Abstract—In this lab, students learned how to use the Instron Universal Testing Machine to create stress vs. strain plots. Using the data obtained in lab, students were responsible for finding the values of unknown material properties for four different materials. These materials include: An unknown metal, carbon-fiber, nylon and plaster of paris. The students had to determine the unknown metal by finding the appropriate material properties and comparing the found properties to those obtained by a reputable source for a given material. In the second part of this lab, students had to test a copper wire specimen in tension to failure using a fixture provided in lab. Based on data obtained in LabVIEW during this testing, students created a stress-strain-plot and found other material properties based on the specimen’s behavior.

Index Terms—Instron Universal Testing Machine, carbon-fiber, nylon, stress, strain

I. INTRODUCTION

HIS lab demonstrates how to use the Instron Universal Testing Machine to perform tensile/compressive testing.

From the data obtained through the tensile/compressive testing, stress-strain plots were generated. Other material properties found from this data include: Young’s modulus (the slope of the stress-strain curve in the linear region), yield strength (the point during testing that plastic deformation begins to occur), ultimate strength (The greatest amount of stress the specimen experiences during testing), breaking strength (the amount of stress the specimen experiences at fracture), toughness (the total amount of energy the specimen can absorb before fracture), percent elongation (percentage of how much the specimen strained during testing), specific strength (the specimen’s strength to weight ratio) and specific stiffness (the specimen’s stiffness to weight ratio). Also, the uncertainties associated with the values of stress and strain were calculated.

T

Three different materials were tensile tested including: An unknown metal, carbon-fiber and nylon. The first three test performed were tensile test. During this type of testing, the test specimen is clamped into the machine on both ends. After the specimen is clamped, the machine applies equal and opposite forces to the piece in directions away from the center of mass of the material. During the testing, force versus

displacement is recorded until the specimen fractures. Displacement is measure using either an extensometer (a sensor that is connected to the test piece that measures the elongation of the test piece) or by using cross head displacement (a method where strain is measured using the displacement of the machine’s grips). The last material tested, plaster of paris, was placed in a compressive test. Like in tensile testing, the piece was first clamped into the machine. After properly clamping the material, the machine applies equal and opposite forces to the piece in directions towards the materials center of mass. Unlike in tensile testing, an extensometer is not used to measure strain. In the second part of this lab, a copper wire specimen was tested using a fixture provided in lab. Strain during testing was measured using a LVDT (linear variable differential transformer). Using LabVIEW, students tested the copper wire specimen to failure using brass weights and created stress-strain plots based on the materials behavior as well as other material properties.

II.PROCEDURE

Lab 3a

A. Specimen MeasurementsThe first part of this required students to take turns

measuring the various specimens. For the first specimen (unknown metal) ten measurements of width and thickness were performed and recorded as well as the specimen’s mass. For the second/third specimens (carbon-fiber/nylon respectively) width and thickness were measured and recorded. Finally, for the fourth specimen (plaster of paris) diameter and height were measured and recorded.

B. Specimen Testing After all the necessary measurements were found and

recorded, the specimens were tested. The first step in testing is to clamp the specimen to the machine’s grips. This provides proper security of the specimen during testing. The second step of testing (for tensile test) is to attach the extensometer and measure the initial length between the grips. Lastly, the Instron software is opened to provide an interface to the machine for testing. After all these steps are

Lab 3: Determining Unknown Materials Based on Stress vs. Strain Plots

Ballingham, RylandSection 3236 3/1/2016

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performed, testing can begin. The test last until the specimen fractures (except for the compressive test of plaster of paris).

C. Post TestingAfter the test were performed, the method of failure for

each specimen was noted and a photograph was taken (except for carbon-fiber due to its method of failure). The data and photographs for test was placed into a zip file on canvas for analysis.

Lab 3b

A. LabVIEW VIIn this part of the lab, a LabVIEW VI is required to properly

obtain the data during the testing of the copper wire specimen. This VI logs the strain based on readings from the LDVT and allows the input of a loading weight value. Based on this data, the VI calculates the stress that the wire undergoes during testing. This is all done within a while loop and the data is written to a spreadsheet.

B. Setting up fixture The students were required to properly assemble the fixture to obtain proper data readings. The first step to assembly is to wrap one end of the wire around the top of the tensile loading fixture and anchor it. After this, the students wrapped the other end of the wire around the weight carrier and anchored it. Finally, the students measured the initial length of the wire.

C. Data collection After the fixture is setup, data collection can begin. Weight is incrementally added to the weight carrier and using the LabVIEW VI, data is collected. This is done until the wire fails.

III. RESULTS

0 0.01 0.02 0.03 0.04 0.05 0.060

100

200

300

400

500

600

Strain

Stre

ss (M

Pa)

Fig. 1. Stress vs. strain plot for unknown metal.

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04-2000

2004006008001000120014001600

Strain

Stre

ss (M

Pa)

Fig. 2. Stress vs. strain plot for carbon-fiber.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.60

5

10

15

20

25

30

Strain

Stre

ss (M

Pa)

Fig. 3. Stress vs. strain plot for nylon.

0 0.005 0.01 0.015 0.02-2024681012141618

Strain

Stre

ss (M

Pa)

Fig. 1. Stress vs. strain plot for plaster of paris.

TABLE I MATERIAL RESULTS

Carbon-fiber Nylon Unknown Metal

Young’s Modulus (GPa) 35.486 0.785 54.38

0.2% Offset Yield Strength

(MPa)- 25 500

Ultimate Strength (MPa) 1349.3 28.21 521.8

Breaking Strength (MPa) 1349.3 13.83 503.3

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Percent Elongation (%) 3.702 136.62 5.342

Toughness (mJ*m-3) 115.6 150.89 122.692

IV. DISCUSSION

Unknown Metal The material properties found in Table I are very similar

to SAE J2340 grade 340 X steel. According to [5], this type of steel has a range of yield strength of about from 340 MPa to 440 MPa, a minimum ultimate strength of 410 MPa and a Young’s modulus of 40 GPa.

TABLE IIMECHANICAL PROPERTIES OF SAE J2340 GRADE

340 X STEELTensile

Strength (MPa)Yield Strength

(MPa)Elastic

Modulus (GPa)410 340-440 40

Failure analysis

A. Unknown metalThe metal appears to have been ductile due to the fact that the specimen showed signs of failure before failure occurred. Failure seems to have occurred at approximately 45 degrees with respect to the horizontal (plane of maximum shear stress).

B. Carbon-fiberThe carbon-fiber method of failure was sudden and

catastrophic. The material showed no signs of impending failure suggesting that carbon-fiber is a brittle material. Once it failed, it was a very violent and quick failure with strings of carbon-fiber scattered around the testing machine.

C. NylonThe nylon shows characteristics of a ductile material due

to the fact that a large amount of strain occurs before the specimen fractures. Another characteristic to note is the fact that during testing, pitting occurs in the material. These pits represent microscopic tears in the material due to the induced strain of the testing machine.

D. Plaster of parisThe plaster of paris was the only material tested in

compression. This material exhibits cracking in the vertical direction before failure occurs. This is due to the fact that micro-cracks begin to form in the specimen under compressive loading and propagate in the direction of the maximum normal stress. Plaster of paris is a brittle material due to catastrophic mode of failure.

Extensometer vs. Cross head displacement An extensometer is best used when failure occurs within

the range of the extensometer. If the material failures out of this range, then this data should be discarded as it is no longer accurate. The advantages of an extensometer is higher

accuracy in measurements (due to potential “slipping” of the specimen in the grips when using cross head displacement). Cross head displacement should only be used when fitting an extensometer isn’t practical or possible.

Specific Strength/Specific Stiffness values

TABLE IIISPECIFIC STRENGTH/ SPECIFIC STIFFNESS VALUES

Material Density (kg/m3)

Breaking Strength (MPa)

Young’s Modulus

(GPa)

Specific Strength (N*m/Pa)

Specific Stiffness (N*m/Pa)

Metal 17,000 503.3 54.38 184359 3,198,889

Carbon-fiber 1,600 1349 35.49 843,313

2.218*

107

Nylon 1,140 13.83 0.785 12,135 687,719

The density of the unknown metal was found by dividing the mass that was calculated in lab by the volume of the specimen. The density values for carbon-fiber and nylon were found from reputable sources online. From the table, it appears that carbon-fiber has the highest specific strength and specific stiffness.

V. CONCLUSION

In this lab, students were taught how to use the Instron Universal Testing Machine to test materials in tension and compression. Students also learned how to create stress-strain diagrams from the data collected in these test and how to find other material properties based on the stress-strain plots. By analyzing the data for the unknown metal, students were able to figure out what the unknown metal was simply based on the stress-strain plots generated from the data.

APPENDIX

Uncertainty values for the stress, strain and cross head displacement are located in [1]. The uncertainty values of Young’s modulus were calculated using the Monte Carlo simulation method. The formulas used for this method are located in [1].

TABLE IVUNCERTAINTY CALCULATIONS

Parameter Uncertainty

width ±0.00005 in.

thickness ±0.00005 in.

height ±0.00005 in.

diameter ±0.00005 in.

AM ±0.20 mm2

AN ±0.54 mm2

ACF ±0.16 mm2

APOP ±0.20 mm2

ϵ ±0.6%

σ M ±240 MPa

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σ N ±38 MPa

σ CF ±56 MPa

σ POP ±0.100 MPa

EM ±800 MPa

EN ±10 GPa

ECF ±150 MPa

EPOP ±0.125 MPa

Cross head displacement ±0.5%

0.2% offset equations

TABLE VEQUATION OF 0.2% OFFSET LINE

Material EquationUnknown Metal y=33804x-1.715

Carbon-fiber y=35486x+122.534

Nylon y=784.69x-3.50098

Uncertainty equations used

U A=√( dAdw )

2

(U w )2+( dAdb )

2

( U b )2 (1)

Uσ=√( dσdP )

2

( UP )2+( dσdA )

2

(U A )2 (2)

U ϵ=√(d ϵdL )

2

(U L)2+( d ϵd Lo )

2

(U Lo )2 (3)

U E=√(dEdσ )

2

(Uσ )2+( dEd ϵ )

2

( U ϵ )2 (4)

REFERENCES

[1] Pandkar, A. “Lab 3 Monte Carlo Spring 2016 Students,” EML3301C- Mechanics of Materials Laboratory - Spring 2016

[2] Pandkar, A. “Lab 3 Lecture Slides,” EML3301C- Mechanics of Materials Laboratory - Spring 2016

[3] "Toughness." Wikipedia. Wikimedia Foundation, 05 Mar. 2015. Web. 02 July 2015.

[4] Beer, Ferdinand P., and E. Russell Johnston. Mechanics of Materials. New York: McGraw-Hill, 2015. Print.

[5] High Strength Steel Stamping Design Manual. (2014, July 25). Retrieved March 6, 2016. <http://www.a-sp.org/~/media/Files/ASP/Enabling%20Programs/High_Strength_Steel_Stamping_Design_Manual.pdf

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