of the standard tests, a load is applied slowly by pressing the
indentor perpendicularly onto the surface being tested for a given period of time. The
load and/or the size of the ball may be varied according to the hardness of the material.
An empirical hardness number may be calculated from the results of such tests by
knowledge of the load applied and cross-sectional area or depth of the resulting
impression using appropriate formula. These tests should never be taken near the edge of
a sample or any closer than about three diameters from an existing impression. Most
hardness tests produce plastic deformation in the material and all variables that effect
plastic deformation effect hardness.
For materials which work-harden in a similar
fashion, there is good correlation between hardness and the ultimate tensile strength.
Concept
The basic concept utilized in this test is that a set force is applied to an indenter in
order to determine the resistance of the material to penetration. If the material is hard, a
relatively small or shallow indentation will result, whereas if the material is soft, a fairly
large or deep indentation will result.
Methods of hardness measurement
Brinell, Rockwell, Vickers, and Knoop are frequently used methods for
determining hardness. These tests are often classified in one of two ways: either by the
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e e
e e
ce a
Lab Manual
ed
e
ea
to a test where a load >1 kg is app ed;
1
ce
a
ed. Add
a
,
e e
e
a
c
e
e
d
ee
ed. A
ac
a e
a e ca ab e
e
ee
e e a load of
c
d c
e
with loads as light as 0.01 g and are commonly referred to as ultralight or
nanoindentation testers.
Rockwell and Brinell testers fall into the macro category, whereas Knoop testers
are used for microindentation tests. Vickers testers are employed for both macro and
microindentation tests (This technique is applied in the laboratory of GUC (C5)). The
measurement methods available include a visual observation of the indentation or a depth
measurement of the indentation. Rockwell and some nanoindentation testers are capable
of determining the depth of the indentation, whereas Brinell, Knoop, and Vickers testers
require an indentation diameter measurement.
Principal
The basis of static indentation tests is that an indenter is forced into the surface of
the material being tested for a set duration. When the force is applied to the test piece
through contact with the indenter, the test piece will yield. After the force is removed,
some plastic recovery in the direction opposite to the initial flow is expected, but over a
smaller volume. Because the plastic recovery is not complete, biaxial residual stresses
remain in planes parallel to the free surface after the force is removed. The hardness
value is calculated by the amount of permanent deformation or plastic flow of the
material observed relative to the test force applied. The deformation is quantified by the
area or the depth of the indentation. The numerical relationship is inversely proportional,
such that as the indent size or depth increases, the hardness value decreases.
Hardness values can be directly compared only if the same test is used, since the
geometry of the indenter and force applied influence the outcome of the test. For each
type of hardness test conducted, a different equation is used to convert the measured
dimension, depth or diameter, to a hardness value. The Brinell hardness value is
calculated by dividing the test force by the surface area of the indentation. The test
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parameters taken into account are the test force and ball diameter while the indentation
diameter is measured. For Rockwell tests, the hardness value is determined by the depth
of indentation made by a constant force impressed upon the indenter. The test parameters
taken into account are the test force (major and minor load) and the indenter geometry
(ball or diamond cone), while the depth of penetration between the application of the
minor load and major load is measured. Vickers hardness values are calculated in the
same manner as Brinell tests. The projected area, instead of the surface area, is used when
computing Knoop values. Table1 lists common applications for the tests.
The test parameters taken into account for Vickers and Knoop tests are identical
and include the test force and diamond indenter geometry while the indentation diameter
is measured. The illustrations in Figure1 demonstrate the indentations.
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Procedures
1-Adjust the Microscope illumination so that all edges
are sharp, but without a halo.
2- First of all set the vertical middle line parallel to the
indentation diagonal in the field of view. Whereby the
indentation should be near to the vertical middle line.
3-Use the lower adjustment knob to set the indentation so
that
-The lower tip extends past the lowest short
measurement line, and
-The upper tip touches one of the short measurement
lines.
4- Use the lateral adjustment knob to bring the next long measurement line to the lower
tip of the indentation. Whereby the upper edge of the measurement line and the tip of
the indentation must just touch one another.
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Hidden setting knob
5-Count the whole measurement line separations
between the indentation tips to be measured.
Read off the scale value from (a) the table for the
objective lenses. Multiply scale value (a) by the
number of whole measurement line distances.
6- Now read off the numerical value from the scale
and read the scale constant (b) from the table for
the objective lenses. These values are also
multiplied by one another.
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7- Add both measured values in step 5 and 6
8- The resulting length of the diagonal is then converted to HV (Vicker hardness) using
the following table
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{Group 3}: Mechanical tests
Exp. (D): Tensile
Objectives
The objective of the experiment is to demonstrate the elastic and plastic properties of
metals. Students will learn about:
How to perform a tensile test on metals.
Measurements of stress and strain in tensile tests
Interpretation of stress strain curves
De a
ae a
e e
eY
d
,
stress, tensile strength and other mechanical properties.
ed
e /0.2%
1. Introduction
The tensile test, also known as tension test, is one of the most important and most
fundamental tests in mechanical testing of materials. Tensile tests provide information on
the strength and ductility of materials under uniaxial tensile stresses for almost all types
of materials. Tensile tests are simple, relatively inexpensive, and fully standardized. The
result of the tensile test is the so-called stress-strain-curve. From this curve, several
material properties can be derived, like elastic (Youn )
d
, ed e , e e
strength and strain at fracture. Other data, which might be obtained, are elastic limit or
proportional limit, reduction of area and other properties. This information may be useful
in comparisons of materials, alloy development, quality control, and design under certain
circumstances.
The direct, but simplified result of the test uses the engineering stress and engineering
strain. An advanced evaluation of the test yields also true stresses and true strains.
The test procedures are outlined in several standards: ASTM E-8, DIN EN 10002-1, ISO
6892, JIS Z2241.
3. Test Samples
For different materials different standardized sample shapes have been developed. A
tensile sample in general has a central part with a constant reduced cross section, and
ends with a larger cross section where the sample will be fixed in the machine. The
design of the specimen has to guarantee that the multi-axial stresses due to gripping and
fixing the sample do not disturb the uniaxial stress state in the central reduced section.
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The elongation of the sample will be measured at the central part of the sample. There,
the so-called gauge length l0 shall be marked. The actual gauge length depends on the
cross section of the sample. The parallel part with the reduced cross section must be
larger than the gauge length, at least by the sample width or diameter. The transition
between the central parallel part and the ends of the specimen must be a smooth curve
with radius larger than a specified minimal radius.
In this experiment hot and cold rolled steel samples and a non-ferrous alloy (brass) shall
be compared. The flat specimen shape will be used (see figure and table below).
Figure 1: Flat tensile specimens according to the ASTM standard
2. Test Procedure
The tensile test makes use of a tensile machine, which consists of a very stiff load frame,
a movable cross-head, suitable devices to grip the sample, a load cell, motors and a
control unit. A tensile machine shall include also a device to measure the elongation of
the sample (extensometer).
The tensile test is performed by gripping the ends of the sample and elongating the
sample. The force, acting on the sample, is measured by a load cell continuously during
the experiment and may be plotted versus the elongation. I.e. we measure and record the
force, necessary to obtain the elongation of the sample during the experiment.
In order to obtain material properties, which do not depend on the sample size and shape,
rather the stress-strain-curve then the force-elongation-curve is used to evaluate the test.
It shall be noted, that not all properties are actually independent on the sample size and
a e. T a
c ca
e a da d ed a
e.
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The test is performed at a uniform constant strain rate and the strain rate shall be
controlled by the testing machine. The strain rates are usually small. In our experiment,
we will use a strain rate of 0.005 s-1.
The basic result is the so-called engineering stress
engineering strain curve. The
engineering stress is the force acting on the sample divided by the minimal initial cross
sectional area.
F
A0
The engineering strain, measured at the gauge length, is the elongation of the gauge
length, dl, divided by the initial gauge length l0.
li
l0
l0
l
l0
For the experiment, a computerized static tensile machine Zwick Z100 will be used. The
entire experiment is computer controlled and all results can automatically be obtained
from the program. The test program will be explained in detail by the supervisor of the
experiment.
Before starting the test, the initial dimensions of the sample must be measured using a
vernier caliper and entered into the computer program. The sample shall then be fixed in
the machine. It should be noted, that the sample must be fixed so that the axis of the
sample is exactly in the load axis of the machine in order to prevent any bending, and the
load cell is set to zero when no force is acting on the sample, i.e. before fixing the
sample. It must be checked, that all additional testing parameters are entered.
The elongation of the gauge length will be measured during the test with the
extensometer. The wedges of the extensometer must be set to the gauge length and
attached to the sample.
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Figure 2: Universal Testing Machine Zwick/Roell Z100
After starting the test, the program controls the elongation of the sample with the desired
strain rate until the sample breaks. As all material parameters show some statistical
scattering, the test shall be repeated at least three times for each type of material.
3. Evaluation of the Test
After finishing the tensile test and plotting the stress strain curve, the following material
properties can be derived from the curve. In the stress different parts can be
distinguished:
1. The elastic region with small strains at the begin of the test. In the elastic region
the stress is proportional to the strain and the curve is a straight line here. If the
sample will be unloaded in this region, it will return to its original size and shape.
2. At a certain point, the curve will depart from the linear relationship between stress
and strain. The part of the curve from this point till the rupture point is called the
plastic region. If the sample will be unloaded in this region, it will not return to
a
e.
3. Some materials, e.g. interstitial alloys like steels show the so-called yield point
elongation (yield point phenomenon), where the plastic deformation is initiated at
the upper yield point with an actual decrease in stress. Then, the stress is
oscillating about a constant stress.
4. Metals exhibit strain hardening, which causes an increase of the necessary force
and stress with continuing plastic deformation. In the stress-strain-curve the
hardening region is characterized by a non-linear cause with increasing stress.
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5. Most materials, which can be deformed plastically, will exhibit a localization of
the plastic deformation at a certain plastic strain. This effect gives rise to a rapid
local decrease of the cross section, which is called necking. As the true cross
section becomes smaller, the actual force, necessary to continue the deformation
decreases which causes a decreasing engineering stress. Thus, the necking
phenomenon causes a maximum in the stress-strain-curve and the necking region
is characterized by decreasing engineering stresses.
The following material properties can be derived from the stress-strain-curve:
Elastic Modulus E: T e e a c
d
( Y
modulus) is the constant of
a
be ee
e a d a b H
a . I
e
e
e ea
segment of the stress-strain-curve in the elastic region.
Y
Yield stress
: The yield stress characterizes the onset of plastic deformation.
Depending on the characteristics of the stress-strain-curve, different measures are
defined:
The proportional limit Re is the point, where the stress-strain-curve deviates from linear
elastic behavior.
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Figure 3: Stress strain curves and derived properties
0.2% proof stress Rp0,2: The proportional limit is often difficult to determine precisely.
Instead, the intersection of the stress-strain-curve with a straight line parallel to the elastic
part of the curve is used to characterize the yield strength. The strain-offset of this
straight line has to be specified and is usually 0.2%. The stress is often called proof stress.
Upper yield stress ReU: Materials which exhibit the yield point phenomenon, this stress
characterizes the onset of plastic deformation and is defined by the initial decrease of the
stress after the
Lower yield stress ReL: is the lower stress bound during the yield point elongation.
Tensile strength (ultimate strength) Rm is the maximum engineering stress.
Several elongation and strain measures are additionally used to describe the elastic-plastic
response of a material. These are: elastic strain, yield point elongation or Lüders
strain, uniform elongation or strain, total elongation and strain at fracture. The
definition of these strains can be taken from fig. 3. As the deformation after the the onset
of necking is no longer homogeneous over the sample, for all properties derived after
uniform strain, the gauge length must be specified, as this properties depend then on the
sample size and geometry.
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Additionally, the reduction of cross-section area at fracture is often used to characterize
the ductility of a material. The reduced area is the minimum cross section at the location
of fracture. The reduction of area is then divided by initial cross section and is usually
given in percent (%).
A0 A
A0
Z
Note, that the engineering strain is an approximation to the true strain for small
deformations but usually sufficient to characterize the mechanical behavior. The true
strain is the logarithmic strain:
T
ln(1
)
The true stress takes into account the actual instantaneous cross section area A, which is
always small than the instantaneous cross section A0.
T
F
Ai
For the true-stress-curve the minimal
cross section has to be used, which is
often difficult to determine during the
experiment, when necking occurs. For
the elastic region, the cross section and
thus the true stress can be calculated, if
P
s ratio is known:
T
(1
)2
For the uniform strain plastic strain
e
, P
a
a
ae
T
(1 )
0.5 and then
Figure 4: Engineering stress and true stress curves
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4. Results
Material
Gauge length / mm
Parallel length / mm
Width / mm
Thickness / mm
Initial cross section / mm2
Elastic modulus / GPa
Elastic limit / MPa
0.2% proof stress / MPa
Upper yield point / MPa
Lower yield point / MPa
tensile strength / MPa
Elastic strain / %
Lüders strain / %
Total uniform strain / %
Plastic uniform strain / %
Total strain at fracture / %
Plastic strain at fracture / %
Final gauge length / mm
Reduced cross section / mm2
Reduction of area / %
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{Group 3}: Mechanical tests
Exp. (C): Impact
Objectives
The objective of the experiment is to demonstrate the impact bending test. Students will
learn about:
How to perform an impact bending test.
The meaning of impact energy
Factors, that influence the impact energy
1. Introduction
Impact tests are designed to measure the resistance to failure of a material to a suddenly
applied force. The test measures the impact energy, or the energy absorbed prior to
fracture. The most common method of measuring impact energy is the impact bending
test (Charpy test). A notched bar is supported at both ends as a simple beam and broken
by falling pendulum. While most commonly used on metals, it is also used on polymers,
ceramics and composites. The test has particular importance in quality control
applications where it is a fast and economical test. It is used more as a comparative test
rather than a definitive test.
The impact energy is a measure of the relative toughness or impact toughness of
materials. It is measured as the work done to fracture a test specimen. When the striker of
the pendulum hits the specimen, the specimen will absorb a part of the kinetic energy of
the hammer until it breaks. The absorbed energy consists of elastic energy, plastic energy
and the surface energy of the crack. Tough materials absorb a lot of energy, whilst brittle
materials tend to absorb very little energy prior to fracture. The test is often used to
determine also the effect of environmental conditions like temperature and various
treatments of the materials on the toughness.
2. Test Specimen
Charpy test specimens normally measure 55x10x10mm and have a notch machined
across one of the larger faces. The notches may be:
V-notch A V-shaped notch, 2mm deep, with 45° angle and 0.25mm radius along
the base
U-notch or keyhole notch A 5mm deep notch with 1mm radius at the base of the
notch.
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In this experiment we will use two specimens of a mild steel, one in the as-received
condition (normalized, see figure) and one hardened sample (austenized at 920°C/45 min,
water quenched). The samples have a V-notch.
Figure 5: Microstructure of the normalized (left) and the hardened sample (right)
3. Test Procedure
The Charpy test involves striking a suitable specimen with a striker, mounted at the end
of a pendulum. The test piece is fixed in place at both ends and the striker impacts the test
piece immediately behind a machined notch.
Figure 6: Principle of impact bending test
At the point of impact, the striker has a known amount of kinetic energy. The impact
energy is calculated based on the height to which the striker would have risen, if no test
specimen was in place, and this compared to the height to which the striker actually rises.
Thus, the energy, absorbed by the sample can be directly read from a scale at the
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machine. Note, that our machine has two scales for different sizes of the striker. We are
using the 300 Joule striker.
Figure 7: Pendulum impact testing machine
.
4. Factors Affecting Impact Energy
Factors that affect the Charpy impact energy of a specimen will include:
Yield strength and ductility
For a given material the impact energy will be seen to decrease if the yield
strength is increased, i.e. if the material undergoes some process that makes it
more brittle and less able to undergo plastic deformation. Such processes may
include cold working or precipitation hardening.
Notches
The notch serves as a stress concentration zone and some materials are more
sensitive towards notches than others due to the presence of internal stress raisers
such as grain boundary inclusions, internal cracks and second phases. The notch
depth and tip radius are therefore very important
Temperature and strain rate
Most of the impact energy is absorbed by means of plastic deformation during the
yielding of the specimen. Therefore, factors that affect the yield behavior and
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hence ductility of the material such as temperature and strain rate will affect the
impact energy. This type of behavior is more prominent in materials with a body
centered cubic structure, where lowering the temperature reduces ductility more
markedly than face centered cubic materials.
Therefore, by doing the test for such materials over a range of temperatures, the
brittle-ductile transition temperature for a particular material may be determined.
Fracture mechanism
Metals tend to fail by one of two mechanisms, micro-void coalescence or
cleavage. Cleavage can occur in body centered cubic materials, where cleavage
takes place along the {001} crystal plane. Micro-void coalescence is the more
common fracture mechanism where voids form as strain increases, and these
voids eventually join together and failure occurs. Of the two fracture mechanisms
cleavage involved far less plastic deformation ad hence absorbs far less fracture
energy.
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{Group 3}: Mechanical tests
Exp. (I): Strain gauge
Introduction
Strain gauges are used in materials science to characterize the mechanical properties of
different materials. Strain Gauges are thin wires that can be glued to a metal structure.
When the structure flexes under a load the resistance of the strain gauges changes and this
can be used to measure the strain in the structure. In this way, the strain in a structure
(e.g. an oil rig or an aircraft wing) can be measured to verify the design calculations.
Strain gauges
Backing Film
Keywords
S ain,
e , Y ng
m d l ,
Poisson
ratio,
strain
gauges,
Wheatstone bridge, Gauge factor
Grid
(electrical resistor)
Copper-plated
Solder tabs
Electrical Properties of the Resistance Gage
The fundamental formula for the resistance of a wire with uniform cross section, A, and
resistivity can be expressed as:
L
(1)
R
A
where L is the wire length. This relation is generally accurate for common metals .
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We are interested in the relative change in R; R/R as a response to the relative change in
the dimensions of the wire L and A.
First take the natural log of Eq. (1) yielding:
ln(R) = ln( ) + ln(L) ln (A);
A=(
D2, D is the Diameter.
and now take the differential of this recalling that d(ln(x))=dx/x to get the simpler result:
dR
R
d
dL dA
L A
The longitudinal strain is = dL/L, and the transversalal strain is
For linearly elastic and isotropic material:
D
D
= dD/D.
=-
where is the Poisson ratio
Using these results:
dA/A = d((
D2)/dD = 2 D = - dL/L
then the resistance change per unit resistance ( R/R) can then be written:
(2)
dR d
(1 2 )
R
A measure of the sensitivity of the material ( resistance change per unit applied strain) is
the Gage Factor
GF
dR / R
dR
R
d /
GF
1
(3)
GF
(4)
2
Example 1
Assume a gage with GF = 2.0 and resistance 350 Ohms. It is subjected to a strain of 5
microstrain). Then
R = GF R
= 2 x 5x10-6 x350 = 0.0035
change!
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MATS 402 Materials Lab (I)
Lab Manual
It is apparent thus far that quite small resistance changes must be measured if
resistance strain gages are to be used.
Direct measurement of 0.0035 Ohm out of 350 Ohms would require a meter with
a resolution of better than one part in 100,000, in other words, a 6 digit ohmmeter!
Several measuring techniques are available for this purpose but the Wheatstone
Bridge circuit has proven the most useful for a number of important reasons. This
circuit will be described shortly but first several fundamental techniques will be
discussed.
Preliminary
Q1: What is a potential divider? Make sure that you understand this simple concept.
R1
R2
V
Figure 2
Q2:What is the potential difference across R1 and across R2.?
First you can give numeric values e.g. V = 10 Volt, R1 = 10 and R2 = 20
V1 and V2.
Make sure that you understand the simple relations
and
V
1
R1
R1 R2 V
(5)
V
2
R2
R1 R2 V
(6)
Now imagine that R1 is a strain gage.
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MATS 402 Materials Lab (I)
Lab Manual
We know that:
a strain gage is a resistor
and the relative change in its length ( L/L)
give a relative change in its resistance ( R/R)
An important question is when the gage R1 subjects to stress it will have a strain
L/L i.e. R1 will change to R1 + R
V1 will change to V1 + V1:
Q3: How we calculate the change in the voltage V1 across the gage R1 due to
this change R1?
The Answer is simple; we differentiate Eq. (5) with respect to R1 ; that is R1 is the
variable and R2 is a constant:
dV1
dV1
[
dR1
R1
R1dR1
R2
R1 R2
( R1
We know that
R2 )
( R1
2
dR1
V
R2 )
2
]V
dR1
R1
GF
R1
dV1
R1 R2
( R1
R2 )
2
(7)
V GF
Q4: what is the optimal value of the resistance R2 which give maximum change dV1?
A: we differentiate the function dV1 with respect to R2 and equate with zero.
This gives the result R1 = R2, that is the optimal value of R2 = R1.
Then Eq. (7) will be:
dV1
1
V GF
(8)
4
This eq. relates the strain in the gage and the resulting change in the voltage across the
gage resistance. Make sure you understand this equation and how you drive it.
Example:
When V = 10 Volt,
GF = 2
= 5 x 10-6
dV1 = ¼ x 10 x 2 x 5 x 10-6 = 0.0025 V = 2.5 mV
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Note that V1 = 5 Volt!4 >> dV1 [dV1/V1 = 0.0005]!
When you measure the potential difference across R1, it will be V1 + dV1, i.e. 5.0025Volt.
The important Question is:
Q5: How we measure dV1 without influence of the huge V1. [How we see only the 0.025
Volt][ dV1 is the measue of the strain]
The Answer is the
W h e a t e s t o ne B r i d g e
Wheatstone bridge enables us to see only the small dV1 [the measure of the strain]
without the very large value of V1!.
HERE WE ARE NOT INTERESTED IN MEASURING AN UNKNOWN
RESISTANCE
BUT TO MEASURE THE CHANGE IN THE RESISTACE DUE TO THE
APPLEIED STRAIN.
4
R1 = R2 in the potential divider, see Eq. (5)
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To understand the Wheatstone bridge we model it as two potential dividers:
V2
R2
R1
V2
R2
R1
V2_3
R3
R4
V2_3
<=>
R3
V3
V Volt
R4
0 Volt
V
Wheatstone Bridge as
two potential dividers
<=>
V Volt
V3
V
Wheatestone Bridge
Figure 3
Q6: What is the potential diference V2 across R2 & the potential diference V3 across R3?
A: See equation (2) or (3) for potential divider.
Q7: What is the potential diference V2_3 = V2
A: V2_3 = V2
V3 =
R2
V
R1 R 2
R3
V
R3 R4
V3?
R 2 R 4 R 1R 3
V
(R 1 R 2 )( R 3 R 4 )
(9)
When
R2R4 = R1R3
(10)
the Bridge is said to be balanced, and the output voltage V2_3 is equal to zero.
Now when the four resistors R1, R2, R3 & R4 are all strain gages, that is we have a full
bridge crcuit and all the four gauge resistors have the same resistance:
Q8: What will be the output voltage V2_3?
A: Acc d
(10)
be
..
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MATS 402 Materials Lab (I)
Lab Manual
Q9: When one or two or all the four gages are subjected to a strain, what will happen to
the output V2_3? [this is exactly Q3, but here we have 4 resistor strain gaes in a
Wheatestone Bride]
A: the answer is the same as to Q3; we differentiate Eq. (9) with respect to R1 R2, R3 & R4
[do not forget that the bridge was originally balanced that is V2_3 was zero].
dV2 _ 3
dV2 _ 3
V2 _ 3
R1
V2 _ 3
dR 1
R2
V2 _ 3
dR 2
R 1R 2
dR
[
( 1
(R 1 R 2 ) 2 R 1
R3
dR 2
)
R2
V2 _ 3
dR 3
R4
R 3R 4
dR
( 3
(R 3 R 4 ) 2 R 3
dR 4
5
dR 4
)]V
R4
the bridge is balanced which means R1 = R2 = R3 = R4
dV2 _ 3
1 dR 1
[
4 R1
dR 3
R3
dR 2
R2
dR 4
]V
R4
we know from eq. (3) that
dV2 _ 3
GF
[
4
1
2
3
4
dR
R
GF
]V
where e1 is the gage placed in the 1st arm of the bride.
The bride was originally balamced which means V2_3 was zero
Now V2 _ 3 dV2 _ 3 0 GF [ 1 2 3 4 ]V
V2 _ 3
4
GF
[
4
1
2
3
4
]V
(11)
This is the basic equation relating the Wheatstone Bridge output voltage to strain in gaes
placed in each arm:
The equation identifies the first order (differential) effects only, and so this is the
ea ed
.I
a d
a (
e a ) e a ce c a e .
Large resistance changes produce nonlinear effects.
Output is directly proportional to the excitation voltage and to the Gage Factor.
Increasing either will improve measurement sensitivity.
Equal strain in gages in adjacent arms in the circuit produce no output. Equal
strain in all gages produces no output either.
Fixed resistors rather than strain gages may be used as bridge arms. In this case
e a c
b
e a d eee e
e e ed a a d
element or gage.
5
do yourself the differentiation of eq (9) wih respect to all four resistors
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Questions
1. De e e e
Ga e ac , e a c a , Y
d
.
2. What is the principle purpose of using a Wheatstone bridge in these experiments?
3. Here is a schematic diagram of a simple Wheatstone bridge circuit:
True or False and explain your answer: A standard Wheatstone bridge is
balanced when R1R3 = R2R4.
True
False
4. True or False and explain your answer: Wire resistance increases with axial
strain.
True
False
5. A strain gage has a resistance of 350 ohms when no strain is applied. Its strain
gage factor is 2.00. When an axial strain of 0.0002 is applied, calculate the change
in resistance, dR, in ohms.
6. Consider the Wheatstone bridge circuit shown in problem 3 above. Resistors R1
and R3 are strain gages, while the other two resistors are fixed resistors. This
circuit is used to measure the axial strain on a cantilevered beam. Which of the
following statements is most correct? and explain your answer
The two strain gages should be mounted on the same surface (top or bottom)
of the cantilevered beam.
The strain gages should be mounted on opposite surfaces (top and bottom) of
the cantilevered beam.
7. In a full bridge circuit, the sensitivity improves by a factor of ________ compared
to a quarter bridge circuit.
. Explain your answer.
8. In which region of the stress-strain diagram are strain gages designed to work? .
Explain your answer.
the plastic deformation region
just beyond the elastic limit
the region where stress is nearly constant
the region where stress decreases with strain
none of the above
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9. What are the S.I. units of strain gage factor S? . Explain your answer.
m
ohms
m/s
s
ohms/V
N/m2
m2/N
none of the above
10. Consider the Wheatstone bridge circuit shown in problem 3 above. Resistors R1
and R3 are strain gages, while the other two resistors are fixed resistors. What
kind of Wheatstone bridge circuit is this? Explain your answer. . Explain your
answer.
a quarter bridge circuit
a half bridge circuit
a full bridge circuit
none of the above
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MATS 402 Materials Lab (I)
Lab Manual
Necessary devices
Traveler Strain Master [a fully automated 8-channel measurement system for strain
measurements using quarter-, half-, and full bridge circuits.]. See the Traveler Strain Master
manual.
Cantilever beam
Strain gages
Cables [to connect strain gauges to the Traveler Strain Master.
A variable resistance
2 x 1k resistors
Multimeters
Power Supply
1 kg set of 50g, 100g, 200 g and 500g masses
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MATS 402 Materials Lab (I)
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Experiment 1
Figure 4
The gauges are a distance D from the load (see figure 4), a load of mass m and weight mg
is suspended from the cantilever beam (g is the acceleration due to gravity). The beam
has thickness t and width w and is made from stainless steel with a Young's Modulus
E
. The calculated strain due to the suspended mass is:
(12)
Therefore the relative change in the resistance of the strain gauge is given by:
R
R
GF
GF
6 mg
Ewt 2
The resistance changes in the strain gauges are very small, therefore the gauges are
connected in a Wheatstone Bridge Circuit (see figure 5). The gage on top of the beam is
in tension, the gage underneath the beam is in compression, hence strain causes equal
and opposite resistance changes in the gages. By using two gauges the effects of
temperature variations on the gauge resistances are cancelled out.
The right hand end of the bridge circuit is at zero volts (see figure 5), the circuit is
powered by the bridge excitation voltage V applied to the left hand end of the bridge (see
figure 5).
If the strain increases the resistance of Gauge One from R to R + R then the resistance
of Gauge Two is decreased from R to R - R. Hence the voltage VG (see figure 5) is
given by Eq. (11):
V2 _ 3
GF
4
[ 1
2
0
0]V
GF
4
111
[ 1
2 ]V
GF
2
V
MATS 402 Materials Lab (I)
Lab Manual
Q10: Why we put zeros in the 3rd and 4th terms? Why we changed the sign of
sure you understand this equation.
Using equation (12) we get:
V2 _ 3
GF
2
6 mgD
V
Ewt 2
2?
Make
(13)
V2_3
0V
1k
1k
-
+
Figure 5: Strain Gauge Wheatstone Bridge Circuit.
Preliminary Experiment
1. With the cantilever beam unloaded, measure and note the resistance of one of the
gauges using a Digital Multimeter (in resistance mode). What is the change in
gauge resistance when a 1 kg load is suspended from the beam?
Setting up the Wheatstone Bridge Circuit
1. Assemble the Wheatstone Bridge Circuit as shown in figure 5.
2. Connect the high sensitivity voltmeter to measure output voltage.
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3. The Bridge Power Supply and the digital multimeter (in voltage mode) used to
measure the Bridge Excitation Voltage are connected using separate wires. This
eliminates errors due to the resistance in the wires and connections.
4. Adjust the Zero Adjust resistor to obtain a zero output voltage when the cantilever
beam is unloaded.
Experiment
1. Measure the bridge output voltage with beam loadings from 0.00 to 1.00 kg in
0.10 kg steps.
2. Plot a graph of output voltage (in Volts) on the vertical axis versus beam loading
(in kg) on the horizontal axis.
3. Hooke's Law states that for elastic behaviour that the strain is proportional to the
load applied, does your graph verify Hooke's Law?
4. If the design of the apparatus is correct, the output voltage of the strain gauge
circuit should be V2 _ 3
GF
6 mgD
V . Use this formula to calculate the
Ewt 2
2
output voltage you expect for one of the loadings you have measured.
5. Calculate the maximum experimental error in the expected value of Vo using the
propagation of error formula.
6. Does the output voltage you expect agree with output voltage you have measured
within their respective experimental errors? What does this tell you?
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Experiment 2
1
On the cantilever beam (2) there are 4 strain gauges bonded on the upper
surface. Measure the distance D for each strain gauge according to the
formula
6mgD
Ewt 2
2
The four strain gauges are connected to canals 1, 2, 3 & 4 of the Traveler
Strain Master.
3
Follow the instructions from the Traveler Strain Master manual [copied
below] to read the strains at the four different positions.
4
In every canal choose Bridge Excitation = 2.5 V, the Bridge Type ¼ Bridge
and the gage factor = 2.07.
5
Put a load of 100 g. Wait until the beam is not more vibrating. Increase the
load in steps of 200 g till 900 g and repeat step 3 to measure the four strains.
6
Write your data in the data sheet. Calculate the strains according to the
formula above. Calculate the experimental uncertainty and compare the
measured and calculated strains
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IV. Data sheet
Cantilever beam:
Load: m = 100 g
.
Distance from gage to
load [mm]
calculated strain
measured
strain
% Difference
calculated strain
measured
strain
% Difference
calculated strain
measured
strain
% Difference
Load: m = 300 g
.
Distance from gage to
load [mm]
Load: m = 500 g
.
Distance from gage to
load [mm]
Load: m = 700 g
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.
Distance from gage to
load [mm]
calculated strain
measured
strain
% Difference
calculated strain
measured
strain
% Difference
Load: m = 900 g
Distance from gage to
load [mm]
Calculation
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V. Results and conclusion
Please present your results in a clear and structured way (including calculated errors).
Supervisor:
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MATS 402 Materials Laboratory I