Chapter 8 Mechanical Failure PDF

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...

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 Computer chip-cyclic Hip implant-cyclic from waves. thermal loading. loading from walking. Adapted from chapter-opening Adapted from Fig. 22.30(b), Callister 7e. Adapted from Fig. 22.26(b), photograph, Chapter 8, Callister 7e. (by (Fig. 22.30(b) is courtesy of National Callister 7e. Neil Boenzi, The New York Times.) Semiconductor Corporation.) Chapter 8 - 1  Outline Failure -Introduction Safety factor Types of failure-Ductile fracture- Brittle fracture Fractography Principles of fracture mechanics Stress concentration Griffith theory Fracture Creep Impact test Chapter 8 - 2 Chapter 8 - 3 Chapter 8 - 4 Chapter 8 - 5 Chapter 8 - 6  Ductile vs Brittle Failure Classification: Fracture Very Moderately Brittle behavior: Ductile Ductile Adapted from Fig. 8.1, Callister 7e. %AR or %EL Large Moderate Small Ductile Ductile: Brittle: fracture is usually warning before No desirable! fracture warning Chapter 8 - 7  Moderately Ductile Failure Evolution to failure: void void growth shearing necking and linkage fracture nucleation at surface s Resulting 50 50mm mm fracture surfaces (steel) 100 mm 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. 11.28, p. 294, John Wiley and Roehrig, CC Technologies, Dublin, nucleation Sons, Inc., 1987. (Orig. source: P. OH. Used with permission. sites. Thornton, J. Mater. Sci., Vol. 6, 1971, pp. 347-56.) Chapter 8 - 8  Microvoid Coalescence (mechanically induced micropores) 1. Microvoid 2. Growth of microvoid 3. Eventually coalescence a. TEM of dimples b. SEM of dimples Chapter 8 - 9  Microvoid Coalescence a. Tensile stress microvoid b. Pure shear microvoid c. Tearing associated with nonuniform stress. TEM SEM fractograph fractograph of elongated of dimples dimples Chapter 8 - 10  Ductile vs. Brittle Failure cup-and-cone fracture brittle fracture Adapted from Fig. 8.3, Callister 7e. Chapter 8 - 11  Brittle Failure Arrows indicate pt at which failure originated Adapted from Fig. 8.5(a), Callister 7e. Chapter 8 - 12  Brittle Fracture Surfaces Intergranular Intragranular (between grains) 304 S. Steel (within grains) (metal) 316 S. Steel Reprinted w/permission (metal) 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.) 160 mm 4 mm National Lab.) Polypropylene Al Oxide (polymer) (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. Chapter 8 - 13 3, ICF4, Waterloo, CA, 1977, p. 1119.)  Ideal vs Real Materials Stress-strain behavior (Room T): s perfect mat’l-no flaws E/10 TSengineering sc  2E s  sc    or Kt > Kc  a  where – E = modulus of elasticity – s = specific surface energy – a = one half length of internal crack – Kc = sc/s0 For ductile => replace s by s + p where p is plastic deformation energy Chapter 8 - 35  Design Against Crack Growth Crack growth condition: K ≥ Kc = Ys a Largest, most stressed cracks grow first! --Result 1: Max. flaw size --Result 2: Design stress dictates design stress. dictates max. flaw size. 2 Kc 1  K c  sdesign  amax  Y amax   Ysdesign  amax s fracture fracture no no fracture amax fracture s Chapter 8 - 36  Problem 8.6 (10e) Some aircraft component is fabricated from an aluminum alloy that has a plane strain fracture toughness of 35 MPa√m. It has been determined that fracture results at a stress of 250 MPa (36,250 psi) when the maximum (or critical) internal crack length is 2.0 mm (0.08 in.). For this same component and alloy, will fracture occur at a stress level of 325 MPa (47,125 psi) when the maximum internal crack length is 1.0 mm (0.04 in.)? Why or why not? Chapter 8 - 37  Problem 8.21(10e) A cylindrical rod of diameter 12.5 mm fabricated from a 70Cu-30Zn brass alloy (Figure 8.21) is subjected to a repeated tension-compression load cycling along its axis. Compute the maximum and minimum loads that will be applied to yield a fatigue life of 1.0 × 106 cycles. Assume that data in Figure 8.21 were taken for repeated axial tension-compression tests, that stress plotted on the vertical axis is stress amplitude, and data were taken for a mean stress of 30 MPa. Chapter 8 - 38 Problem 8.21(10e) Chapter 8 - 39  Loading Rate Increased loading rate... Why? An increased rate -- increases sy and TS gives less time for -- decreases %EL dislocations to move past obstacles. s TS e sy larger e TS smaller sy e Chapter 8 - 40  Impact Testing Impact loading: (Charpy) -- severe testing case -- makes material more brittle -- decreases toughness 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.) final height initial height Chapter 8 - 41  Temperature Increasing temperature... --increases %EL and Kc Ductile-to-Brittle Transition Temperature (DBTT)... FCC metals (e.g., Cu, Ni) Impact Energy BCC metals (e.g., iron at T < 914°C) polymers Brittle More Ductile High strength materials ( s y > E/150) Adapted from Fig. 8.15, Callister 7e. Temperature Ductile-to-brittle transition temperature Chapter 8 - 42  Design Strategy: Stay Above The DBTT! Pre-WWII: The Titanic WWII: Liberty ships Reprinted w/ permission from R.W. Hertzberg, Reprinted w/ permission from R.W. Hertzberg, "Deformation and Fracture Mechanics of Engineering "Deformation and Fracture Mechanics of Engineering Materials", (4th ed.) Fig. 7.1(a), p. 262, John Wiley and Materials", (4th ed.) Fig. 7.1(b), p. 262, John Wiley and Sons, Inc., 1996. (Orig. source: Dr. Robert D. Ballard, Sons, Inc., 1996. (Orig. source: Earl R. Parker, The Discovery of the Titanic.) "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. Chapter 8 - 43  Fatigue Fatigue = failure under cyclic stress. specimen compression on top Adapted from Fig. 8.18, Callister 7e. (Fig. 8.18 is motor from Materials Science in bearing bearing counter Engineering, 4/E by Carl. A. Keyser, Pearson flex coupling Education, Inc., Upper tension on bottom Saddle River, NJ.) Stress varies with time. s smax -- key parameters are S, sm, and sm S frequency smin time Key points: Fatigue... --can cause part failure, even though smax < sc. --causes ~ 90% of mechanical engineering failures. Chapter 8 - 44  Fatigue Design Parameters Fatigue limit, Sfat: S = stress amplitude case for --no fatigue if S < Sfat unsafe steel (typ.) Sfat safe Adapted from Fig. 8.19(a), Callister 7e. 10 3 10 5 10 7 10 9 N = Cycles to failure Sometimes, the fatigue limit is zero! S = stress amplitude case for unsafe Al (typ.) safe Adapted from Fig. 8.19(b), Callister 7e. 10 3 10 5 10 7 10 9 N = Cycles to failure Chapter 8 - 45  Fatigue Mechanism Crack grows incrementally typ. 1 to 6 da  K  m dN ~ s  a increase in crack length per loading cycle crack origin Failed rotating shaft --crack grew even though Kmax < Kc --crack grows faster as s increases Adapted from Fig. 8.21, Callister 7e. crack gets longer (Fig. 8.21 is from D.J. loading freq. increases. Wulpi, Understanding How Components Fail, American Society for Metals, Materials Park, OH, 1985.) Chapter 8 - 46  Improving Fatigue Life 1. Impose a compressive S = stress amplitude Adapted from surface stress Fig. 8.24, Callister 7e. (to suppress surface Increasing near zero or compressive sm cracks from growing) sm moderate tensile sm Larger tensile sm N = Cycles to failure --Method 1: shot peening --Method 2: carburizing shot C-rich gas put surface into compression 2. Remove stress bad better concentrators. Adapted from Fig. 8.25, Callister 7e. bad better Chapter 8 - 47  Creep Sample deformation at a constant stress (s) vs. time s s,e 0 t Primary Creep: slope (creep rate) decreases with time. Secondary Creep: steady-state i.e., constant slope. Adapted from Fig. 8.28, Callister 7e. Tertiary Creep: slope (creep rate) increases with time, i.e. acceleration of rate. Chapter 8 - 48  Creep Occurs at elevated temperature, T > 0.4 Tm tertiary primary secondary elastic Adapted from Figs. 8.29, Callister 7e. Chapter 8 - 49  Secondary Creep Strain rate is constant at a given T, s -- strain hardening is balanced by recovery stress exponent (material parameter)  Qc  e s  K 2s exp  n  activation energy for creep strain rate  RT  (material parameter) material const. applied stress Strain rate 200 Stress (MPa) 427°C increases 100 538 °C for higher T, s 40 20 649 °C 10 10 -2 10 -1 1 Steady state creep rate es (%/1000hr) Chapter 8 - 50  Larson–Miller parameter (L) Larson–Miller parameter is the most extensively used extrapolation technique for predicting creep life of metallic materials The Larson-Miller parameter describes the equivalence of time at temperature for a steel under the thermally activated creep process of stress rupture. It permits the calculation of the equivalent times necessary for stress rupture to occur at different temperatures Chapter 8 - 51  Creep Failure Failure: Estimate rupture time along grain boundaries. S-590 Iron, T = 800°C, s = 20 ksi g.b. cavities 100 applied Stress, ksi 20 stress 10 data for S-590 Iron 1 12 16 20 24 28 L(10 3 K-log hr) 24x103 K-log hr Time to rupture, tr T ( 20  logt r )  L T ( 20  logt r )  L temperature function of 1073K applied stress time to failure (rupture) Ans: tr = 233 hr Chapter 8 - 52  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 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 s increases. - for higher T (T > 0.4Tm): - time to fail decreases as s or T increases. Chapter 8 - 53