Principles of Metal Manufacturing Processes - Lab Report Example

? Young Modulus Presented by Introduction Different materials have different mechanical properties that make them fit for various uses. Aluminum, Low Carbon Steel and High Carbon Steel have different strengths and they break at different loads (John 1992). The Young’s Modulus (E) is a measure of stiffness of an elastic material defined as the ration of stress to the corresponding strain when a material is put under tension or compression. The most commonly used test specimens are cylindrical in shape as shown in figure 1. For this experiment, however, a wire was used as a specimen. When more loads are applied the specimen breaks at the centre as shown in figure 1 (b). The data of load versus extension of the specimen is collected and used in calculation of stress and strain. The values are plotted on an X-Y graph and yield a typical graph as shown in figure 2. From the graph several material properties could be calculated and observed ((Ashby & Jones 2005). Figure 1: Sample test specimen for a tensile test. ao - original thickness of a flat test piece or wall thickness of a tube bo - original width of the parallel length of a flat test piece Lc - parallel length Lo - original gauge length Lt - total length of test piece Lu - final gauge length after fracture So - original cross-sectional area of the parallel length 1 - gripped ends The following experiment investigates the Young’s Modulus of a piece of wire subjected to tension. To get the Young’s Modulus, stress and strain of the wire must be calculated from the recorded results. Formula I and 2 below shows calculation for stress while 3 shows calculation for strain. .............................................................. 1 Area A0 = ?r2.................................................. 2 Where r is the specimen radius On the other hand, strain will be calculated by dividing change in length by the original length as shown in formula 2. .................................................... 3 As shown from figure 2, the linear section of the graph is referred to as the yield strength where the material shows elastic behavior and it is used in the calculation of E. On the other hand, the other part of the graph is referred to as the non linear section. The yield point is the transition between the linear and the non-linear sections, and the magnitude of stress at this section is termed as the yield strength (?Y). The slope of the linear section of the curve gives the material’s Young’s modulus, given in GPa. The formula for calculating young’s modulus is shown below. ..................................... 4 .............................. 5 Figure 2: A typical stress v strain plot from a tensile test Objectives The objective of this experiment is to determine the Young’s Modulus when a piece of wire is subjected to varying forces. Apparatus The following apparatus were used during the experiment: 1 x G-clamp, approximately 10 cm jaw 1 x 2 wooden blocks 1 x single pulley placed on a bench clamp 1 x meter rule 1 x Adhesive tape 2 x cardboard bridges 1 x mass hanger with 8 slotted masses, 100g each 2 x lengths of copper wire 1 x safety spectacles Wire rolls and threads Procedure The experiment set up was as shown in figure 3 below. Figure 3: Experimental setup 1. After the set up was made, a copper wire was stretched and fixed horizontally along the bench as shown in figure 3 above 2. A maker was made from the adhesive tape and it was attached to the wire to make it less 2 m from the clamp and approximately 5 cm from the pulley. The marker was set to line up with the meter rule so that it could be used to measure the extension of the wire. A loop was made in the end of the wire for loading 3. The original length of the wire was measured and recorded. This was the length from the clamp to the marker. A small mass of 100g was then placed to stretch the wire and the length recorded. 4. The masses were increased gradually in steps of 200g while the force and the corresponding extension was recorded in each case. The recordings were taken up to a maximum weight of 2 kgs. 5. The forces were then removed gradually and the wire length measured to check whether it measured the original length. 6. The procedure I to 6 was repeated using the second wire (thread sample). Results Experiment 1 (copper wire) Diameter 2r = 0.33 cm = 33 x 10-5 m Original length = 1.91 m Mass (g) Force (N) Extension (mm) Stress (NM-2) Strain 309.38 2.992 0.1 35200000 0.052356 404.4 3.963 0.1 46623529.41 0.052356 503.48 4.934 0.2 58047058.82 0.104712 602.2 5.901 0.2 69423529.41 0.104712 705.82 6.917 0.3 81376470.59 0.157068 908.14 8.899 0.5 104694117.6 0.26178 1006.53 9.863 0.6 116035294.1 0.314136 1108.92 10.867 1 127847058.8 0.52356 1207.1 11.829 2.5 139164705.9 1.308901 1306.96 12.808 2.7 150682352.9 1.413613 1406.15 13.78 3 162117647.1 1.570681 Table 1: Experimental results for copper wire Experiment 2 (wire thread) Diameter 2r = 0.17mm = 17 x 10-5 m Original length = 1.47m Mass (g) Force (N) Extension (mm) 103.20 1.011 0.45 Av 202.25 1.986 1.00 Av 301.97 2.959 1.45 Av 405.56 3.974 1.95 Av 504.12 4.940 2.45 Av 609.98 5.928 2.90 Av 703.69 6.895 3.30 Av 802.81 7.867 3.70 Av 901.92 8.838 4.20 Av Table 2: Experimental results for thread wire Calculations Experiment 1 Area = ?r2 = 85 x 10-10 m2 Mass (g) Force (N) Extension (mm) Stress (NM2) Strain 309.38 2.992 0.1 35200000 0.052356 404.4 3.963 0.1 46623529.41 0.052356 503.48 4.934 0.2 58047058.82 0.104712 602.2 5.901 0.2 69423529.41 0.104712 705.82 6.917 0.3 81376470.59 0.157068 908.14 8.899 0.5 104694117.6 0.26178 1006.53 9.863 0.6 116035294.1 0.314136 1207.1 11.829 2.5 139164705.9 1.308901 1306.96 12.808 2.7 150682352.9 1.413613 1406.15 13.78 3 162117647.1 1.570681 ‘ Table 3: calculations for copper wire Experiment 2 Area = ?r2 = 2.269 x 10-8 m2 Mass (g) Force (N) Extension (mm) Stress (NM2) Strain 103.2 1.011 0.45 4455707.36 0.306122 202.25 1.986 1 8752754.52 0.680272 301.97 2.959 1.45 13040987.2 0.986395 405.56 3.974 1.95 17514323.5 1.326531 504.12 4.94 2.45 21771705.6 1.666667 609.98 5.928 2.9 26126046.7 1.972789 703.69 6.895 3.3 30387836.1 2.244898 802.81 7.867 3.7 34671661.5 2.517007 901.92 8.838 4.2 38951079.8 2.857143 Table 4: calculations for thread wire Data analysis Figure 4: Stress versus strain curve for copper wire Figure 5: Stress versus Strain curve for thread wire Young’s modulus Copper wire = (120000000-65000000)/ (0.5-0.2) = 183 Gpa Wire thread = (25000000-15000000)/(600-400) = 5GPa Discussion From the experiment, the Young’s modulus for a copper wire was found out to be 183Gpa while that of wire thread was 5Gpa. Materials with strong bonds have a higher resistant to fracturing forces making them have high elastic modulus. The metallic bonds found in copper wire resist deformation by the applied force making it take long to fracture and eventually more force was applied (Furness 2011). The force applied on the wire thread specimen was small because it is a light metal and can be easily deformed (Beddoes and Bibby 120-180). References ASHBY, M. F., & JONES, D. R.(2005). Engineering materials 1: an introduction to properties, applications and design (3rd ed.). Amsterdam: Elsevier Butterworth-Heinemann. BEDDOES, J. AND BIBBY, M. J. (1999). Principles of metal manufacturing processes. London: Arnold, FURNESS, J. (2011). Properties of copper. Retrieved from: http://www.azom.com/article.aspx?ArticleID=400 JOHN, VERNON. (1992). Introduction to engineering materials. 3rd ed. Basingstoke: ELBS with Macmillan. Read More