MAAE2202_Lab A

Carleton University Laboratory Report Course #: MAAE 2202 Lab #: A Lab Section #: Load Deformation Behaviour for Engineering Materials Summary

The purpose of the lab was to obtain the stress – strain relationship from tensile force testing for aluminum 2011 series and brass 360 series. Using the TECQUIPMENT Universal Testing Machine SM100, an increasing tensile force was applied to each of the specimens and measured using the software. By attaching an extensometer, the change in length of the specimens due to the tensile force was measured precisely. Using these values as well as the measured cross-sectional area, the stresses and strains on the specimens were calculated. With this a stress – strain curve was plotted, and the elastic modulus was determined by the slope of the linear portion of the curve. The elastic modulus for aluminum was calculated to be 65 GPa and brass 81 GPa. The yield stress was determined by offsetting the line for Young’s modulus by 0.2% strain and finding the point in which it intercepted with the original curve. The yield stress for aluminum was calculated to be 316 MPa and brass 261 MPa. Nomenclature Symbol Parameter Unit F Tensile Load kN ΔL Extension mm L original Original Length mm ε Strain Unitless σ Stress GPa σ y Yield Stress MPa E Elastic/Young’s Modulus GPa A Cross-Sectional Area mm 2 d Diameter mm %error Error Percentage % Table 1: Nomenclature used for this lab report. Theory and Analysis Strain is the ratio of extension to original length of a component, and can be represented by equation 1: ε = ∆ L L original Stress is the force per unit area within a component, with area being the cross-sectional area. Stress can be represented by equation 2: σ = F A = 4 F π d 2 Young’s modulus of a material is a property that describes how easily it can stretch and deform. It is the ratio between stress and strain, and can be represented by equation 3: E = σ ε = ∆σ ∆ε Since Young’s modulus is the gradient between stress and strain, the slope of the line on a stress-strain graph will be the elastic modulus. P a g e 2 | 12

Figure 1: Determination of Young’s modulus from stress-strain relation. Furthermore, yield stress can be determined by offsetting the linear elastic region by 0.2% and finding the point in which the new line intercepts with the original curve. Figure 2: Determination of Yield Stress from 0.2% residual strain approach. Experimental Setup and Procedure Figure 3: Experiment apparatus schematic drawing with labeled components. The experiment was conducted exactly as outlined in the lab manual. Results and Discussion Requirement A P a g e 3 | 12

Load, F Gauge Extension, ΔL Strain, ε Stress, σ kN mm unitless GPa 0.0 0.00 0 0 0.2 0.00 0.00006 0.002640688 0.7 0.00 0.00018 0.009242409 2.2 0.00 0.00032 0.029047571 2.8 0.00 0.00042 0.036969636 3.6 0.04 0.00064 0.047532389 4.5 0.08 0.00084 0.059415486 5.9 0.09 0.001 0.077900304 6.6 0.10 0.00116 0.087142713 7.3 0.12 0.0013 0.096385122 8.6 0.14 0.0015 0.113549596 9.3 0.17 0.00164 0.122792005 9.9 0.19 0.0018 0.13071407 10.5 0.21 0.00196 0.138636135 11.8 0.24 0.0021 0.155800609 12.4 0.27 0.00224 0.163722674 12.9 0.28 0.0024 0.170324394 13.8 0.32 0.00262 0.182207492 15.0 0.34 0.00274 0.198051621 15.7 0.37 0.00292 0.20729403 16.4 0.39 0.0031 0.216536439 17.1 0.43 0.00334 0.225778848 18.4 0.46 0.00348 0.242943322 19.2 0.50 0.00376 0.253506075 19.8 0.53 0.00404 0.26142814 20.4 0.55 0.0042 0.269350205 21.5 0.59 0.00444 0.283873991 22.1 0.64 0.00484 0.291796055 22.6 0.69 0.00512 0.298397776 23.1 0.74 0.00566 0.304999497 23.8 0.84 0.00666 0.314241906 24.1 0.94 0.0079 0.318202938 24.3 1.04 0.00948 0.320843627 24.5 1.12 0.01052 0.323484315 24.8 1.20 0.01118 0.327445347 24.8 1.28 0.01144 0.327445347 24.9 1.32 0.0116 0.328765691 25.0 1.36 0.0118 0.330086036 25.2 1.45 0.01184 0.332726724 P a g e 4 | 12