Uniaxial Tension Tests

UNIAXIAL TENSION TESTS

OF

STRUCTURAL STEEL

CE 332

MECHANICS OF DEFORMABLE BODIES

By

Walter Fish

9 October, 1998

Department of Civil Engineering

The City College of New York

Table of Contents

page

Abstract1

Introduction1

Procedure & Results1

Discussion of Results7

Conclusion7

Appendix A – Formulas8

Appendix B – INSTRON Analysis Output9

Abstract

This report describes a uniaxial tension experiment conducted on a specimen of 0.2% carbon steel. The goal of this lab is to study the behavior of a steel member under increasing tension until rupture. The data collected – applied force versus deformation– allow us to plot a stress-strain diagram and calculate various properties of the material (modulus of elasticity, proportional limit, yield strength, ductility, ultimate strength and rupture stress). The values obtained for each of these properties falls within expected ranges. The lab provides with an insight into the meaning of each of these properties and the stress-strain diagram.

Introduction

In the design of structural systems, it is important that we fully understand how the different materials we use in construction will react under certain outside forces and conditions. For instance, how much load can a particular member sustain before permanent and irreparable damage is done? Or, under a given force, how much will a certain material deform? These questions and many others can be answered only if we know the mechanical properties of the material.

In this lab, we observe the effects of a specific kind of external force – uniaxial tension – on a specific type of material – 0.2% carbon steel rod, 8 inches long and .5 inches in diameter. Although the scope of this lab is limited, it illuminates the underlying concepts behind published values for mechanical properties of materials and tools such as stress-strain diagrams.

We begin by completing the steps as outlined in the procedure, followed by the processing of the data obtained, both by direct calculation and by plotting relationships between properties (stress-strain diagram). Once we have values for the properties of interest, we can compare them to the values obtained from the testing machine and those published in engineering design manuals.

Procedure & Results

This test is carried out using the INSTRON 8500 Testing system located in the Strength of Materials Laboratory of the Civil Engineering Department, on a sample of 0.2% carbon steel. The steel is in the form of a rod 8 inches long and .5 inches in diameter. The rod is placed in the gripping mechanism of the machine and a 2 in. extensometer is placed on the exposed portion of the rod (this increases the sensitivity of the machine’s internal distance measurement apparatus during the low-deformation stage of the process).

The setup and calibration of the testing machine is covered exhaustively in the lab hand-out and will not be covered herein. Suffice it to say that the machine is properly calibrated and the correct parameters are entered. Once this is done and the machine is ready, a tension force is applied. As the tension force increases, the machine notes both elongation and the tensile force every second. The ramp load is applied such that the bar is tensioned at a strain rate of 0.25% per minute. This continues until the extensometer is removed, at which time the tensioning proceeds at 0.25 inches per minute.

The experiment is concluded when the bar finally ruptures. At this point, the broken bar is removed from the testing machine and the data is collected from the testing machine’s PC terminal.

The data received from the computer is simply the measurements of total elongation and tensile load, taken at 1-second intervals. These numbers are then transferred to a spreadsheet for further analysis.

Table 1 shows a sample of the original and processed data. First, we compute the stress at each data point by dividing the load by the original cross-sectional area. Next, we calculate the strain, which is simply the total elongation divided by 2 inches (the span of the extensometer). Finally, the strain is converted to a percentage by multiplying by 100. We are now ready to extract some meaningful information from this data.

Figure 1 shows a plot of stress vs. strain. This is a graphical representation of what is happening within the bar from the beginning of loading until rupture. The various stages can be seen on this graph, beginning with the linear elastic range (0 – 0.2%), the yielding stage (0.2 – 1.4%), the strain-hardening phase (1.4 – 17%) and finally the necking stage (17 – 25%), ending in rupture. Although this graph gives an excellent overall picture of our data, the most interesting portion, the linear-elastic range, needs a little magnification.

Figure 2 shows a portion of the original data, specifically the stress vs. strain from 0 to 0.225% strain. This magnification allows us to do a best-fit trend line along the linear-elastic range, thus yielding a value for the modulus of elasticity E (30 x 106 psi).

Figure 3 is again a detail of the original data, but this time ranging from 0 to 1.4% strain. From this plot, we can obtain the yielding stress (y) by the 0.2% offset method. A line is drawn starting at 0.2% strain with the same slope E as the linear-elastic range. This gives a value for y of approximately 64 ksi (highlighted in blue in Table 1). This method is not really necessary in this case, because since we are dealing with steel, the yielding point is very well defined. Had we simply taken the value for y at the end of the linear elastic range and the beginning of the horizontal yielding phase (highlighted in orange in Table 1), we would have obtained essentially the same answer.

Finally, we can read directly from Table 1 a few more pieces of important data. By looking for the largest value for stress, we find that the ultimate strength of the sample occurs at 102393.9 lbs and 17.29% strain (highlighted in green in Table 1). Next, we read that the last value for elongation is 0.50618 inches and dividing by the original length of 2 inches, we get a value for ductility in percent elongation (25.31%). Lastly, reading the final value for stress gives us a value for rupture stress (82551.76 psi).

Table 1. Sample Set of Collected and Processed Data

Figure 1. Stress Strain Diagram for Structural Steel.

Figure 2. Stress-Strain Diagram for Linear-Elastic Range.

Figure 3. Stress-Strain Diagram Detailing the Plastic Zone.

Discussion of Results

The calculated values of the desired properties are summarized in Table 2. They correspond directly with the results obtained from the testing machine’s analysis package, with the exception of the modulus of elasticity. Although we do not have charts for this specific type of steel, we see that our results fall comfortably within the range of values for similar materials.

For most of the results for which we have a known value to compare to, the only error is due to rounding off. The one exception to this is the modulus of elasticity E.

Table 2. Summary of Results

Formulas used in analyzing our data are found in Appendix A. Also included is the output from the INSTRON analysis package (Appendix B).

Conclusion

Although this lab is relatively straight-forward, it offers a useful insight into the source of information that is used in many day-to-day engineering tasks. Aside from seeing the process from which tables of material properties are derived, we can gain a better understanding of what it is we are calculating, computing or designing.

The stress-strain diagram is an especially useful tool in that once it has been plotted for a given material, it is representative of that material in any member in any number of configurations. It also gives a clear picture of what can happen if material limitations are not taken into consideration when constructing a structural system.

Appendix A

Stress = Force / Original Cross-sectional Area = P / A

Ultimate Stress = Ultimate Force / Cross-sectional AreaU = PU / A

Strain = Deformation / Original Length =  / L

Ductility = 100 x [(LFinal – LInitial) / LInitial]

% error = 100 x [(Measured Value – Known Value) / Known Value]

Appendix B

INSTRON Analysis Output

Not included in this web-page version