2nd Chapter Failure (Chapter 8)

Transcription

1 2nd Chapter Failure (Chapter 8) 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 1Neil 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.

2 Learning Objectives 1. Describe the mechanism of crack propagation for both ductile and brittle modes of fracture. 2. Explain why the strengths of brittle materials are much lower than predicted by theoretical calculations. 3. Define fracture toughness in terms of (a) a brief statement (b) an equation; define all parameters in this equation. 4. Make a distinction between fracture toughness and plane strain fracture toughness. 5. Name and describe the two impact fracture testing techniques. 2 School of Materials Science and Engineering

3 Learning Objectives 6. Define fatigue and specify the conditions under which it occurs. 7. From a fatigue plot for some material, determine (a) the fatigue lifetime (at a specified stress level) (b) the fatigue strength (at a specified number of cycles). 8. Define creep and specify the conditions under which it occurs. 9. Given a creep plot for some material, determine (a) the steady-state creep rate (b) the rupture lifetime. 3 School of Materials Science and Engineering

4 2.1 Fracture mechanisms Ductile fracture Accompanied by significant plastic deformation with high energy absorption before fracture. Brittle fracture Accompanied by Little or no plastic deformation With low energy absorption before fracture. Catastrophic Brittle fracture 4 Ductile fracture

5 Ductile and brittle are relative terms; whether a particular fracture is one mode or the other depends on the situation. Ductility may be quantified in terms of percent elongation (Equation 6.11) and percent reduction in area (Equation 6.12). Furthermore, ductility is a function of temperature of the material, the strain rate, and the stress state. Engineering tensile stress, smaller %EL larger %EL 5 Engineering tensile strain,

6 Any fracture process involves two steps crack formation + propagation The mode of fracture is highly dependent on the mechanism of crack propagation. Ductile fracture is characterized by extensive plastic deformation in the vicinity of an advancing crack. Furthermore, the crack propagation proceeds relatively slowly. Such a crack is often said to be stable it resists any further extension unless there is an increase in the applied stress. Brittle fracture: cracks may spread extremely rapidly, with very little accompanying plastic deformation. 6 Such cracks may be said to be unstable crack propagation, once started, will continue spontaneously without an increase in magnitude of the applied stress.

7 Ductile fracture is almost always preferred for two reasons: First, brittle fracture occurs suddenly and catastrophically without any warning. Ductile fracture, the presence of plastic deformation gives warning that fracture is imminent, allowing preventive measures to be taken. Second, more strain energy is required to induce ductile fracture because ductile materials are generally tougher. Under an applied tensile stress, most metal alloys are ductile, ceramics are typically brittle, polymers may exhibit both types of fracture. 7

8 Ductile vs Brittle Failure Fracture behavior: Very Ductile Moderately Ductile Brittle Classification: %RA or %EL Large Moderate Small (a) Ductile Highly fracture ductile is fracture in which Ductile: the specimen necks down Brittle: to a point. usually more Warning before No (b) desirable Moderately than ductile fracture fracture after some necking. warning brittle fracture! (c) Brittle fracture without any plastic deformation.

9 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. 9

10 Moderately Ductile Failure Failure Stages: necking void nucleation void growth and coalescence to form crack shearing at surface fracture 10 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.

11 Fractographic Studies Much more detailed information regarding the mechanism of fracture is available from microscopic examination. Moderately Ductile vs. Brittle Failure 11 cup-and-cone fracture In aluminum brittle fracture In a mild steel 低碳钢

12 Ductile Failure Shear lip 剪切唇区 Fiber region 纤维区 Radiation region 辐射区 Focus point--- crack source 12

13 Ductile Failure Fibrous region Shear lip Scanning electron fractograph (a) spherical dimples ductile fracture resulting from uniaxial tensile loads. (b) parabolic-shaped dimples ductile fracture resulting from shear loading. 13

14 Brittle Failure Arrows indicate point at which failure originated V-shaped markings Fanlike patterns 14

15 Grain Path of crack propagation Cleavage:crack propagation corresponds to the successive and repeated breaking of atomic bonds along specific crystallographic planes.--transgranular (or transcrystalline) : the fracture cracks pass through the grains. The fracture surface may have a grainy or faceted texture. 15

16 Intergranular fracture: crack propagation is along grain boundaries. Three-dimensional nature of grains can be seen on the fracture surface. Grain boundaries Path of crack propagation 16

17 Brittle Fracture Surfaces Intergranular (between grains) 304 S. Steel (metal) Transgranular (through grains) 316 S. Steel (metal) 4mm Polypropylene 聚丙烯 (polymer) Al Oxide (ceramic) 160 mm 3mm 17 1mm

18 2.2 Principles of fracture mechanics I. Stress Concentration t where m 2 o a t 1/ 2 t = radius of curvature a = half crack length o = applied tensile stress m = stress at crack tip K t o Measured fracture strength < theoretical calculation 18 the presence of microscopic flaws in the bulk material The stress may be amplified or concentrated at the tip of cracks.

19 Concentration of Stress at Crack Tip Stress concentration factor the degree to which a stress is amplified 19 Stress amplification Microscopic cracks; Macroscopic voids sharp corners notches 2a

20 Engineering Fracture Design Avoid sharp corners! r, Fillet radius w max h 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 max 0 r/h 20

21 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 Stress concentration is more significant in brittle than in ductile materials. 21 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 Criterion for Crack Propagation Crack propagates if crack-tip stress ( m ) exceeds a critical stress ( c ) i.e., m > c where E = modulus of elasticity s = specific surface energy a = one half length of internal crack c 2E s a 1/ 2 brittle materials For ductile materials => replace s with s + p where p is plastic deformation energy 22 EXAMPLE PROBLEM 8.1

23 II. Fracture Toughness Fracture toughness:a measure of a material s resistance to brittle fracture when a crack is present. Unit: Y is a dimensionless parameter or function that depends on both crack and specimen sizes and geometries, as well as the manner of load application. thin specimens: K c ----depend on specimen thickness. thick specimens: independent of thickness; under these conditions a condition of plane strain exists. 23 plane strain fracture toughness

24 Fracture Toughness Fracture toughness: K IC is fracture toughness for most situations. 24 The three modes of crack surface displacement. (a) Mode I, opening or tensile mode; (b) Mode II, sliding mode (c) Mode III, tearing mode.

25 KIc(MPa m 0.5 ) ---especially useful in predicting catastrophic Fracture Toughness Ranges Metals/ Alloys Steels Ti alloys Al alloys Mg alloys Graphite/ Ceramics/ Semicond Polymers PP PC failure in materials having intermediate ductilities. Composites/ fibers Brittle materials--low values,vulnerable to catastrophic C-C( fibers) failure; 1 Ductile materials-- relatively large values. --one of fundamental material property --Influencing factors: Al/Al oxide(sf) Temperature 2 Y 2 O 3 /ZrO 2 (p) 4 C/C( fibers) Strain rate 1 Al oxid/sic(w) 3 Diamond Si nitr/sic(w) 5 Al oxid/zro 2 (p) 4 Si carbide Microstructure: Al oxide PET Glass/SiC(w) grain size 6 Si nitride Yield strength PVC 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 <100> Si crystal PS Glass 6 <111> 0.7 Glass -soda Polyester Concrete Table

26 III. Design Against Crack Growth Crack growth condition: K K c = Y a Largest, most highly stressed cracks grow first! --Scenario 1: Max. flaw size dictates design stress. design Y K c a max --Scenario 2: Design stress dictates max. flaw size. 2 1 Kc a max Ydesign a max fracture fracture no fracture a max no fracture 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 Use... c Y K Ic a max Design B --use same material --largest flaw is 4 mm --failure stress =? Key point: Y and K Ic are the same for both designs. --Result: Y K Ic = a = constant 112 MPa 9 mm 4 mm c amax a A c max B 27 Answer: ( c ) B 168 MPa

28 Dye penetrant inspection 着色渗透探伤 Acoustic emission 声发射检测 28

29 DESIGN EXAMPLE 8.1 Material Specification for a Pressurized Spherical Tank 29

30 1. Yielding criterion: y, using y instead of, introduce a factor of safety N 30

31 2. Leak before break criterion: a = t The medium carbon steel will be the best candidate material. 31

32 Questions 1. What are the two fracture mechanisms? (classification) 2. What factors may influence fracture toughness of a material? 3. Please re-arrange the following figures according to the time-sequence during fracture. a b c d e 32

33 Fracture toughness testing --Impact Testing Impact loading: -- severe testing case -- makes material more brittle -- decreases toughness -- qualitative results (Charpy) final height initial height 33

34 Influence of Temperature on Impact Energy Ductile-to-Brittle Transition Temperature (DBTT)... Low-strength (FCC and HCP) metals (e.g., Cu, Ni) Impact Energy Brittle BCC metals (e.g., iron at T < 914ºC) Low-strength steels, polymers More Ductile High-strength materials ( y > E/150) Ductile-to-brittle transition temperature Temperature 34 One of the primary functions of the impact tests is to determine whether a material experiences a ductile-to-brittle transition with decreasing temperature.

35 Design Strategy: Stay Above The DBTT! Pre-WWII: The Titanic WWII: Liberty ships 35 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.

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37 2.3 Fatigue Fatigue = failure under applied cyclic stress. Axial:tension-compression; Flexural:bending; Torsional:twisting bearing specimen Stress varies with time. compression on top bearing -- key parameters are a, m, and cycling frequency motor flex coupling tension on bottom max m min counter 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.) a time 37 Key points: Fatigue... --can cause part failure, even though max < y (or TS). --responsible for ~ 90% of mechanical engineering failures. --catastrophic, without warning

38 Mean stress Reversed stress cycle: symmetrical; Range of stress Repeated stress cycle: asymmetrical; Stress amplitude Random stress cycle: random Stress ratio 38

39 The S N curve becomes horizontal at higher N values. Types S fat represent of largest Fatigue value of Behavior fluctuating stress that will not cause failure for an infinite number of cycles. 39 Fatigue limit, S fat : --no fatigue if S < S fat Fatigue strength, Fatigue life --there is no fatigue limit! S = stress amplitude S = stress amplitude S 1 Fatigue strength at N 1 S fat safe safe unsafe unsafe N Fatigue life at S 1 N = Cycles to failure case for steel (typ.) Adapted from Fig. 8.19(a), Callister & Rethwisch 8e. Fatigue strength: the stress level 10 at 3 which 10 5 failure 10 7 will 10occur 9 for some specified number of cycles. N = Cycles to failure Fatigue life: cycle number to cause failure at a specified stress level. case for Al (typ.) Adapted from Fig. 8.19(b), Callister & Rethwisch 8e.

40 Rate of Fatigue Crack Growth Crack grows gradually da dn K m ~ typ. 1 to 6 a The process of fatigue (1) crack initiation; (2) crack propagation (3) final failure increase in crack length per loading cycle Failed rotating shaft -- crack grew even though crack origin K max < K c fracture toughness crack grows faster as increases crack gets longer loading freq. increases. beachmarks /clamshell mark Adapted from Fig. 8.21, Callister & Rethwisch 8e

41 Factors affact Fatigue Life Mean stress mean stress fatigue life Surface effects Fatigue life is especially sensitive to the condition and configuration of the component surface. Design criteria as well as various surface treatments may be the factors that affect fatigue life. 41

42 Improving Fatigue Life 1. Impose compressive surface stresses (to suppress surface cracks from growing) surface strengthening --Method 1: shot peening shot put surface into compression --Method 2: Case hardening: Carburizing or nitriding C-rich gas Remove stress concentrators. Chamfer: rounding bad bad better better Adapted from Fig. 8.25, Callister & Rethwisch 8e.

43 2.4 Creep < yield stress Sample deformation at a constant stress () vs. time Plastic deformation, > yield stress Constant-load creep of metals 0 t 初始蠕变 / 暂态蠕变 Primary / transient Creep: slope (creep rate) decreases with time. Secondary Creep: steady-state creep 稳态蠕变 i.e., constant slope /t) 43 Tertiary Creep: slope (creep rate) increases with time, i.e. acceleration of rate. 加速蠕变

44 Creep: Temperature Dependence Occurs at elevated temperature, T > 0.4 T m (in K) (1) instantaneous strain at the time of stress application increases; primary secondary tertiary (2) steady-state creep rate (slope) is increased; (3) rupture lifetime decreases. elastic 44 Adapted from Fig. 8.29, Callister & Rethwisch 8e.

45 Secondary Creep Strain rate is constant at a given T, -- strain hardening is balanced by recovery stress exponent (material parameter) 45 strain rate material const. Strain rate increases with increasing T, s Stress (MPa) activation energy for creep (material parameter) applied stress ºC 538ºC 649ºC Steady state creep rate (%/1000hr) s 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.)

46 Prediction of Creep Rupture Lifetime The Larson Miller parameter in terms of temperature and rupture lifetime. temperature constant time to failure (rupture) Estimate rupture time S-590 alloy, T = 800ºC, = 140 MPa ( 1073 K)(20 log t ) r 3 24x10 Ans: t r = 233 hr 46

47 Estimate the rupture time for S-590 alloy, T = 750ºC, s = 140 MPa Solution: 47 Time to rupture, t r T(20 logtr ) ( 1023 K)(20 logt ) r L temperature function of applied stress time to failure (rupture) Ans: t r = 2887 hr 3 24x10 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).) 47 1 Stress (10 3 psi)

48 48 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 < 0.4T m), 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 > 0.4T m ): - time to rupture decreases as or T increases.

49 49 SUMMARY Three usual causes of failure: - Improper materials selection and processing. - Inadequate component design. - Component misuse. measures to extend fatigue fatigue life: - Reducing the mean stress level. - Eliminating sharp surface discontinuities. - Improving the surface finish by polishing - Imposing surface residual compressive stresses by shot peening. - Case hardening by using a carburizing or nitrding process

50 Homeworks

51 That s all for today, thanks!

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

54 Example: Superhard aluminum alloy -- aircraft industry T ---TS, Elastic modulus, Necking, Ductility, 54 Resistance to deformation