Lecture 6
Mechanical Properties
Problem 1
A cylindrical specimen of aluminum having a diameter of 12.8 mm) and a gauge
length of (50.800 mm) is pulled in tension. Use the load–elongation characteristics
tabulated below to complete problems a through f.
Load(N)
Length(mm)
(a) Plot the data as engineering stress versus engineering strain.
(b) Compute the modulus of elasticity.
(c) Determine the yield strength at a strain offset of 0.002.
(d) Determine the tensile strength of this alloy.
(e) What is the approximate ductility, in percent elongation?
Solution
(a) The data are plotted below on two plots: the first corresponds to the entire stressstrain curve, while for the second; the curve extends just beyond the elastic region of
deformation
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Lecture 6
Mechanical Properties
(b) The elastic modulus is the slope in the linear elastic region as
(c) For the yield strength, the 0.002 strain offset line is drawn dashed. It intersects the
stress-strain curve at approximately 285 MPa
(d) The tensile strength is approximately 370 MPa, corresponding to the maximum
stress on the complete stress-strain plot.
(e) The ductility, in percent elongation, is just the plastic strain at fracture, multiplied
by one hundred.
The total fracture strain at fracture is 0.165; subtracting out the elastic strain (which is
about 0.005) leaves a plastic strain of 0.160. Thus, the ductility is about 16%EL.
Problem 2
From the tensile stress–strain behavior for the brass specimen shown in Figure
determine the following
(a) The modulus of elasticity.
(b) The yield strength at a strain offset of 0.002.
(c) The maximum load that can be sustained by a cylindrical specimen having an
original diameter of 12.8 mm.
(d) The change in length of a specimen originally 250 mm long that is subjected to a
tensile stress of 345 MPa.
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Lecture 6
Mechanical Properties
SOLUTION
(a) The modulus of elasticity is the slope of the elastic or initial linear portion of the
stress–strain curve. The strain axis has been expanded in the inset, Figure to facilitate
this computation. The slope of this linear region is the rise over the run, or the change
in stress divided by the corresponding change in strain; in mathematical terms,
Inasmuch as the line segment passes through the origin, it is convenient to take both
σ1 and ε1 as zero. If σ2 is arbitrarily taken as 150 MPa, then ε2 will have a value of
0.0016. Therefore
(b) The 0.002 strain offset line is constructed as shown in the inset; its intersection
with the stress–strain curve is at approximately 250 MPa, which is the yield strength
of the brass.
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Lecture 6
Mechanical Properties
(c) The maximum load that can be sustained by the specimen is calculated by using
Equation, in which _ is taken to be the tensile strength, from Figure, 450. Solving for
F, the maximum load, yields
(d) To compute the change in length, ∆L, it is first necessary to determine the strain
that is produced by a stress of 345 MPa. This is accomplished by locating the stress
point on the stress–strain curve, point A, and reading the corresponding strain from
the strain axis, which is approximately 0.06. Inasmuch as Lo = 250 mm, we have
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Lecture 6
Mechanical Properties
Hardness Test
Hardness is resistance of material to plastic deformation caused by indentation.
Sometimes hardness refers to resistance of material to scratching or abrasion
Principle of any hardness test method is forcing an indenter into the sample surface
followed by measuring dimensions of the indentation (depth or actual surface area of
the indentation).
Benefits of hardness test:
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Easy
Inexpensive
Quick
Non-destructive
May be applied to the samples of various dimensions and shapes
May be performed in-situ
Depending on the loading force value and the indentation dimensions, hardness is
defined as a macro- , micro- or nano-hardness.
Macro-hardness tests (Rockwell, Brinell, and Vickers) are the most widely used
methods for rapid routine hardness measurements. The indenting forces in macrohardness tests are in the range of 50N to 30000N.
Micro-hardness tests (micro-Vickers, Knoop) is applicable when hardness of
coatings, surface hardness, or hardness of different phases in the multi-phase material
is measured. Small diamond pyramid is used as indenter loaded with a small force of
10 to 1000gf.
Nano-hardness test uses minor loads of about 1 nano-Newton followed by precise
measuring depth of indentation.
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Lecture 6
Mechanical Properties
Brinell hardness Test
In this test a hardened steel ball of 2.5, 5 or 10 mm in diameter is used as indenter.
The loading force is in the range of 300N to 30000N (300N for testing lead alloys,
5000N for testing aluminum alloys, 10000N for copper alloys, 30000 N for testing
steels).
The Brinell Hardness Number (HB) is calculated by the formula:
HB = 2F/ (3.14D*(D-(D² - Di²)½))
Where
F- applied load, kg
D – indenter diameter, mm
Di – indentation diameter, mm.
Rockwell Hardness Test
In the Rockwell test the depth of the indenter penetration into the specimen surface is
measured. The indenter may be either a hardened steel ball with diameter 1/16”, 1/8”
or a spherical diamond cone of 120º angle (Brale).
Loading procedure starts from applying a minor load of 10 kgf (3kgf in Rockwell
Superficial Test) and then the indicator, measuring the penetration depth, is set to
zero. After that the major load (60, 100 or 150 kgf) is applied. The penetration depth
is measured after removal of the major load.
Hardness is measured in different scales (A, B, C, D, E, F, G, H, K) and in numbers,
having no units (in contrast to Brinell and Vickers methods).
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Lecture 6
Mechanical Properties
Aluminum alloys, copper alloys and soft steels are tested with 1/16” diameter steel
ball at 100 kgf load (Rockwell hardness scale B).
Harder alloys and hard cast iron are tested with the diamond cone at 150 kgf
(Rockwell hardness scale C).
An example of Rockwell test result: 53 HRC. It means 53 units, measured in the scale
C by the method HR (Hardness Rockwell).
Vickers Hardness Test
The principle of the Vickers Hardness method is similar to the Brinell method. The
Vickers indenter is a 136 degrees square-based diamond pyramid. The impression,
produced by the Vickers indenter is clearer, than the impression of Brinell indenter,
therefore this method is more accurate.
The load, varying from 1kgf to 120 kgf, is usually applied for 30 seconds.
The Vickers number (HV) is calculated by the formula:
HV = 1.854*F/ D²
Where
F-applied load, kg
D – length of the impression diagonal, mm
The length of the impression diagonal is measured by means of a microscope, which
is usually an integral part of the Vickers Tester.
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Lecture 6
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Mechanical Properties