1. Lecture 14 Fracture and Impact ME 330 Engineering Materials Fracture Process Ductile Fracture Brittle Fracture Impact Testing Stress Concentration Factor, K t Case Study - Silver Bridge Disaster Read Chapter 8

2. Fracture mechanics: Study of cracks and crack-like defects with a view of understanding and predicting the crack’s growth tendencies. Such growth may be either stable (slow and safe) or unstable (instantaneous and catastrophic). FRACTURE MECHANICS: An Introduction

3. 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. 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 Adapted from chapter-opening photograph, Chapter 8, Callister 7e. (by Neil Boenzi, The New York Times.)

4. Collapse of Molasses tank in Boston in 1919 Cargo ships failures (World War II) (Liberty ships) -Due to presence of stress concentrations in the ship structure -ability of cracks to transverse welds joining adjacent steel plates -faulty welds -inferior steel quality These ships were first to have an all welded hull, could be fabricated much faster than earlier riveted designs. Today all ships are welded but sufficient knowledge was gained to avoid similar failures. FRACTURE FAILURES: Examples

5. Several bridges fractured and collapsed in Belgium, Canada, Australia, US (last 50 years), e.g. Duplessis Bridge in Quebec, Canada 1951 - due to preexistent crack in steel microstructure Minnesota Bridge in Minneapolis, 2007 - due to design flaw and extra weight Sinking of Titanic in 1912 -due to brittle fracture of steel with high sulfur content Challenger Space Shuttle - O-ring seal failed in one of the main boosters due to cold weather Columbia Shuttle Accident (2003) - hole was punctured in one of the wings made of carbon- carbon composite (a piece of insulating foam from the external fuel tank peeled off, puncturing the wing) FRACTURE FAILURES: Examples (cont)

7. FRACTURE MECHANICS : Historical Perspective 1.Experiments of Leonardo da Vinci (500 years ago) He measured strength of iron wires and found that the strength varied inversely with wire length. These results implied that flaws in the material controlled strength. 2.Inglis (1913) Stress field in the presence of elliptical hole 3. Griffith (1920) Quantitative connection between fracture stress and flaw size He applied a stress analysis of an elliptical hole to the unstable propagation of a crack. Theory applied to brittle materials only. 4.Westergaard (1938) semi-inverse technique for analyzing stresses and displacements near a sharp crack tip.

8. 5.Irwin (1956) energy release rate concept 6.Irwin (1957) introduced crack tip characterizing parameter called stress intensity factor All above: Linear elastic fracture mechanics (LEFM) 7.Irwin, Dugdale, Barenblatt, Wells (1960’s) analysis of yielding at crack tip 8. Rice (1968) J- integral (parameter to characterize nonlinear behavior of crack tip) 9. Begley and Landes (1971) used J integral to characterize fracture toughness of steels 10. Shih and Hutchinson (1976) mathematical relationship between fracture toughness, stress, and flaw size. FRACTURE MECHANICS : Historical Perspective

9. Fracture Process Crack formation (initiation) Crack propagation –Dictates mode of fracture –Ductile Extensive plastic deformation - often visible deformation Proceeds relatively slowly Stable - crack resists further extension unless there is an increased stress –Brittle Small plastic deformation Spread rapidly Unstable - crack propagation will occur without increased stress

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

11. Ductile failure: --one piece --large 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. Example: Failure of a Pipe Brittle failure: --many pieces --small deformation

12. Typical Tensile Fracture Surfaces  Soft metals (Ag, Au)  Metals, polymers, glasses at high temperatures  Ductile Metals  Brittle Metals (Cast Iron)  Ceramics  Brittle Plastics From: Callister

13. Ductile vs Brittle Failure Very Ductile Moderately Ductile Brittle Fracture behavior: LargeModerate%AR or %EL Small Ductile fracture is usually desirable! Adapted from Fig. 8.1, Callister 7e. Classification: Ductile: warning before fracture Brittle: No warning

14. Evolution to failure: Resulting fracture surfaces (steel) 50 mm particles serve as void nucleation sites. 50 mm 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. Moderately Ductile Failure necking  void nucleation void growth and linkage shearing at surface fracture

15.  (MPa)  (%)  Necking begins at UTS *  Microvoids form in neck  3-D stress state *  Microvoid enlargement, coalescence, & growth *  Further microvoid growth  Rapid crack propagation around outer neck * “Fibrous” region “Shear” region ~45º Ductile Tensile Fracture- Cup-and-cone formation From: Callister

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

17. Brittle Tensile Fracture No appreciable deformation “Rapid” crack propagation –Perpendicular to applied load –“Flat” fracture surface Fracture surfaces show point of crack formation –Often visible with naked eye –“Chevron” marks point to center –Fan-like patterns Transgranular - bond breaking along crystallographic planes –Cracks pass through grains, change orientation –Also called “cleavage” Intergranular - cracking along grain boundaries From: Hertzberg, Callister

18. 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. 3 mm 4 mm 160 mm 1 mm (Orig. source: K. Friedrick, Fracture 1977, Vol. 3, ICF4, Waterloo, CA, 1977, p. 1119.) Brittle Fracture Surfaces

19. Intergranular (between grains) Intragranular (within grains)

20. Stress-strain behavior (Room T): Ideal vs Real Materials TS << TS engineering materials perfect materials   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.

21. By analyzing an “infinite” plate with elliptical hole, Inglis found: For a crack, typically have –a = 10 -3 –  = 10 -9 – Often define a stress concentration factor, K t as: Obviously, there are some limitations Stress Concentration  applied 2a   local  applied

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

23. Macroscopic Stress Concentrators Stress amplification often encountered in macroscopic structures Complete tabulated values for many geometries in: –Pilkey, Walter D. Peterson’s Stress Concentration Factors,Wiley, New York, 2 nd Ed., 1997 From: Callister

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

25. Engineering Fracture Design r/hr/h sharper fillet radius increasingw/hw/h 00.51.0 1.5 2.0 2.5 Stress Conc. Factor, K t  max  o = Avoid sharp corners!  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.) r, fillet radius w h o  max

26. Loading Rate Increased loading rate... -- increases  y and TS -- decreases %EL Why? An increased rate gives less time for dislocations to move past obstacles.   yy yy TS larger  smaller 

27. Torsional Fracture From: Dowling Simple test to conduct Uncomplicated by necking Ductile –Fail on planes of maximum shear Traverse and longitudinal to specimen axis Jagged square peaks Angle of twist proportional to shear strain Brittle Failure –Fail on planes of maximum tension 45° to specimen axis Helical spiral fracture

28. Impact Testing Initial attempts to “qualify” fracture characteristics Izod & Charpy or Falling weight –Measure impact energy (“notch toughness”) –Designed for worst case failures Low temperature High strain rate Triaxial stress (notch generates constraint) –Simple to perform Specimens cheap to make Equipment is inexpensive From: Callister

29. Testing Apparatus Instrumented Load Cell Indenting Wedge Pendulum –Measures change in height (h - h`) Falling weight –Instrumented tup –Load cell similar to tensile test From: Instron, Callister

30. Impact Measures Instrumented test measures: –Load during impact Important measure: Maximum load –Deflection of impacting tup Plot deflection versus load –Integrate to find energy Important measure: Total energy absorbed Run several tests at different temperatures –Plot energy versus temperature –Find ductile-to-brittle transition Note: variability between tests * From: Callister

31. Trends with Temperature As temperature increases –Larger % shear lip –Increased impact energy –More shear failure –More ductile in behavior From: Hertzberg, Callister

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

33. Ductile-to-Brittle Transition Higher temperatures show higher energy absorption –Can see a distinct temperature (or range) where absorption characteristics change drastically Appearance of fracture surface also changes –Ductile - fibrous or dull (shear), 45º surfaces –Brittle - granular or shiny (cleavage) –Usually see some combination Most materials show some form of transition –BCC and HCP metals (not FCC - yield stress always lower than stress to cause brittle failure, regardless of temperature) –Most polymers - closely related to glass transition temperature –Ceramics at very high temperatures

34. Pre-WWII: 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: Stay Above The DBTT!