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Ch8: Mechanical Prop of Materials 1. Eng Stress: σ = F/Ao 2. Eng Strain: ε = (li – lo)/lo 3. Shear stress: t = F/Ao 4. Stress-strain behavior (Hooke’s Law): σ=Eε (E = Young’s modulus) 5. Shear stress and strain: t = Gy Anelasiticity: Elastc deformation that cont. after stress application with t needed to recover 6. Poison’s ration: v = -εx/εz = - εy/ εz 7. Moduli relations: E = 2G(1+v)

To determine phase amounts: use Lever rule! (other phase boundary) Eutectic=easily melted Eutectic strcutre: solid that results from eutectic transformation of alternating layers of a and b phases that form. Eutectoid reaction: delta = lamda + epsilon (with cooling/heating on = sign), therefore solid into two other solids and vica versa Peritectic Reaction: delta + lamda = epsilon, one liquid and solid phase turns into solid phase and vica versa. Congruent transformation: no compositional transformations Iron-Iron Carbide Phase Diagram:

grain boundary; Transgranular: fracture cracks pass through grains. Principles for fract mechanics: Stress concentration, amplified stress at the tip, , applied tensile stress, length surf crack, radius of curve. Design using fracture mechanics: Critical/design stress:

(Y will be given, or 1) Max allow flaw size and Crit stress for crack prop in brittle materials

(zeta-spec surf Slow diffusion at low temperatures leads to fine-grained microstructure with thin-layered structure of pearlite (fine pearlite). At higher temperatures, high diffusion rates allow for larger grain growth and formation of thick layered structure of pearlite (coarse pearlite). Bainite: consists of ferrite and cementite phases, forms as needles or plates, so fine only visible under electron micros. Spheriodite: If steel alloy having pearlitic or bainitic microstrucs is heated and left at temp below eutectoid for long time. Fe3C is spherelike. Martensite: when austenized ironcarbonalloys are rapidly cooled (quenched).

8. Ductility: %EL or (%AR) = eng strain x 100 Ductility is a measure of degree of plastic deformation sustained at fracture. Resilience is capacity of material to absorb energy when it it’s deformed elastically and then have energy recovered upon unloading Toughness is indication of a material’s resistance to fracture when there’s a crack. True stress/strain: is the stress/strain at that moment (instantaneous). Hardness: measure of material’s resistance to localized plastic deformation Rockwell: most common method Ch7 Diffusion Diffusion: Material transport by atomic motion. Impurity dif: atoms of one metal to another Self dif: same metal Vacancy dif: Interchange of atom from normal lattice pos to adjacent vacant pos Interstitial dif: Atoms migrate from interstitial position to neighbouring empty 1 1: Steady state diff: Diffusion flux Fick’s first law: J = M/At (M – nr. of atoms, A = area, t = time) or J = -D(dC/dx) (dC/dX = conc grad, D = diff coeff, m^2/s) 2. Non-steady state diff: Fick’s 2nd law (D and dC/dx vary with time): dC/dt = D(d^2C/dx^2) 3. Factors that infl. Diff: Diff species Temp: D = Do*exp(-Qd/RT) (D=coef of dif, Qd=activ. Energy J/mol, R = 8.31j/mol.K, T = temp (K= celcius + 273) Activ energy = ener req to diff 1 mole of ato. Ch9 Disloc + strength mech Slip-process by which plast defor is prod by disloc motion Equiaxed-same dim in all directions Strength mechanisms: -Grain size reduction, plastic deform, grain boundar(improves strength and toughness) Hall Petch: σy = σo + kyd^(-0.5) (yield strength, d = avg grain diam, rest is const) -Solid-solution strengthening: alloying with impurity atoms that go into subs or interst solid solution. Incr in impurity conc = incr in tensile and yield strength - Strain Hardening/cold working/work hardening: Duct metals become hard and strong as plast deformed.(becomes less ductile) %CW = (Ao-Ad)/Ao x 100 Rec. Recr. Grain growth -Recovery: Stored interal energy is relieved by disloc motion as result of atomic diff at elevated temp -Recrys: formation of new set of strainfree equiaxed grains with low disloc densities characteristic of precoldworked cond. (Recr temp (1H) normally 0.4Tm) -Grain Growth: Strainfree grains will grow if specimen is left at high temp. Migration of grain boundaries Ch6 Microscopy -Optical – uses light, needs surf prep, then etching (chem reagent), small grooves form that are more visible, max mag = 2000X -Electron – uses beams of electrons, for smaller microstrucs that need more mag .Transmission Electron Micr – passes beam of electrons through material, differ in diffract between elem produc the image, spec must be thin foil, max mag=1000000X .Scanning Electron Micr – surf is scanned with electron beam, then collected, surf must not be polished, can be etched, must be conductive, otherw metal coat is appl, max mag = 10X to 50000X -Scanning Probe Micr – Generates topograph map, tiny probe with sharp tip brought to surf, raster scannes plane, probe exp deflections, in vac, air or liq, max mag = 10^9X Ch11 Phase Diagrams Solubility limit: max conc of solute atoms that may dissolve in the solvent to form solid solution. Isomorphous:compl liq and solid solubility of components. Solvent: greatest amount, solute: minor amount, Metastable: persists indef and experi imperceptible changes with time

Eutectic reaction: L gamma + Fe3C Eutectoid reaction: γ(0.76 wt% C) ↔ α (0.022 wt% C) + Fe3C(6.7 wt% C) Microstructure of eutectoid steel:

Microstructure of hypoeutectoid steel:

Microstructure of hypereutectoid steel:

Ch12 Phase Transformations Most phase transformations involve change in composition ⇒ redistribution of atoms via diffusion is required. Nucleation of the new phase - formation of stable small particles (nuclei) of the new phase. Nuclei are often formed at grain boundaries and other defects. Growth of new phase at the expense of the original phase. Avrami: y = 1−exp(−kt^n) (y=fraction of phase transformation) Time and temperature dependant Isothermal Transformation Diagrams:

Isothermal Transformation Diagram:

Mechanical behavior of Fe-C alloys: Considering microstructure we can predict that, Spheroidite is the softest, Fine pearlite is harder and stronger than coarse pearlite, Bainite is harder and stronger than pearlite, Martensite is the hardest, strongest and the most brittle. Tempered martensite: Tempered martensite is less hard/strong as compared to regular martensite but has enhanced ductility (ferrite phase is ductile). ¾ Mechanical properties depend upon cementite particle size: fewer, larger particles means less boundary area and softer, more ductile material - eventual limit is spheroidite. ¾ Particle size increases with higher tempering temperature and/or longer time (more C diffusion) - therefore softer, more ductile material. CCT Diagrams: A plot containing modified beginning and ending reaction curves  Bainite will not form when alloy of eutectoid composition or, any plain carbon steel is continuously cooled to room temperature  Austenite will have transformed to pearlite by the time the bainite transformation has become possible  For continuous cooling of a steel alloy – critical quenching rate - represents min. rate off quenching that will produce a totally martensite structure  Only martensite will exist for quenching rates greater than the critical o Range of rates over which pearlite and martensite are produced o Until finally a totally pearlitic structure develops for low cooling rates Ch17 Frabrication and Processing Forming: Hot working, cold working, forging, rolling, extrusion, drawing Casting: Sand casting(most common, gating), die casting, investment casting, lost foam(polystyrene), continuous(casting+rolling, large ingots). Annealing: heated then slowly cooled. To: increase softness, relieve stress, produce specific microstructure. Annealing for ferrous alloys: Lower crit temp: below which all austenite transf into ferrite and cementite; Upper crit temp: lines for hypo and hyper steels, above only auste. Normalise: decrease grain size(55 above upper crit temp); Full anneal(>50 upper crit temp); spheriodizing(having uniform grain struct results Precipitation hardening: Strength and hardness of metals alloys can be increased by formation of small second phase particles dispersed in original phase mix. Ch10 Failure Simple fracture: separation of body into two or more pieces in response to imposed stress that is changing with time and at temperatures that below the melting temp. Two modes: Ductile: Different materials different fracture surfaces; Fracture occurs after stages of initial deformation; Quantified: % elongation; High energy absorption and plastic deformation before fracture. Brittle: Direction of crack is perpendicular to the applied tensile stress and yields a flat fracture surface; Crack profile can happen through interior of grains or along a grain boundary; Takes place without any appreciable deformation and by a rapid crack propagation; Intergranular: crack propagation along

energy) Fracture toughness:

Fracture toughness testing: Impact test techn: to attain fracture char of mater at high loads; Test cond were chosen to repr those most severe rela to poten for fract: Deformation at low temps, high strain rate, triaxial stress state. Two methods: Charpy V-notch test: Shape of bar with squar crosection into which a v-notch is machined, Load is applied as impact from weighted hammer strikes spec, Difference between two methods is based on the manner of specimen support. Realeased from a height h, Knife edge on tip of hammer. Izod, Ductiletobrittle testing, Ductile surface = fibrous or dull, Brittle surface = granular (shiny ) texture; Ductile to brittle transition features of both types will exist; Structures from alloys that show ductile to brittle behaviour should be used at T above transition temp to avoid brittle failure; Relates to temperature dependence; Higher temperatures the CVN energy is large, linked to ductile mode of fracture; As temp decreases the impact energy does too over a narrow temperature range below which the energy has a constant but small value, mode of fracture is then brittle. Fatigue: Occurs in structures subjected to dynamic and fluctuating stresses. Failure can occur at stress level < yieldstrength. Occurs over a lengthy period time. Fatigue is of brittle like behavior even in ductile metals. Process starts with small cracks in surface loodreg to applied tensile stress. Cyclic stresses:

S-N Curve: Series of tests comence by subj spec 2 strescycl at large maximum stress ampl. Nr’s of cycls to failure R counted. Proc is repeat on other spec at decreasing maxstress ampl. Data is plotted on S (stress amplitudes) vs N(number of cycles to failure); Fatigue strength: stress level at which failure will occur for some specified number of cycles; Fatigue/ endurance limit: limiting stress level. Crack prop: Fatiguefail has 3 steps:1.Crack initiation,small crack forms at point of high stress concent.2.Crack prop,crack grows each stress cycle. 3.Final failure occurs rapidly once advancing crack has reached critical size. Fracture surface formed during crack prop char by two types: beachmarks and striations. Both features indicate the position of the crack tip at some point in time. Presence of beach marks or striations on fracture surface confirms cause of failure was fatigue. Can be 1000s of striat in one beachmark Factors that affect fatigue life: 1.Meanstress: incr meanstreslevel leads to decr in fatigue life; Repr on a series of S-N curves. 2. Surface effects: Most cracks on surface lead to fatigue failure; Proper management of factors can improve fatigue life; Max stress component occurs at surface. Design factors; Avoid these structural irregularities = chance of fatigue lowered; Reduce sudden contour change leading to sharp corners; Notches or geometric discontinuity can act as stress raiser and fatigue crack initiator – groves, holes, keyways, and threads; The shaper the discontuity more sever the stress concentration; Surface treatments: Case hardening: both surface hardness and fatigue life are enhanced for steel alloys - Carbon or nitriding process (component is exposed to carbonaceous or nitrogenous atmosphere at elevated temp); Scratches and grooves introduced onto surface by cutting tool; Polishing materials surface will increase fatigue life. Environmental effects: Thermal fatigue: induced at elevated temperatures by fluctuating thermal stresses: Origin of thermal stresses is the restraint to expansion and contraction as temp changes.

Propagation rate increases due to corrosive environment; Prevention: eliminate or reduce, restraint the source Creep: Deformation undr high temps and mater is exposed to mechstres. Creep test: subject exposed to constant load/stress wile maintaining cons temp. Creep curves have three regions: Primary/ transient creep: Cont decr creep rate; Increased creep resistance or strain hardening; Deform becomes harder; Secondary creep: Rate is constant; Longest duration of creep; Constancy of creep rate is explained on the basis of balance between the competing process of strain hardening and recovery (the process where the material becomes softer and retains ability to experience deformation).; Tertiary creep: Accelerated rate of creep and ultimate failure(rupture); Results from: grain boundary separation and formation of internal cracks. For tensile loads, necking; Consstres tests display better underst of creep; Strain is measured and

plotted as a function of elapsed time; Uniaxial creep test more appropriate for brittle materials; Most nb param of creep test is steady state creep rate (eps(s)); minimum creep rate is the slope of the linear segment in the secondary region

deformation can occur in response to applied tensile load; Brittle fracture process: formation of cracks through the cross section of material in direction perpendicular to the applied load.; Crack growth in ceramics: through the grains or along grain boundaries (transgranular and intergranular); Measured fracture strengths of most ceramic materials are substantially lower than predicted by theory from bonding forces; Single phase: stress amplification depends on crack length and tip radius of curvature. Stress strain behavior: Flexural strength: Stress strain behavior ceramics can’t be determined by tensile test because: Ceramics fail after only about 0.1%strain that which necessitates the tensile specimens to be perfectly aligned for the test to avoid bending stresses; Difficult to prep and test the specimen having the required geometry; Difficult to grip brittle materials without fracturing . Transverse bending test is used  Rod specimen is bent until fracture using three or four

Several factors affect the creep: temp, elastic mod, grain size. In general: smaller grains increase grain boundary sliding and therefore creep rates increase; Stainless steels and super alloys are resistant to creep; The higher the temp the higher the elastic mod and the larger the grain size = the better resist to creep. Ch4: Structure of Crystalline Solids Ceram are inorganic and nonmetal maters. Props of them are normally achieved through hightemperature heat treatment process (firing). Ceram structs are composed of at least two elements. Crystal structs are more complex than those for metals. Bonds are purely ionic to totally covalent often combo of these two types. Ionic arrangement and geometry: Two components of the component ions in crystalline structure influence the crystal structure: Magnitude of electrical charge; Relative size of cations and anions. For atomic bonding that is predominantly ionic – thought to be composed of electrically charged ions instead of atoms: Metallic ions = cation = + charged, Non metallic ions = anion = - charged; The entire crystal must be electrically neutral; Ionic radii of cations and anions: Cat < ani=(rc/ra) Ax type crystal struct: A=cat,X=Ani. 3 Types: 1.Rock Salt: Coord number for cat + ani is 6. FCC struct. (NaCl).

point loading technique. , 2nd one for round crosssec. Stress is computed from: specimen thickness, bending moment, and moment of inertia of cross section; Max tensile stress exists at bottom surface directly below point of load; Three point: top surface state of compression and bottom state of tension. Types of ceramics: Glasses: containers, lenses, fiberglass. Non crystalline ceramics containing other oxides. GlassCeramics: Prod of crystalliz is a finegrained polycrystalline material; Dielectric properties; Biocompatibility, May be optically transparent. Overware, tableware. Clay products: Widely used raw material;Dried to remove moisture, then fired at elevated temp. 2 classes: structural clay products: applications in which structural integrity is important. Whitewares: become white after high temperature firing. China, tableware. Refractories: Withstand high temperatures without melting: Remain unreactive and inert when exposed to severe environments. Metal refining, glass manuf. Fire clay refractories: Consists large+fine particles: Fine particles involved in bonding during firing, increase strength of the material. Silica Refractories: Aluminia content kept to a minimum; Resistant to slugs. Abrasives: particles bonded to grinding wheels as coat abrasive and as loose grains by means of glassy ceramics; Surface structure has some porosity for air flow or liquid coolants. Cements: Some of these cement materials act as bonding phase that chemically binds particulate aggregates into a single cohesive structure; Bonds develop at room temperature. Ch17 Frabrication of glasses and g-ceramics Glass properties: Importants for fabrication and processing on visc scale:1.Melting point: corresponds to temp at which viscosity is 10 Ra.s ; glass is fluid enough to be liquid. 2.Working point: temp at which viscosity is 10³ ; glass is easily deformed. 3.Softening point: temp at which viscosity is 4*10⁶ Ra.s ; max temp at which glass piece may be handled without causing dimensional alterations. 4. Annealing point: temp, viscosity = 10¹² Ra.s; at this temp atomic diffusion is rapid and residual stresses may be removed within 15 min. 5. Strain point: temp where viscosity = 3*10¹³ Pa.s; temp below, fracture will occur before plastic deformation. Glass transition temp will be above strain point; Forming occurs between 3 and 2. Glass forming: Homogenous achieved by complete melting and mixing of the raw ingredients. Porosity,proper adjustment of the viscosity of the molten material. 5 types of forming: Blowing: by hand. Drawing: used to form long glass pieces. Process: Molten glass passes from furnace 1, On to a tin bath in furnace 2, Continuous glass ribbon ‘floats’ on tin, gravitational and surface tension forces = faces become perfectly flat and parallel = sheet uniform thickness, sheet then passes into an annealing furnace, Cut into sections. Pressing: used for thick walled pieces. Formed by pressure application in a graphite-coated cast iron mold having the desired shape. Sheet, Fibre forming. Heat treating glasses Annealing: Avoid thermal stresses by cooling at slower rates; Once stresses are introduced remove annealing heat treatment; Glass Tempering: Increase strengthening by introducing compressive residual stresses; Thermal tempering. Characteristics of clay: Strong ceramic may be formed during firing without complete melting; Fusion temp range depends on the composition of clay; When water is added they become very plastic (hydroplasticity) – important in forming operations. Fabrication techniques: Hydroplastic forming: Low yield strengths; Maintains shape during handling and drying; mixed with water. SlipCasting: Cast pieces dry and then begin to pull away from the mold wall; Nature of slip: high specific gravity and very fluid; Mold porosity varied to control the casting rate. Drying and firing: Green body = formed and dried but not fired; Evaporation rate controlled by temperature, humidity and rate of air flow; Factors that influence shrinkage:Body thickness,Water content, Clay particle size. Firing: Cooling fused phase forms a glossy matrix(dense and strong); Final microstructure = vitrified phase, any unreached quarts particles and some porosity; Degree of vitrification...