Date post: | 04-Apr-2018 |
Category: |
Documents |
Upload: | bhagwan-jane |
View: | 221 times |
Download: | 0 times |
of 17
7/29/2019 Lab 1 ASE 324 Utexas
1/17
The Tension Test of Steel (LAB 1)
Tomasz Sudol
ASE 324LUniversity of Texas at Austin
6/15/2006
7/29/2019 Lab 1 ASE 324 Utexas
2/17
1.0 ABSTRACT
Tensile tests were done at the University of Texas at Austin on both cold rolledsteel (CRS) and hot rolled steel (HRS) specimens. A constant ramp load was applied to
the specimens by an alectromechanical loading device until fracture occurred. Two
extensometers measured the radial and axial strains on the test specimens. After fracture
had occurred, the stress-strain curves were analyzed to obtain a basic understanding ofhow CRS and HRS differ in behavior. The Youngs Modulus for CRS and HRS was
found to be 26773 ksi and 30108 ksi, respectively. Furthermore, CRS was found to have
a lower Poissons Ratio than HRS. Upper and lower yielding stress was determined forHRS and compared to the yielding stress obtained from the 0.2% proof stress of the CRS.
The CRS proved to have a higher yielding stress. Also, the CRS had a higher ultimate
tensile strength than HRS. However, the HRS was found to be much more malleable thanCRS. The hardening exponent and ductility were used to compare malleability. It was
shown that CRS is stronger while HRS is generally more malleable.
7/29/2019 Lab 1 ASE 324 Utexas
3/17
2.0 INTRODUCTION
A base knowledge of material properties is essential to todays practicing engineers.
This knowledge of how materials respond to loads is essential and the concepts of
mechanics of solids span most of the engineering fields in some way or another. The
elasticity of material used in the frame of an aircraft, for example, has to be strong
enough so that the it can withstand the forces it is subjected to in flight and yet flexible
enough to be able to damp the effects of turbulence for the sake of the passengers
comfort. Aerospace engineers refer to this subject as the study of aeroelasticity. Civil and
architectural engineers, on the other hand, use properties of materials to determine which
materials to use in the construction of buildings, bridges, and countless other structures
whose reliability depends on how the material deforms when subjected to a load.
The purpose of this lab is to investigate the behavior of hot and cold rolled 1020 steel
when subjected to a uniform ramp loading. Familiarization with methods of tension
testing is also part of this experiment. A solid base of discerning material characteristics
from stress-strain curves is another objective of the lab.
7/29/2019 Lab 1 ASE 324 Utexas
4/17
3.0 EXPERIMENTAL AND DATA REDUCTION PROCEDURES
3.1 Experimental Procedure
A specimen of hot rolled steel (HRS) was loaded onto a screw-driven loading
device to provide the displacement control. Then some preliminary measurements were
made. These included the specimen diameter and gage length. The gage length was
marked on the specimen for later measuring purposes.
A transducer with a linear response was used to acquire data. The calibration
constant for the transducer was taken to be 2 kips/V. An extensometer with a calibration
of 5%/V was used to measure the specimen axial strain. The calibration output of the
diametrical extensometer used to measure radial strain was 0.0427 in/V.
The tensile test of the HRS consisted of applying a ramp displacement by the
loading device until the specimen broke. The data gathered was in terms of load and
deformation which were converted to stress and strain and graphed on a stress-strain
curve. The same was then repeated for cold rolled steel (CRS).
3.2 Data Reduction Procedures
The linear response of the transducers used in the measurements can be described
by the relation
VQ = (1)
where Q is the quantity being measured, is a constant of proportionality specific to the
machine, and Vis the output voltage. In this case, the constant of proportionality is equal
to 5%/V for the axial extensometer and 2 kips/V for the load cell.
Stress and strain are related through Hookes Law, a linear relationship between
stress and strain as a multiple of Youngs Modulus. Hookes Law states
E= (2)
where is stress, Eis Youngs Modulus (the stiffness of the material), and is the strain.
Eq. (2) only applies to the elastic region, where strain and stress are linearly proportional
to each other. Deformation in the elastic region is reversible, whereas deformation in the
plastic region of the strain-stress curve permanently deforms the material. A good
7/29/2019 Lab 1 ASE 324 Utexas
5/17
measure of the effect of stiffness is Poissons Ratio, which is the ratio of radial strain to
axial strain
a
t
= . (3)
where t is the radial strain and a is the axial strain. The Poissons Ratio depends on
where on a stress-strain curve a material lies.
Ductility is a measure of how malleable a material is by describing its
deformation as it is axially loaded. Ductility can be discussed in terms of elongation and
area reduction. When describing elongation, ductility is a measure of how the length of a
specimen changes, and is given by
100
= o
of
l L
LL
D (4)
where fL is the final length after deformation has stopped, and oL is the initial length of
the specimen before it is subjected to a load. Area reduction ductility pertains to how the
cross-sectional area of the specimen deforms when subjected to a load, and is given by
100
=o
fo
aA
AAD . (5)
In this expression, oA is the original cross-sectional area before deformation occurs due
to a load. fA is the final cross-sectional area after the material stops deforming. A
number of ductility data are presented later in the lab, but for example purposes. The
following is an elongation ductility calculation for HRS:
%5.31100315.01002
263.2==
=lD
The hardening exponent is described by
n
p HE
1
==
(6)
and stems from the sum of the elastic and plastic strains and reduces to Eq. (6) with the
use of Eq. (2). In Eq. (6), n is the hardening exponent, which in this lab was found by
plotting the log functions of axial and radial strains.
7/29/2019 Lab 1 ASE 324 Utexas
6/17
The toughness was calculated by obtaining the area under the stress-strain graphs
which is mathematically described by the integral
=f
dT
0
(7)
Where material stress is integrated with respect to axial strain f . Due to the fact that
the integral in Eq. (7) cannot be easily performed, an approximation using the trapezoidal
rule was obtained.
7/29/2019 Lab 1 ASE 324 Utexas
7/17
3.0 RESULTS
3.1 Experimental Parameters
A number of initial measurements were first taken before performing the tests on
the tensile specimens. After the tensile tests were done, the specimens were again
measured for comparison. Observations about the nature of the fracture were also made.
All of these data are listed in Table 1.
CRS HRS
Initial Diameter 05 in 0.495 in
Initial Length 2 in 2 in
Initial Area (cross-
sectional)0.1964 in 0.1901 in
Final Diameter 0.306 in 0.389 in
Final Length 2.377 in 2.63 in
Final Area 0.0735 in 0.1188 in
Neck Out Out
Fracture cup/cone cup/cone
TABLE 1 Measured and Observed Data Before and After Tensile Tests on
CRS and HRS
3.2 Extensometer and Crosshead for CRS
When comparing the extensometer stress-strain data to that obtained with the
crosshead in Fig. 1, it is clear that the crosshead data is shifted significantly to the right.
This is due to the fact that while the load was applied to the tensile specimen, the
crosshead itself was deforming. This deformation is the cause of the shift of the
crosshead data in Fig. 1.
7/29/2019 Lab 1 ASE 324 Utexas
8/17
Figure 1 - Stress vs. Strain for Extensometer and Crosshead
(CRS)
-10
0
10
20
30
40
50
60
70
80
90
-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
axial strain
stress
(ksi) extensometer
crosshead
When examining Fig. 2, the same shift can be noticed despite the fact that HRS is
being analyzed. Once again, deformation of the crosshead is to blame for this.
Fig. 2 - Stress vs. Strain for Extensometer and Crosshead
(HRS)
-10
0
10
20
30
40
50
60
70
80
90
- 0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6
strain
s
tress(
ksi)
extensometer
crosshead
7/29/2019 Lab 1 ASE 324 Utexas
9/17
3.3 Basic Stress-Strain Curve
A number of basic material properties can be obtained from analyzing a simple stress-
strain plot. Fig. 3 shows some of these properties of CRS.
Figure 3 - Stress vs. Strain (CRS)
-10
0
10
20
30
40
50
60
70
80
90
-0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
axia l strain
stress
(ksi)
Series1
The elastic region of the CRS can be seen in Fig. 3 to exist approximately below the
strain of 0.01. The plastic region exits at all values of strain above the elastic region. The
ultimate tensile strength is the maximum value of the entire plot and can be eyeballed to
be around 85 ksi. From the hooking of the data past the strain of about 0.08, it is evident
that upon fracture, the neck occurs outside of the gage and the fracture itself resembles a
cup/cone. The fracture point is the last point on the plot, and is about 57 ksi. More precise
values of some of these data will be presented later. The basic stress-strain behavior of
HRS can be determined by re-examining Fig. 2.
3.4 Derivation of Youngs Modulus
Youngs Modulus can be derived from the stress-strain curve for both CRS andHRS in Figs. 3 and 2. It applies to the elastic portions of the graphs where the stress is
proportionally related to the strain. Youngs Modulus, otherwise known as the modulus
of elasticity, is equal to the slope of the elastic region of both CRS and HRS plots. Fig. 4
shows a cropped set of data from the elastic region of Fig. 3.
7/29/2019 Lab 1 ASE 324 Utexas
10/17
Figure 4 - Youngs Modulus (CRS)
y = 26773x - 3.0576
-10
0
10
20
30
40
50
60
-0.0005 0 0.0005 0.001 0.0015 0.002 0.0025
strain
stress
(ksi)
A trendline is fitted to the data and the slope of the equation of the trendline is, in fact,
Youngs Modulus for CRS, which equals 26773 ksi. A similar approach was taken to
obtain Youngs Modulus for HRS. Fig. 5 shows a similar cropping of data to Fig. 4, but
this time for the elastic region of the extensometer data in Fig. 2.
Figure 5 - Young's Modulus (HRS)
y = 30108x - 2.9349
-10
0
10
20
30
40
50
60
70
-0.0005 0 0.0005 0.001 0.0015 0.002 0.0025
strain
stress
(ksi)
7/29/2019 Lab 1 ASE 324 Utexas
11/17
From Fig. 5, it can be seen that the Youngs Modulus for HRS is 30108 ksi the slope of
the trendline fitted to the data.
3.5 Poissons Ratio
Poissons Ratio was obtained by graphing the radial strain verse the axial strain.
This relationship is represented by Eq. (3).
3.5.1 Poissons Ratio of CRS
Cropping of data was once again used to find an elastic property of CRS. This
time, the Poissons Ratio for the elastic portion of radial vs. axial strain curve was
analyzed. This data is shown in Fig. 6.
Figure 6 -Poisson's Ratio Plot (CRS)
y = -0.23x + 3E-05
-0.0008
-0.0007
-0.0006
-0.0005
-0.0004
-0.0003
-0.0002
-0.0001
00 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035
axial strain
radialstrain
Once again, it is the slope of the trendline that gives the value of interest. Poissons Ratio
for the elastic region of CRS is equal to 0.23. It is positive due to the nature of Eq. (3),
which states that Poissons Ratio is the negative of the ratio of the two strains. Similarly,
a portion of a plastic region of the stress was analyzed, and once again the slope of thetrendline equaled Poissons Ratio. This is seen in Fig. 7.
7/29/2019 Lab 1 ASE 324 Utexas
12/17
Figure 7 - Poissants Ratio (CRS)
y = -0.4036x + 0.0004
-0.0018
-0.0016
-0.0014
-0.0012
-0.001
-0.0008
-0.0006
-0.0004
-0.0002
0
0 0.001 0.002 0.003 0.004 0.005 0.006
axia l strain
radialstrain
Fig. 7 shows the Poissons Ratio of the plastic region of CRS to be 0.40.
3.5.2 Poissons Ratio of HRS
The same methods used in section 3.5.1 were employed to obtain the Poissons Ratios for
HRS. The cropped data on which trendlines were fitted to are seen in Figs. 8 and 9.
Figure 8 - Poissants Ratio (elastic - HRS)
y = -0.4203x - 8E-05
-0.0025
-0.002
-0.0015
-0.001
-0.0005
0
-0.001 0 0.001 0.002 0.003 0.004 0.005 0.006
axia l strain
radialstrain
7/29/2019 Lab 1 ASE 324 Utexas
13/17
Figure 9 - Poissons Ratio (plastic - HRS)
y = -0.5093x - 3E-05
-0.0006
-0.0005
-0.0004
-0.0003
-0.0002
-0.0001
0
-0.0002 0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012
axial strain
radialstrain
Fig. 8 shows that Poissons Ratio for the elastic region of HRS was 0.42. Furthermore,
the Poissons Ratio for the plastic region of HRS was 0.51, as seen in Fig. 9.
3.6 Proof Stress for CRS
The 0.2% proof stress is a universal method for determining where the elastic
region of a material transitions to the plastic region. The stress-strain data in Fig. 3 was
used to illustrate this concept. A 0.2% offset is plotted in Fig. 10.
Figure 10 - 0.2% Offset
0
10
20
30
40
50
60
70
80
90
-0.001 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007
strain
stress
(k
7/29/2019 Lab 1 ASE 324 Utexas
14/17
The point where the 0.2% offset line crosses the data is the 0.2% proof stress. This point
is considered the yield stress of CRS. Closer inspection of the data in Fig. 10 in a
spreadsheet showed that the 0.2% proof stress (yield stress) was 74.31 ksi for CRS.
3.7 Yield Strength for HRS
The upper and lower yield strengths were obtained from the plot of stress vs.
strain for HRS, shown in Fig. 11.
Figure 11 - Stress vs Strain (HRS)
-10
0
10
20
30
40
50
60
70
80
90
-0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25
strain
stress(
ksi)
The upper yield strength is the greatest value of the elastic region of Fig. 11. The lower
yield strength is the lowest value of the small notch which forms at the end of Luders
Band (small region of no stress growth following elastic region.) From examining the
values in Fig. 11 more closely on a spreadsheet, the upper and lower yield strengths were
found to be 62.12 ksi and 55.9 ksi, respectively.
7/29/2019 Lab 1 ASE 324 Utexas
15/17
3.8 Ultimate Tensile Strength
The ultimate tensile strength is the highest value on a stress-strain curve. From Fig. 3, the
ultimate tensile strength for CRS is obtained by reading the largest value of the entire
plot, which equals 85.56 ksi. The ultimate tensile strength for HRS can be obtained from
Fig. 11. The highest value of this plot is 79.53 ksi.
3.9 Hardening Exponent
The hardening exponent was obtained by plotting the natural logs of stress vs. strain. The
data was then fitted with a linear trendline whose slope represented the inverse of the
hardening exponent. Fig. 12 shows this data for CRS.
Figure 12 - Hardening Exponent
y = 0.0659x + 4.7081
4.18
4.2
4.22
4.24
4.26
4.28
4.3
4.32
4.34
4.36
-9 -8 -7 -6 -5 -4 -3 -2 -1 0
ln(Ep)
ln(stress)
From Fig. 12, it is seen that the hardening exponent for CRS is 1/0.0659 which is equal to
15.17.
Fig. 13 shows similar data for HRS.
7/29/2019 Lab 1 ASE 324 Utexas
16/17
Figure 13 - Hardening Exponent
y = 0.8625x - 0.0532
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
-1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0
ln(Ep)
ln(stre
The hardening exponent for HRS is 1/0.8625 which equals 1.16 much lower than that
of CRS.
4.0 Toughness
The toughness of both CRS and HRS was measured by summing up the are below the
stress-strain curve. This followed from Eq. (7), which states that the toughness is the
integral of stress. The area under the stress-strain plots was obtained by using integral
approximation methods and is therefore just that an approximation. In any case, the
area under the curve in Fig. 3 was estimated to obtain a value of the toughness of CRS.
This approximation turned out to be around 19.8 ksi. Similarly, the area under Fig. 11
was estimated to obtain the HRS toughness, which turned out to be somewhat higher ~
34.74 ksi.
4.1 Ductility
The ductility of CRS and HRS was calculated using Eqs. (4) and (5). Both, the
elongation and area reduction ductility were obtained which led to the conclusion that
HRS is, for the most part, more malleable. The crosshead and extensometer ductilities
were also calculated, and all of these values are listed in Table 2.
Ductility CRS HRS
Elongation18.85
%31.5%
Area Reduction62.55
%37.49%
Crosshead 30.6% 53.9%
7/29/2019 Lab 1 ASE 324 Utexas
17/17
Extensometer 9.58% 20.24%
TABLE 2 Ductility Values
5.0 CONCLUSIONThis experiment proved that CRS is noticeably stronger than HRS. CRS not only had
a higher Youngs Modulus, but it also had a higher yield strength and ultimate tensile
strength. However, the HRS was found to be considerably more malleable than CRS.
HRS was found to have a higher value of toughness and a generally higher value of
ductility. The HRS also had a much lower hardening exponent. These data suggest that in
cases where a strong, stiff material is needed, CRS is better suited for the job. On the
other hand, if a tough material that easily changes shape is needed, HRS is better suited.