Mechanical Failure - Case Studies in Materials - Lab | MATE 410, Lab Reports of Materials science

Download Mechanical Failure - Case Studies in Materials - Lab | MATE 410 and more Lab Reports Materials science in PDF only on Docsity! 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? 1 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. MECHANICAL FAILURE Very Ductile Moderately Ductile Brittle Fracture behavior: Large Moderate%AR or %EL : Small 2 • Ductile fracture is desirable! • Classification: Ductile: warning before fracture Brittle: No warning DUCTILE VS BRITTLE FAILURE JOM, 50 (1) (1998), pp. 12-18. It made the Titanic sink ☺ 4 • Evolution to failure: necking void nucleation void growth and linkage shearing at surface fracture σ • Resulting fracture surfaces (steel) 50 μm particles serve as void nucleation sites. 50 μm 100 μm 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.) Fracture surface of tire cord wire loaded in tension. Courtesy of F. Roehrig, CC Technologies, Dublin, OH. MODERATELY DUCTILE FAILURE 5 • 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, "Defor-mation and Fracture Mechanics of Engineering Materials", (4th ed.) Fig. 7.35(d), p. 303, John Wiley and Sons, Inc., 1996. 3μm 4 mm 160μm 1 mm (Orig. source: K. Friedrick, Fracture 1977, Vol. 3, ICF4, Waterloo, CA, 1977, p. 1119.) BRITTLE FRACTURE SURFACES 6 • DaVinci (500 yrs ago!) observed... --the longer the wire, the smaller the load to fail it. • Reasons: --flaws cause premature failure. --Larger samples “are more flawed”! Code Atlanticus 16th century EARLY STUDIES IN BRITTLE FRACTURE Before fracture mechanics There was the Charpy test ASTM E23-07ae1 Standard Test Methods for Notched Bar Impact Testing of Metallic Materials We get an energy absorbed during fracture. Results vary depending on the details of the notch – comparison of materials is tricky Success stories of the Charpy test BDTT=Brittle to ductile temperature transition Irradiation effects Old nuclear reactors are deemed safe based on Charpy specimens that were stored in the reactor when the reactor was installed Initially design for 10-20 years some of these reactors have lasted for 30-40 years. The Charpy specimens are running out. Ideal strength (newer calculations) IN REALITY WE ARE FAR BELOW 7 • Elliptical hole in a plate: σ σo 2a FLAWS ARE STRESS CONCENTRATORS! ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ += b a21max σσ • Maximum stress at the tip σσ σσ 2110 3 max max =⇒= =⇒= ba ba ρ ρ abaab =⇔= //2 )(221max ρρ σ ρ σσ >>≈⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ += aaa For sharp cracks stress → ∞ • ρ at a crack tip is very small! • Result: crack tip stress is very large. WHEN DOES A CRACK PROPAGATE? A.A. Griffith (1920) said: A crack will propagate if the energy released is larger than the energy spent during the propagation of the crack Energy versus crack size S CR S CRA SBA E at E ta da dU at E taUU γπσγπσ γπσ 20420 4 22 22 =⇒=+−⇒= +−+= a UA Stable Unstable aCR growscrack grow) tonot tend (does stable iscrack CR CR aa aa > < Alternatively a ES π γσ 2FAILURE = For an existing crack of size 2a there is a stress that makes this crack critical 9 • Crack propagates when the elastic released due to crack growth is higher than the surface energy created by the additional crack surface (Griffith’s criterion for brittle materials – Linear elastic fracture mechanics) WHEN DOES A CRACK PROPAGATE? F w t a a E S critical π γσ 2= wt F =σ 321321 CK S K Ea γπσ 2= energysurface=Sγ 11 Graphite/ Ceramics/ Semicond Metals/ Alloys Composites/ fibersPolymers 5 K Ic (M P a · m 0 .5 ) 1 Mg alloys Al alloys Ti alloys Steels Si crystal Glass-soda Concrete Si carbide PC Glass6 0.5 0.7 2 4 3 10 20 30 <100> <111> Diamond PVC PP Polyester PS PET C-C(|| fibers)1 0.6 6 7 40 50 60 70 100 Al oxide Si nitride C/C( fibers)1 Al/Al oxide(sf)2 Al oxid/SiC(w)3 Al oxid/ZrO2(p)4 Si nitr/SiC(w)5 Glass/SiC(w)6 Y2O3/ZrO2(p)4 Kc metals Kc comp Kc cer≈ Kc poly in c re a si n g Based on data in Table B5, Callister 6e. 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. FRACTURE TOUGHNESS 1000 100 3S Fracture toughness Ki./MN m-22 o 0.01 O41 ENGINEERING Al 1 YIELD BEFORE / roo8 FRACTURE GUIDE LINES ‘ 4 vo ENGINEERING” 4 bz- COMPOSITES 10 a= M7) exonecrne | 7 POLYMERS r 7 ‘ q eee) | ENGINEERING “| ‘CERAMICS 7 7 POROUS 7 7” CERAMICS ee 7 4 af 4 FRACTURE 4 BEFORE YIELD 7 53 at 4 10 10° mm pK pedis) a 1 10 100 1000 10.000 Strength o,/MN m-2 Fracture-toughness, X,,. plotted against strength. a,. The contours show the value of KL ma?—roughly, the diameter of the process-zone at a crack tip (units: mm). The guide lines of constant Kit, and Kije, are used in yield-before-break and leak-before-break design. Figure 8.32 Ashby property chart of fracture toughness versus strength (Ashby, 1989, pp. 1273-93; with permission of Geometry factor Y —2b take 4 ieee 1.8F—- Ki =v Bae 4 Le t Kye fighe yo 17 =] Figi= (Sec jira oO 0.1 0.2 0.3 o4 os 0.6 2a/W i) Krefiglo wo Higi=L12- 0.231 (a/b) +10,5Storb¥* -2L7atarbP + 3039(o/b)* 34 (ob) 3.2 3.0 28 Ate ys Ky = y Stee Bw’ Where Mi is the bending moment 2.6 |— Y te Thickness. 2.4 )— Kj stale Wa o=6M/tb® 22 fig) L12+ O203{e6)-L197iovp)? r= Nolo vro +180 lor bl fale L122-140(a/ble%33ta/bi -13.08tarbi%s Latta" 20 Pure bending we sw =8 {c) {0} 18 SEN pi sw =4 16 0 Of O02 O83 O04 05 06 ” K 71a PLANE STRAIN vs. PLANE STRESS a <—_ —_e w-a Frachire z bp tearing (relieved by on 45 degree Poisson plane contraction) Bafore Frachire After Fracture section AA Pg OF —n| Lg =< —_- Gre Fracture bur & = 0 by cleavage (Poisson on AE contraction plane revented bp urrounding material) Pojore Fracture ’ After Fracture section A-A PLANE STRAIN FRACTURE TOUGHNESS KIC We focus on KIC because it is a true material property (i.e., it does not depend on geometry of the specimen) FRACTURE TOUGHNESS TESTING | ry ne f “O (a) ‘Single edge-notched bend SE(B) (b) Compact specimen, om € (c) Arc-shape tension specimen, A(T) (d) Disk-shape compact specimen, DC(T) (e) _Arc-shape bend specimen, A(B) Small scale yielding? • Griffiths approach needs to be modified: In addition to the surface energy term, the irreversible energy lost due to plasticity needs to be considered. ( ) a E plasticityS critical π γγ σ + = 2 Yplasticity <A W P/ da atda What about fracture toughness of ductile materials? • A design approach for ductile materials exists (J-integral) but it is mathematically complex (albeit extremely important in applications such as aerospace engineering) • We can apply the Griffith’s theory (Linear elastic fracture mechanics ) if yielding of the material occurs at small scale. Why small scale yielding is needed for valid testing? bad OK Plastically yielded area around crack tip Summary of conditions • Sharp crack • Pmax /PQ <1.1 • Plane strain • Small scale yielding • If not iterate with larger specimen Modes of Fracture -Mode I (Opening mode) -Mode II (Sliding mode) -Mode III (Tearing mode) (c) (a) Figure 7.1 “Goofy duck Crack/beak elosed.(b) 0 (Courtesy of M. H. for three modes of crack loading, (a) ode. (c) Sliding mode. (d) Tearing mode. Mode superposition • Stresses from different modes can be superimposed outside the plastic zone. • Complex mode criteria exist but are out of scope here. Homework I 1. Compute the stresses (normalized by KI /(2πa)0.5 around a crack loading in plane strain and mode I at: θ=0, 45, 90, 135, and 180o . Draw the principal directions of stress in each location. 2. Find two examples of inclusions with significant differences of strength than the surrounding matrix (one harder inclusion and one softer than the matrix). Provide data (with references of the strength of each phase, i.e., inclusion and matrix). Photos are welcome. 3. Find as many as possible online, fully readable textbooks and handbooks on fracture and fatigue that exist in our library (In about 10 minutes I found 8; see if you can find more ☺ ).