Laboratory Experiment:

Uniaxial Testing of

Civil Engineering Materials

Table of Contents

Introduction 1
Procedure 1
Experimental 1
Analysis 1
Results 2
Conclusion 4
References 5

Introduction

In this set of laboratory experiments, uniaxial tests were performed on two specimens: 1) a steel bar in tension, and 2) an aluminum bar in tension. The specific types of materials used in this experiment are grade 50 for the steel, and type 2017-T351 for the aluminum. The experimental procedure and analysis give a better insight to the behavior of different ductile materials under normal stresses. Through the analysis of the experimental data, various properties of the material can be found and these properties are used in the design of engineering structures which use these materials. Through the use of plots of the stress versus strain for each material, and tables providing material properties, the report will include the following objectives for all materials:

• Describe the behavior in the elastic range by determining the moduli of elasticity, and yielding stresses. • Describe the behavior of the materials beyond yielding by determining plastic stresses, ultimate stresses, rupture stresses, and ductility as well as indicating the range of strain hardening and necking. • Compare computed values obtained from the test results to expected values found for steel and aluminum.

Further, the report will assist in obtaining the objectives stated above by giving and organized presentation of the experimental and analysis procedure, and conclusions of the experiment.

Procedure

Experimental

In this set of laboratory experiments, uniaxial tests were performed on two specimens: 1) a steel bar in tension, and 2) an aluminum bar in tension. The procedure of the experiment is very similar to that given in the Mechanics of Materials textbook1. The diameter of the central circular cross section of the specimens has been accurately determined to be 0.335 inches and an extensometer with a two inch gage length, Lo has been placed on the specimen. The test specimens are then placed in a testing machine which is used to apply a centric tensile load, P. As the load increased, the length of the deformation, δ increases (with respect to the gage length), and the machine electronically transfers this data (P and δ) to a Microsoft excel spreadsheet. The bars were loaded and unloaded a number of times while still in the linear elastic range and then also beyond the elastic range until they ruptured.

Analysis

• The Excel data obtained from the experiment was used to calculate the stresses, σ, and strains, ε, of the specimens using equations (1) σ = P/A, and (2) ε= δ/Lo, respectively. • The cross sectional area, A, found in equation (1) was computed using the formula for the area of a circle, A = (1/4)πd2, where d is the determined diameter of the specimen. • From the computed stresses and strains, an Excel scatterplot was plotted to observe the stress-strain relationship. • After plotting the initial stress-strain diagram, it was observed that there were some data that qualified as outliers of the data set and removed from the analysis. These outliers include measurements taken: while the machine was adjusting (the test begins with arbitrary measurements), or after rupture. • The modulus of elasticity for aluminum and steel was determined by performing a linear regression using the range of values of the stress and strain above the excluded measurements and below what appeared to be the proportional limit. • It was observed that the data was not zeroed so that a 0 strain equals 0 stress. The strain data was then modified by using the equation from the regression analysis to solve for strain when the stress equals zero. The value of the strain obtained by solving was then subtracted from each computed strain (from the data) to get the final adjusted (zeroed) strains. Performing a second regression analysis using the original stresses computed and the new strains illustrated that the data had been zeroed. • For the steel, the yielding stress and elastic limit were found by taking an average of the values of the stress which appeared, in the stress-strain diagram, to be somewhat constant directly after the initial yielding. • For the aluminum, the 0.2% offset method and also visual inspection of the stress-strain diagram were used to determine the yielding stress and elastic limit. The 0.2% offset line was found using the slope of the line obtained from the regression analysis (which is the modulus of elasticity) to find the equation of a line passing through .002 in./in. The value of the stress where the 0.2% offset line intersects the scatterplot is considered the yielding stress and elastic limit. However, by visually inspecting the stress-strain diagram closely, one can see that the elastic or proportional limit of the material is actually less than the value indicated by the 0.2% offset method and closer to the expected value. Therefore the value for the yielding stress obtained by visually inspecting the aluminum stress-strain diagram was the computed value used when comparing expected values to computed values (see Table 2). • Ultimate stresses for each material were obtained by using the maximum function in Microsoft excel over the range of values computed for the stress. • For each material the rupture stresses were taken as the last computed value of the stress before the machine began giving inconsistent (negative) values for the load. • The ductility ratios for each material were found by taking the rupture strain and multiplying it by 100. • A final adjusted (zeroed) stress-strain diagram was created for each specimen. The diagrams label various material properties and is presented in the results. • Tables were created to compare the properties of the materials found from the analysis to expected values. Equation (3), below was used to compute the percent difference between the expected values and the computed values.

% difference = ((Computed value – Expected value)/Expected Value)*100 (3)

Results

Figures 1 and 2 below are the stress-strain diagrams created for the steel and aluminum bars respectively. The figures label the elastic limit, and also the extents strain-hardening, and necking. The figures also label the yielding, rupture, and ultimate stresses. Further, because these materials yield differently the stress-strain diagram for the steel labels the extent of the plastic zone while the aluminum diagram labels the point of yield as found by visual inspection and the .2% offset method.
[pic]
Figure 1 – Stress vs Strain diagram for steel bar in tension

[pic]
Figure 2 – Stress vs Strain diagram for aluminum bar in tension
Tables 1 and 2 below - for the steel and aluminum respectively - compare expected values for the materials to values obtained through the analysis. Expected values for steel are found in the Mechanics of Materials textbook1 and expected values for the aluminum were found online2.

Table 1 – Computed Values versus expected values for steel bar in tension
| |Computed Value |Expected Value |Percentage Error (%) |
|Modulus of Elasticity (ksi) |2.98E+04 |2.90E+04 |2.6 |
|Yielding Stress (ksi) |57.9 |50 |15.8 |
|Ultimate Stress (ksi) |78.4 |65 |20.6 |
|Rupture Stress (ksi) |56.2 |- |- |
|Ductility (%) |27.2 |21 |29.4 |

Table 2 – Computed Values versus expected values for aluminum bar in tension
| |Computed Value |Expected Value |Percentage Error (%) |
|Modulus of Elasticity (ksi) |1.060E+04 |1.050E+04 |0.920 |
|Yielding Stress (ksi) |40.5 |40 |1.24 |
|Ultimate Stress (ksi) |67.2 |62 |8.40 |
|Rupture Stress (ksi) |58.0 |- |- |
|Ductility (%) |22.5 |22 |2.49 |

Conclusion

In summary, the steel and aluminum behaved as expected and the stress-strain diagrams resembled that found in the textbook1. Although steel seemed to be slightly off from the expected values, the aluminum was right on target. The experiment assisted in understanding axial loads, normal stress versus strain, how certain properties of engineering materials are determined and how different engineering materials behave due to varying loads.

References

1 Beer FP, Johnston ER, Dewolf JT. Mechanics of Materials. 4th ed. New York: McGraw-Hill; 2006.800p.

2 Laboratory Devices Company. 2004. Materials List. Laboratory Devices Company. < http://www.laboratorydevicesco.com/materialspec.html>. Accessed 2007 Sep 23.