Elastic modulus

Roberto Barraza
EML 3301
Report 3
Elastic Modulus and Creep
February 28, 2010
Introduction
Strain is among one of the most important measurements of a material. Moreover, the elastic modulus is a measure of the stiffness of an isotropic material and it is essential in that it helps determine how a material will react to an applied tensile or compressive force. For instance, a particularmaterial has a unique point of buckling in which the material will no longer return back to its original shape.
Temperature can also be an important factor when trying to calculate the total stress and strain because materials react differently upon heating or cooling. Thus, a thermocouple is used to obtain the ambient experimental temperature to conclude what is the effect of temperature on thedata measured.
Creep may be defined as the tendency of a material to continually deform under steady stress, and a linear plastic-strain behavior can be observed in a wide range of area of the strain vs time graph for a particular material under tensile stress. In the case of plastics, creep occurs rapidly and abruptly at room temperature, where as in metals creep occurs at a much lower rate.Procedure
Using a LVDT voltage output, one can create a LabView program that will measure the displacement of a metal wire under tension using a conversion factor of 0.000487 V/µm. Having the displacement in hand, equations (1) and (2) can be used to calculate the elastic modulus. This is done several times and with different values of forces (weights) that will produce differentdisplacement.
(1) (2)
To measure the ambient temperature, a thermocouple analog converter is used with a conversion constant of 1mV=degree temperature.
A monofilament fiber wire with a diameter of 3.048 mm is used as an example to measure creep. For this, the same LVDT with a 12V output voltage is used in combination with a LabView programthat will convert the voltage output into a displacement using a conversion factor of: 486.63 mV/mm. This is done several times so that accurate data will be collected and a standard deviation will be calculated.
Results
After measuring the diameter of the wire (0.0006µm), the results are tabulated in table (1)
Table (1) Stress, strain and modulus of elasticity of three experiments
MODULUSOF ELASTICITY |
|
First experiment |
Starting output voltage=0.609 Volts |
Starting displacement=1252.0 Micrometers |
Mass (Kg) | Voltage | Displacement | (∆Disp) | Applied force (N) | Stress (σ) N/m^2 | Strain (ε) | Modulus |
0.05 | 0.5863 | 1203 | 49 | 0.4905 | 1734784.823 | 0.0391374 | 44325522.42 |
0.1 | 0.5525 | 1135 | 117 | 0.981 | 3469569.646 | 0.0934505 | 37127360.66 |0.2 | 0.5069 | 1043 | 209 | 1.962 | 6939139.292 | 0.1669329 | 41568432.51 |
0.3 | 0.4601 | 944.7 | 307.3 | 2.943 | 10408708.94 | 0.2454473 | 42407105.73 |
| | | | | | | |
Second experiment |
Starting output voltage=0.5790 |
Starting displacement=1189 |
Mass (Kg) | Voltage | Displacement | (∆Disp) | Applied force (N) | Stress (σ) N/m^2 | Strain | Modulus |
0.5 | 0.5588 | 1148| 41 | 4.905 | 17347848.23 | 0.0344828 | 503087598.7 |
0.1 | 0.537 | 1105 | 84 | 0.981 | 3469569.646 | 0.0706476 | 49110932.25 |
0.2 | 0.4999 | 1024 | 165 | 1.962 | 6939139.292 | 0.1387721 | 50003858.29 |
0.3 | 0.4531 | 932.8 | 256.2 | 2.943 | 10408708.94 | 0.2154752 | 48305835 |
| | | | | | | |
Third experiment |
Starting output voltage = 0.5701 |
Starting displacement=1173|
Mass (Kg) | Voltage | Displacement | (∆Disp) | Applied force (N) | Stress (σ) N/m^2 | Strain | Modulus |
0.5 | 0.557 | 1144 | 29 | 4.905 | 17347848.23 | 0.0247229 | 701690550.8 |
0.1 | 0.5372 | 1106 | 67 | 0.981 | 3469569.646 | 0.0571185 | 60743361.12 |
0.2 | 0.4941 | 1012 | 161 | 1.962 | 6939139.292 | 0.1372549 | 50556586.27 |
0.3 | 0.4459 | 913.8 | 259.2 | 2.943 | 10408708.94 |...