ISSUES TO ADDRESS... Stress and strain: What are they and why are they used instead of load and deformation? Elastic behavior: When loads are small, how much deformation occurs? What materials deform least? Plastic behavior: At what point do dislocations cause permanent deformation? What materials are most resistant to permanent deformation? 1 Toughness and ductility: What are they and how do we measure them? CHAPTER 1: MECHANICAL PROPERTIES Ceramic Materials: What special provisions/tests are made for ceramic materials?

2 1. Initial2. Small load3. Unload Elastic means reversible! ELASTIC DEFORMATION

3 1. Initial2. Small load3. Unload Plastic means permanent! PLASTIC DEFORMATION (METALS)

4 Tensile stress,  : Shear stress,  : Stress has units: N/m 2 or lb/in 2 ENGINEERING STRESS

Typical tensile specimen 9 Other types of tests: --compression: brittle materials (e.g., concrete) --torsion: cylindrical tubes, shafts. Typical tensile test machine Adapted from Fig. 6.2, Callister 6e. Adapted from Fig. 6.3, Callister 6e. (Fig. 6.3 is taken from H.W. Hayden, W.G. Moffatt, and J. Wulff, The Structure and Properties of Materials, Vol. III, Mechanical Behavior, p. 2, John Wiley and Sons, New York, 1965.) STRESS-STRAIN TESTING

Modulus of Elasticity, E: (also known as Young's modulus) 10 Hooke's Law:  = E  Poisson's ratio, : metals: ~ 0.33 ceramics: ~0.25 polymers: ~0.40 Units: E: [GPa] or [psi] : dimensionless LINEAR ELASTIC PROPERTIES

13 Metals Alloys Graphite Ceramics Semicond Polymers Composites /fibers E(GPa) YOUNG’S MODULI: COMPARISON

15 Simple tension test: (at lower temperatures, T < T melt /3) PLASTIC (PERMANENT) DEFORMATION

16 Stress at which noticeable plastic deformation has occurred. when  p = YIELD STRENGTH,  y

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

19 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 AFRE, GFRE, & CFRE = aramid, glass, & carbon fiber-reinforced epoxy composites, with 60 vol% fibers. TENSILE STRENGTH: COMPARISON

Plastic tensile strain at failure: 20 Another ductility measure: Note: %AR and %EL are often comparable. --Reason: crystal slip does not change material volume. --%AR > %EL possible if internal voids form in neck. Adapted from Fig. 6.13, Callister 6e. DUCTILITY, %EL

Energy to break a unit volume of material Approximate by the area under the stress-strain curve. 21 TOUGHNESS

25 Compare to responses of other polymers: --brittle response (aligned, cross linked & networked case) --plastic response (semi-crystalline case) Stress-strain curves adapted from Fig. 15.1, Callister 6e. Inset figures along elastomer curve (green) adapted from Fig , Callister 6e. (Fig is from Z.D. Jastrzebski, The Nature and Properties of Engineering Materials, 3rd ed., John Wiley and Sons, 1987.) TENSILE RESPONSE: ELASTOMER CASE

26 Decreasing T... --increases E --increases TS --decreases %EL Increasing strain rate... --same effects as decreasing T. Adapted from Fig. 15.3, Callister 6e. (Fig is from T.S. Carswell and J.K. Nason, 'Effect of Environmental Conditions on the Mechanical Properties of Organic Plastics", Symposium on Plastics, American Society for Testing and Materials, Philadelphia, PA, 1944.) T AND STRAIN RATE: THERMOPLASTICS

27 Stress relaxation test: --strain to   and hold. --observe decrease in stress with time. Relaxation modulus: Data: Large drop in E r for T > T g. (amorphous polystyrene) Sample T g (C) values: PE (low M w ) PE (high M w ) PVC PS PC Adapted from Fig. 15.7, Callister 6e. (Fig is from A.V. Tobolsky, Properties and Structures of Polymers, John Wiley and Sons, Inc., 1960.) Selected values from Table 15.2, Callister 6e. TIME DEPENDENT DEFORMATION

Design uncertainties mean we do not push the limit. Factor of safety, N 29 Often N is between 1.2 and 4 Ex: Calculate a diameter, d, to ensure that yield does not occur in the 1045 carbon steel rod below. Use a factor of safety of 5. 5 DESIGN OR SAFETY FACTORS

Stress and strain: These are size-independent measures of load and displacement, respectively. Elastic behavior: This reversible behavior often shows a linear relation between stress and strain. To minimize deformation, select a material with a large elastic modulus (E or G). Plastic behavior: This permanent deformation behavior occurs when the tensile (or compressive) uniaxial stress reaches  y. 30 Toughness: The energy needed to break a unit volume of material. Ductility: The plastic strain at failure. Note: For materials selection cases related to mechanical behavior, see slides 20-4 to SUMMARY

Type Ionic Covalent Metallic Secondary Bond Energy Large! Variable large-Diamond small-Bismuth Variable large-Tungsten small-Mercury smallest Comments Nondirectional (ceramics) Directional semiconductors, ceramics polymer chains) Nondirectional (metals) Directional inter-chain (polymer) inter-molecular SUMMARY: BONDING

Bond length, r Bond energy, E o Melting Temperature, T m T m is larger if E o is larger. PROPERTIES FROM BONDING: T M

Elastic modulus, E E ~ curvature at r o E is larger if E o is larger. PROPERTIES FROM BONDING: E E ~ curvature at r o

Coefficient of thermal expansion,   ~ symmetry at r o  is larger if E o is smaller. PROPERTIES FROM BONDING: 

3 tend to be densely packed. have several reasons for dense packing: -Typically, only one element is present, so all atomic radii are the same. -Metallic bonding is not directional. -Nearest neighbor distances tend to be small in order to lower bond energy. have the simplest crystal structures. 74 elements have the simplest crystal structures – BCC, FCC and HCP We will look at three such structures... METALLIC CRYSTALS

14 different point lattices, called Bravais lattices, make up the crystal system. The lengths of the sides, a, b, and c, and the angles between them can vary for a particular unit cell.

Three simple lattices that describe metals are Face Centered Cubic (FCC) Body Centered Cubic (BCC) and Hexagonal Close Packed (HCP)

4 Rare due to poor packing (only Po has this structure) Close-packed directions are cube edges. Coordination # = 6 (# nearest neighbors) (Courtesy P.M. Anderson) SIMPLE CUBIC STRUCTURE (SC) Click on image to animate

6 Coordination # = 12 Adapted from Fig. 3.1(a), Callister 6e. (Courtesy P.M. Anderson) Close packed directions are face diagonals. --Note: All atoms are identical; the face-centered atoms are shaded differently only for ease of viewing. FACE CENTERED CUBIC STRUCTURE (FCC) Click on image to animate

Coordination # = 8 8 Adapted from Fig. 3.2, Callister 6e. (Courtesy P.M. Anderson) Close packed directions are cube diagonals. --Note: All atoms are identical; the center atom is shaded differently only for ease of viewing. BODY CENTERED CUBIC STRUCTURE (BCC) Click on image to animate

10 Coordination # = 12 ABAB... Stacking Sequence APF = D Projection 2D Projection Adapted from Fig. 3.3, Callister 6e. HEXAGONAL CLOSE-PACKED STRUCTURE (HCP)

11 Example: Copper Data from Table inside front cover of Callister (see next slide): crystal structure = FCC: 4 atoms/unit cell atomic weight = g/mol (1 amu = 1 g/mol) atomic radius R = nm (1 nm = 10 cm) -7 THEORETICAL DENSITY, 

12 Adapted from Table, "Charac- teristics of Selected Elements", inside front cover, Callister 6e. Characteristics of Selected Elements at 20C

13 Why? Metals have... close-packing (metallic bonding) large atomic mass Ceramics have... less dense packing (covalent bonding) often lighter elements Polymers have... poor packing (often amorphous) lighter elements (C,H,O) Composites have... intermediate values Data from Table B1, Callister 6e. DENSITIES OF MATERIAL CLASSES

14 Bonding: --Mostly ionic, some covalent. --% ionic character increases with difference in electronegativity. Adapted from Fig. 2.7, Callister 6e. (Fig. 2.7 is adapted from Linus Pauling, The Nature of the Chemical Bond, 3rd edition, Copyright 1939 and 1940, 3rd edition. Copyright 1960 by Cornell University. Large vs small ionic bond character: CERAMIC BONDING

21 Compounds: Often have similar close-packed structures. Close-packed directions --along cube edges. Structure of NaCl (Courtesy P.M. Anderson) STRUCTURE OF COMPOUNDS: NaCl Click on image to animate

Diamond, BeO and GaAs are examples of FCC structures with two atoms per lattice point

22 Some engineering applications require single crystals: Crystal properties reveal features of atomic structure. (Courtesy P.M. Anderson) --Ex: Certain crystal planes in quartz fracture more easily than others. --diamond single crystals for abrasives --turbine blades Fig. 8.30(c), Callister 6e. (Fig. 8.30(c) courtesy of Pratt and Whitney). (Courtesy Martin Deakins, GE Superabrasives, Worthington, OH. Used with permission.) CRYSTALS AS BUILDING BLOCKS

23 Most engineering materials are polycrystals. Nb-Hf-W plate with an electron beam weld. Each "grain" is a single crystal. If crystals are randomly oriented, overall component properties are not directional. Crystal sizes typ. range from 1 nm to 2 cm (i.e., from a few to millions of atomic layers). Adapted from Fig. K, color inset pages of Callister 6e. (Fig. K is courtesy of Paul E. Danielson, Teledyne Wah Chang Albany) 1 mm POLYCRYSTALS

24 Single Crystals -Properties vary with direction: anisotropic. -Example: the modulus of elasticity (E) in BCC iron: Polycrystals -Properties may/may not vary with direction. -If grains are randomly oriented: isotropic. (E poly iron = 210 GPa) -If grains are textured, anisotropic. 200  m Data from Table 3.3, Callister 6e. (Source of data is R.W. Hertzberg, Deformation and Fracture Mechanics of Engineering Materials, 3rd ed., John Wiley and Sons, 1989.) Adapted from Fig. 4.12(b), Callister 6e. (Fig. 4.12(b) is courtesy of L.C. Smith and C. Brady, the National Bureau of Standards, Washington, DC [now the National Institute of Standards and Technology, Gaithersburg, MD].) SINGLE VS POLYCRYSTALS

atoms pack in periodic, 3D arrays typical of: 26 Crystalline materials... -metals -many ceramics -some polymers atoms have no periodic packing occurs for: Noncrystalline materials... -complex structures -rapid cooling crystalline SiO 2 noncrystalline SiO 2 "Amorphous" = Noncrystalline Adapted from Fig. 3.18(b), Callister 6e. Adapted from Fig. 3.18(a), Callister 6e. MATERIALS AND PACKING

28 Quartz is crystalline SiO 2 : Basic Unit: Glass is amorphous Amorphous structure occurs by adding impurities (Na +,Mg 2+,Ca 2+, Al 3+ ) Impurities: interfere with formation of crystalline structure. (soda glass) Adapted from Fig , Callister, 6e. GLASS STRUCTURE

3 Vacancies: -vacant atomic sites in a structure. Self-Interstitials: -"extra" atoms positioned between atomic sites. POINT DEFECTS

Edge Dislocation An edge dislocation results from a mismatch in the rows of atoms, as if an extra plane of atoms was inserted. The burger’s vector, b, represents how far we would have to move an atom to bring it back into registry. The burgers vector is perpendicular to the dislocation line.

Screw Dislocation Screw dislocations result from “shearing” in the crystal. The burgers vector, b, is parallel to the slip plane

Mixed Dislocation Dislocations virtually never are purely “edge” or “screw” type. They are usually combinations of the two, or “mixed”