AERO 214. Introduction to Aerospace Mechanics of Materials. Lecture 2

Transcription

1 AERO 214 Introduction to Aerospace Mechanics of Materials Lecture 2

2 Materials for Aerospace Structures Aluminum Titanium Composites: Ceramic Fiber-Reinforced Polymer Matrix Composites High Temperature Materials: Superalloys and Ceramics

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4 Mechanical Behavior: Elastic and Plastic

5 Elastic Deformation 1. Initial 2. Small load 3. Unload bonds stretch Elastic, no remaining deformation upon unloading Due to stretching of bonds F F return to initial Linear Elastic Non-Linear Elastic 2

6 Linear Elastic Isotropic Modulus of Elasticity, E: (also known as Young's modulus) Hooke's Law: s E Linearelastic e 10

7 Comparison of Elastic Moduli E(GPa) Metals Alloys Graphite Ceramics Semicond Diamond Si carbide Tungsten Al oxide Molybdenum Si nitride Steel, Ni Tantalum <111> Platinum Si crystal Cu alloys <100> Zinc, Ti Silver, Gold Aluminum Glass-soda Magnesium, Tin Concrete Graphite Polymers Polyester PET PS PC Composites /fibers Carbon fibers only CFRE( fibers)* Aramid fibers only AFRE( fibers)* Glass fibers only GFRE( fibers)* GFRE* CFRE* GFRE( fibers)* CFRE( fibers)* AFRE( fibers)* Epoxy only Based on data in Table B2, Callister 6e. Composite data based on reinforced epoxy with 60 vol% of aligned carbon (CFRE), aramid (AFRE), or glass (GFRE) fibers PP HDPE PTFE Wood( grain) 0.2 LDPE 13

8 Plastic Deformation in Metals 1. Initial 2. Small load 3. Unload F Plastic means permanent! Permanent set Proportional/elastic limit Yielding point linear elastic plastic linear elastic 3

9 Plastic Deformation in Metals Simple tension test: tensile stress, s (at lower temperatures, T < T melt /3) Elastic+Plastic at larger stress initially Elastic e p plastic strain permanent (plastic) after load is removed engineering strain, e 15

10 Tensile Properties tensile stress, s when e p = engineering strain, e 16

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13 since in tension, fracture usually occurs before yield. Hard to measure, in ceramic matrix and epoxy matrix composites, since in tension, fracture usually occurs before yield. Comparison of Yield Strength Yield strength, s y (MPa) Metals/ Alloys Steel (4140) qt Ti (5Al-2.5Sn) W (pure) a Cu (71500) Mo (pure) cw Steel (4140) a Steel (1020) cd Al (6061) ag Steel (1020) hr Ti (pure) a Ta (pure) Cu (71500) hr Al (6061) a Graphite/ Ceramics/ Semicond Hard to measure, Polymers PC Nylon 6,6 PET humid PVC PP H DPE dry Composites/ fibers sy(ceramics) >>sy(metals) >> sy(polymers) Room T values Based on data in Table B4, Callister 6e. a = annealed hr = hot rolled ag = aged cd = cold drawn cw = cold worked qt = quenched & tempered 10 Tin (pure) LDPE 17

14 Tensile Strength (TS) Maximum possible engineering stress in tension Adapted from Fig. 6.11, Callister 6e. Metals: occurs when noticeable necking starts. Ceramics: occurs when crack propagation starts. Polymers: occurs when polymer backbones are aligned and about to break. 18

15 Ductile vs Brittle Failure Fracture behavior: Very Ductile Moderately Ductile Brittle Adapted from Fig. 8.1, Callister 7e. %AR or %EL Large Moderate Small Ductile: warning (large plastic deformation) before fracture Brittle: No warning

16 Ductile vs Brittle Failure ductile brittle

17 Evolution to failure: Necking is the localization of damage necking s Moderately Ductile Failure void nucleation void growth and linkage shearing at surface fracture 100 mm Fracture surface of tire cord wire loaded in tension. Courtesy of F. Roehrig, CC Technologies, Dublin, OH. Used with permission. 17

18 Ductility Tensile strain at failure, %EL: %EL L f L o L o x100 Adapted from Fig. 6.13, Callister 6e. %AR A o A f Reduction in the area at failure, %AL: A o Note: %AR and %EL are often comparable. crystal slip does not change material volume. %AR > %EL possible if internal voids form in neck. x100 20

19 Toughness Ability to absorb energy up to fracture Engineering tensile stress, s smaller toughness (ceramics) larger toughness (metals, PMCs) W f e s d e 0 Engineering tensile strain, e smaller toughnessunreinforced polymers Usually ductile materials have more toughness than brittle one Areas below the curves 21

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21 True Stress & Strain st F A i e T s e T T ln i ln 1 e o s 1 e Curve fit to the stress-strain of plastic deformation: s T K e n T hardening exponent: n = 0.15 (some steels) to n = 0.5 (some coppers) true stress (F/A) true strain: ln(l/l o )

22 True stress & strain Curve fit to the stress-strain response: s Ke n T T n = hardening exponent n = 0.15 (some steels) n = 0.5 (some copper) 22

23 Properties of Common Aerospace Structural Materials Material Elastic Modulus (E) [GPa] Strength (S) [MPa] % Elongation Aluminum Al 7075-T6 Titanium Ti-6Al-4V 71.7 Yield Strength: % Yield Strength: % Epoxy 2.41 Tensile Strength: 40 5% Carbon Fiber 230 Tensile Strength: % Carbon fiber-epoxy Composite (V f =60%) Longitudinal: 220 Tensile Strength: Transverse: 6.9 Tensile Strength:

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26 Hardness

27 Hardness Measure of resistance to localized plastic deformation Simple, non-destructive, not a well-defined material property 1. Scratch hardness: Mohs scale, 2. Indentation hardness: Rockwell, Vickers, Brinell, Shore 3. Rebound (Dynamic) hardness: Leeb, scleroscope Larger hardness: smaller indent resistance to plastic deformation or cracking in compression better wear properties most plastics brasses Al alloys easy to machine steels file hard cutting tools nitrided steels diamond increasing hardness

28 Indentation Hardness

29 Brinell Hardness (HB) D=10 mm hardened steel Keep at least 3 indentation diameters away from the edge or previous mark Hardness can be related to tensile strength For steel: TS (MPa) = 3.45 HB 10 mm sphere F= 10,000 N measure size of indent after removing load D d Smaller indents mean larger hardness.

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31 Appendix

32 Stress and strain are point-wise and can vary over the space.

33 Photoelasticity

34 Stress-strain of iron at several temperatures c07f14

35 Stress-Strain Behaviors of Polymers brittle polymer Tensile strength of polymer ca. 10% that of metals elastic modulus less than metal Plastic polymer elastomer Strains deformations > 1000% possible (for metals, maximum strain ca. 10% or less)

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37 Dislocation Motion Dislocations & plastic deformation Cubic & hexagonal metals - plastic deformation by plastic shear or slip where one plane of atoms slides over adjacent plane by defect motion (dislocations). If dislocations don't move, deformation doesn't occur! Adapted from Fig. 7.1, Callister 7e. 37