Failure Studies in Materials_ch8

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 loadingfrom waves.Computer chip-cyclicthermal loading.Hip implant-cyclicloading from walking.Adapted from Fig. 22.30(b), Callister 7e. (Fig. 22.30(b) is courtesy of National Semiconductor Corporation.)Adapted from Fig. 22.26(b), Callister 7e.Chapter 8: Mechanical Failure & Failure AnalysisAdapted from chapter-opening photograph, Chapter 8, Callister 7e. (by Neil Boenzi, The New York Times.)

Fracture mechanismsDuctile fractureOccurs with plastic deformation

Brittle fractureOccurs with Little or no plastic deformationThus they are Catastrophic meaning they occur without warning!

Ductile vs Brittle Failure Ductile fracture is nearly always desirable!Ductile: warning before fractureBrittle: No warning

Ductile failure: --one piece --large deformationFigures 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.Example: Failure of a Pipe

Evolution to failure:Moderately Ductile Failure

Ductile vs. Brittle FailureAdapted from Fig. 8.3, Callister 7e.cup-and-cone fracturebrittle fracture

Brittle FailureArrows indicate point at which failure originatedAdapted from Fig. 8.5(a), Callister 7e.

Intergranular(between grains) Intragranular (within grains)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.)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.)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.)Polypropylene(polymer)Reprinted w/ permission from R.W. Hertzberg, "Deformation and Fracture Mechanics of Engineering Materials", (4th ed.) Fig. 7.35(d), p. 303, John Wiley and Sons, Inc., 1996.3 mm4 mm160 mm1 mm(Orig. source: K. Friedrick, Fracture 1977, Vol. 3, ICF4, Waterloo, CA, 1977, p. 1119.)Brittle Fracture Surfaces: Useful to examine to determine causes of failure

Failure Analysis Failure AvoidanceMost failure occur due to the presence of defects in materialsCracks or Flaws (stress concentrators) Voids or inclusionsPresence of defects is best found before hand and they should be determined non-destructivelyX-Ray analysisUltra-Sonic InspectionSurface inspectionMagna-fluxDye Penetrant

Stress-strain behavior (Room Temp):Ideal vs Real Materials

Considering Loading Rate Effect Increased loading rate... -- increases sy and TS -- decreases %EL Why? An increased rate allows less time for dislocations to move past obstacles.s

Impact (high strain rate) Testing Impact loading (see ASTM E23 std.): -- severe testing case -- makes material act more brittle -- decreases toughness Useful to compare alternative materials for severe applicationsAdapted 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.)

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

Figure 8.3 Variation in ductile-to-brittle transition temperature with alloy composition. (a) Charpy V-notch impact energy with temperature for plain-carbon steels with various carbon levels (in weight percent). (b) Charpy V-notch impact energy with temperature for FeMn0.05C alloys with various manganese levels (in weight percent). (From Metals Handbook, 9th ed., Vol. 1, American Society for Metals, Metals Park, OH, 1978.)

Pre-WWI: The Titanic WWII: Liberty ships Problem: Used a type of steel with a DBTT ~ Room temp.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.)Design Strategy: Build Steel Ships Quickly!As a Designer: Stay Above The DBTT!

Flaws are Stress Concentrators!Results from crack propagationGriffith Crack Model:

where t = radius of curvature of crack tipso = applied stresssm = stress at crack tip

tAdapted from Fig. 8.8(a), Callister 7e.

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

Engineering Fracture Design Avoid sharp corners!sAdapted from G.H. Neugebauer, Prod. Eng. (NY), Vol. 14, pp. 82-87 1943.)max is the concentrated stress in the narrowed region

Crack PropagationCracks propagate due to sharpness of crack tip A plastic material deforms at the tip, blunting the crack. deformed regionbrittle

Energy balance on the crackElastic strain energy- energy is stored in material as it is elastically deformedthis energy is released when the crack propagatescreation of new surfaces requires (this) energyplastic

When Does a Crack Propagate?Crack propagates if applied stress is above critical stress

whereE = modulus of elasticitys = specific surface energya = one half length of internal crackKc = sc/s0

For ductile materials replace gs by gs + gp where gp is plastic deformation energyi.e., sm > sc or Kt > Kc

Fracture ToughnessComposite 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.K1c plane strain stress concentration factor with edge crack; A Material Property we use for design, developed using ASTM Std: ASTM E399 - 09 Standard Test Method for Linear-Elastic Plane-Strain Fracture Toughness K Ic of Metallic Materials

Crack growth condition: Largest, most stressed cracks grow first!As Engineers we must Design Against Crack GrowthY is a material behavior shape factor

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

Lets look at Another SituationSteel subject to tensile stress of 1030 MPa, it has K1c of 54.8 MPa(m) a handbook valueIf it has a largest surface crack .5 mm (.0005 m) long will it grow and fracture?

What crack size will result in failure?

Figure 8.7 Two mechanisms for improving fracture toughness of ceramics by crack arrest. (a) Transformation toughening of partially stabilized zirconia involves the stress-induced transformation of tetragonal grains to the monoclinic structure, which has a larger specific volume. The result is a local volume expansion at the crack tip, squeezing the crack shut and producing a residual compressive stress. (b) Microcracks produced during fabrication of the ceramic can blunt the advancing crack tip

Fatigue behavior: Fatigue = failure under cyclic stress Stress varies with time. -- key parameters are S (stress amplitude), sm, and frequency Key points when designing in Fatigue inducing situations: -- fatigue can cause part failure, even though smax < sc. -- fatigue causes ~ 90% of mechanical engineering failures. Because of its importance, ASTM and ISO have developed many special standards to assess Fatigue Strength of materials (Fig. 8.18 is from Materials Science in Engineering, 4/E by Carl. A. Keyser, Pearson Education, Inc., Upper Saddle River, NJ.)

Some important Calculations in Fatigue Testing

Figure 8.8 Fatigue corresponds to the brittle fracture of an alloy after a total of N cycles to a stress below the tensile strength.

Fatigue limit, Sfat: --no fatigue failure if S < Sfat Fatigue Limit is defined in: ASTM D671

Adapted from Fig. 8.19(a), Callister 7e. Fatigue Design Parameters

Lets look at an Example

For metals other than Ferrous alloys, F.S. is taken as the stress that will cause failure after 108 cycles

Figure 8.21 Fatigue behavior for an acetal polymer at various temperatures. (From Design Handbook for Du Pont Engineering Plastics, used by permission.)For polymers, we consider fatigue life to be (only) 106 cycles to failure thus fatigue strength is the stress that will lead to failure after 106 cycles

Cracks in Material grows incrementallytyp. 1 to 6increase in crack length per loading cycle Failed rotating shaft --crack grew even though Kmax < Kc --crack grows faster as Ds increases crack gets longer loading freq. increases.Adapted fromfrom D.J. Wulpi, Understanding How Components Fail, American Society for Metals, Materials Park, OH, 1985.Fatigue Mechanism

Figure 8.11 An illustration of how repeated stress applications can generate localized plastic deformation at the alloy surface leading eventually to sharp discontinuities.

Figure 8.12 Illustration of crack growth with number of stress cycles, N, at two different stress levels. Note that, at a given stress level, the crack growth rate, da/dN, increases with increasing crack length, and, for a given crack length such as a1, the rate of crack growth is significantly increased with increasing magnitude of stress.

Improving Fatigue Life1. Impose a compressive surface stresses (to suppress surface crack growth)Adapted fromFig. 8.24, Callister 7e.

Figure 8.17 Fatigue strength is increased by prior mechanical deformation or reduction of structural discontinuities.

Other Issues in Failure Stress Corrosion CrackingWater can greatly accelerate crack growth and shorten life performance in metals, ceramics and glasses Other chemicals that can generate (or provide H+ or O2-) ions also effectively reduce fatigue life as these ions react with the metal or oxide in the material

Figure 8.18 The drop in strength of glasses with duration of load (and without cyclic-load applications) is termed static fatigue. (From W. D. Kingery, Introduction to Ceramics, John Wiley & Sons, Inc., New York, 1960.)

Figure 8.19 The role of H2O in static fatigue depends on its reaction with the silicate network. One H2O molecule and one Si OSi segment generate two SiOH units, which is equivalent to a break in the network.

Figure 8.20 Comparison of (a) cyclic fatigue in metals and (b) static fatigue in ceramics.

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.SUMMARY

*****************Stress concentrated at crack tip****************************