Mechanical Properties Of Metals - II CHAPTER 7 Mechanical Properties Of Metals - II 7-1

Recovery and Recrystallization Cold worked metals become brittle. Reheating, which increases ductility results in recovery, recrystallization and grain growth. This is called annealing and changes material properties. 7-2 (Adapted from Z.D. Jastrzebski, “The Nature and Properties of Engineering Materials,” 2d ed., Wiley, 1976, p.228.)

Structure of Cold Worked Metals Strain energy of cold work is stored as dislocations. Heating to recovery temperature relieves internal stresses (Recovery stage). Polygonization (formation of sub-grain structure) takes place. Dislocations are moved into lower energy configuration. Structure of 85% Cold worked metal TEM of 85% Cold worked metal Polyganization Figure 6.4 Dislocations Grain Boundaries Slip bands Structure of stress relived metal TEM of stress relived metal Figure 6.2 and 6.3 7-3 (After “Metals Handbook,” vol 7, 8th ed., American Society of Metals, 1972, p.243)

Recrystallization If metal is held at recrystallization temperature long enough, cold worked structure is completely replaced with recrystallized grain structure. Two mechanisms of recrystallization Expansion of nucleus Migration of grains. More deformed region Structure and TEM of Recrystallized metal Migration Expansion Nucleus of recrystallized grain Figure 6.5 Figure 6.2 and 6.3 7-4 (After “Metals Handbook,” vol 7, 8th ed., American Society of Metals, 1972, p.243)

Effects on Mechanical Properties Annealing decreases tensile strength, increases ductility. Example: Factors affecting recrystalization: Amount of prior deformation Temperature and time Initial grain size Composition of metal 85% Cu & 15% Zn 50% cold rolled Annealed 1 h 4000C Tensile strength 75 KSI Ductility 3% Tensile strength 45 KSI Ductility 38 % Figure 6.6 7-5 (After “Metals Handbook,” vol 2, 9th ed., American Society of Metals, 1979, p.320)

Facts About Recrystallization A minimum amount of deformation is needed. Smaller the deformation, higher the recrystallization temperature. Higher the temperature, lesser is the time required. Greater the degree of deformation, smaller are the recrystallized grains. Larger the original grain size, greater amount of deformation is required to produce equivalent temperature. Recrystallization temperature increases with purity of metals. Figure 6.7b Continuous annealing 7-6 (After W.L. Roberts, “Flat Processing of steel,” Marcel Dekker, 1988.)

Fracture of Metals – Ductile Fracture Fracture results in separation of stressed solid into two or more parts. Ductile fracture : High plastic deformation & slow crack propagation. Three steps : Specimen forms neck and cavities within neck. Cavities form crack and crack propagates towards surface, perpendicular to stress. Direction of crack changes to 450 resulting in cup-cone fracture. 7-7

Brittle Fracture No significant plastic deformation before fracture. Common at high strain rates and low temperature. Three stages: Plastic deformation concentrates dislocation along slip planes. Microcracks nucleate due to shear stress where dislocations are blocked. Crack propagates to fracture. Example: HCP Zinc ingle crystal under high stress along {0001} plane undergoes brittle fracture. SEM of ductile fracture SEM of brittle fracture Figure 6.11 & 6.13 7-8 (From ASM handbook vol 12, page 12 and 14)

Ductile and Brittle Fractures Ductile fracture Brittle Fracture

Brittle Fractures (cont..) Brittle fractures are due to defects like Folds Undesirable grain flow Porosity Tears and Cracks Corrosion damage Embrittlement due to atomic hydrogen At low operating temperature, ductile to brittle transition takes place

Toughness and Impact Testing Toughness is a measure of energy absorbed before failure. Impact test measures the ability of metal to absorb impact. Toughness is measured using impact testing machine Figure 6.14 7-9 (After H.W. Hayden, W.G. Moffatt, and J.Wulff, “The structure and Properties of Materials,” vol. III, Wiley, 1965, p.13.)

Impact testing (Cont…) Also used to find the temperature range for ductile to brittle transition. Sinking of Titanic: Titanic was made up of steel which has ductile brittle transition temperature 320C. On the day of sinking, sea temperature was –20C which made the the structure highly brittle and susceptible to more damage. Figure 6.15 Figure 6.16 7-10 (After J.A.Rinebolt and W.H. Harris, Trans. ASM, 43: 1175(1951))

Fracture Toughness Cracks and flaws cause stress concentration. K1 = Stress intensity factor. σ = Applied stress. a = edge crack length Y = geometric constant. Figure 6.17 KIc = critical value of stress intensity factor.(Fracture toughness) Example: Al 2024 T851 26.2MPam1/2 4340 alloy steel 60.4MPam1/2 7-11

Measuring Fracture Toughness A notch is machined in a specimen of sufficient thickness B. B > > a plain strain condition. B = 2.5(KIc/Yield strength)2 Specimen is tensile tested. Higher the KIc value, more ductile the metal is. Used in design to find allowable flaw size. Figure 6.18 7-12 Courtesy of White Shell research)

Fatigue of Metals Metals often fail at much lower stress at cyclic loading compared to static loading. Crack nucleates at region of stress concentration and propagates due to cyclic loading. Failure occurs when cross sectional area of the metal too small to withstand applied load. Fracture started here Figure 6.19 Fatigue fractured surface of keyed shaft Final rupture 7-13 (After “Metals Handbook,” vol 9, 8th ed., American Society of Metals, 1974, p.389)

Fatigues Testing Alternating compression and tension load is applied on metal piece tapered towards center. Stress to cause failure S and number of cycles required N are plotted to form SN curve. Figure 6.21 Figure 6.20 Figure 6.23 7-14 (After H.W. Hayden, W.G. Moffatt, and J.Wulff, “The structure and Properties of Materials,” vol. III, Wiley, 1965, p.15.)

Cyclic Stresses Different types of stress cycles are possible (axial, torsional and flexural). Figure 6.24 Stress amplitude = Mean stress = Stress range = Stress range = 7-15

Structural Changes in Fatigue Process Crack initiation first occurs. Reversed directions of crack initiation caused surface ridges and groves called slipband extrusion and intrusion. This is stage I and is very slow (10-10 m/cycle). Crack growth changes direction to be perpendi- cular to maximum tensile stress (rate microns/sec). Sample ruptures by ductile failure when remaining cross-sectional area is small to withstand the stress. Persistent slip bands In copper crystal Figure 6.26 7-16 Courtesy of Windy C. Crone, University of Wisconsin

Factors Affecting Fatigue Strength Stress concentration: Fatigue strength is reduced by stress concentration. Surface roughness: Smoother surface increases the fatigue strength. Surface condition: Surface treatments like carburizing and nitriding increases fatigue life. Environment: Chemically reactive environment, which might result in corrosion, decreases fatigue life. 7-17

Fatigue Crack Propagation Rate Notched specimen used. Cyclic fatigue action is generated. Crack length is measured by change in potential produced by crack opening. Figure 6.27 7-18 (After “Metals Handbook,” Vol 8, 9th ed., American Society of Metals, 1985, p.388.)

Stress & Crack Length Fatigue Crack Propagation. When ‘a’ is small, da/dN is also small. da/dN increases with inc- reasing crack length. Increase in σ increases crack growth rate. σ2 σ1 Δa ΔN Δa ΔN = fatigue crack growth rate. α f(σ,a) Figure 6.28 ΔK = Kmax-Kmin = stress intensity factor range. A,m = Constants depending on material, environment, frequency temperature and stress ratio. 7-19

Fatigue Crack Growth rate Versus ΔK Straight line with slope m Limiting value of ΔK below Which there is no measurable Crack growth is called stress intensity factor range threshold ΔKth Figure 6.29 7-20 (After P.C. Paris et al. Stress analysis and growth of cracks, STP 513 ASTM, Philadelphia, 1972, PP. 141-176

Fatigue Life Calculation But Therefore Therefore Integrating from initial crack size a0 to final crack size af at number of fatigue cycles Nf Integrating and solving for Nf (Assuming Y is independent of crack length) 7-21

Creep in Metals Creep is progressive deformation under constant stress. Important in high temperature applications. Primary creep: creep rate decreases with time due to strain hardening. Secondary creep: Creep rate is constant due to simultaneous strain hard- ening and recovery process. Tertiary creep: Creep rate increases with time leading to necking and fracture. Figure 6.30 7-22

Creep Test Creep test determines the effect of temperature and stress on creep rate. Metals are tested at constant stress at different temperature & constant temperature with different stress. High temperature or stress Medium temperature or stress Figure 6.33 Creep strength: Stress to produce Minimum creep rate of 10-5%/h At a given temperature. Low temperature or stress Figure 6.32 7-23

Creep Test (Cont..) Creep rupture test is same as creep test but aimed at failing the specimen. Plotted as log stress versus log rupture time. Time for stress rupture decreases with increased stress and temperature. Figure 6.35 Figure 6.34 7-24 (After H.E. McGannon [ed]. “ The making, shaping and Treating of Steel,” 9th ed., United States Steel, 1971, p. 1256

Larsen Miller Parameter Larsen Miller parameter is used to represent creep-stress rupture data. P(Larsen-Miller) = T[log tr + C] T = temperature(K), tr = stress-rupture time h C = Constant (order of 20) Also, P(Larsen-Miller) = [T(0C) + 273(20+log tr) or P(Larsen-Miller) = [T(0F) + 460(20+log tr) At a given stress level, the log time to stress rupture plus constant multiplied by temperature remains constant for a given material. 7-25

Larsen Miller Parameter If two variables of time to rupture, temperature and stress are known, 3rd parameter that fits L.M. parameter can be determined. Example: For alloy CM, at 207 MPa, LM parameter is 27.8 x 103 K Then if temperature is known, time to rupture can be found. Figure 6.36 7-26 (After “Metals Handbook,” vol 1, 10th ed., ASM International, 1990, p.998.)

L.M. Diagram of several alloys Figure 6.37 Example: Calculate time to cause 0.2% creep strain in gamma Titanium aluminide at 40 KSI and 12000F From fig, p = 38000 38000 = (1200 + 460) (log t0.2% + 20) t=776 h 7-27 After N.R. Osborne et. al., SAMPE Quart, (4)22;26(1992)

Case Study – Analysis of Failed Fan Shaft Requirements Function – Fan drive support Material 1045 cold drawn steel Yield strength – 586 Mpa Expected life – 6440 Km (failed at 3600 km) Visual examination (avoid additional damage) Failure initiated at two points near fillet Characteristic of reverse bending fracture

Failed Shaft – Further Analysis Tensile test proved yield strength to be 369 MPa (lower than specified 586 MPa). Metallographic examination revealed grain structure to be equiaxed ( cold drawn metal has elongated grains). Conclusion: Material is not cold drawn – it is hot rolled !. Lower fatigue strength and stress raiser caused the failure of the shaft.

Recent Advances: Strength + Ductility Coarse grained – low strength, high ductility Nanocrystalline – High strength, low ductility (because of failure due to shear bands). Ductile nanocrystalline copper : Can be produced by Cold rolling at liquid nitrogen temperature Additional cooling after each pass Controlled annealing Cold rolling creates dislocations and cooling stops recovery 25 % microcrystalline grains in a matrix of nanograins.

Fatigue Behavior of Nanomaterials Nanomaterials and Ultrafine Ni are found to have higher endurance limit than microcrystalline Ni. Fatigue crack growth is increased in the intermediate regime with decreasing grain size. Lower fatigue crack growth threshold Kth observed for nanocrystalline metal.