Fatigue Damage and Cracking

Transcription

1 Fatigue Daage and Cracking Figure 9.9 During high-cycle fatigue the tension cycle produces a tiny plastic zone which is folded forward during copression During low-cycle fatigue the plastic zone is large enough for voids to nucleate and coalesce which advances the crack 1

2 Fatigue Metals often fail at uch lower stress at cyclic loading copared to static loading. Crack nucleates at region of stress concentration and propagates due to cyclic loading. Failure occurs when cross sectional area of the etal too sall to withstand applied Fracture started here load. Fatigue fractured surface of keyed shaft Final rupture Vibration and Resonance Loading and unloading a part is never copletely reversible energy is always lost this fact is pronounced when loading is in vibration Daping coefficient η Measures the degree to which a aterial dissipates vibrational energy Loss coefficient η Fraction of the stored energy not returned on unloading 2

3 Types of Cyclic Loading Figure 9.1 (a) Low aplitude acoustic vibration (b) High-cycle fatigue: cycling below or slightly above the yield strength ( y ) (c) Low-cycle fatigue: cycling above the yield strength ( y ) but below the ultiate tensile strength ( ts ) High-cycle fatigue loading is ost significant in engineering ters Fatigue Fatigue failures occur due to cyclic loading at stresses below a aterial s yield strength Depends on the aplitude of the stress and the nuber of cycles Figure 9.2 Loading cycles can be in the illions for an aircraft; fatigue testing ust eploy illions of fatigue cycles to provide eaningful design data 3

4 S-N Curves Fatigue characteristics are easured and plotted on S-N curve S (MPa) S S Stress aplitude Mean stress Figure 9.3 R = -1: = 0 R = 0: in = 0 R <0: in is copressive Endurance liit σ e : stress aplitude below which fracture does not occur at all or only after a very large nuber of cycles (>10 7 ) Predicting Fatigue Life Coffin s law for low-cycle fatigue Basquin s law for high-cycle fatigue Figure 9.4 These laws describe the fatigue failure of uncracked coponents cycled at a constant aplitude about a ean stress of zero Stress range, not stress aplitude 4

5 Mean Stress and Variable Aplitude Goodan s rule The corrected stress range can be plugged into Basquin s law Miner s rule of cuulative daage Figure 9.5 When the cyclic stress aplitude changes, the life is calculated using Miner s rule Exaple: We applied a cyclic loading = 20 Mpa for 20,000 cycles, and then changed the stress range to 40 MPa. How any cycles can we still apply before the fatigue failure happens? S 2 20 MPa 2/3 of total fatigue tolerance has been consued 1 30,000 N 5

6 Fatigue Loading of Cracked Coponents Fatigue crack growth is studied by cyclically loading speciens containing a sharp crack Cyclic stress intensity range: driven force of fatigue crack growth Y Stress range, not stress aplitude Figure 9.6 The range ΔK increases with tie under constant cyclic stress because the crack grows in length Crack Growth During Cyclic Loading Initial crack tip a 0 a f Fatigue Fracture End of fatigue; onset of fracture 6

7 Crack Growth During Cyclic Loading Figure 9.7 dc Log Log ( A K ) dn. Log ( K ) Log( A) Paris law The figure shows crack growth per cycle with respect to the stress intensity factor Safe design requires calculating the nuber of loading cycles possible before the crack grows to a dangerous length Straight line with slope Paris Law: But Therefore Therefore dc dn K Y K dc dn A K Y A Y c 2 2 c 2 2 ( c ) Integrating fro initial crack size a 0 to final crack size a f at nuber of fatigue cycles N f c f N f dc AY 2 c 2 dn ( ) 1 ( ) 1 c0 0 c 2 2 f c0 Integrating and solving for N f N f 2 AY ( 1) 2 (Assue Y is independent of crack length) The nuber of loading cycles to drive the crack to grow fro c 0 to c f 7

8 Factors Affecting Fatigue Strength Stress concentration: Fatigue strength is reduced by stress concentration. Surface roughness: Soother surface increases the fatigue strength. Surface condition: Surface treatents like carburizing and nitriding increases fatigue life. Environent: Cheically reactive environent, which ight result in corrosion, decreases fatigue life. Endurance Liit Strength Chart Endurance liit is the ost iportant property characterizing fatigue strength Metals/Polyers Glasses/Ceraics Figure 9.8 8

9 Fatigue Ratio Figure 9.10 Correlation between endurance liit and yield strength not as strong as with tensile strength Cracks only propagate during the tensile part of a stress cycle copressive stress forces the crack faces together, claping it shut Copressive forces on the surface a aterial act resist crack growth one ethod of producing this is shot peening Figure

10 Creep Creep is progressive deforation under constant stress. Iportant in high teperature applications. Priary creep: creep rate decreases with tie due to strain hardening. Secondary creep: Creep rate is constant due to siultaneous strain hardening and recovery process. Tertiary creep: Creep rate Most iportant stage increases with tie leading to necking and fracture. Figure 6.30 Steady-State Creep Rate The constants ε 0, σ o, n, and Q c are experientally found and vary fro aterial to aterial Figure

11 Creep Mechanis: Diffusion Diffusion is the spontaneous interixing of atos over tie the rate of diffusion is expressed by Fick s law: D: diffusion constant dc/dx: concentration gradient In a crystalline solid, two things are needed for an ato to switch sites: 1) Enough theral energy 2) An adjacent vacancy Figure 13.9 Interdiffusion Diffusion of cheically different atos Figure Q d activation energy per ole D o constant based on oscillation of atos and atoic size 11

12 Figure The ean distance that one type of ato travels fro diffusion is given by Low Stress: Diffusional Flow Diffusion can change the grain shape of polycrystalline aterials Grain boundaries act as sources and sinks for vacancies If a vacancy joins a boundary, an ato ust leave it if a vacancy leaves a boundary, and ato ust join it Figure

13 High Stress: Dislocation Clib Diffusion can allow a dislocation to ove beyond particles in its path The half-plane of atos is eaten away by diffusion, allowing the dislocation to clib over the ipeding particle This is the basis of power-law-creep which is defined by: Figure Deforation Mechaniss Materials can defor by dislocation plasticity, or at high teperatures, by diffusional flow or power-law creep Deforation echanis aps show the range of stress and teperature in which we expect to find each sort of deforation and the strain rate that any cobination of the produces < T /2: No creep > T /2: Creep Figure T is easured in Kelvin ( o K) 13

14 Creep Fracture Diffusion can cause creep as well as fracture due to creep by creating voids that nucleate on grain boundaries Figure Materials to Resist Creep < T /2: No creep > T /2: Creep Figure T is easured in Kelvin ( o K) 14

15 Creep Test Specien is loaded in tension or copression, usually at a constant load, inside a furnace that is aintained at a constant teperature Figure 13.3 Creep Test Creep test deterines the effect of teperature and stress on creep rate. Metals are tested at constant stress at different teperature & constant teperature with different stress. High teperature or stress Figure 6.33 Figure 6.32 Low teperature or stress Creep strength: Stress to produce Miniu creep rate of 10-5 %/h At a given teperature. 15

16 Creep Test (Cont..) Creep rupture test is the sae as creep test but aied at failing the speciens. Plotted as log stress versus log rupture tie. Tie for stress rupture, t r, decreases with increased stress and teperature. Figure 6.35 Figure 6.34 Larsen Miller Paraeter Larsen Miller paraeter is used to represent creep-stress rupture data. P(Larsen-Miller) = T[log t r + C] P = Larson Miller paraeter T = teperature(k), t r = stress-rupture tie h C = Constant (order of 20) Usually, P(Larsen-Miller) = [T( 0 C) + 273](20+log 10 t r ) or P(Larsen-Miller) = [T( 0 F) + 460](20+log 10 t r ) Note: P is a function of stress At a given stress level, the log tie to stress rupture plus constant ultiplied by teperature reains constant for a given aterial. 16

17 Larsen Miller Paraeter If two variables of tie to rupture, teperature and stress are known, 3 rd paraeter that fits L.M. paraeter can be deterined. Exaple: For alloy CM, at 207 MPa, LM paraeter is 27.8 x 10 3 K Then if teperature is known, tie to rupture can be found. Figure 6.36 L.M. Diagra of several alloys Figure 6.37 Exaple: Calculate tie to cause failure in gaa Titaniu aluinide at 40 KSI and F Fro figure above, P = 38, = ( ) (log 10 t r + 20) t r =776 h 17

18 High-Teperature Pipework Typical operating conditions of 650 C at a pressure of 15 MPa Figure Design For a known design life, use the chart to find the stress below which fracture will not occur then plug the stress value into the equation to find the iniu pipe thickness Figure Turbine Blades Figure At typical stress and teperature levels, pure nickel would defor by power-law creep at an unacceptable level the ipact of strengthening echaniss on MAR-M200 nickel alloy reduces this rate by a factor of 10 6 diffusional creep can then be slowed by increasing the grain size Figure

19 Theral Barrier Coatings Design against creep can include the use of theral barrier coatings Figure For the turbine blade shown in Figure 13.23, a ceraic coating is applied to the etal surface allowing for an increase in gas teperature with no increase in that of the blade itself Airfraes Aircraft flying above speeds of Mach 1 are subject to creep due to high teperatures and theral expansion caused by the ΔT of the jet and the atosphere Figure Material selection for this application has several potential liiting factors a cobination of tensile strength and high teperature perforance is required, but weight often forces a aterial with lower than desired values to achieve optial speed Figure