Material Science Studio Lab Tensile Test of Thin Engineering Sheet Materials

OBJECTIVE The objective of this lab is to determine the relationship of engineering stress and engineering strain, as well as the material property when subjected to axial tensile load with an emphasis on being able to fully analyze the data. INTRODUCTION AND THEORY The tensile test is a common material testing procedure for determining material response to axial pulling of a sample until total fracture occurs. Information gained from the test is the following: Young’s Modulus, elastic limit, yield strength, ultimate tensile strength, percent elongation and area reduction. The data measured in the experiment are load and length change of the sample. The load versus the length change data can be used to generate the engineering stress-strain curve. If one considers the elongation and its associated reduction in area then a true stress-strain curve can be developed. In the tensile test when a load is applied to a sample it deforms or elongates in a way that obeys Hook’s Law. This deformation is considered to be elastic and will be restored when the load is removed provided the elastic limit has not been exceeded. If the elastic limit is exceeded then the deformation includes both elastic and plastic parts. The plastic part cannot be recovered with the removal of the load. The ratio of the force (F) applied to the original cross-sectional area (Ao) of a material is called the engineering stress:

oA

FStress = units: Newton per square meter (N/m2) or Pascal (Pa)

The ratio of the change in length (∆L) to the original length (Lo) of a material is called the engineering strain:

oLLStrain ∆

= No units (mm/mm)

Figure 1: Stress-strain curve

Stre

ss (N

/m2 )

Strai

Elastic

Plastic

Yield

The initial slope of this curve gives Young’s Modulus for the material. The point at which the curve deviates from being linear is called the Elastic Limit. Stress values above the elastic limit result in permanent deformation or plastic strain, which are not recoverable by the removal of the stress. The yield strength of most engineering material is identified by construction a line on the stress-strain graph parallel to the Young’s Modulus with a 0.2% offset on the strain axis. The intersection of the constructed line with the stress-strain curve denotes the Yield Strength. The yield strength on the graph is denoted by a change in the slope of the curve. Some materials exhibit a pronounced change in slope at the yield point whereas it may be slight change in slope. Ductile materials exhibit large strains prior to fracture. In contrast brittle materials have limited strain prior to fracture. As the material resists deformation more dislocations are generated and their interaction occurs with the result being work hardening of the material. In samples that have polished surfaces the generation and motion of dislocation can be observed in the form of Luders bands. If the stain hardening is rapid and uniform over the gage length this causes a constant reduction in the area over the gage length and the sample elongates uniformly. However, if the strain hardening is slow or non-uniform then an area of localized reduction in cross sectional area occurs which is called necking. The highest stress the material obtained is called the Ultimate Tensile Strength (UTS). The toughness of the material can be related to the area under the stress-strain curve. SET-UP for ScienceWorkshop System 1. Plug the sensors into the interface. Connect the Force Sensor to Channel A of the interface.

Connect the yellow plug of the RMS to Channel 1 and the black plug to Channel 2.

Figure 2: Setup of interface 2. Start Capstone by opening the activity file MENG3331 Tensile Test.cap.

Figure 2: Apparatus Setup

3. Check RMS orientation. While monitoring data in Capstone, turn the crank clockwise. Watch the "Displacement" digits display. If displacement decreases, swap the positions of the yellow and black RMS plugs on the interface.

1. Rotary Motion Sensor (RMS) 6. 3- Step Pulley 2. Force Sensor 7. Belt 3. Force Sensor Attachment 8. Groove 4. Setscrew 9. Coupon Clamps 5. Stress-Strain Platform 10. Lever Arm 11. Thumbscrew

PROCEDURE Apparatus Calibration During the experiment, as the crank turns, force will be applied to the test coupon, causing it to stretch. However, this force will also cause the apparatus platform and the Force Sensor to bend. The displacement registered by the RMS will be the combination of the coupon stretching and the rest of the apparatus bending. Regardless of how much the coupon stretches, the deformation of the rest of the apparatus is constant for a given force. One can measure this deformation directly by using the calibration bar (which does not stretch significantly) in place of a coupon as force is applied. The goal is to create a plot of Displacement versus Force for the calibration bar, in which the displacement is due only to bending of the apparatus. Later, subtract this plot from a similar plot made with a coupon, in which the displacement results from both bending of the apparatus and stretching of the coupon. The result will be a plot in which the displacement is due only to stretching of the coupon.

Figure 3: Calibration bar setup Use the following steps to acquire Displacement versus Force data: 1. Install the calibration bar by removing all the nuts, washers, and springs and then sliding the bar over the posts. See Figure 3. Do not use the nuts to attach the calibration bar. 2. Preload the bar so the slack is taken up:

a. Turn the crank so the lever bar does not touch the force sensor. Then zero the force sensor. b. Start recording and turn the crank until the force reads about 5 N. Then stop cranking and stop recording and zero the force sensor again.

3. Start recording and turn the crank slowly to stretch the apparatus. The recording will automatically stop when the force reaches 235 N. 4. To get a relationship between the force and the amount of stretch that is due to the apparatus stretching:

a. Turn on a Power Fit for the Position vs. F calibration data. b. Click on the Power Fit annotation box on the graph and look at the Curve Fit editor at left.

If it cannot find a fit, try selecting data on the graph so the endpoints of the plot are not included. Lock x0 equal to zero and lock B equal to zero.

c. The Power Fit has n=4 locked initially. Unlock it and change n to 0.5 and lock it again and

This workbook already contains a rough calibration, so you can proceed without further calibration.

then click on Update Fit in the Curve Fit Editor. d. Once it finds a fit, unlock n and click on Update Fit again. This gives the final equation

for position as a function of force. e. Open the calculator (at left) and enter the values for A and n.

DATA COLLECTION 1. Installing coupons

Remove the calibration bar and re-install the springs, clamps, washers, and nuts as shown in Figure 4.

Figure 4: a) Coupon attachment b) Washer Configuration

When installing coupons, loosen the nuts but do not remove them. The coupon should be slid completely under the clamp top on each end. Turn the crank to make room for the coupon so the coupon does not buckle and is straight. Then tighten the nuts with the wrench as tight as possible, making sure the coupon does not twist. First the spring goes on. Then the curved-inward washer goes on with the flat side down. Then the curved-outward washer goes on with the curved side down. Finally, the smaller flat washer goes on last, followed by the nut.

2. Calculating Stress and Strain.

a. Stress is related to the force by Equation (1). Measure the cross-sectional area of the coupon and enter it into the calculator as the Area in units mm² (this will make the stress be in units of MPa). Make a calculation for "Metal Stress" and "Plastic Stress" because they have different cross-sectional areas.

b. Strain is the related to the measured position by Equation

(2). Measure the initial length of the coupon and enter it into the calculator as L0 in meters. Measure the length of only the part of the coupon that is narrow, for which we can say the cross-sectional area is the same as in the stress calculation. Make a calculation for "Metal Strain" and "Plastic Strain" because each has a different length.

3. Pre-loading Coupons This is the procedure you will follow each time you test a coupon. You must pre-load the coupon so the initial slack is taken up and the force sensor is zeroed at position zero.

a) Turn the crank so the lever bar does not touch the force sensor. Then zero the force

sensor.

Figure 5: Interface of calculator

b) Start recording and turn the crank and watch the digits display of the force. When the force reaches about 5N, stop recording and press the zero button on the force sensor. Do not let go of the crank and do not move the crank.

c) Now the apparatus is ready to record the curve for the coupon. You should immediately start recording again and proceed to stretch the coupon over the entire range.

4. Collecting Data.

Press the Tare button on the Force Sensor. Click the Record button. Turn the crank clockwise. Starting just before the lever arm comes into contact with the Force sensor, turn the crank very slowly. When finished collecting data, click Stop. (If the maximum force is reached, Capstone will stop automatically.) If the coupon breaks, it should break in the middle. If the coupon breaks near the end, it was probably twisted slightly when it was mounted, resulting in a point of higher stress where it broke.

DATA ANALYSIS On the Stress-Strain graph, identify and record the elastic region, the plastic region, the yield point, and the break point (if available). To calculate Young's modulus, select a data region covering the linear, lower left-hand part of the graph. (The very first part of the plot may not be linear. This nonlinearity likely is due to the straightening of bends and twists in the coupon as force is first applied. Do not include this region in the selection.) Apply a linear curve fit to the selected data. The slope of the line is Young's modulus in units of MPa (106N/m2) or Pa (N/mm2). Record Young’s Modulus. DETAIL REQUIREMENT 1. Define engineering stress and strain in your own words and include a sketch. Discuss what is

physically happening to a coupon when it is experiencing stress and strain. 2. Sketch graphs of stress-strain from your data. Identify different regions. Discuss the

relationship between stress and strain in these regions. 3. Do the graphs agree with Hooke’s Law? Explain. 4. Determine Young's modulus, elastic limit, yield strength, ultimate tensile strength, and

percent elongation in each curve, and list all the values in a table. 5. Compare the stress-strain curves of the materials you tested, discuss in detail, find trend and

make your points. 6. Does the coupon that can withstand the greatest force also experience the greatest stress?

Explain.

LIST OF SAMPLES No. of Sample

Material Quantity of the Sample

Detail Dimension of the Sample

1 Steel 3 2 Brass 3 3 Brass 3 4 Aluminum 3 5 Polycarbonate 3

Material Properties Item cold-rolled

steel annealed steel aluminum brass (thin) brass (thick)

Cross-sectional area

0.303 mm2 0.303 mm2

0.303 mm2 0.303 mm2 0.506 mm2

Tensile strength

620 MPa/ 90,000 psi

300 MPa/ 44,000 psi

145 MPa/ 21,000 psi

430 MPa/ 44,000 psi

430 MPa/ 44,000 psi

Tensile elongation

none 42-45% 6% 25% 25%

Modulus of elasticity

200,000 MPa/ 29,000,000 psi

200,000 MPa/ 29,000,000 psi

69,000 MPa/ 10,000,000 psi

117,000 MPa/ 17,000,000 psi

117,000 MPa/ 17,000,000 psi

Item HIPS nylon 6(+ 15%

glass) ABS polypropylene

Color code orange black blue white Cross-sectional area

2.482 mm2 2.482 mm2 2.482 mm2 2.482 mm2

Tensile strength 23 MPa/ 3410 psi

98 MPa/ 14000 psi

47 MPa/ 6800 psi

34 MPa/ 4900 psi

Tensile elongation 40% 2.5% 20% 9% Modulus of elasticity

2000 MPa/ 280000 psi

2900 MPa/ 420000 psi

2300 MPa/ 380000 psi

1900 MPa/ 239000 psi