Lab 2 Torsion Testing

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2355

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Mechanical Engineering

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Jan 9, 2024

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ME 2356 Laboratory Template 1 Department of Mechanical and Industrial Engineering ME 2356: Laboratory for Mechanics of Materials Torsion Testing Submitted by Sydney Rodriguez Date Submitted: 11/2/2023 Date Performed: 10/19/2023 Lab Section: 12 Lab TA: Lindsey Young Course Instructor: Marguerite Matherne

ME 2356 Laboratory Template 2 1. Introduction The objective of this experiment was to investigate the correlation between torsional stress and strain in various materials and to assess shear stress and strain data to determine the shear modulus and Young's modulus 2. Methods and results 2.1 Instron Procedure To conduct this experiment first the initial length and diameter of the material was measured. Subsequently, group mates were split up to load the specimen into the Instron machine, while the others set up the software for data collection. Finally, the test was conducted and captured images of the fracture surface. Results  Sample material and measurements table Table 1. Aluminum measurements. Parameter Initial value Unit Length 66.91 mm Diameter 6.47 mm J 172.0351 mm 4  Torque vs. angle of twist plot Figure 1: Torque vs. Angle of Twist plot

ME 2356 Laboratory Template 3  Stress vs. strain plot Figure 2: Stress vs. Strain Plot  Mechanical properties table Table 2. Mechanical properties. Parameter Value Unit Shear modulus 2.48e+04 MPa Yield strength 964.66 MPa Ultimate strength 1.08e+03 MPa Calculated elastic modulus 6.64e+04 MPa

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ME 2356 Laboratory Template 4 Discussion  The fracture type is ductile as you can see by the photo below, the surface is smooth. Figure 3: Fracture Surface  The calculated shear modulus was 2.48e+04 MPa, while the accepted shear modulus for aluminum ranges from 26 to 28 GPa. Meanwhile the elastic modulus of aluminum ranges from 69-71 GPa, which is around 3 GPa from the calculated value of 6.64e+04 MPa. Both expected values are close to the calculated values of this experiment. Possible sources of error could be the calibration of the Isotron machine. If others were to reconduct this experiment they would most likely gain results similar to this.

ME 2356 Laboratory Template 5 2.2 Manual tester Procedure During this part of the lab students were provided with the initial length and diameter of the sample. Following this, they loaded the sample, then unloaded and reloaded it. The data was collected and recorded in an Excel file. Results  Sample material and measurements table Table 3. “Brass” sample. Parameter Initial value Unit Length 80 mm Diameter 6 mm  Torque vs. angle of twist plot Figure 4: Torque vs. Angle of Twist Plot

ME 2356 Laboratory Template 6  Stress vs. strain plot Figure 5: Stress vs. Strain Plot  Mechanical properties table Table 4. Mechanical properties. Parameter Value Unit Initial shear modulus 1279 MPa First yield strength 336 MPa Unloading shear modulus 1236 MPa Second yield strength -417 MPa Discussion  The yield stresses calculated were .336 GPa and -.417 GPa, both values correspond to the Bauschinger effect in which one is negative (compressive yield stress) and the other positive (tensile yield stress).  The calculated initial shear modulus is 1.279 GPa while the expected value was 40 GPa. This could be due to improper calibration of the tester or because of a small data sample. If this is repeated by others the data should be closer to 40 GPa.

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ME 2356 Laboratory Template 7 2.3 Poisson’s ratio Procedure In this procedure an axial Instron machine was operated to investigate the axial and transverse deformation of a cork sample and a rubber band sample. Initially, the initial dimensions were assessed, including width/diameter and height, for both samples and photographed in their undeformed state. Subsequently, the samples were positioned within the Instron machine, and the crank was manually manipulated to induce deformation. Finally, images of the deformed samples were captured, and the final width/diameter and height of each sample were measured. Results  Sample material and measurements table Table 5. Samples. Parameter Initial Length Initial Width/diameter Final Length Final Width/diameter Unit “Rubber” 9.98 9.90 8.43 12.64 mm “Cork” 19.92 17.18 14.40 17.33 mm  Photos of the unloaded and loaded samples Figure 6: Unloaded Rubber Sample

ME 2356 Laboratory Template 8 Figure 7: Loaded Rubber Sample Figure 8: Loaded Cork Sample

ME 2356 Laboratory Template 9 Figure 9: Unloaded Cork Sample  Strain Table 5. Samples. Parameter Axial strain Transverse strain -transverse/axial strain ratio “Rubber” 0.155 -0.277 0.566 “Cork” 0.277 0.00873 0.0272 Discussion  The other way of calculating Poisson’s ratio is by the following equation: υ = E 2G − 1 Equation 1  In which, values for E and G, along with Poisson's ratio, can be determined using data derived from a stress-strain diagram.  The expected value of Poisson’s ratio for rubber is 0.48-0.5 while the value for the cork is 0. The calculated values of 0.566 for the rubber and 0.0272 for the cork are close to the expected values. The cause of the small variation from the expected value is most likely due to human error when taking the measurements. If repeated other’s would likely see similar results.

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ME 2356 Laboratory Template 10 Appendix: MATLAB code % Isotron Test %clear data clearvars; clc; %read file filename = 'Lab2Part1.csv' ; T = readmatrix(filename); %sample properties (mm) di = 6.47; ri = di/2; li = 66.91; Ai = pi*(ri^2); J = pi*(di^4)/32; %conversions time = T(:,2); twist = T(:,3); torque = T(:,4)*1000; %stress and strain calculations Stress = torque.*(di/(2*J))*10^3; Strain = twist.*((di/2)*(pi/180)/li); %plot torque vs twist figure(1) plot(twist, torque); title( 'Torque vs. Angle of Twist' ); xlabel( 'Twist (degrees)' ); ylabel( 'Torque (Nm)' ); hold on ; %plot stress vs. strain figure(2) plot(Strain, Stress); title( 'Stress vs. Strain' ); xlabel( 'Strain' ); ylabel( 'Stress (MPa)' ); %calculate values ultimate_strength = max(Stress); ultimate_torque = max(torque); %young's modulus and shear modulus F = polyfit (Strain (5:100), Stress(5:100),1); E = F(1); G = E/(2*1.34);

ME 2356 Laboratory Template 11 % Manual Tester %clear data clearvars; clc; %read file filename = 'Lab2Part2.csv' ; T = readmatrix(filename); %sample properties (mm) di = 6; ri = di/2; li = 80; Ai = pi*(ri^2); J = pi*(di^4)/32; %conversions twist = T(:,1); torque = T(:,2); %stress and strain calculations Stress = torque.*(di/(2*J))*1000; Strain = twist.*((di/(2*li))); %plot torque vs twist figure(1) plot(twist, torque); title( 'Torque vs. Twist' ); xlabel( 'Twist (degrees)' ); ylabel( 'Torque (Nm)' ); hold on ; %plot stress vs. strain figure(2) plot(Strain, Stress); title( 'Stress vs. Strain' ); xlabel( 'Strain' ); ylabel( 'Stress (MPa)' ); %calculate values G1 = (Stress(2)-Stress(1))/(Strain(2)-Strain(1)); G2 = (Stress(5)-Stress(6))/(Strain(5)-Strain(6)); yield1 = Stress(2); yield2 = Stress(7);