Presentation on theme: "Week 5 Fracture, Toughness, Fatigue, and Creep"— Presentation transcript:
1Week 5 Fracture, Toughness, Fatigue, and Creep Materials Science
2Mechanical Failure ISSUES TO ADDRESS... • How do flaws in a material initiate failure?• How is fracture resistance quantified; how do differentmaterial classes compare?• How do we estimate the stress to fracture?• How do loading rate, loading history, and temperatureaffect the failure stress?Mechanical failure is the change in the structure/material that refrains the specimen to perform its intended operationFlaws include micro-cracks, voids, stress concentrations, etcShip-cyclic loadingfrom waves.Computer chip-cyclicthermal loading.Hip implant-cyclicloading from walking.
3What is a Fracture?Fracture is the separation of a body into two or more pieces in response to an imposed stress that is static and at temperatures that are low relative to the melting temperature of the material.The applied stress may be tensile, compressive, shear, or torsionalAny fracture process involves two steps—crack formation and propagation—in response to an imposed stress.(i.e., constant or slowly changing with time).the present discussion will be confined to fractures that result from uniaxial tensile loads
4Fracture mechanisms Ductile fracture Brittle fracture Occurs with plastic deformationBrittle fractureLittle or no plastic deformationCatastrophic0. Classification is based on the ability of a material to experience plastic deformation.1. Ductile materials typically exhibit substantial plastic deformation with high energy absorption before fracture
5Ductile vs Brittle Failure • Classification:VeryDuctileModeratelyBrittleFracturebehavior:LargeModerate%AR or %ELSmall• Ductilefracture is usuallydesirable!Ductile:warning before fractureBrittle: No warning
6Example: Failure of a Pipe • Ductile failure:--one/two piece(s)--large deformation• Brittle failure:--many pieces--small deformation
7Moderately Ductile Failure • Evolution to failure:voidnucleationvoid growthand linkageshearingat surfaceneckingsfracture• Resultingfracturesurfaces(steel)50 mmparticlesserve as voidnucleationsites.100 mm
8Ductile vs. Brittle Failure 2. Brittle fracture takes place without any appreciable deformation, and by rapid crack propagation. The direction of crack motion is very nearly perpendicular to the direction of the applied tensile stress and yields a relatively flat fracture surface, as indicated in Figurecup-and-cone fracturebrittle fracture
9Transgranular vs Intergranular Fracture 1. For most brittle crystalline materials, crack propagation corresponds to the successive and repeated breaking of atomic bonds along specific crystallographic planes (Figure a); such a process is termed cleavage. This type of fracture is said to be transgranular, because the fracture cracks pass through the grains.2. In some alloys, crack propagation is along grain boundaries this fracture is termed intergranular3. Scanning electron fractograph showing an intergranular fracture surface. 50 magnificationIntergranular FractureTransgranular Fracture
10Brittle Fracture Surfaces • Intergranular(between grains)• Transgranular(within grains)304 S. Steel (metal)316 S. Steel (metal)160 mm4 mmPolypropylene(polymer)Al Oxide(ceramic)3 mm1 mm
11Ideal vs Real Materials • Stress-strain behavior (Room T):TS << TSengineeringmaterialsperfectseE/10E/1000.1perfect mat’l-no flawscarefully produced glass fibertypical ceramictypical strengthened metaltypical polymer• DaVinci (500 yrs ago!) observed...-- the longer the wire, thesmaller the load for failure.• Reasons:-- flaws cause premature failure.-- Larger samples contain more flaws!Steel Young’s Modulus Elasticity is 200,000MPa and UTS is 800MPaDa Vinci -> Italian scientist, inventer
12Flaws are Stress Concentrators! Results from crack propagationGriffith Crackwhere t = radius of curvatureso = applied stresssm = stress at crack tipKt = Stress concentration factortThe measured fracture strengths for most brittle materials are significantly lower than those predicted by theoretical calculations based on atomic bonding energies. This discrepancy is explained by the presence of very small, microscopic flaws or cracks that always exist under normal conditions at the surface and within the interior of a body of material. These flaws are a detriment to the fracture strength because an applied stress may be amplified or concentrated at the tip, the magnitude of this amplification depending on crack orientation and geometry. This phenomenon is demonstrated in Figure.Due to their ability to amplify an applied stress in their locale, these flaws are sometimes called stress raisers.
14Engineering Fracture Design • Avoid sharp corners!sr/hsharper fillet radiusincreasingw/h0.51.01.52.02.5Stress Conc. Factor, Ktsmaxo=r ,filletradiuswhosmaxExplain effect of increasing W/h on Kt
15Crack Propagation Cracks propagate due to sharpness of crack tip A plastic material deforms at the tip, “blunting” the crack.deformed regionbrittleEnergy balance on the crackElastic strain energy-energy stored in material as it is elastically deformedthis energy is released when the crack propagatescreation of new surfaces requires energyplasticBlunt -> make less intenseElastic strain energy is also called as Resilience energy
16When Does a Crack Propagate? Crack propagates if above critical stresswhereE = modulus of elasticitys = specific surface energy (J/m2)a = one half length of internal crackFor ductile => replace gs by gs + gpwhere gp is plastic deformation energyi.e., sm > scAll brittle materials contain a population of small cracks and flaws that have a variety of sizes, geometries, and orientations.When the magnitude of a tensile stress at the tip of one of these flaws exceeds the value of this critical stress, a crack forms and then propagates, which results in fracture
17Fracture Toughness: Design Against Crack Growth • Crack growth condition:K ≥ Kc =• Largest, most stressed cracks grow first!--Result 1: Max. flaw sizedictates design stress.samaxnofracture--Result 2: Design stressdictates max. flaw size.amaxsnofractureKc is the fracture toughnessY is a dimensionless parameter or function that depends on both crack and specimen sizes and geometries, as well as the manner of load application. Relative to this Y parameter, for planar specimens containing cracks that are much shorter than the specimen width, Y has a value of approximately unity. For example, for a plate of infinite width having a through-thickness crack Y=0; whereas for a plate of semi-infinite width containing an edge crack of length Y=1.1
18Fracture ToughnessFor relatively thin specimens, the value of Kc will depend on specimen thickness. However, when specimen thickness is much greater than the crack dimensions, Kc becomes independent of thickness.The Kc value for this thick-specimen situation is known as the plane strain fracture toughness KIC
19Fracture Toughness ) (MPa · m K 0.5 Ic Kc = Graphite/ Ceramics/ SemicondMetals/AlloysComposites/fibersPolymers5KIc(MPa · m0.5)1Mg alloysAl alloysTi alloysSteelsSi crystalGlass-sodaConcreteSi carbidePC60.724310<100><111>DiamondPVCPPPolyesterPSPETC-C(|| fibers)0.67100Al oxideSi nitrideC/C( fibers)Al/Al oxide(sf)Al oxid/SiC(w)Al oxid/ZrO(p)Si nitr/SiC(w)Glass/SiC(w)YO/ZrOKc =
20Design Example: Aircraft Wing • Material has Kc = 26 MPa-m0.5• Two designs to consider...Design A--largest flaw is 9 mm--failure stress = 112 MPaDesign B--use same material--largest flaw is 4 mm--failure stress = ?• Use...• Key point: Y and Kc are the same in both designs.9 mm112 MPa4 mm--Result:Pay off -> Yield a profit or resultAnswer:• Reducing flaw size pays off!
21Loading Rate s sy e -- increases sy and TS gives less time for • Increased loading rate...-- increases sy and TS-- decreases %EL• Why? An increased rategives less time fordislocations to move pastobstacles and form into a crack.sesyTSlargersmallerThat’s why a piece ruptured by impact loading doesn’t show much plastic deformation before getting ruptured
22Impact Testing -- severe testing case -- makes material more brittle • Impact loading:-- severe testing case-- makes material more brittle-- decreases toughness(Charpy)final heightinitial height
23Impact TestsA material may have a high tensile strength and yet be unsuitable for shock loading conditionsImpact testing is testing an object's ability to resist high-rate loading.An impact test is a test for determining the energy absorbed in fracturing a test piece at high velocityTypes of Impact Tests -> Izod test and Charpy Impact testIn these tests a load swings from a given height to strike the specimen, and the energy dissipated in the fracture is measured3. Impact energy is a measure of the work done to fracture a test specimen4. Izod -> (notched or unnotched)5. The test is particularly useful in showing the decrease in ductility and impact strength of materials of bcc structure at moderately low temperatures
24A. Izod TestThe Izod test is most commonly used to evaluate the relative toughness or impact toughness of materialsIzod test sample usually have a V-notch cut into themMetallic samples tend to be square in cross section, while polymeric test specimens are often rectangularIt is used more as a comparative test rather than a definitive test… although specimens with no notch as also used on occasion
25Izod Test - MethodIt involves striking a suitable test piece with a striker, mounted at the end of a pendulumThe test piece is clamped vertically with the notch facing the striker.The striker swings downwards impacting the test piece at the bottom of its swing.
26Determination of Izod Impact Energy At the point of impact, the striker has a known amount of kinetic energy.The impact energy is calculated based on the height to which the striker would have risen, if no test specimen was in place, and this compared to the height to which the striker actually rises.Tough materials absorb a lot of energy, whilst brittle materials tend to absorb very little energy prior to fracture
27B. Charpy TestCharpy test specimens normally measure 55 x 10 x 10mm and have a notch machined across one of the larger facesThe Charpy test involves striking a suitable test piece with a striker, mounted at the end of a pendulum.The test piece is fixed in place at both ends and the striker impacts the test piece immediately behind a machined notch.… A V-shaped notch, 2mm deep, with 45° angle and 0.25mm radius along the baseThe impact energy for Charpy test is calculated in the same manner as for Izod test
28Factors Affecting Impact Energy For a given material the impact energy will be seen to decrease if the yield strength is increasedThe notch serves as a stress concentration zone and some materials are more sensitive towards notches than othersMost of the impact energy is absorbed by means of plastic deformation during the yielding. Therefore, factors that affect the yield behavior (and hence ductility) of the material such as temperature and strain rate will affect the impact energyif the material undergoes some process that makes it more brittle and less able to undergo plastic deformation. Such processes may include cold working or precipitation hardening.The notch depth and tip radius are therefore very importantThis type of behaviour is more prominent in materials with a body centred cubic structure, where lowering the temperature reduces ductility more markedly than face centred cubic materials
29Effect of Temperature on Toughness • Increasing temperature...--increases %EL and Kc• Ductile-to-Brittle Transition Temperature (DBTT)...FCC metals (e.g., Cu, Ni)BCC metals (e.g., iron at T < 914°C)polymersImpact EnergyBrittleMore DuctileKc -> fracture toughnessA material experiences a ductile-to-brittle transition with decreasing temperature.At higher temperatures the CVN (Charpy V-Notch) energy is relatively large, in correlation with a ductile mode of fracture. As the temperature is lowered, the impact energy drops suddenly over a relatively narrow temperature range, below which the energy has a constant but small value; that is, the mode of fracture is brittleHigh strength materials (sy> E/150)TemperatureDuctile-to-brittletransition temperature
30Fatigue TestFatigue is concerned with the premature fracture of metals under repeatedly applied low stressesA specified mean load (which may be zero) and an alternating load are applied to a specimen and the number of cycles required to produce failure (fatigue life) is recorded.Generally, the test is repeated with identical specimens and various fluctuating loads.Data from fatigue testing often are presented in an S-N diagram which is a plot of the number of cycles required to cause failure in a specimen against the amplitude of the cyclical stress developed3. Loads may be applied axially, in torsion, or in flexure. Depending on amplitude of the mean and cyclic load, net stress in the specimen may be in one direction through the loading cycle, or may reverse direction4. The cyclical stress represented may be Stress Amplitude (One-half the range of fluctuating stress developed in a specimen in a fatigue test.), maximum stress or minimum stress. Each curve in the diagram represents a constant mean stress. Most fatigue tests are conducted in flexure, rotating beam, or vibratory type machines.
31Fatigue Testing Equipment 2. Consider a rotating beam of circular cross-section and carrying a load W
33Fatigue Test - S-N Curve This S–N diagram indicates that some metals can withstand indefinitely the application of a large number of stress reversals, provided the applied stress is below a limiting stress known as the endurance limit0. The standard method of studying fatigue is to prepare a large number of specimens free from flaws, and to subject them to tests using a different range of stress, S, on each group of specimens. The number of stress cycles, N, endured by each specimen at a given stress level is recorded and plotted, as shown in FigureEndurance limit -> it is the maximum stress to which a metal can be subjected for indefinitely long periods without damage. Endurance limit for Carburized iron plot (in figure above) is 200MNm-2 and for Decarburized iron is 110MNm-2
34Fatigue Mechanism --crack grew even though Kmax < Kc • Crack grows incrementallytyp. 1 to 6increase in crack length per loading cyclecrack origin• Failed rotating shaft--crack grew even thoughKmax < Kc--crack grows faster as• Ds increases• crack gets longer• loading freq. increases.ΔK is the change in the stress intensity factor
35Improving Fatigue Life 1. Impose a compressivesurface stress(to suppress surfacecracks from growing)N = Cycles to failuremoderate tensilesmLarger tensileS = stress amplitudenear zero or compressiveIncreasing m--Method 1: shot peeningputsurfaceintocompressionshot--Method 2: carburizingC-rich gasResidual compressive stresses are commonly introduced into ductile metals mechanically by localized plastic deformation within the outer surface region. Commercially, this is often accomplished by a process termed shot peening. Small, hard particles (shot) having diameters within the range of 0.1 to 1.0 mm are projected at high velocities onto the surface to be treated. The resulting deformation induces compressive stresses to a depth of between one-quarter and one-half of the shot diameter.A carbon- or nitrogen-rich outer surface layer (or “case”) is introduced by atomic diffusion from the gaseous phase. The case is normally on the order of 1 mm deep and is harder than the inner core of material. The improvement of fatigue properties results from increased hardness within the case, as well as the desired residual compressive stresses the formation of which attends the carburizing or nitriding process. This process increases bonding strength among molecules at surface, thus, giving rise to compressive stress2. Remove stressconcentrators.badbetter
364. Creep TestCreep is defined as plastic (or irrevresible) flow under constant stressCreep is high temperature progressive deformation at constant stressA creep test involves a tensile specimen under a constant load maintained at a constant temperature.At relatively high temperatures creep appears to occur at all stress levels, but the creep rate increases with increasing stress at a given temperature.2. Another definition of term “creep”3. … Measurements of strain are then recorded over a period of time
37Creep TestCreep occurs in three stages: Primary, or Stage I; Secondary, or Stage II, and Tertiary, or Stage IIIFigure (top) shows the characteristics of a typical creep curveBottom graph -> On y-axis replace “creep” with “strain”
38Creep TestStage I occurs at the beginning of the tests, and creep is mostly transient, not at a steady rate.In Stage II, the rate of creep becomes roughly steadyIn Stage III, the creep rate begins to accelerate as the cross sectional area of the specimen decreases due to necking decreases the effective area of the specimen… or Primary creep …Resistance to creep increases until Stage II is reached. … or Secondary creep. …. This stage is often referred to as steady state creep.… or tertiary creep … If stage III is allowed to proceed, fracture will occur.The creep test is usually employed to determine the minimum creep rate in Stage II. Engineers need to account for this expected deformation when designing systems.
39Creep • Occurs at elevated temperature, T > 0.4 Tm tertiary primary secondaryelastic
40Secondary Creep s stress exponent (material parameter) • Strain rate is constant at a given T, sstress exponent (material parameter)activation energy for creep(material parameter)strain ratematerial const.applied stress• Strain rateincreasesfor higher T, s1024-2-11Steady state creep rate (%/1000hr)esStress (MPa)427°C538°C649R is the Boltzman Constant having units J/mol.K
41Creep Failure S-590 Iron, T = 800°C, s = 20 ksi g.b. cavities applied along grain boundaries.time to failure (rupture)function ofapplied stresstemperatureappliedstressg.b. cavities• Time to rupture, tr• Estimate rupture timeS-590 Iron, T = 800°C, s = 20 ksiL(103K-log hr)Stress, ksi1001011220242816data forS-590 Iron1073KAns: tr = 233 hr24x103 K-log hrLarson-Miller Parameter22.37 = 20 + log trtr = antilog (2.37) = 233
42Numerical ProblemsProblems 8.1 – 8.10; 8.14 – 8.23; and 8.27