Fracture mechanisms. Ductile vs Brittle Failure. Example: Failure of a Pipe

Transcription

1 Lectures and Chapter 8: Mechanical Failure ISSUES TO ADDRESS... How do flaws in a material initiate failure? How is resistance quantified; how do different material classes compare? How do we estimate the stress to? How do loading rate, loading history, and temperature affect the failure stress? Fracture mechanisms Ductile Occurs with plastic deformation Brittle Little or no plastic deformation Catastrophic Ship-cyclic loading from waves. chapter-opening photograph, Chapter 8, (by Neil Boenzi, The New York Times.) Computer chip-cyclic thermal loading. Fig..30(b), (Fig..30(b) is courtesy of National Semiconductor Corporation.) Hip implant-cyclic loading from walking. Fig..6(b), Ductile vs Brittle Failure Classification: Fracture behavior: Very Ductile Moderately Ductile Brittle Example: Failure of a Pipe Ductile failure: --one piece --large deformation Fig. 8., %AR or %EL Ductile is usually desirable! Large Ductile: warning before Moderate Small Brittle: No warning Brittle failure: --many pieces --small deformation Figures from V.J. Colangelo and F.A. Heiser, Analysis of Metallurgical Failures (nd ed.), Fig. 4.(a) and (b), p. 66 John Wiley and Sons, Inc., 987. Used with permission. 3 4

2 Evolution to failure: necking Moderately Ductile Failure void nucleation void growth and linkage shearing at surface Ductile vs. Brittle Failure Resulting surfaces (steel) particles serve as void nucleation sites mm From V.J. Colangelo and F.A. Heiser, Analysis of Metallurgical Failures (nd ed.), Fig..8, p. 94, John Wiley and Sons, Inc., 987. (Orig. source: P. Thornton, J. Mater. Sci., Vol. 6, 97, pp ) 00 mm Fracture surface of tire cord wire loaded in tension. Courtesy of F. Roehrig, CC Technologies, Dublin, OH. Used with permission. 5 cup-and-cone Fig. 8.3, brittle 6 Brittle Failure Arrows indicate pt at which failure originated Intergranular (between grains) 4mm Brittle Fracture Surfaces 304 S. Steel (metal) Reprinted w/permission from "Metals Handbook", 9th ed, Fig. 633, p Copyright 985, ASM International, Materials Park, OH. (Micrograph by J.R. Keiser and A.R. Olsen, Oak Ridge National Lab.) Intragranular (within grains) 36 S. Steel (metal) Reprinted w/ permission from "Metals Handbook", 9th ed, Fig. 650, p Copyright 985, ASM International, Materials Park, OH. (Micrograph by D.R. Diercks, Argonne National Lab.) 60mm Fig. 8.5(a), 7 Polypropylene (polymer) Reprinted w/ permission from R.W. Hertzberg, "Defor-mation and Fracture Mechanics of Engineering Materials", (4th ed.) Fig. 7.35(d), p. 303, John Wiley and Sons, Inc., 996. mm (Orig. source: K. Friedrick, Fracture 977, Vol. 3, ICF4, Waterloo, CA, 977, p. 9.) Al Oxide (ceramic) Reprinted w/ permission from "Failure Analysis of Brittle Materials", p. 78. Copyright 990, The American Ceramic Society, Westerville, OH. (Micrograph by R.M. Gruver and H. Kirchner.) 3mm 8

3 Ideal vs Real Materials Stress-strain behavior (Room T): E/0 E/00 perfect mat l-no flaws carefully produced glass fiber typical ceramic 0. ε TS engineering materials typical strengthened metal typical polymer DaVinci (500 yrs ago!) observed the longer the wire, the smaller the load for failure. Reasons: -- flaws cause premature failure. -- Larger samples contain more flaws! << TS perfect materials Reprinted w/ permission from R.W. Hertzberg, "Deformation and Fracture Mechanics of Engineering Materials", (4th ed.) Fig John Wiley and Sons, Inc., 996. ρ t Flaws are Stress Concentrators! Results from crack propagation Griffith Crack m a = o ρt / = K where ρ t = radius of curvature o = applied stress m = stress at crack tip Fig. 8.8(a), t o 9 0 Concentration of Stress at Crack Tip Fig. 8.8(b), Engineering Fracture Design Avoid sharp corners! o max Stress Conc. Factor, K t = w o max.5 r, fillet radius h Fig. 8.W(c), Callister 6e. (Fig. 8.W(c) is from G.H. Neugebauer, Prod. Eng. (NY), Vol. 4, pp ).0.5 increasing w/h sharper fillet radius r/h 3

4 Crack Propagation When Does a Crack Propagate? Cracks propagate due to sharpness of crack tip A plastic material deforms at the tip, blunting the crack. deformed region brittle plastic Energy balance on the crack Elastic strain energy- energy stored in material as it is elastically deformed this energy is released when the crack propagates creation of new surfaces requires energy Crack propagates if above critical stress i.e., m > c or K t > K c Eγ = πa where E = modulus of elasticity γ s = specific surface energy a = one half length of internal crack K c = c / 0 For ductile => replace γ s by γ s + γ p where γ p is plastic deformation energy c s / 3 4 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 <00> Si crystal <> Glass -soda Concrete Polymers PET PP PC PS PVC Polyester Composites/ fibers C-C( fibers) Al/Al oxide(sf) YO3/ZrO (p) 4 C/C( fibers) Al oxid/sic(w) 3 Si nitr/sic(w) 5 Al oxid/zro (p) 4 Glass/SiC(w) 6 Glass 6 Based on data in Table B5, Composite reinforcement geometry is: f = fibers; sf = short fibers; w = whiskers; p = particles. Addition data as noted (vol. fraction of reinforcement):. (55vol%) ASM Handbook, Vol., ASM Int., Materials Park, OH (00) 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 (986). 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/85-0/, ORNL, (0vol%) F.D. Gace et al., Ceram. Eng. Sci. Proc., Vol. 7 (986) pp Design Against Crack Growth Crack growth condition: K K c = Y πa Largest, most stressed cracks grow first! --Result : Max. flaw size dictates design stress. design no < Y K c πa max a max --Result : Design stress dictates max. flaw size. Kc a max < π Ydesign a max no 6 4

5 Design Example: Aircraft Wing Loading Rate Material has K c = 6 MPa-m 0.5 Two designs to consider... Design A --largest flaw is 9 mm --failure stress = MPa Kc Use... c = Y πa max Design B --use same material --largest flaw is 4 mm --failure stress =? Key point: Y and K c are the same in both designs. --Result: MPa 9 mm 4 mm ( c a max ) = c a max A ( ) B Increased loading rate increases y and TS -- decreases %EL y y TS ε larger TS Why? An increased rate gives less time for dislocations to move past obstacles. ε smaller Reducing flaw size pays off! Answer: ( c ) B = 68 MPa ε 7 8 Impact loading: -- severe testing case -- makes material more brittle -- decreases toughness Fig. 8.(b), (Fig. 8.(b) is adapted from H.W. Hayden, W.G. Moffatt, and J. Wulff, The Structure and Properties of Materials, Vol. III, Mechanical Behavior, John Wiley and Sons, Inc. (965) p. 3.) Impact Testing (Charpy) Increasing temperature... --increases %EL and K c Ductile-to-Brittle Transition Temperature (DBTT)... Impact Energy FCC metals (e.g., Cu, Ni) Brittle Temperature BCC metals (e.g., iron at T < 94 C) polymers More Ductile High strength materials (y > E/50) final height initial height Ductile-to-brittle transition temperature Temperature Fig. 8.5, 9 0 5

6 Design Strategy: Stay Above The DBTT! Pre-WWII: The Titanic Reprinted w/ permission from R.W. Hertzberg, "Deformation and Fracture Mechanics of Engineering Materials", (4th ed.) Fig. 7.(a), p. 6, John Wiley and Sons, Inc., 996. (Orig. source: Dr. Robert D. Ballard, The Discovery of the Titanic.) WWII: Liberty ships Reprinted w/ permission from R.W. Hertzberg, "Deformation and Fracture Mechanics of Engineering Materials", (4th ed.) Fig. 7.(b), p. 6, John Wiley and Sons, Inc., 996. (Orig. source: Earl R. Parker, "Behavior of Engineering Structures", Nat. Acad. Sci., Nat. Res. Council, John Wiley and Sons, Inc., NY, 957.) Problem: Used a type of steel with a DBTT ~ Room temp. Fatigue Fatigue = failure under cyclic stress. bearing specimen compression on top bearing flex coupling tension on bottom Stress varies with time. -- key parameters are S, m, and frequency motor max min Key points: Fatigue... --can cause part failure, even though max < c. --causes ~ 90% of mechanical engineering failures. m counter Fig. 8.8, (Fig. 8.8 is from Materials Science in Engineering, 4/E by Carl. A. Keyser, Pearson Education, Inc., Upper Saddle River, NJ.) S time Fatigue Design Parameters Fatigue limit, S fat : --no fatigue if S < S fat Sometimes, the fatigue limit is zero! S fat S = stress amplitude safe unsafe N = Cycles to failure S = stress amplitude safe unsafe N = Cycles to failure case for steel (typ.) Fig. 8.9(a), case for Al (typ.) Fig. 8.9(b), 3 Crack grows incrementally da dn = Failed rotating shaft --crack grew even though Fatigue Mechanism K max < K c --crack grows faster as increases crack gets longer loading freq. increases. typ. to 6 ( K ) m ~ ( ) a increase in crack length per loading cycle Fig. 8., (Fig. 8. is from D.J. Wulpi, Understanding How Components Fail, American Society for Metals, Materials Park, OH, 985.) crack origin 4 6

7 Improving Fatigue Life. Impose a compressive surface stress (to suppress surface cracks from growing) --Method : shot peening shot. Remove stress concentrators. Increasing m put surface into compression bad bad S = stress amplitude N = Cycles to failure --Method : carburizing C-rich gas better better Fig. 8.4, near zero or compressive m moderate tensile m Larger tensile m Fig. 8.5, 5 Creep Sample deformation at a constant stress () vs. time,ε 0 t Primary Creep: slope (creep rate) decreases with time. Secondary Creep: steady-state i.e., constant slope. Tertiary Creep: slope (creep rate) increases with time, i.e. acceleration of rate. Fig. 8.8, 6 Creep Occurs at elevated temperature, T > 0.4 T m primary elastic secondary Figs. 8.9, tertiary 7 Strain rate is constant at a given T, -- strain hardening is balanced by recovery stress exponent (material parameter) ε = n Q c activation energy for creep s K exp strain rate RT (material parameter) material const. applied stress Strain rate increases for higher T, Secondary Creep Stress (MPa) 47 C 538 C 649 C Steady state creep rate (%/000hr) ε s Fig. 8.3, (Fig. 8.3 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, 980, p. 3.) 8 7

8 Failure: along grain boundaries. g.b. cavities Time to rupture, t r T( 0 + logtr ) = L temperature function of applied stress time to failure (rupture) Creep Failure applied stress From V.J. Colangelo and F.A. Heiser, Analysis of Metallurgical Failures (nd ed.), Fig. 4.3, p. 87, John Wiley and Sons, Inc., 987. (Orig. source: Pergamon Press, Inc.) Estimate rupture time S-590 Iron, T = 800 C, = 0 ksi data for S-590 Iron 6 0 L( K-log hr) Stress, ksi T( 0 + logtr ) = L 073K Ans: t r = 33 hr Fig. 8.3, (Fig. 8.3 is from F.R. Larson and J. Miller, Trans. ASME, 74, 765 (95).) 4x0 3 K-log hr 9 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 and T < 0.4T m, failure stress decreases with: - increased maximum flaw size, - decreased T, - increased rate of loading. - for cyclic : - cycles to fail decreases as increases. - for higher T (T > 0.4T m ): - time to fail decreases as or T increases. 30 8