CHAPTER 8: MECHANICAL FAILURE ISSUES TO ADDRESS... • How do flaws in a material initiate failure? • 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. Computer chip-cyclic thermal loading. Hip implant-cyclic loading from walking. Adapted from Fig. 8.0, Callister 6e. (Fig. 8.0 is by Neil Boenzi, The New York Times.) Adapted from Fig. 18.11W(b), Callister 6e. (Fig. 18.11W(b) is courtesy of National Semiconductor Corporation.) Adapted from Fig. 17.19(b), Callister 6e. 1

Mechanical Failure The usual causes for failure are: Cost of failure Improper materials selection and processing Inadequate design Misuse Cost of failure 1000 Billions of $ or YTL annually Loss of human life !

Fracture mechanisms Ductile fracture Occurs with plastic deformation Brittle fracture Little or no plastic deformation Catastrophic

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

From http://plane-truth.com/comet.htm Heverill Fire Department aerial ladder failure from: http://www.engr.sjsu.edu/WofMatE/FailureAnaly.htm From http://plane-truth.com/comet.htm

Mechanical Failure: How do materials break ? Fracture: crack growth to rupture at a critical load Ductile vs Brittle fracture Principles of Fracture Mechanics Stress Concentration Impact Fracture Testing Fatigue: crack growth due to cycling loads Cyclic stresses, the S-N curve Crack initiation and propagation Factors that effect fatigue behavior Creep: high temperature plastic deformation Stress and temperature effects Alloys for hi-temperature usage

DUCTILE VS BRITTLE FAILURE • Classification: Substantial plastic deformation Absorb high amounts of energy before fracture What is the reduction in x-sectional area ? Adapted from Fig. 8.1, Callister 6e. • Ductile fracture is desirable! Ductile: warning before fracture Brittle: No warning Failure is catastrophic 2

Fracture, in detail Two steps involved in fracture: Crack formation Crack growth Two fracture modes can be defined Ductile (preferred, most metals and some polymers) extensive plastic deformation in the vicinity of a crack Extension of crack length requires an increase in the applied load, hence crack is stable unless stress is increased. Crack propagation is therefore slow Brittle (undesired, ceramics, metals at low temperatures) Takes place w/o appreciable plastic deformation Crack is unstable, will propagate with high speed once formed and w/o increase in applied stress

Ductile vs Brittle Q1:What is ductility ? Q2: What is toughness?

Example: Failure of a Pipe Observe the variation in the amount of plastic deformation • 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., 1987. Used with permission.

Moderately Ductile Failure • Evolution to failure: void nucleation void growth and linkage shearing at surface necking s fracture • Resulting fracture surfaces (steel) 50 mm particles serve as void nucleation sites. 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.) 100 mm Fracture surface of tire cord wire loaded in tension. Courtesy of F. Roehrig, CC Technologies, Dublin, OH. Used with permission.

Ductile Fracture Cup Cone Dimple SEM of the fracture surface: Fractographic studies Dimples, micro-cavities that initiate crack formation, on the surface will be observed during high resolution investigation of the cup and cone type fracture surfaces. Cup Cone Cup and cone fracture in Aluminum Micro-void Dimple

Brittle Fracture Surfaces • Intergranular (between grains) • Intragranular (within grains) 304 S. Steel (metal) Reprinted w/permission from "Metals Handbook", 9th ed, Fig. 633, p. 650. 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. 357. Copyright 1985, ASM International, Materials Park, OH. (Micrograph by D.R. Diercks, Argonne National Lab.) 160 mm 4 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., 1996. 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 1 mm (Orig. source: K. Friedrick, Fracture 1977, Vol. 3, ICF4, Waterloo, CA, 1977, p. 1119.)

BRITTLE FRACTURE SURFACES • INTERgranular (between grains) • TRANSgranular (within grains) 304 S. Steel (metal) 316 S. Steel (metal) Transgranular fracture: Cracks move in and through grains. Fracture surface have faceted texture because of different orientation of cleavage planes . Intergranular fracture: Crack propagation is along grain boundaries (grain boundaries are weak or embrittle due to impurity segregation, etc.) 160mm 4 mm Al Oxide (ceramic) Polypropylene (polymer) No appreciable plastic deformation Fast moving crack Propagation direction is nearly 90º to applied stress Crack often propagates by cleavage, breaking of bonds along specific crystallographic planes, aka cleavage planes 3mm 5 1 mm

Ideal vs Real Materials • Stress-strain behavior (Room T): TS << TS engineering materials perfect s e E/10 E/100 0.1 perfect mat’l-no flaws carefully produced glass fiber typical ceramic 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! 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.

Flaws ; Stress concentrators Fracture strength of a brittle solid is related to the cohesive forces between atoms, bond strength. It can be estimated that the theoretical cohesive strength of a brittle material should be around ~ E/10. But experimental fracture strength is normally E/100 - E/10,000. Much lower fracture strength is explained by the effect of stress concentration at microscopic flaws. The applied stress is amplified at the tips of micro-cracks, voids, notches, surface scratches, corners, etc. that are called stress concentrators raisers. The magnitude of this amplification depends on micro-crack orientations, geometry and dimensions. TABLES 6.1 and 6.2 In chapter 6

FLAWS ARE STRESS CONCENTRATORS! • Elliptical hole in a plate: • Stress distrib. in front of a hole: s max r t » 2 o a æ è ç ö ø ÷ • Stress concentration factor: • Large Kt promotes failure: Sharper cracks amplify stress ! More important for brittle materials as in ductile material Plas. Dfm takes place and stress is distributed more uniformly around a crack ! NOT SO BAD K t =2 7

Flaws are Stress Concentrators! Results from crack propagation Griffith Crack where t = radius of curvature so = applied stress sm = stress at crack tip t Stress concentrated at crack tip Adapted from Fig. 8.8(a), Callister 7e.

Concentration of Stress at Crack Tip Adapted from Fig. 8.8(b), Callister 7e.

Engineering Fracture Design • Avoid sharp corners! s r/h sharper fillet radius increasing w/h 0.5 1.0 1.5 2.0 2.5 Stress Conc. Factor, K t s max o = r , fillet radius w h o s max 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.)

Anything peculiar in this image ! From http://plane-truth.com/comet.htm

GEOMETRY, LOAD, & MATERIAL • Condition for crack propagation: Stress Intensity Factor: Depends on applied stress, crack length & component geometry. K ≥ Kc Fracture Toughness: Depends on the material, temperature, environment, & rate of loading. • Values of K for some standard loads & geometries: Adapted from Fig. 8.8, Callister 6e. 10

When Does a Crack Propagate? Crack propagates if above critical stress where E = modulus of elasticity s = specific surface energy a = one half length of internal crack Kc = sc/s0 For ductile => replace gs by gs + gp where gp is plastic deformation energy i.e., sm > sc or Kt > Kc

WHEN DOES A CRACK PROPAGATE? • rt at a crack tip is very small! • Result: crack tip stress is very large. • Crack propagates when: the tip stress is large enough to make: K ≥ Kc 9

Crack Propagation Cracks propagate due to sharpness of crack tip A plastic material deforms at the tip, “blunting” the crack. deformed region brittle 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 plastic

TOUGHNESS & RESILIENCE • Energy to break a unit volume of material • Approximate by the area under the stress-strain curve. RESILIENCE is energy stored in the material w/o plastic deformation ! Ur = σy2 / 2 E TOUGHNESS is total energy stored in the material upon fracture ! 20

Fracture Toughness ) (MPa · m K increasing Graphite/ Ceramics/ Semicond Metals/ Alloys Composites/ fibers Polymers 5 K Ic (MPa · m 0.5 ) 1 Mg alloys Al alloys Ti alloys Steels Si crystal Glass - soda Concrete Si carbide PC 6 0.7 2 4 3 10 <100> <111> Diamond PVC PP Polyester PS PET C-C (|| fibers) 0.6 7 100 Al oxide Si nitride C/C ( fibers) Al/Al oxide(sf) Al oxid/SiC(w) Al oxid/ZrO (p) Si nitr/SiC(w) Glass/SiC(w) Y O /ZrO increasing Fracture toughness is the resistance of a material to brittle fracture when a crack is present ! Based on data in Table B5, Callister 7e. 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.

Design Against Crack Growth • Crack growth condition: K ≥ Kc = • Largest, most stressed cracks grow first! --Result 1: Max. flaw size dictates design stress. s amax no fracture --Result 2: Design stress dictates max. flaw size. amax s no fracture

Design Example: Aircraft Wing • Material has Kc = 26 MPa-m0.5 • Two designs to consider... Design A --largest flaw is 9 mm --failure stress = 112 MPa Design B --use same material --largest flaw is 4 mm --failure stress = ? • Use... • Key point: Y and Kc are the same in both designs. 9 mm 112 MPa 4 mm --Result: Answer: • Reducing flaw size pays off!

Loading Rate s sy e • Increased loading rate... -- increases sy and TS -- decreases %EL • Why? An increased rate gives less time for dislocations to move past obstacles. s e sy TS larger smaller

Impact Testing • Impact loading: -- severe testing case -- makes material more brittle -- decreases toughness (Charpy) final height initial height Adapted from Fig. 8.12(b), Callister 7e. (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.)

Temperature • Increasing temperature... --increases %EL and Kc • Ductile-to-Brittle Transition Temperature (DBTT)... FCC metals (e.g., Cu, Ni) BCC metals (e.g., iron at T < 914°C) polymers Impact Energy Brittle More Ductile High strength materials ( s y > E/150) Adapted from Fig. 8.15, Callister 7e. Temperature Ductile-to-brittle transition temperature

DBTT As temperature decreases a ductile material can become behave brittle - ductile-to-brittle transition FCC metals remain ductile down to very low temperatures. For ceramics, this type of transition occurs at much higher temperatures than for metals. The ductile-to-brittle transition can be measured by impact testing: the impact energy needed for fracture drops suddenly over a relatively narrow temperature range – temperature of the ductile-to-brittle transition.

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., 1996. (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., 1996. (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.

FATIGUE • Fatigue = failure under cyclic stress. Explain! Load Adapted from Fig. 8.16, Callister 6e. (Fig. 8.16 is from Materials Science in Engineering, 4/E by Carl. A. Keyser, Pearson Education, Inc., Upper Saddle River, NJ.) • Stress varies with time. --key parameters are S and sm • Key points: Fatigue... --can cause part failure, even though smax < scritical. --causes ~ 90% of mechanical engineering failures. 17

FATIGUE How ? Important ? What is the failure type ? Under fluctuating / cyclic stresses, failure can occur at loads considerably lower than tensile or yield strengths of material under a static load: Important ? Estimated to causes 90% of all failures of metallic structures (bridges, aircraft, machine components, etc.) What is the failure type ? Fatigue failure is brittle-like (relatively little plastic deformation) - even in normally ductile materials. Thus sudden and catastrophic! Applied stresses causing fatigue may be axial (tension or compression), flextural (bending) or torsional (twisting). Fatigue failure proceeds in three distinct stages: Crack initiation in the areas of stress concentration (near stress raisers), incremental crack propagation, final catastrophic failure.

Periodic and symmetrical Rotating Car axle Periodic and asymmetrical Random stress fluctuations

Fatigue Design Parameters • Fatigue limit, Sfat: --no fatigue if S < Sfat Sfat case for steel (typ.) N = Cycles to failure 10 3 5 7 9 unsafe safe S = stress amplitude Adapted from Fig. 8.19(a), Callister 7e. • Sometimes, the fatigue limit is zero! Adapted from Fig. 8.19(b), Callister 7e. case for Al (typ.) N = Cycles to failure 10 3 5 7 9 unsafe safe S = stress amplitude

FATIGUE DESIGN PARAMETERS • Fatigue limit, Sfat: --no fatigue if S < Sfat case for unsafe Steel % Ti Endurance Limit S = stress amplitude For steels Sfat = 35%-60% of YS Think about design criteria factor, N in chapter 6 S fat safe Adapted from Fig. 8.17(a), Callister 6e. 3 5 7 9 10 10 10 10 N = Cycles to failure • Sometimes, the fatigue limit is zero! case for unsafe Al (typ.) S = stress amplitude safe Adapted from Fig. 8.17(b), Callister 6e. Low cycle fatigue: high loads, plastic and elastic deformation High cycle fatigue: low loads, elastic deformation (N > 105) 3 5 7 9 10 10 10 10 N = Cycles to failure 18

FATIGUE MECHANISM • Crack grows incrementally • Failed rotating shaft typ. 1 to 6 increase in crack length per loading cycle crack origin • Failed rotating shaft --crack grew even though Kmax < Kc --crack grows faster if • Ds increases • crack gets longer • loading freq. increases. Adapted from Fig. 8.19, Callister 6e. (Fig. 8.19 is from D.J. Wulpi, Understanding How Components Fail, American Society for Metals, Materials Park, OH, 1985.) 19

Improving Fatigue Life 1. Impose a compressive surface stress (to suppress surface cracks from growing) N = Cycles to failure moderate tensile s m Larger tensile S = stress amplitude near zero or compressive Increasing m Adapted from Fig. 8.24, Callister 7e. --Method 1: shot peening put surface into compression shot --Method 2: carburizing C-rich gas 2. Remove stress concentrators. Adapted from Fig. 8.25, Callister 7e. bad better

IMPROVING FATIGUE LIFE 1. Impose a compressive surface stress (to suppress surface cracks from growing) Adapted from Fig. 8.22, Callister 6e. POLISH THE SURFACE ! --Method 1: shot peening --Method 2: carburizing 2. Remove stress concentrators. Adapted from Fig. 8.23, Callister 6e. 20

CREEP • Occurs at elevated temperature, T > 0.4 Tmelt • Deformation changes with time. Adapted from Figs. 8.26 and 8.27, Callister 6e. 21

SECONDARY CREEP • Most of component life spent here. • Strain rate is constant at a given T, s --strain hardening is balanced by recovery stress exponent (material parameter) . activation energy for creep (material parameter) strain rate material const. applied stress Adapted from Fig. 8.29, Callister 6e. (Fig. 8.29 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.) • Strain rate increases for larger T, s 22

CREEP FAILURE • Failure: along grain boundaries. • Estimate rupture time S 590 Iron, T = 800C, s = 20 ksi g.b. cavities Adapted from Fig. 8.45, Callister 6e. (Fig. 8.45 is from F.R. Larson and J. Miller, Trans. ASME, 74, 765 (1952).) 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.) 24x103 K-log hr • Time to rupture, tr temperature function of applied stress 1073K Ans: tr = 233hr time to failure (rupture) 23

SUMMARY (I) • 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 s and T < 0.4Tm, failure stress decreases with: increased maximum flaw size, decreased T, increased rate of loading. -for cyclic s: cycles to fail decreases as Ds increases. -for higher T (T > 0.4Tm): time to fail decreases as s or T increases. 24

SUMMARY (II)

ANNOUNCEMENTS Reading: Chapter 8 and Chapter 9 at least twice ! Use the CD and review Chapter 7 and 8 ! Core Problems: 8.7,8.10, 8.13, 8.17, 8.22 Self-help Problems: 8.1, 8.2, 8.3, 8.15, 8.20, 8.21 Homework due January 5th , 2009