Presentation on theme: "Chapter Outline: Failure"— Presentation transcript:
1Chapter Outline: Failure How do Materials Break?Ductile vs. brittle fracturePrinciples of fracture mechanicsStress concentrationImpact fracture testingFatigue (cyclic stresses)Cyclic stresses, the S—N curveCrack initiation and propagationFactors that affect fatigue behaviorCreep (time dependent deformation)Stress and temperature effectsAlloys for high-temperature use
2Brittle vs. Ductile Fracture Ductile materials - extensive plastic deformation and energy absorption (“toughness”) before fractureBrittle materials - little plastic deformation and low energy absorption before fracture
3Brittle vs. Ductile Fracture A B CVery ductile: soft metals (e.g. Pb, Au) at room T, polymers, glasses at high TModerately ductile fracturetypical for metalsBrittle fracture: ceramics, cold metals,
4Ductile fracture is preferred in most applications Steps : crack formationcrack propagationDuctile vs. brittle fractureDuctile fracture is preferred in most applicationsDuctile - most metals (not too cold):Extensive plastic deformation before crackCrack resists extension unless applied stress is increasedBrittle fracture - ceramics, ice, cold metals:Little plastic deformationCrack propagates rapidly without increase in applied stress
5Ductile Fracture (Dislocation Mediated) Crack grows 90o to applied stress45O - maximum shear stress(a) Necking, (b) Cavity Formation,(c) Cavities coalesce form crack(d) Crack propagation, (e) Fracture
6(Cup-and-cone fracture in Al) Ductile Fracture(Cup-and-cone fracture in Al)Scanning Electron Microscopy. Spherical “dimples” micro-cavities that initiate crack formation.
7Brittle Fracture (Low Dislocation Mobility) Crack propagation is fastPropagates nearly perpendicular to direction of applied stressOften propagates by cleavage - breaking of atomic bonds along specific crystallographic planesNo appreciable plastic deformationBrittle fracture in a mild steel
8Brittle FractureTransgranular fracture: Cracks pass through grains. Fracture surface: faceted texture because of different orientation of cleavage planes in grains.Intergranular fracture: Crack propagation is along grain boundaries (grain boundaries are weakened/ embrittled by impurity segregation etc.)AB
9Stress Concentration Fracture strength of a brittle solid: related to cohesive forces between atoms.Theoretical strength: ~E/10Experimental strength ~ E/100 - E/10,000Difference due to:Stress concentration at microscopic flawsStress amplified at tips of micro-cracks etc., called stress raisersFigure byN. Bernstein &D. Hess, NRL
10Stress Concentration Crack perpendicular to applied stress: maximum stress near crack tip 0 = applied stress; a = half-length of crack;t = radius of curvature of crack tip.Stress concentration factor
11Impact Fracture Testing Two standard tests: Charpy and Izod. Measure the impact energy (energy required to fracture a test piece under an impact load), also called the notch toughness.IzodCharpyhh’Energy ~ h - h’
12Ductile-to-Brittle Transition As temperature decreases a ductile material can become brittle
13Ductile-to-brittle transition Low temperatures can severely embrittle steels. The Liberty ships, produced in great numbers during the WWII were the first all-welded ships. A significant number of ships failed by catastrophic fracture. Fatigue cracks nucleated at the corners of square hatches and propagated rapidly by brittle fracture.
15Failure under fluctuating stress FatigueFailure under fluctuating stressUnder fluctuating / cyclic stresses, failure can occur at lower loads than under a static load.90% of all failures of metallic structures (bridges, aircraft, machine components, etc.)Fatigue failure is brittle-like –even in normally ductile materials. Thus sudden and catastrophic!
16Fatigue: Cyclic Stresses Characterized by maximum, minimum and meanRange of stress, stress amplitude, and stress ratioMean stress m = (max + min) / 2Range of stress r = (max - min)Stress amplitude a = r/2 = (max - min) / 2Stress ratio R = min / maxConvention: tensile stresses positivecompressive stresses negative
17Fatigue: S—N curves (I) Rotating-bending test S-N curvesS (stress) vs. N (number of cycles to failure)Low cycle fatigue: small # of cycleshigh loads, plastic and elastic deformationHigh cycle fatigue: large # of cycleslow loads, elastic deformation (N > 105)
18Fatigue: S—N curves (II) Fatigue limit (some Fe and Ti alloys)S—N curve becomes horizontal at large NStress amplitude below which the material never fails, no matter how large the number of cycles is
19Fatigue: S—N curves (III) Most alloys: S decreases with N.Fatigue strength: Stress at which fracture occurs after specified number of cycles (e.g. 107)Fatigue life: Number of cycles to fail at specified stress level
20Fatigue: Crack initiation+ propagation (I) Three stages:crack initiation in the areas of stress concentration (near stress raisers)incremental crack propagationrapid crack propagation after crack reaches critical sizeThe total number of cycles to failure is the sum of cycles at the first and the second stages:Nf = Ni + NpNf : Number of cycles to failureNi : Number of cycles for crack initiationNp : Number of cycles for crack propagationHigh cycle fatigue (low loads): Ni is relatively high. With increasing stress level, Ni decreases and Np dominates
21Fatigue: Crack initiation and propagation (II) Crack initiation: Quality of surface and sites of stress concentration(microcracks, scratches, indents, interior corners, dislocation slip steps, etc.).Crack propagationI: Slow propagation along crystal planes with high resolved shear stress. Involves a few grains.Flat fracture surfaceII: Fast propagation perpendicular to applied stress.Crack grows by repetitive blunting and sharpening process at crack tip. Rough fracture surface.Crack eventually reaches critical dimension and propagates very rapidly
22Factors that affect fatigue life Magnitude of stressQuality of the surfaceSolutions:Polish surfaceIntroduce compressive stresses (compensate for applied tensile stresses) into surface layer.Shot Peening -- fire small shot into surfaceHigh-tech - ion implantation, laser peening.Case Hardening: Steel - create C- or N- rich outer layer by atomic diffusion from surfaceHarder outer layer introduces compressive stressesOptimize geometryAvoid internal corners, notches etc.
23Factors affecting fatigue life Environmental effects Thermal Fatigue. Thermal cycling causes expansion and contraction, hence thermal stress.Solutions:change design!use materials with low thermal expansion coefficientsCorrosion fatigue. Chemical reactions induce pits which act as stress raisers. Corrosion also enhances crack propagation.decrease corrosiveness of mediumadd protective surface coatingadd residual compressive stresses
24Creep Time-dependent deformation due to constant load at high temperature(> 0.4 Tm)Examples: turbine blades, steam generators.Creep test:FurnaceCreep testing
25Stages of creep Instantaneous deformation, mainly elastic. Primary/transient creep. Slope of strain vs. time decreases with time: work-hardeningSecondary/steady-state creep. Rate of straining constant: work-hardening and recovery.Tertiary. Rapidly accelerating strain rate up to failure: formation of internal cracks, voids, grain boundary separation, necking, etc.
26Parameters of creep behavior Secondary/steady-state creep:Longest durationLong-life applicationsTime to rupture ( rupture lifetime, tr):Important for short-life creep/ttr
27Creep: stress and temperature effects With increasing stress or temperature:The instantaneous strain increasesThe steady-state creep rate increasesThe time to rupture decreases
28Creep: stress and temperature effects Stress/temperature dependence of the steady-state creep rate can be described byQc = activation energy for creepK2 and n are material constants
29Grain boundary diffusion Dislocation glide and climb Mechanisms of CreepDifferent mechanisms act in different materials and under different loading and temperature conditions:Stress-assisted vacancy diffusionGrain boundary diffusionGrain boundary slidingDislocation motionDifferent mechanisms different n, Qc.Grain boundary diffusion Dislocation glide and climb
30Alloys for High-Temperatures (turbines in jet engines, hypersonic airplanes, nuclear reactors, etc.)Creep minimized in materials withHigh melting temperatureHigh elastic modulusLarge grain sizes(inhibits grain boundary sliding)Following materials (Chap.12) are especially resilient to creep:Stainless steelsRefractory metals (containing elements of high melting point, like Nb, Mo, W, Ta)“Superalloys” (Co, Ni based: solid solution hardening and secondary phases)
31Summary Make sure you understand language and concepts: Brittle fractureCharpy testCorrosion fatigueCreepDuctile fractureDuctile-to-brittle transitionFatigueFatigue lifeFatigue limitFatigue strengthImpact energyIntergranular fractureIzod testStress raiserThermal fatigueTransgranular fracture