CHAPTER 8: and alloys? DEFORMATION AND STRENGTHENING MECHANISMS - PowerPoint PPT Presentation

• Why are dislocations observed primarily in metals CHAPTER 8: and alloys? DEFORMATION AND STRENGTHENING MECHANISMS • How are strength and dislocation motion related? • How do we manipulate properties? Strengthening Heat treating 1

Slip on close packed planes • In a given crystal, slip is easiest – on the most densely packed plane – in the most densely packed direction Single crystal Zn (hcp)

DISLOCATIONS Edge Screw • Produce plastic deformation, • Incrementally breaking/reforming bonds. 3

Stress at dislocation Highest stress with no impurity at core From: Van Vlack, 1985 Under shear, atoms in the highly strained area will shift more easily

BOND BREAKING AND REMAKING • Dislocation motion requires the successive bumping of a half plane of atoms (from left to right here). • Bonds across the slipping planes are broken and remade in succession. Atomic view of edge dislocation motion from left to right as a crystal is sheared. (Courtesy P.M. Anderson) 5

DISLOCATIONS & MATERIALS CLASSES • Metals: Disl. motion easier. + + + + + + + + -non-directional bonding + + + + + + + + -close-packed directions + + + + + + + + for slip. electron cloud ion cores • Covalent Ceramics (Si, diamond): Motion hard. -directional (angular) bonding • Ionic Ceramics (NaCl): + - + - + - + Motion hard. -need to avoid ++ and -- - - - - + + + neighbors. - - - + + + + 2

DISLOCATION MOTION - SLIP • Strain field around dislocation core • Interaction between strain fields can effect motion Edge Dislocations allow slip at lower shear stress, but when they become entangled the metal is stronger. 3

DISLOCATIONS & CRYSTAL STRUCTURE • close-packed planes & directions are preferred. WHY? – more nearest neighbors, easier to transfer bond from one atom to next 6

FCC slip directions Ex.: In (111) plane Along [10-1] direction (100)<011> • How many slip directions? FCC (110)<-110>

Slip plane/directions • Comparison among crystal structures: FCC: many close-packed planes/directions; HCP: only one plane, 3 directions; BCC: none NO CLOSE-PACKED PLANES, but still has preferred slip directions and planes

Shear stress Applied tensile stress produces shear on internal planes Resolved components of pure shear and pure tension for the plane of interest ′ σ = σ θ 2 cos ′ τ = σ θ θ sin cos Max shear stress at this angle (45) shear and normal stress on plane 3

STRESS AND DISLOCATION MOTION Crystals slip due to a resolved shear stress, τ R . • on favorably oriented plane/direction τ R = σ cos λ cos φ Plastically stretched for shear stress on zinc particular single plane and crystal. direction Adapted from Fig. 7.9, Callister 6e. (Fig. 7.9 is from C.F. Elam, The Distortion of Metal Crystals , Oxford University Press, London, 1935.) 7

CRITICAL RESOLVED SHEAR STRESS (CRSS) τ R > τ CRSS • Condition for dislocation motion Material property • Orientation of slip system (crystal orientation) can make it easy or hard to move dislocation on typically that system 10-4G to 10-2G τ R = σ cos λ cos φ σ σ σ τ R = 0 τ R = σ /2 τ R = 0 φ =90° λ =90° λ =45° φ =45° 8

DISL. MOTION IN POLYCRYSTALS σ • Slip planes & directions ( λ , φ ) change from one crystal to another. τ R • for most favorable direction will vary from one crystal to another. • The crystal with the largest τ R yields first. • Other (less favorably oriented) crystals Adapted from Fig. 7.10, yield later. Callister 6e. (Fig. 7.10 is courtesy of C. Brady, National • Unfavorably oriented grains Bureau of Standards inhibit deformation of favorably [now the National Institute of Standards oriented grains 300 μ m and Technology, Gaithersburg, MD].) 9

Manipulation of properties 1. Strengthening 2. Heat treating

3 STRATEGIES FOR STRENGTHENING: 1: REDUCE GRAIN SIZE • Grain boundaries are barriers to slip. • Barrier "strength" slip plane B n i increases with a r g misorientation. grain A grain boundary • Smaller grain size: Adapted from Fig. 7.12, Callister 6e. (Fig. 7.12 is from A Textbook of Materials more barriers to slip. Technology , by Van Vlack, Pearson Education, Inc., Upper Saddle River, NJ.) σ yield = σ o + k y d − 1/2 • Hall-Petch Equation: Example: Solidification conditions can change grain size 10

ANISOTROPY IN σ yield • Can be induced by rolling a polycrystalline metal -before rolling -after rolling Adapted from Fig. 7.11, Callister 6e. (Fig. 7.11 is from W.G. Moffatt, G.W. Pearsall, and J. Wulff, The Structure and Properties of Materials , Vol. I, Structure , p. 140, John Wiley and Sons, New York, 1964.) rolling direction 235 μ m -isotropic -anisotropic since grains are since rolling affects grain approx. spherical orientation and shape. & randomly oriented. 12

STRENGTHENING STRATEGY 2: SOLID SOLUTIONS • Impurity atoms distort the lattice & generate stress. • Stress can produce a barrier to dislocation motion. • Smaller substitutional • Larger substitutional impurity impurity A C D B Impurity generates local shear at Impurity generates local shear at A and B that opposes disl motion C and D that opposes disl motion to the right. to the right. 14

STRENGTHENING STRATEGY 2: SOLID SOLUTIONS • Impurity atoms distort the lattice & generate stress. • Stress can produce a barrier to dislocation motion. 14

Solid Solution: Stress at dislocation Highest stress with no impurity at core From: Van Vlack, 1985 Under shear, atoms in the highly strained area will shift more easily � Effect of adding impurity at core of dislocation – added stress needed to move dislocation past the impurity

EX: SOLID SOLUTION STRENGTHENING IN COPPER • Tensile strength & yield strength increase w/wt% Ni. Tensile strength (MPa) Yield strength (MPa) 180 400 Adapted from Fig. 7.14 (a) and (b), 120 Callister 6e. 300 60 200 0 10 20 30 40 50 0 10 20 30 40 50 wt. %Ni, (Concentration C) wt. %Ni, (Concentration C) σ 1 / 2 • Empirical relation: y C ~ impurity Alloying increases σ y • and TS. 15

STRENGTHENING STRATEGY 3: COLD WORK (%CW) • Room temperature deformation. – increase # of dislocations • Common forming operations change the cross sectional area: -Forging -Rolling force roll Ad die Ao Ao Ad blank roll Adapted from Fig. 11.7, Callister 6e. force -Drawing -Extrusion Ao container die die holder Ad force tensile ram Ao Ad billet extrusion force die die container %CW = A o − A d x100 A o 16

DISLOCATIONS DURING COLD WORK • Ti alloy after cold working: • Dislocations entangle with one another during cold work. • Dislocation motion becomes more difficult. Adapted from Fig. 4.6, Callister 6e. (Fig. 4.6 is courtesy of M.R. Plichta, Michigan Technological 0.9 μ m University.) 17

RESULT OF COLD WORK Dislocation density ( ρ d ) goes up: • Carefully prepared sample: ρ d ~ 10 3 mm/mm 3 Heavily deformed sample: ρ d ~ 10 10 mm/mm 3 • Measuring dislocation density: 40 μ m Area, A dislocation pit N dislocation pits (revealed by etching) d = N ρ A σ • Yield stress increases large hardening σ y1 as ρ d increases: σ y0 small hardening ε 18

IMPACT OF COLD WORK Yield strength ( σ • ) increases. y • Tensile strength (TS) increases. • Ductility (%EL or %AR) decreases. Stress Adapted from Fig. 7.18, Callister % cold work 6e. (Fig. 7.18 is from Metals Handbook: Properties and Selection: Iron and Steels , Vol. 1, Strain 9th ed., B. Bardes (Ed.), American Society for Metals, 1978, p. 221.) 21

COLD WORK ANALYSIS • What is the tensile strength & ductility after cold working? Copper Cold work -----> Do=15.2mm Dd=12.2mm 2 − π r d 2 π r o %CW = x100 = 35.6% 2 π r o Ductility decreased, Tensile strength increased 22

Effect of Temperature on Strength

σ - ε BEHAVIOR VS TEMPERTURE 800 -200°C • Results for 600 Stress (MPa) polycrystalline iron: -100°C 400 25°C 200 00 0.1 0.2 0.3 0.4 0.5 Strain σ y • and TS decrease with increasing test temperature. • %EL increases with increasing test temperature. • Why? Vacancies 3. disl. glides past obstacle help dislocations 2. vacancies replace past obstacles. atoms on the obstacle disl. half 1. disl. trapped plane by obstacle 23

Heat treatment: EFFECT OF HEATING AFTER %CW • 1 hour treatment at T anneal ... decreases TS and increases %EL. • Effects of cold work are reversed! • 3 Annealing Annealing Temperature (°C) stages to 100 300 500 700 60 tensile strength (MPa) 600 discuss... tensile strength Recovery 50 Recrystallization ductility (%EL) 500 Grain growth 40 400 30 ductility 20 Adapted from Fig. 7.20, Callister 6e. (Fig. 7.20 is adapted from G. Sachs and K.R. van Horn, 300 Recovery Recrystallization Grain Growth Practical Metallurgy, Applied Metallurgy, and the Industrial Processing of Ferrous and Nonferrous Metals and Alloys , American Society for Metals, 1940, p. 139.) 24