Chapter 9: Mechanical Failure - Clarkson University
Chapter 9: Mechanical Failure ISSUES TO ADDRESS... How do cracks that lead to failure form? How is fracture resistance quantified? How do the fracture resistances of the different material classes compare? How do we estimate the stress to fracture? How do loading rate, loading history, and temperature affect the failure behavior of materials? Ship-cyclic loading from waves. Adapted from chapter-opening photograph, Chapter 9, Callister & Rethwisch 4e. (by Neil Boenzi, The New York Times.) Computer chip-cyclic thermal loading. Adapted from Fig. 22.30(b), Callister 7e. (Fig. 22.30(b) is courtesy of National Semiconductor Corporation.) Hip implant-cyclic loading from walking. Adapted from Fig. 22.26(b), Callister 7e. Chapter 9 - 1 Fracture mechanisms Ductile fracture Accompanied by significant plastic deformation
Brittle fracture Little or no plastic deformation Catastrophic Chapter 9 - 2 Ductile vs Brittle Failure Classification: Fracture behavior: Very Ductile Moderately Ductile Brittle Large Moderate Small Adapted from Fig. 9.1, Callister & Rethwisch 4e. %AR or %EL Ductile fracture is
usually more desirable than brittle fracture! Ductile: Warning before fracture Brittle: No warning Chapter 9 - 3 Example: Pipe Failures Ductile failure: -- one piece -- large deformation Brittle failure: -- many pieces -- small deformations 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., 1987. Used with permission. Chapter 9 - 4 Moderately Ductile Failure Failure Stages: necking
Resulting fracture surfaces void nucleation shearing void growth and coalescence at surface 50 50mm mm (steel) particles serve as void nucleation sites. fracture 100 mm From V.J. Colangelo and F.A. Heiser, Analysis of Metallurgical Failures (2nd ed.), Fig. 11.28, p. 294, John Wiley and Sons, Inc., 1987. (Orig. source: P.
Thornton, J. Mater. Sci., Vol. 6, 1971, pp. 347-56.) Fracture surface of tire cord wire loaded in tension. Courtesy of F. Roehrig, CC Technologies, Dublin, OH. Used with permission. Chapter 9 - 5 Moderately Ductile vs. Brittle Failure cup-and-cone fracture brittle fracture Adapted from Fig. 9.3, Callister & Rethwisch 4e. Chapter 9 - 6 Brittle Failure Arrows indicate point at which failure originated Adapted from Fig. 9.5(a), Callister & Rethwisch 4e. Chapter 9 - 7 Brittle Fracture Surfaces Transgranular Intergranular (between grains)
4 mm 304 S. Steel (metal) (through grains) 316 S. Steel (metal) Reprinted w/permission from "Metals Handbook", Reprinted w/ permission 9th ed, Fig. 633, p. 650. from "Metals Handbook", Copyright 1985, ASM 9th ed, Fig. 650, p. 357. International, Materials Copyright 1985, ASM Park, OH. (Micrograph by International, Materials J.R. Keiser and A.R. Park, OH. (Micrograph by Olsen, Oak Ridge D.R. Diercks, Argonne National Lab.) National Lab.) Polypropylene (polymer)
160 mm Al Oxide (ceramic) Reprinted w/ permission Reprinted w/ permission from R.W. Hertzberg, from "Failure Analysis of "Defor-mation and Brittle Materials", p. 78. Fracture Mechanics of Copyright 1990, The Engineering Materials", American Ceramic (4th ed.) Fig. 7.35(d), p. Society, Westerville, OH. 303, John Wiley and (Micrograph by R.M. Sons, Inc., 1996. Gruver and H. Kirchner.) 3 mm 1 mm (Orig. source: K. Friedrick, Fracture 1977, Vol. 3, ICF4, Waterloo, CA, 1977, p. 1119.) Chapter 9 - 8 Ideal vs Real Materials Stress-strain behavior (Room T):
E/10 perfect matl-no flaws TSengineering << TS perfect carefully produced glass fiber E/100 typical ceramic 0.1 materials 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 longer flaws! Reprinted w/ permission from R.W. Hertzberg,
"Deformation and Fracture Mechanics of Engineering Materials", (4th ed.) Fig. 7.4. John Wiley and Sons, Inc., 1996. Chapter 9 - 9 Flaws are Stress Concentrators! Griffith Crack a m 2o t t 1/ 2 K t o where t = radius of curvature o = applied stress m = stress at crack tip Adapted from Fig. 9.8(a), Callister & Rethwisch 4e. Chapter 9 - 10
Concentration of Stress at Crack Tip Adapted from Fig. 9.8(b), Callister & Rethwisch 4e. Chapter 9 - 11 Engineering Fracture Design Avoid sharp corners! max Stress Conc. Factor, K t = 0 w max r, fillet radius 2.5 h Adapted from Fig. 8.2W(c), Callister 6e. (Fig. 8.2W(c) is from G.H. Neugebauer, Prod. Eng. (NY), Vol. 14, pp. 82-87 1943.)
2.0 increasing w/h 1.5 1.0 0 0.5 1.0 sharper fillet radius r/h Chapter 9 - 12 Crack Propagation Cracks having sharp tips propagate easier than cracks having blunt tips A plastic material deforms at a crack tip, which blunts the crack. deformed region brittle ductile 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 Chapter 9 - 13 Criterion for Crack Propagation Crack propagates if crack-tip stress (m) exceeds a critical stress (c) i.e., m > c 2Es c a 1/ 2 where E = modulus of elasticity s = specific surface energy a = one half length of internal crack For ductile materials => replace s with s + p where p is plastic deformation energy Chapter 9 - 14 Fracture Toughness Ranges Metals/ Alloys 100 K Ic (MPa m0.5 )
70 60 50 40 30 Graphite/ Ceramics/ Semicond Polymers C-C(|| fibers) 1 Steels Ti alloys Al alloys Mg alloys Based on data in Table B.5, Callister & Rethwisch 4e. 20 Al/Al oxide(sf) 2 Y2 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 10 7 6 5 4 Diamond Si carbide Al oxide Si nitride 3 0.7 0.6 0.5 PET PP PVC 2 1 Composites/ fibers PC
<100> Si crystal <111> Glass -soda Concrete PS Polyester 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. 606. 2. (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. 61-73. 4. 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/85-22011/2, ORNL, 1992. 6. (20vol%) F.D. Gace et al., Ceram. Eng. Sci. Proc., Vol. 7 (1986) pp. 978-82. Glass 6
Chapter 9 - 15 Design Against Crack Growth Crack growth condition: K Kc = Y a Largest, most highly stressed cracks grow first! --Scenario 1: Max. flaw size dictates design stress. design Kc Y amax fracture no fracture --Scenario 2: Design stress dictates max. flaw size. amax amax 1 K c Ydesign
2 fracture amax no fracture Chapter 9 - 16 Design Example: Aircraft Wing Material has KIc = 26 MPa-m0.5 Two designs to consider... Design A --use same material --largest flaw is 4 mm --failure stress = ? --largest flaw is 9 mm --failure stress = 112 MPa K Ic Use...
Design B c Y amax Key point: Y and KIc are the same for both designs. K Ic = a =constant Y --Result: 112 MPa c 9 mm amax A 4 mm c amax
Answer: (c )B 168 MPa B Chapter 9 - 17 Brittle Fracture of Ceramics Characteristic Fracture behavior in ceramics Origin point Initial region (mirror) is flat and smooth After reaches critical velocity crack branches mist hackle Adapted from Figs. 9.14 & 9.15, Callister & Rethwisch 4e. Chapter 9 - 18 Crazing During Fracture of Thermoplastic Polymers Craze formation prior to cracking during crazing, plastic deformation of spherulites and formation of microvoids and fibrillar bridges aligned chains
fibrillar bridges microvoids crack Adapted from Fig. 9.16, Callister & Rethwisch 4e. Chapter 9 - 19 Impact Testing Impact loading: (Charpy) -- severe testing case -- makes material more brittle -- decreases toughness Adapted from Fig. 9.18(b), Callister & Rethwisch 4e. (Fig. 9.18(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. (1965) p. 13.) final height initial height
Chapter 9 - 20 Influence of Temperature on Impact Energy Ductile-to-Brittle Transition Temperature (DBTT)... Impact Energy FCC metals (e.g., Cu, Ni) BCC metals (e.g., iron at T < 914C) polymers Brittle More Ductile High strength materials ( y > E/150) Temperature Adapted from Fig. 9.21, Callister & Rethwisch 4e. Ductile-to-brittle transition temperature Chapter 9 - 21 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. 7.1(a), p. 262, John Wiley and Sons, Inc., 1996. (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. 7.1(b), p. 262, John Wiley and Sons, Inc., 1996. (Orig. source: Earl R. Parker, "Behavior of Engineering Structures", Nat. Acad. Sci., Nat. Res. Council, John Wiley and Sons, Inc., NY, 1957.) Problem: Steels were used having DBTTs just below room temperature. Chapter 9 - 22 Fatigue Fatigue = failure under applied cyclic stress. specimen compression on top bearing bearing motor counter flex coupling tension on bottom
Stress varies with time. -- key parameters are S, m, and cycling frequency Adapted from Fig. 9.24, Callister & Rethwisch 4e. (Fig. 9.24 is from Materials Science in Engineering, 4/E by Carl. A. Keyser, Pearson Education, Inc., Upper Saddle River, NJ.) max m S time min Key points: Fatigue... --can cause part failure, even though max < y. --responsible for ~ 90% of mechanical engineering failures. Chapter 9 - 23 --no fatigue if S < Sfat For some materials, there is no fatigue
limit! S = stress amplitude Fatigue limit, Sfat: S = stress amplitude Types of Fatigue Behavior unsafe case for steel (typ.) Sfat safe 10 3 Adapted from Fig. 9.25(a), Callister & Rethwisch 4e. 10 5 10 7 10 9 N = Cycles to failure unsafe safe 10 3
10 5 10 7 10 9 N = Cycles to failure case for Al (typ.) Adapted from Fig. 9.25(b), Callister & Rethwisch 4e. Chapter 9 - 24 Fatigue Behavior of Polymers Fatigue limit: - PMMA, PP, PE No fatigue limit: - PET, Nylon (dry) Adapted from Fig. 9.27, Callister & Rethwisch 4e. Chapter 9 - 25 Rate of Fatigue Crack Growth Crack grows incrementally da Km dN
typ. 1 to 6 ~ a increase in crack length per loading cycle crack origin Failed rotating shaft -- crack grew even though Kmax < Kc -- crack grows faster as increases crack gets longer loading freq. increases. Adapted from Fig. 9.28, Callister & Rethwisch 4e. (Fig. 9.28 is from D.J. Wulpi, Understanding How Components Fail, American Society for Metals, Materials Park, OH, 1985.) Chapter 9 - 26 1. Impose compressive surface stresses (to suppress surface cracks from growing)
S = stress amplitude Improving Fatigue Life --Method 1: shot peening r m Adapted from Fig. 9.31, Callister & Rethwisch 4e. near zero or compressive m moderate tensile m Larger tensile m N = Cycles to failure --Method 2: carburizing shot put surface into compression 2. Remove stress
concentrators. c In ing s ea bad bad C-rich gas better better Adapted from Fig. 9.32, Callister & Rethwisch 4e. Chapter 9 - 27 Creep Sample deformation at a constant stress () vs. time 0 t
Primary Creep: slope (creep rate) decreases with time. Secondary Creep: steady-state i.e., constant slope /t) Tertiary Creep: slope (creep rate) increases with time, i.e. acceleration of rate. Adapted from Fig. 9.35, Callister & Rethwisch 4e. Chapter 9 - 28 Creep: Temperature Dependence Occurs at elevated temperature, T > 0.4 Tm (in K) tertiary primary secondary elastic Adapted from Figs. 9.36, Callister & Rethwisch 4e. Chapter 9 - 29 Secondary Creep Strain rate is constant at a given T, -- strain hardening is balanced by recovery stress exponent (material parameter)
Qc s K 2 exp RT n strain rate material const. applied stress Stress (MPa) Strain rate increases with increasing T, activation energy for creep (material parameter) 200 100 40 20 10 10 -2 10 -1 Steady state creep rate
Adapted from Fig. 9.38, Callister & 427C Rethwisch 4e. (Fig. 9.38 is from Metals 538 C Handbook: Properties and Selection: Stainless Steels, Tool Materials, and Special Metals, Vol. 3, 649 C Purpose 9th ed., D. Benjamin (Senior Ed.), American Society for Metals, 1980, p. 131.) 1 s (%/1000hr) Chapter 9 - 30 Creep Failure Failure: along grain boundaries. g.b. cavities 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., 1987. (Orig. source: Pergamon Press, Inc.) Chapter 9 - 31
Prediction of Creep Rupture Lifetime Estimate rupture time S-590 Iron, T = 800C, = 20,000 psi Time to rupture, tr 20 10 data for Stress (103 psi) 100 T (20 log t r ) L function of applied stress time to failure (rupture) temperature S-590 Iron 12 16 20 24
28 1 (1073 K )(20 log t r ) 24 x103 103 L (K-h) Adapted from Fig. 9.39, Callister & Rethwisch 4e. (Fig. 9.39 is from F.R. Larson and J. Miller, Trans. ASME, 74, 765 (1952).) Ans: tr = 233 hr Chapter 9 - 32 Estimate the rupture time for S-590 Iron, T = 750C, = 20,000 psi Solution: T (20 log t r ) L 20 function of applied stress time to failure (rupture) temperature 10 data for (1023 K )(20 log t r ) 24 x10 3
S-590 Iron 12 Ans: tr = 2890 hr Stress (103 psi) 100 Time to rupture, tr 16 20 24 28 1 103 L (K-h) Adapted from Fig. 9.39, Callister & Rethwisch 4e. (Fig. 9.39 is from F.R. Larson and J. Miller, Trans. ASME, 74, 765 (1952).) Chapter 9 - 33 SUMMARY Engineering materials not as strong as predicted by theory Flaws act as stress concentrators that cause failure at
stresses lower than theoretical values. Sharp corners produce large stress concentrations and premature failure. Failure type depends on T and : -For simple fracture (noncyclic and T < 0.4Tm), failure stress decreases with: - increased maximum flaw size, - decreased T, - increased rate of loading. - For fatigue (cyclic : - cycles to fail decreases as increases. - For creep (T > 0.4Tm): - time to rupture decreases as or T increases. Chapter 9 - 34 ANNOUNCEMENTS Reading: Core Problems: Self-help Problems: Chapter 9 - 35
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