Lab 1 ASE 324 Utexas

7/29/2019 Lab 1 ASE 324 Utexas

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The Tension Test of Steel (LAB 1)

Tomasz Sudol

ASE 324LUniversity of Texas at Austin

6/15/2006


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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.


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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.


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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


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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.


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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.


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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.


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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


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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.


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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)


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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.


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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


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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


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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.


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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.


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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%


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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.

Lab 1 ASE 324 Utexas

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