Experiment 1: Solid Mechanics

Solid mechanics plays a role in almost all aspects of engineering. Hence it is crucial that the engineer be familiar with the methods for quantifying material properties and relationships such as stress versus stain. An important part of this process is the use of extensometers for determining local strain values. You will utilize a tension test machine to acquire physical insight into the constitutive relationships between stress and strain for tool steel and aluminum.

Introduction

In this experiment, tension test data for carbon steel 1018 and 6061 aluminum alloy is collected and used to determine several material properties. The ASTM standard flat tensile specimens are used, having a cross-section in the gage region of approximately 0.125 x 0.5 in. for both tool steel and aluminum. Specimen elongation during the linear part of the test is measured with use of an MTS strain gage extensometer, with a gage length of 1 in. The experiment is performed with the MTS universal testing machine in Link 0021.

Equipment

MTS Testing Machine

The universal testing machine can be used to either determine material properties or to determine how a mechanical part behaves under load. The machine consists of two "dog bone" grips, one of which is attached to a moving hydraulic actuator. During a tension test, this actuator moves at a constant rate, thereby causing the specimen to elongate. During this process, a load cell is used to measure the amount of force that results as the specimen is elongated. Both the elongation and load data are output to a computer equipped with DAQ15.3 data acquisition software for later analysis.

Most universal testing machines have features that allow the operator to adjust the loading rate and scale the output. The behavior of the material is often dependent on the loading rate; most materials require a higher load to produce the same elongation as the loading rate is increased. The load is often scaled in such a way that the output is converted from force to stress. In this lab we will use the cross-sectional area (original area) of the specimen for this conversion.

 

Strain Measurement

There are different methods for measuring the amount of extension that takes place in the specimen during the test. An extensometer or strain gauges are used to measure the elongation of the specimen directly. In this experiment, an extensometer is used to measure elongation in the linear part of the load-up, and the relative position of the actuator is used to determine the elongation of the specimen throughout the entire test.

There is some error associated with the latter method. The displacement of the actuator not only includes the deformation of the specimen, but also includes the deformation of the machine. The deformation of the machine is elastic, and can generally be regarded as being directly proportional to the load that is applied to the specimen. The percent error associated with the machine deformation is quite large during the initial portion of the test when the deformation of the specimen is relatively small. The percent error decreases as the material yields and the strain values become larger. Hence we use an extensometer in this initial part of the test, obtaining a direct measurement in the gage region of the specimen.

Data Collection and Reduction

In this experiment, the strain and stress data are collected using a computer and DAQ15.3 data acquisition software. The raw data is not collected in units of stress and strain, but rather in units of load and elongation. Consequently, stress in the gage region is directly proportional to the applied load:

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where s is the stress, P is the applied load, and A is the cross-sectional area of the gage region. Strain in the gage region is proportional to the elongation of the material in that region:

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where e is the strain, D L is the elongation of the extensometer or displacement of the actuator, and L0 is the initial gage length.

Material Properties and the Stress vs. Strain Curve

Typical stress strain curves for steel are shown in Figure 1. Stress strain curves for different materials often take on very different shapes. This curve is an extremely useful source of information. Its shape alone is a valuable indication of the behavior of the material under an applied load. Values for the yield stress, ultimate stress, and rupture stress can generally be read directly from the curve, while other material properties can be attained using simple post processing (data reduction) methods.

Stress vs. Strain

Figure 1. Stress/Strain Curve (need reference)

The area under the elastic portion of the curve is known as the modulus of resilience, UR. For a material such as steel where the initial portion of the curve is a straight line, the modulus of resilience is given by:

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The energy absorbed per unit volume of the specimen up to the rupture point is called the modulus of toughness, UT and is equal to the area under the entire curve.

Procedure

1. Use a caliper or a micrometer to accurately measure the specimen’s width and thickness at several locations along the gage region. Take the average result to compute the area of your specimen and use this in all subsequent calculations. The individual measurements, the averages, and the cross-sectional area should appear in your report.

2. Following the above, the TA will instruct you on how prepare the surface of the gage region for extensometer mounting, and how to place the specimen in the grips.

3. Note down the initial gage length of the extensometer (1 in.), and mount it securely onto the gage region using two rubber bands. Once in place, make sure to REMOVE the zeroing pin from the extensometer.

4. Set-up DAQ15.3, TestStar, and TestWare programs as indicated by the TA (TAKE NOTES). Record the load rate, deflection and load limits, trigger increment, gain, etc.

5. Apply the tensile load to the specimen by pressing RUN. This can be done either in the TestWare program, or on the pod controller.

6. Continue applying load until the load vs. elongation curve turns non-linear. At this point HOLD the test, and carefully remove the extensometer. Resume the test by pressing RUN, and continue loading the specimen until failure. STOP the load ramp and end data acquisition. NOTE: For the composite material with 90 degree fiber orientation, the extensometer need to be removed when the load is about 1500 lbf.

7. Carefully remove the failed specimen from grips, and examine the fractured region. Note down the character of fracture, and measure width and thickness of the necked region so that you can compute the final area.

The data sets from all groups will be posted on the web page.

Exercises

For each material calculate or record the following properties for the test data obtained by your lab group.

  1. Yield stress and strain (using 0.2% offset method). Calculate with both extensometer data and grip data for comparison.
  2. Ultimate stress and strain.
  3. Rupture stress and strain.
  4. True rupture stress and percent elongation - use the final cross sectional area and length.
  5. Percent reduction in area.
  6. Experimental modulus of elasticity.
  7. Modulus of resilience (include your software in appendix). Calculate with both extensometer data and grip data for comparison.
    1. Trapezoidal rule what is required, feel free to attempt a higher order accuracy method.
  8. Modulus of toughness (include your software in appendix).
    1. Trapezoidal rule what is required, feel free to attempt a higher order accuracy method.
  9. For the steel specimen estimated Brinell Hardness No. (yield stress/500).
  10. Poisson Ratio
  11. Uncertainties of all results.
  12. Percent difference from published values.

Topics for Discussion