AE321_HW6

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University of Illinois, Urbana Champaign *

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Mechanical Engineering

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Feb 20, 2024

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AE 321 – Homework 6 1. 1045 cold rolled steel: a) b) 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0 100 200 300 400 500 600 700 800 900 Yield point Point of onset necking Failure point 1045 Steel Stress-Strain Curve Strain (mm/mm) Stress (MPa) c) Proportional limit: (0.002446, 452.056 MPa) 0.2% offset stress: 369.63 MPa (stress when strain = 0.002) Ultimate tensile strength: 809.205 MPa (maximum stress) Failure strain: 15.59% (maximum strain) d) E = σ ε Slope from (0, 0) to proportional limit (0.002446, 452.056 MPa): E = 452.056 MPa − 0 0.002446 − 0 = 184814.391 MPa = 184.8 GPa

e) 0 0.01 0.02 0.03 0.04 -200 0 200 400 600 800 1000 1200 f(x) = 184814.39 x − 4755.46 1045 Steel unloaded after 3% straining Strain (mm/mm) Stress (MPa) 3% offset stress = 788.975 MPa Unloading curve: σ = ( ε − 0.03 ) E + 788.975 σ = ( 184814.391 MPa ) ε − 4755.5 MPa Final plastic strain: Unloading curve at σ = 0 0 = ( 184814.391 MPa ) ε − 4755.5 MPa ε = 4755.5 184814.391 = 0.0257 = 2.57% New Yield stress = 788.975 MPa

6061-T6 aluminum alloy: a) b) 0 0.05 0.1 0.15 0.2 0 50 100 150 200 250 300 350 Yield point Point of onset necking Failure point 6061-T6 Al Stress-Strain Curve Strain (mm/mm) Stress (MPa) c) Proportional limit: (0.004749, 285.411 MPa) 0.2% offset stress: 127.760 MPa Ultimate tensile strength: 324.761MPa Failure strain: 18.25% d) E = σ ε Slope from (0, 0) to proportional limit (0.004749, 285.411 MPa): E = 285.411 MPa − 0 0.004749 − 0 = 60099.1788 MPa = 60.1 GPa e) 3% offset stress = 185.116 MPa Unloading curve: σ = ( ε − 0.03 ) E + 185.116 σ = ( 60099.1788 MPa ) ε − 1617.859 MPa Final plastic strain: Unloading curve at σ = 0 0 = ( 60099.1788 MPa ) ε − 1617.859 MPa ε = 1617.859 60099.1788 = 0.0269 = 2.69% New Yield stress = 185.116 MPa

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7075-T6 aluminum alloy: a) b) 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 -2 98 198 298 398 498 598 Yield Point Point of onset necking Failure point 7075-T6 Al Stress-Strain Curve Strain (mm/mm) Stress (MPa) c) Proportional limit: (0.00579, 469.403 MPa) 0.2% offset stress: 539.762 MPa Ultimate tensile strength: 573.799 MPa Failure strain: 14.83% d) E = σ ε Slope from (0, 0) to proportional limit (0.00579, 469.403 MPa) E = 469.403 MPa − 0 0.00579 − 0 = 81071.3299 MPa = 81.07 GPa e) 3% offset stress = 549.923 MPa Unloading curve: σ = ( ε − 0.03 ) E + 549.923 σ = ( 81071.3299 MPa ) ε − 1882.217 MPa Final plastic strain: Unloading curve at σ = 0 0 = ( 81071.3299 MPa ) ε − 1882.217 MPa ε = 1882.217 81071.3299 = 0.0232 = 2.32% New Yield stress = 549.923 MPa

f) The stress-strain curve of 7075-T6 is more linear and does not bend as much as 6061-T6 meaning 7075-T6 is more brittle. It exhibits this as it fractures suddenly instead of deforming gradually. This is also reflected in modulus of elasticity, as a more brittle material will have a higher elastic modulus. 2. The Boeing 787 Dreamliner uses epoxy/carbon fiber composite for its many advantages. For one, composite materials have remarkable tensile strength, with structural strength comparable to metallic alloys. Along the direction of the fibers and measured at RTA (72°F, 22°C), the tensile strength of the expoy/carbon fiber composite is 1034 MPa. Composites show exceptional tensile strength when compared to other metals under the same conditions; for example, 1045 cold-rolled steel has a tensile strength of 809.205 MPa, 6061-T6 aluminum at 324.761MPa, and 7075-T6 aluminum at 573.799 MPa. The composite has a tensile modulus of 69 GPa at RTA along the direction of fibers. This range of elastic modulus allows the material to be flexible while still resistant to deformation given its high tensile strength. However, the lack of stiffness has caused problems for the development of the Boeing 787 Dreamliner [1]. The composite’s tensile strength is between the 7075-T6 aluminum, which has a tensile strength of 81.70 GPa, and 6061-T6 aluminum, which has a tensile strength of 60.10 GPa. It sits on the lower end in terms of material stiffness when compared to 1045 cold-rolled steel, which has a tensile modulus of 184.80 GPa. These properties are important for determining materials for aircraft, as they must be designed to withstand stress and fatigue. Additionally, they should withstand extreme temperatures. Composite material measured at CTA (-65°F, -54°C) holds up very well, with tensile strength and tensile modulus within the range of that in RTA. A huge advantage of composite is its lightweight property, which lets it compete with metallic alloys. The 787 Dreamliner reduced its weight by 20% by making its components from composite materials [1]. The reduction in weight helps with reducing fuel consumption. It will also reduce transportation costs for materials. References [1] B.S.Kukreja, Johan Löfström, "Composites in the Aircraft Industry," Appropedia Available: https://www.appropedia.org/Composites_in_the_Aircraft_Industry