CHAPTER 7: MECHANICAL FAILURE

Transcription

1 CHAPTER 7: MECHANICAL FAILURE ISSUES TO ADDRESS... Failure mechanism? How is fracture resistance quantified; how do different material classes compare? How do we estimate the stress to fracture? How do loading rate, loading history, and temperature affect the failure stress? Ship-cyclic loading from waves. Adapted from Fig. 8.0, Callister 6e. (Fig. 8.0 is by Neil Boenzi, The New York Times.) Computer chip-cyclic thermal loading. Adapted from Fig W(b), Callister 6e. (Fig W(b) is courtesy of National Semiconductor Corporation.) Department of Materials Engineering at Isfahan University of Technology Hip implant-cyclic loading from walking. Adapted from Fig (b), Callister 6e. 1

2 DUCTILE VS BRITTLE FAILURE Fracture: Separation of a body into two ore more pieces in response to an imposed stress. Classification: Fracture behavior: Very Ductile Moderately Ductile Brittle Ductile fracture is desirable! %AR or %EL : Large Ductile: warning before fracture Moderate Department of Materials Engineering at Isfahan University of Technology Small Brittle: No warning 2

3 EX: FAILURE OF A PIPE Ductile failure: --one piece --large deformation Brittle failure: --many pieces --small deformation Figures from V.J. Colangelo and F.A. Heiser, Analysis of Metallurgical Failures (2nd ed.), Fig. 4.1(a) and (b), p. 66 John Wiley and Sons, Inc., Used with permission. Department of Materials Engineering at Isfahan University of Technology 3

4 MODERATELY DUCTILE FAILURE Evolution to failure: necking σ void nucleation void growth and linkage shearing at surface fracture Resulting fracture surfaces (steel) μm 100 μm particles From V.J. Colangelo and F.A. Heiser, Fracture surface of tire cord wire serve as void Analysis of Metallurgical Failures (2nd loaded in tension. Courtesy of F. ed.), Fig , p. 294, John Wiley and Roehrig, CC Technologies, Dublin, nucleation Sons, Inc., (Orig. source: P. OH. Used with permission. sites. Thornton, J. Mater. Sci., Vol. 6, 1971, pp. Department of Materials ) Engineering at Isfahan University of Technology 4

5 BRITTLE FRACTURE SURFACES Brittle fracture is due to rapid crack propagation without any major deformation. Fracture surface Characteristics: 1. V-shaped marking in the centre of the cross section (crack initiation) 2. Contain lines that radiate from the origin of the crack Department of Materials Engineering at Isfahan University of Technology 5

6 BRITTLE FRACTURE SURFACES Cleavage: Crack propagation corresponds to breaking of atomic bonds along specified crystallographic planes 1. Transgranular (within grains) 160μm Department of Materials Engineering at Isfahan University of Technology 5

7 BRITTLE FRACTURE SURFACES 2. Intergranular (between grains) 4 mm Department of Materials Engineering at Isfahan University of Technology 5

8 IDEAL VS REAL MATERIALS Stress-strain behavior (Room T): E/10 E/100 σ perfect mat l-no flaws carefully produced glass fiber typical ceramic 0.1 typical strengthened metal typical polymer DaVinci (500 yrs ago!) observed... --the longer the wire, the smaller the load to fail it. Reasons: --Defects cause premature failure. --Larger samples are more defected! Department of Materials Engineering at Isfahan University of Technology 6 ε TS << TS engineering materials perfect materials

9 DEFECTS ARE STRESS CONCENTRATORS! Elliptical hole in a plate: Stress distrib. in front of a hole: Department of Materials Engineering at Isfahan University of Technology 7

10 DEFECTS ARE STRESS CONCENTRATORS! Elliptical hole in a plate: σ o σ Stress distrib. in front of a hole: σ max σ a o ρ t 2a ρ t Stress conc. factor: K t = σ max /σ o Large K t promotes failure: NOT SO BAD Kt=3 BAD! Kt>>3 Department of Materials Engineering at Isfahan University of Technology 7

11 ENGINEERING FRACTURE DESIGN Avoid sharp corners! w σ max σ o r, fillet radius h Adapted from Fig. 8.2W(c), Callister 6e. (Fig. 8.2W(c) is from G.H. Neugebauer, Prod. Eng. (NY), Vol. 14, pp ) Department of Materials Engineering at Isfahan University of Technology 8

12 WHEN DOES A CRACK PROPAGATE? ρ t at a crack tip is very small! σ Result: crack tip stress is very large. σ tip σ tip = K 2 π x Crack propagates when: the tip stress is large enough to make: K K c increasing K distance, x, from crack tip Department of Materials Engineering at Isfahan University of Technology 9

13 GEOMETRY, LOAD, & MATERIAL Condition for crack propagation: K K c Stress Intensity Factor: --Depends on load & geometry. Values of K for some standard loads & geometries: σ Fracture Toughness: --Depends on the material, temperature, environment, & rate of loading. σ 2a units of K: MPa m or ksi in Adapted from Fig. 8.8, Callister 6e. a K =σ πa K = 1.1σ πa Department of Materials Engineering at Isfahan University of Technology 10

14 Plane Strain Fracture Toughness For thin specimens: Kc depends on thickness, Plain Stress For thick specimens (thickness is much greater than the crack dimensions: Kc becomes independent of thickness, Plain Strain Mode I: Opening or Tensile Mode II: Sliding Mode III: Tearing K IC : Plane Strain fracture toughness = Kc for thick specimen Department of Materials Engineering at Isfahan University of Technology

15 FRACTURE TOUGHNESS Department of Materials Engineering at Isfahan University of Technology

16 KIc(MPa m 0.5 ) FRACTURE TOUGHNESS Metals/ Alloys Steels Ti alloys Al alloys Mg alloys Graphite/ Ceramics/ Semicond Diamond Si carbide Al oxide Si nitride <100> Si crystal <111> Glass -soda Polymers PET PP PC PS PVC Polyester Composites/ fibers C-C ( fibers) 1 Al/Al oxide(sf) 2 Y 2 O 3 /ZrO 2 (p) 4 C/C ( fibers) 1 Al oxid/sic(w) 3 Si nitr/sic(w) 5 Al oxid/zro 2 (p) 4 Glass/SiC(w) 6 Glass 6 K c metals K c comp K c cer K c poly Department of Materials Engineering Concrete at Isfahan University of Technology 11 increasing Based on data in Table B5, Callister 6e. Composite reinforcement geometry is: f = fibers; sf = short fibers; w = whiskers; p = particles. Addition data as noted (vol. fraction of reinforcement): 1. (55vol%) ASM Handbook, Vol. 21, ASM Int., Materials Park, OH (2001) p (55 vol%) Courtesy J. Cornie, MMC, Inc., Waltham, MA. 3. (30 vol%) P.F. Becher et al., Fracture Mechanics of Ceramics, Vol. 7, Plenum Press (1986). pp Courtesy CoorsTek, Golden, CO. 5. (30 vol%) S.T. Buljan et al., "Development of Ceramic Matrix Composites for Application in Technology for Advanced Engines Program", ORNL/Sub/ /2, ORNL, (20vol%) F.D. Gace et al., Ceram. Eng. Sci. Proc., Vol. 7 (1986) pp

17 DESIGN AGAINST CRACK GROWTH Crack growth condition: K K c Yσ πa Largest, most stressed cracks grow first! --Result 1: Max flaw size dictates design stress. σ design < σ K c Y πa max --Result 2: Design stress dictates max. flaw size. a max < 1 π a max K c Yσ design 2 fracture fracture no fracture a max no fracture σ Department of Materials Engineering at Isfahan University of Technology 12

18 DESIGN EX 1: AIRCRAFT WING Material has K c = 26 MPa-m 0.5 Two designs to consider... Design A --largest flaw is 9 mm --failure stress = 112 MPa K c Design B --use same material --largest flaw is 4 mm --failure stress =? Use... σ c = Y πa max Key point: Y and K c are the same in both designs. --Result: 112 MPa 9 mm 4 mm ( σ c a max ) = σ c a max A ( ) B Reducing flaw size pays off! Answer: ( σ c ) = 168MPa B Department of Materials Engineering at Isfahan University of Technology 13

19 DESIGN EX 2: Pressurized Spherical Tank a) Yielding of the wall before failure, Yielding before crack rapid propagation b) Leak-before-break, critical crack length equal to the thickness Department of Materials Engineering at Isfahan University of Technology

20 (a) DESIGN EX 2: Pressurized Spherical Tank (b) Department of Materials Engineering at Isfahan University of Technology

21 LOADING RATE Increased loading rate... --increases σ y and TS --decreases %EL Why? An increased rate gives less time for disl. to move past obstacles. σ y σ y σ TS larger ε TS small er ε ε Department of Materials Engineering at Isfahan University of Technology 14

22 Impact Test Impact loading: --severe testing case --more brittle --smaller toughness Department of Materials Engineering at Isfahan University of Technology

23 Increasing temperature... --increases %EL and K c TEMPERATURE Ductile-to-brittle transition temperature (DBTT)... FCC metals (e.g., Cu, Ni) Impact Energy Brittle Ductile-to-brittle transition temperature BCC metals (e.g., iron at T < 914C) polymers More Ductile High strength materials ( Temperature σy>e/150) Adapted from C. Barrett, W. Nix, and A.Tetelman, The Principles of Engineering Materials, Fig. 6-21, p. 220, Prentice-Hall, Electronically reproduced by permission of Pearson Education, Inc., Upper Saddle River, New Jersey. Department of Materials Engineering at Isfahan University of Technology 15

24 DESIGN STRATEGY: STAY ABOVE THE DBTT! Pre-WWII: The Titanic WWII: Liberty ships Reprinted w/ permission from R.W. Hertzberg, "Deformation and Fracture Mechanics of Engineering Materials", (4th ed.) Fig. 7.1(a), p. 262, John Wiley and Sons, Inc., (Orig. source: Dr. Robert D. Ballard, The Discovery of the Titanic.) Reprinted w/ permission from R.W. Hertzberg, "Deformation and Fracture Mechanics of Engineering Materials", (4th ed.) Fig. 7.1(b), p. 262, John Wiley and Sons, Inc., (Orig. source: Earl R. Parker, "Behavior of Engineering Structures", Nat. Acad. Sci., Nat. Res. Council, John Wiley and Sons, Inc., NY, 1957.) Problem: Used a type of steel with a DBTT ~ Room temp. Department of Materials Engineering at Isfahan University of Technology 16

25 Fatigue = failure under cyclic stress. specimen bearing compression on top bearing motor flex coupling tension on bottom Stress varies with time. --key parameters are S and σ m FATIGUE σmax σmin σm counter Key points: Fatigue... --can cause part failure, even though σ max < σ c. --causes ~ 90% of mechanical engineering failures. σ Adapted from Fig. 8.16, Callister 6e. (Fig is from Materials Science in Engineering, 4/E by Carl. A. Keyser, Pearson Education, Inc., Upper Saddle River, NJ.) S time Department of Materials Engineering at Isfahan University of Technology 17

26 Fatigue Reverse stress cycle Repeated stress cycle Random stress cycle Department of Materials Engineering at Isfahan University of Technology

27 FATIGUE TEST Fatigue = failure under cyclic stress. Stress varies with time. --key parameters are S and σ m σmax σmin σm σ S time Department of Materials Engineering at Isfahan University of Technology 17

28 FATIGUE DESIGN PARAMETERS Fatigue limit, S fat : --no fatigue if S < S fat Sometimes, the fatigue limit is zero! Sfat S = stress amplitude safe unsafe N = Cycles to failure S = stress amplitude unsafe case for steel (typ.) Adapted from Fig. 8.17(a), Callister 6e. case for Al (typ.) N = Cycles to failure Department of Materials Engineering at Isfahan University of Technology 18 safe Adapted from Fig. 8.17(b), Callister 6e.

29 Important Parameters: Sample Preparation Surface Preparation Metallurgical Variables Specimen Alignment Mean Stress Fatigue Test Department of Materials Engineering at Isfahan University of Technology

30 FATIGUE MECHANISM Crack grows incrementally da dn = ΔK ( ) m typ. 1 to 6 ~ ( Δσ) a increase in crack length per loading cycle Failed rotating shaft --crack grew even though K max < K c --crack grows faster if Δσ increases crack gets longer loading freq. increases. Beachmarks Striations Department of Materials Engineering at Isfahan University of Technology 19

31 IMPROVING FATIGUE LIFE 1. Mean Stress Effect Department of Materials Engineering at Isfahan University of Technology

32 IMPROVING FATIGUE LIFE 2. Impose a compressive surface stress (to suppress surface cracks from growing) shot put surface into compression C-rich gas --Method 1: shot peening --Method 2: carburizing Department of Materials Engineering at Isfahan University of Technology 20

33 IMPROVING FATIGUE LIFE 3. Design factor: Remove stress concentrators. bad bad better better Adapted from Fig. 8.23, Callister 6e. 4. Surface preparation and polishing 5. Environmental Effects: Thermal Fatigue Corrosion Fatigue Department of Materials Engineering at Isfahan University of Technology

34 CREEP Occurs at elevated temperature, T > 0.4 T melt Deformation changes with time. σ,ε σ 0 t Adapted from Figs and 8.27, Callister 6e. Department of Materials Engineering at Isfahan University of Technology 21

35 Most of component life spent here. Strain rate is constant at a given T, σ --strain hardening is balanced by recovery strain rate material const. SECONDARY CREEP. ε s = K 2 σ n exp Q c RT stress exponent (material parameter) applied stress activation energy for creep (material parameter) Department of Materials Engineering at Isfahan University of Technology 22

36 EFFECT OF STRESS Strain rate increases for larger T, σ Stress (MPa) 427C 538 C 649 C Steady state creep rate (%/1000hr) ε s Adapted from Fig. 8.29, Callister 6e. (Fig is from Metals Handbook: Properties and Selection: Stainless Steels, Tool Materials, and Special Purpose Metals, Vol. 3, 9th ed., D. Benjamin (Senior Ed.), American Society for Metals, 1980, p. 131.) Department of Materials Engineering at Isfahan University of Technology

37 EFFECT OF TEMPERATURE strain, ε INCREASING T tertiary primary secondary elastic 0 T < 0.4 T m time Department of Materials Engineering at Isfahan University of Technology

38 CREEP FAILURE Failure: along grain boundaries. g.b. cavities Time to rupture, t r T(20 + log t r ) = L applied stress From V.J. Colangelo and F.A. Heiser, Analysis of Metallurgical Failures (2nd ed.), Fig. 4.32, p. 87, John Wiley and Sons, Inc., (Orig. source: Pergamon Press, Inc.) Estimate rupture time S 590 Iron, T = 800C, σ = 20 ksi data for S-590 Iron L(10 3 K-log hr) Stress, ksi T(20 + log t r ) = L Adapted from Fig. 8.45, Callister 6e. (Fig is from F.R. Larson and J. Miller, Trans. ASME, 74, 765 (1952).) 24x10 3 K-log hr temperature function of applied stress time to failure (rupture) 1073K Ans: t r = 233hr Department of Materials Engineering at Isfahan University of Technology 23

39 Creep Characteristics Factor Factors Melting point Elastic modulus Grain size Department of Materials Engineering at Isfahan University of Technology

40 SUMMARY Engineering materials don't reach theoretical strength. Flaws produce stress concentrations that cause premature failure. Sharp corners produce large stress concentrations and premature failure. Failure type depends on T and stress: -for noncyclic σ and T < 0.4T m, failure stress decreases with: increased maximum flaw size, decreased T, increased rate of loading. -for cyclic σ: cycles to fail decreases as Δσ increases. -for higher T (T > 0.4T m ): time to fail decreases as σ or T increases. Department of Materials Engineering at Isfahan University of Technology 24