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# Material properties_1_ by hcj

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Pupil Sheet

Young’s Modulus
Experimental details
The device used in this experiment to determine Young’s Modulus and Poisson’s ratio is the electrical resistance strain gauge. This is the most widely used device for measuring elastic strains. It is essentially a strip of metal foil which is firmly glued to the surface where the strain is to be measured, so that when the material is strained, the strain at the surface is fully transmitted to the metal foil. Elastic strain along the length of the strip causes a small change in resistance of the gauge, largely because of the change in length and crosssectional area of the strip, although there is also a slight change in its resistivity. Small changes in resistance are easy to measure accurately, and so the gauge gives an accurate reading of the small elastic strain along the direction of the strip in the gauge. The change in resistance, and hence the voltage across the strain gauge for a constant current, is proportional to the strain; the gauge manufacturer supplies the value of the constant of proportionality. For the strain gauges and current used here ε = 3.803×10-7 V (a conversion factor provided by the manufacturer), where ε = strain (No units – a dimensionless quantity) and V = voltage across strain gauge (measured in microvolts). This practical uses a simulation, based on a University experiment, of the simple cantilever bending of the beam to which the strain gauges are attached. The sidearm is not used in this experiment. Identify the 3 strain gauges on the cantilever arm. For this experiment you will use only two gauges; the one that is lined up along the cantilever, the “x” direction and the one lined up laterally across the cantilever, the “y” direction. These are represented in the diagram, above, by the strain gauges on the left and right respectively. Measurements are taken using a single meter, which is attached in turn to different strain gauges on the top and bottom of the beam. You will use four of these. TOP – denotes the gauges measuring tension on the upper surface. BOTTOM – denotes the gauges measuring compression on the lower surface. ALONG – denotes the strain in the x direction, along the beam. LATERAL – denotes the strain in the y direction, across the beam.

Activity YM1

Pupil Sheet

The experimental work in this practical is very simple and proper working out of the results will take some time. A results table is provided at the back of this booklet for you to record your results. To make calculations easier, a spreadsheet is available to enter your data and process the results. Alternatively you can use graph paper to plot graphs manually.

Method – Measurements
1. Select the strain gauge labeled TOP, ALONG – x direction in tension 2. Take a reading with no load. There may be some drift in this value. Wait until a steady reading is obtained, or estimate the average value. 3. Suspend weights from point “A”, and apply successively larger loads to the end of the beam. Record the strain gauge outputs (in μV) produced in each case. It may be useful to remove some weights from time to time to check that you get the same (or almost the same) readings. 4. Repeat the method selecting the following strain gauges: TOP, LATERAL – y direction in tension. BOTTOM, ALONG – x direction in compression. BOTTOM, LATERAL – y direction in compression.

Treatment of Results
To verify Hooke’s Law for this material Plot suitable graphs of the gauge readings as a function of the applied load. The linearity of the graphs will demonstrate the validity of Hooke's law. To determine Young’s Modulus for this material Convert the strain gauge readings to strains ε x and εy, (Use the conversion factor provided by the manufacturer) and the loads to Newtons (1 kg = 9.81N). From the εx and εy readings (no units), the loads applied (in Newtons) and the dimensions of the beam (measure these yourself), calculate the Young's modulus E and Poisson's ratio v of the beam. Use the gradients of the stress/strain lines, rather than individual readings. NOTE: The LINEST function in Excel is useful here; or you could plot the graphs on graph paper. Make an estimate of the accuracy of your values. The theory for this part of the practical is given in the Information Sheet.

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Activity YM1

Pupil Sheet

Results Tables – Use the Interactive Young’s Modulus simulation to collect data. Enter your readings in these tables, then transfer them to the Excel Spreadsheet Dimensions of material tested Distance of weights to strain gauge Width of the beam Thickness of the beam = = = l w h 1 (cm) 2 (cm) 3 (cm)

page 3 of 4

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Activity YM1

Pupil Sheet

Using the Information Sheet provided, and the results obtained from experimental work, answer the questions below. What is Hooke’s law?

Explain what happens when the elastic limit is exceeded:

Explain what is meant by Young’s Modulus:

How is knowledge of Young’s Modulus helpful to an engineer when selecting materials for use in a given project? Give examples:

Explain what is meant by Poisson’s ratio:

Young’s modulus can be measured by loading a wire and measuring the strain. Which method is likely to be more accurate? Explain your answer

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