Chapter 8: Mechanical Failure

Transcription

1 Chapter 8: 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 8, Callister & Rethwisch 8e. (by Neil Boenzi, The New York Times.) Computer chip-cyclic thermal loading. Adapted from Fig (b), Callister 7e. (Fig (b) is courtesy of National Semiconductor Corporation.) Hip implant-cyclic loading from walking. Adapted from Fig (b), Callister 7e. 1

2 Fracture mechanisms Ductile fracture Accompanied by significant plastic deformation Brittle fracture Little or no plastic deformation Catastrophic 2

3 Classification: Ductile vs Brittle Failure Fracture behavior: Very Ductile Moderately Ductile Brittle Adapted from Fig. 8.1, Callister & Rethwisch 8e. %AR or %EL Ductile fracture is usually more desirable than brittle fracture! Large Ductile: Warning before fracture Moderate Small Brittle: No warning 3

4 DUCTILE FRACTURE Highly ductile materials Pure gold and lead at room temperature, and other metals, polymers, and inorganic glasses at elevated temperatures. They neck down to a point fracture Showing virtually 100% reduction in area. Moderate ductile fracture The most common type of tensile fracture profile for ductile materials Brittle fracture Happens without any appreciable deformation and by rapid crack growth The direction of crack growth is very nearly perpendicular to the direction of the applied stress and yields a briefly flat surface. 4

5 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., Used with permission. 5

6 Moderately Ductile Failure Failure Stages: necking s void nucleation void growth and coalescence shearing at surface fracture Resulting fracture surfaces (steel) particles serve as void nucleation sites mm From V.J. Colangelo and F.A. Heiser, Analysis of Metallurgical Failures (2nd ed.), Fig , p. 294, John Wiley and Sons, Inc., (Orig. source: P. Thornton, J. Mater. Sci., Vol. 6, 1971, pp ) 100 mm Fracture surface of tire cord wire loaded in tension. Courtesy of F. Roehrig, CC Technologies, Dublin, OH. Used with permission. 6

7 Moderately Ductile vs. Brittle Failure cup-and-cone fracture brittle fracture Adapted from Fig. 8.3, Callister & Rethwisch 8e. 7

8 Moderately Ductile Failure Occurs in several stages: 1) initial necking, 2) small cavity formation, 3) coalescence of cavities to form a crack, 4) crack propagation, 5) final shear fracture at a 45 angle relative to the tensile direction 45 with the tensile axis is the angle at which the shear stress is maximum 8

9 Fractography-Ductile materials In a cop-and-cone fracture, the central interior region of the surface has an irregular and fibrous appearance, which is indicative of plastic deformation High magnification: consists of numerous spherical dimples. Each dimple is one half of a microvoid that formed and then separated during fracture process (elongated and C-shaped). Figure 8.4 9

10 Fractography-Brittle materials In brittle fracture, the sign of gross plastic deformation is absent. A series of V-shaped chevron marking may form near the center of the fracture cross section that point back toward the crack initiation site. Other brittle fracture surfaces contain lines or ridges that radiate from the origin of the crack in a fanlike pattern Brittle fracture in amorphous materials, such as ceramic glasses, yields a relatively shiny and smooth surface 10

11 Brittle Failure Arrows indicate point at which failure originated Adapted from Fig. 8.5(a), Callister & Rethwisch 8e. 11

12 CLEAVAGE FRACTURE For most brittle crystalline materials, crack propagation corresponds to the successive and repeated breaking of atomic bonds along specific crystallographic planes (Cleavage). This type of fracture is transgranular (or transcrystalline), as the fracture cracks pass through the grains. Macroscopically, the fracture surface may have a grainy or faceted texture, because the orientation of the cleavage planes were changed from grain to grain. 12

13 Brittle Fracture Surfaces Intergranular (between grains) 4 mm 304 S. Steel (metal) Reprinted w/permission from "Metals Handbook", 9th ed, Fig. 633, p Copyright 1985, ASM International, Materials Park, OH. (Micrograph by J.R. Keiser and A.R. Olsen, Oak Ridge National Lab.) 316 S. Steel (metal) Reprinted w/ permission from "Metals Handbook", 9th ed, Fig. 650, p Copyright 1985, ASM International, Materials Park, OH. (Micrograph by D.R. Diercks, Argonne National Lab.) Transgranular (through grains) 160 mm 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., mm (Orig. source: K. Friedrick, Fracture 1977, Vol. 3, ICF4, Waterloo, CA, 1977, p ) Al Oxide (ceramic) Reprinted w/ permission from "Failure Analysis of Brittle Materials", p. 78. Copyright 1990, The American Ceramic Society, Westerville, OH. (Micrograph by R.M. Gruver and H. Kirchner.) 3 mm 13

14 INETRGRANULAR FRACTURE Normally results subsequent to the occurrence of processes that weaken or embrittle grain boundary regions. 14

15 Ideal vs Real Materials Stress-strain behavior (Room T): E/10 E/100 s perfect mat l-no flaws carefully produced glass fiber typical ceramic 0.1 e 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 longer 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.,

16 STRESS CONCENTRATION Theoretical calculations of fracture strength is based on atomic bonding energies. The measured fracture strengths of materials are significantly lower than the theoretical values, because of the presence of microvoid flaws or cracks that always exist under normal conditions. The applied stress is amplified or concentrated at the crack tips. The flaws are called stress risers 16

17 Flaws are Stress Concentrators! Griffith Crack s m 2s o a t 1/2 Ks t o t where t = radius of curvature s o = applied stress s m = stress at crack tip Adapted from Fig. 8.8(a), Callister & Rethwisch 8e. 17

18 Concentration of Stress at Crack Tip Adapted from Fig. 8.8(b), Callister & Rethwisch 8e. 18

19 ENGINEERING FRACTURE DESIGN Stress amplification is not restricted to these microscopic defects, and may occur at macroscopic internal discontinuities (e.g., voids or inclusions), at sharp corers, scratches, and notches. When the magnitude of a tensile stress at the tip of one of the flaws exceeds the value of critical stress, a crack forms and then propagate, which result in fracture. 19

20 ENGINEERING FRACTURE DESIGN 20

21 Engineering Fracture Design Avoid sharp corners! r, fillet radius w s max h s Adapted from Fig. 8.2W(c), Callister 6e. (Fig. 8.2W(c) is from G.H. Neugebauer, Prod. Eng. (NY), Vol. 14, pp ) Stress Conc. Factor, K t = increasing w/h sharper fillet radius s max s 0 r/h 21

22 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 22

23 Criterion for Crack Propagation Crack propagates if crack-tip stress (s m ) exceeds a critical stress (s c ) i.e., s m > s c s where E = modulus of elasticity s = specific surface energy a = one half length of internal crack c 2E a s 1/2 For ductile materials => replace s with s + p where p is plastic deformation energy 23

24 Example Brittle Fracture Given Glass Sheet with Tensile Stress, s = 40 Mpa E = 69 GPa = 0.3 J/m Find Maximum Length of a Surface Flaw Plan Set s c = 40Mpa Solve Griffith Eqn for Edge-Crack Length 2E s Solving a 269 a s 2 applied N/m N/m 0.3N/m 6 a m 8.2µm

25 K Ic (MPa m 0.5 ) Fracture Toughness Ranges 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 Concrete 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 Based on data in Table B.5, Callister & Rethwisch 8e. 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

26 Design Against Crack Growth Crack growth condition: K K c = Ys a Largest, most highly stressed cracks grow first! --Scenario 1: Max. flaw size dictates design stress. s K c design Y a max s --Scenario 2: Design stress dictates max. flaw size. 2 Kc a 1 max Ys design a max fracture fracture no fracture a max no fracture s 26

27 Design Example: Aircraft Wing Material has K Ic = 26 MPa-m 0.5 Two designs to consider... Design A --largest flaw is 9 mm --failure stress = 112 MPa s Answer: K Ic Y ( ) B 168MPa s c Design B --use same material --largest flaw is 4 mm --failure stress =? Use... c a max Key point: Y and K Ic are the same for both designs. K Ic constant --Result: Y =s a= 112 MPa 9 mm 4 mm sc amax s a A c max B 27

28 Design using fracture mechanics Example: Compare the critical flaw sizes in the following metals subjected to tensile stress 1500MPa and K = 1.12 s a. K Ic (MPa.m 1/2 ) Al 250 Steel 50 Zirconia(ZrO2) 2 Toughened Zirconia 12 SOLUTION Critical flaw size (microns) Where Y = Substitute values

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31 Impact loading: -- severe testing case -- makes material more brittle -- decreases toughness Impact Testing (Charpy) Adapted from Fig. 8.12(b), Callister & Rethwisch 8e. (Fig. 8.12(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 31

32 Impact Energy Influence of Temperature on Impact Energy Ductile-to-Brittle Transition Temperature (DBTT)... FCC metals (e.g., Cu, Ni) BCC metals (e.g., iron at T < 914ºC) polymers Brittle More Ductile High strength materials ( s y > E/150) Ductile-to-brittle transition temperature Temperature Adapted from Fig. 8.15, Callister & Rethwisch 8e. 32

33 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: Steels were used having DBTT s just below room temperature. 33

34 FATIGUE Fatigue = failure under applied cyclic stress. bearing specimen compression on top bearing Stress varies with time. -- key parameters are S, s m, and cycling frequency S = stress amplitude motor flex coupling tension on bottom s max s min s m counter s Adapted from Fig. 8.18, Callister & Rethwisch 8e. (Fig is from Materials Science in Engineering, 4/E by Carl. A. Keyser, Pearson Education, Inc., Upper Saddle River, NJ.) S time Key points: Fatigue... --can cause part failure, even though s max < s y. --responsible for ~ 90% of mechanical engineering failures. -- occurs suddenly and catastrophically (brittle-like) 34

35 Fatigue Fatigue = failure under applied cyclic stress. Adapted from Fig. 8.17, Callister & Rethwisch 8e. max and min stresses are asymmetrical relative to the zero stress 35

36 Fatigue Source: 36

37 RANGE OF STRESS,STRESS AMPLITUDE, AND STRESS RATIO Mean stress Range of stresses One-half of the range (stress amplitude) Stress ratio 37

38 Question make a schematic sketch of a stress-versus-time plot for the situation when the stress ratio R has a value of

39 Types of Fatigue Behavior Fatigue limit, S fat : --no fatigue if S < S fat S = stress amplitude S fat safe unsafe N = Cycles to failure case for steel (typ.) Adapted from Fig. 8.19(a), Callister & Rethwisch 8e. For some materials, there is no fatigue limit! S = stress amplitude safe unsafe N = Cycles to failure case for Al (typ.) Adapted from Fig. 8.19(b), Callister & Rethwisch 8e. 39

40 CREEP time-dependent and permanent deformation of materials when subjected to constant load or stress normally an undesirable phenomenon and reduces the lifetime of the mechanical parts for metals, it becomes important at T>0.4T m (absolute temperature) amorphous polymers are specially sensitive to creep deformation 40

41 CREEP Sample deformation at a constant load or stress (s) vs. time (T = constant) s s,e 0 t Primary Creep: slope (creep rate) decreases with time. Secondary Creep: steady-state i.e., constant slope De/Dt). Tertiary Creep: slope (creep rate) increases with time, i.e. acceleration of rate. elastic deformation Adapted from Fig. 8.28, Callister & Rethwisch 8e. 41

42 CREEP CURVE Primary region: the material is experiencing an increase in creep resistance or strain hardening (the deformation becomes more difficult as the material is strained) Secondary region: the longest duration ( a balance between the competing processes of strain hardening and recovery) Tertiary region: the acceleration of the rate of creep. The failure is termed rupture 42

43 ENGINEERING DESINS in the long-life applications (e.g., nuclear power plant), De/Dt) is the most important parameter from a creep rupture test. in short-life creep situations (e.g., turbine blades), time to rupture or rupture lifetime is the dominant design consideration. 43

44 UNDERESTANDING CREEP Source: 44

45 Creep: Temperature Dependence Occurs at elevated temperature, T > 0.4 T m (in K) tertiary primary secondary elastic Adapted from Fig. 8.29, Callister & Rethwisch 8e. 45

46 Creep: Temperature Dependence with either increasing stress or temperature: the instantaneous strain at the tie of stress application increases the steady-state creep rate is increased the rupture life is diminished 46

47 Stress (MPa) Secondary Creep Strain rate is constant at a given T, s -- strain hardening is balanced by recovery e s strain rate material const. Strain rate increases with increasing T, s s n K Qc 2 exp RT stress exponent (material parameter) applied stress activation energy for creep (material parameter) Steady state creep rate (%/1000hr) e s 427ºC 538ºC 649ºC Adapted from Fig. 8.31, Callister 7e. (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.) 47

48 Prediction of Creep Rupture Lifetime prolonged creep tests are sometimes not practical! one solution is to perform creep rupture tests at temperatures in excess of those required, for shorter time periods, and at a comparable stress level, and then making a suitable extrapolation to the in-service condition. a common extrapolation procedure is Larson-Miller parameter. 48

49 Stress (10 3 psi) Prediction of Creep Rupture Lifetime Estimate rupture time S-590 Iron, T = 800ºC, s = 20,000 psi Time to rupture, t r T(20 logt ) r L temperature function of applied stress time to failure (rupture) data for S-590 Iron L (K-h) 1 ( 1073K)( 20 logt ) 24x10 r 3 Adapted from Fig. 8.32, Callister & Rethwisch 8e. (Fig is from F.R. Larson and J. Miller, Trans. ASME, 74, 765 (1952).) Ans: t r = 233 hr 49

50 Estimate the rupture time for S-590 Iron, T = 750ºC, s = 20,000 psi Stress (10 3 psi) Solution: Time to rupture, t r T(20 logt ) r L temperature function of applied stress time to failure (rupture) ( 1023K)( 20 logt ) 24x10 3 Ans: t r = 2890 hr r data for S-590 Iron L (K-h) Adapted from Fig. 8.32, Callister & Rethwisch 8e. (Fig is from F.R. Larson and J. Miller, Trans. ASME, 74, 765 (1952).)

51 SUMMARY Failure type depends on T and s : -For simple fracture (noncyclic s and T < 0.4T m), failure stress decreases with: - increased maximum flaw size, - decreased T, - increased rate of loading. - For fatigue (cyclic s : - cycles to fail decreases as Ds increases. - For creep (T > 0.4T m ): - time to rupture decreases as s or T increases. 51