ENGR-45_Lec-19_Failure-1.ppt 1 Bruce Mayer, PE Engineering-45: Materials of Engineering Bruce Mayer, PE Licensed Electrical & Mechanical Engineer Engineering 45 Material Failure (1)

ENGR-45_Lec-19_Failure-1.ppt 2 Bruce Mayer, PE Engineering-45: Materials of Engineering Learning Goals.1 – Failure  How Flaws In A Material Initiate Failure  How Fracture Resistance is Quantified How Different Material Classes Compare  How to Estimate The Stress at Fracture  Factors that Change the Failure Stress Loading Rate Loading History Temperature

ENGR-45_Lec-19_Failure-1.ppt 3 Bruce Mayer, PE Engineering-45: Materials of Engineering Learning Goals.2 – Failure  FATIGUE Failure Fatigue Limit Fatigue Strength Fatigue Life  CREEP at Elevated Temperatures Incremental Yielding at <σ y Over a Long Time Period at Elevated Temperature

ENGR-45_Lec-19_Failure-1.ppt 4 Bruce Mayer, PE Engineering-45: Materials of Engineering Ductile vs Brittle Fracture Classification: Ductile fracture is desirable! Ductile: warning before fracture Brittle: No warning Very Ductile Moderately Ductile Brittle Fracture behavior: LargeModerate%Ra or %EL: Small Ductility:

ENGR-45_Lec-19_Failure-1.ppt 5 Bruce Mayer, PE Engineering-45: Materials of Engineering Example: Pipe Failure  Ductile Failure One Piece Large Deformation LEAK before BURST  Brittle Failure Many Pieces Small Deformation EXPLOSIVE Burst –NOT Good 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.

ENGR-45_Lec-19_Failure-1.ppt 6 Bruce Mayer, PE Engineering-45: Materials of Engineering Fracture Formation  Fracture Formation Steps 1.Crack Initiation 2.Crack Propagation  DUCTILE Fracture Significant PLASTIC Deform. at Crack Tip Crack(s) Grow Relatively Slowly  BRITTLE Fracture Once Brittle-Crack Starts Propagation can NOT be stopped –Can Proceed at Speeds up to MACH-1

ENGR-45_Lec-19_Failure-1.ppt 7 Bruce Mayer, PE Engineering-45: Materials of Engineering Moderately Ductile Fracture  Stages to Fracture upon Loading necking void nucleation void growth and linkage shearing at surface fracture    Resulting fracture surfaces (steel) 50  m 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 ) Particles serve as void nucleation sites 100  m Fracture surface of tire cord wire loaded in tension. Courtesy of F. Roehrig, CC Technologies, Dublin, OH. Used with permission.

ENGR-45_Lec-19_Failure-1.ppt 8 Bruce Mayer, PE Engineering-45: Materials of Engineering Ductile vs. Brittle Tensile Failure  Ductile Failure  “Cup-and-Cone” Fracture Surface  Brittle Failure  “Matted” Fracture Surface

ENGR-45_Lec-19_Failure-1.ppt 9 Bruce Mayer, PE Engineering-45: Materials of Engineering Brittle-Fracture Surfaces Intergranular (between grains) Intragranular (within/across 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 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 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., m3m 4 mm 160  m 1 mm

ENGR-45_Lec-19_Failure-1.ppt 10 Bruce Mayer, PE Engineering-45: Materials of Engineering Brittle-Fracture  Characteristics of Brittle Fracture No Significant Deformation Proceeds by Rapid Crack Propagation Crack Direction Almost  to Applied Load Relatively Flat Fracture Surface

ENGR-45_Lec-19_Failure-1.ppt 11 Bruce Mayer, PE Engineering-45: Materials of Engineering 6 Reprinted w/ permission from R.W. Hertzberg, "Deformation and Fracture Mechanics of Engineering Materials", (4th ed.) Fig John Wiley and Sons, Inc., Ideal vs Real materials   E/10 E/ perfect mat’l-no flaws carefully produced glass fiber typical ceramictypical strengthened metal typical polymer  Rm-Temp Stress-Strain Behavior DaVinci (500 yrs ago!) Observed –The LONGER the Wire, the SMALLER to Load Needed to Cause Failure Reasons –Matl Flaws Cause Premature Failure –Larger samples have more flaws

ENGR-45_Lec-19_Failure-1.ppt 12 Bruce Mayer, PE Engineering-45: Materials of Engineering Stress Concentration  Elliptical hole in a plate:  σ distrib. in front of hole:   o 2a  Define Stress Concentration Factor:  Large K t Promotes Facture-Failure NOT SO BAD K t =3 BAD! K t >>3 ρ t  Local Hole, or CrackTip, Radius

ENGR-45_Lec-19_Failure-1.ppt 13 Bruce Mayer, PE Engineering-45: Materials of Engineering 8 Avoid sharp corners! Engineering Fracture Design r = Fillet Radius w h  o  max r/h sharper fillet radius increasingw/h Stress Conc. Factor, K t  max  o =

ENGR-45_Lec-19_Failure-1.ppt 14 Bruce Mayer, PE Engineering-45: Materials of Engineering Griffith Theory of Brittle Fracture  A. A. Griffith (1920s) proposed that very small, MICROSCOPIC cracks weaken brittle materials This is why the theoretical Tensile strength of a brittle elastic solid (~E/10) is not achieved  Griffith proposed that all brittle materials contain a POPULATION of small cracks and flaws that have a VARIETY of sizes, shapes, and orientations  Fracture occurs when the THEORETICAL cohesive strength of the material is exceeded at the TIP of one of these flaws This was shown with glass, where very fine and super- strong WHISKERS were shown to have strengths CLOSE to the THEORETICAL However, larger samples very quickly form surface flaws, and the strength drops!

ENGR-45_Lec-19_Failure-1.ppt 15 Bruce Mayer, PE Engineering-45: Materials of Engineering Glass Rod Bending Fracture  Cantilever-Load on Glass Rod  Load to Failure by Brittle Fracture  The Fracture Surface  The Facture Surface displays 3, more or less, Distinct Regions

ENGR-45_Lec-19_Failure-1.ppt 16 Bruce Mayer, PE Engineering-45: Materials of Engineering Glass Rod Bending Fracture  Mirror Zone  A smooth region surrounding the fracture origin  Mist Zone  A small band of rougher surface surrounding the mirror region.  Hackle Zone  Area composed of large irregularly oriented facets.

ENGR-45_Lec-19_Failure-1.ppt 17 Bruce Mayer, PE Engineering-45: Materials of Engineering Crack Propagation  Cracks propagate due to SHARPNESS of the crack tip  A PLASTIC material DEFORMS at the tip, “blunting” the crack plasticBrittle Deformed Region  Perform Energy balance on the crack Elastic 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

ENGR-45_Lec-19_Failure-1.ppt 18 Bruce Mayer, PE Engineering-45: Materials of Engineering Griffith Brittle-Fracture Theory  When a Crack Propagates There is a RELEASE of Elastic Strain Energy There is Energy CONSUMED To Extend The Crack By Creating NEW Fracture Surfaces  Griffith’s Proposal for Crack Propagation Propagation Requires –[release of elastic strain energy] > [energy required to form new crack surfaces] –  c  Critical Stress for Crack Propagation (Pa) –E  Elastic Modulus (Pa) –  s  Surface Energy (J/m) –a  Crack Length (m)

ENGR-45_Lec-19_Failure-1.ppt 19 Bruce Mayer, PE Engineering-45: Materials of Engineering Example – Brittle Fracture  Given Glass Sheet with Tensile Stress,  = 40 Mpa E = 69 GPa  = 0.3 J/m  Find Maximum Length of a Surface Flaw  Plan Set  c = 40Mpa Solve Griffith Eqn for Edge-Crack Length  Solving

ENGR-45_Lec-19_Failure-1.ppt 20 Bruce Mayer, PE Engineering-45: Materials of Engineering When Does a Crack Propagate?  The Crack Tip Radius, ρ t, can be Quite Small  Thus σ Crk-Tip can be Very Large distance,x, from crack tip  tip  K 2  a  increasing K  Crack propagates when the tip stress is large enough to make: K ≥ K c Kc  Fracture Toughness (MPa  m) –Cool units

ENGR-45_Lec-19_Failure-1.ppt 21 Bruce Mayer, PE Engineering-45: Materials of Engineering K, K c : Geometry, Load, Matl  Recall Condition for Crack Propagation Values of K for Some Standard Loads & Geometries K ≥ K c Stress Intensity Factor: --Depends on load & geometry. Fracture Toughness: --Depends on the material, temperature, environment, & rate of loading.  2a  a a

ENGR-45_Lec-19_Failure-1.ppt 22 Bruce Mayer, PE Engineering-45: Materials of Engineering Crack Extension Modes  Cracks can Extend in 3 Modes: I, II, III  Combination of Modes Can Occur; Particularly Modes I+III (think Drive Shaft)  Mode- I is By Far the Most Common Mode-I: Opening Mode Mode-II: Shearing or Sliding Mode Mode-III: Tearing or AntiPlane Mode

ENGR-45_Lec-19_Failure-1.ppt 23 Bruce Mayer, PE Engineering-45: Materials of Engineering K I c for Several Metals  Higher Values of K I c are Desired

ENGR-45_Lec-19_Failure-1.ppt 24 Bruce Mayer, PE Engineering-45: Materials of Engineering 11 increasing 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 (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 Fracture Toughness

ENGR-45_Lec-19_Failure-1.ppt 25 Bruce Mayer, PE Engineering-45: Materials of Engineering 12 Crack growth condition: Largest, most stressed cracks grow first --Result 1: Max flaw size dictates design stress. --Result 2: Design stress dictates max. flaw size. K ≥ K c Design Against Crack Growth (Y  Unitless Geometry Factor)

ENGR-45_Lec-19_Failure-1.ppt 26 Bruce Mayer, PE Engineering-45: Materials of Engineering The Y-Parameter  Y for Some Geometries and Loading B  Material Base-depth (into Screen/Page)

ENGR-45_Lec-19_Failure-1.ppt 27 Bruce Mayer, PE Engineering-45: Materials of Engineering 13 Two designs to consider... Design A --largest physical flaw is 9 mm --failure stress = 112 MPa Design B --use same material --largest physical flaw is 4 mm --failure stress = ? Use... Key point: Y and K I c are the same in both designs. --Result: 9 mm112 MPa 4 mm Answer: Reducing flaw size pays off! Material has K I c = 26 MPa-m 0.5 Design Ex: Aircraft Wing

ENGR-45_Lec-19_Failure-1.ppt 28 Bruce Mayer, PE Engineering-45: Materials of Engineering Loading Rate  Increased Loading Rate INcreases σ y and TS DEcreases %EL  Reason An increased rate gives less time for dislocations to move past obstacles  Thus Material Deformation Can Be Different based on the DYNAMICS of the Load Application    y  y TS Larger d  /dt Smaller d  /dt

ENGR-45_Lec-19_Failure-1.ppt 29 Bruce Mayer, PE Engineering-45: Materials of Engineering Temperature Effects  Increasing Temperature Increases %EL & K c As Discussed Previously, Some Materials Exhibit a Ductile-to-Brittle Transition-Temperature (DBTT) BCC metals (e.g., iron at T < 914C) Impact Energy Temperature FCC metals (e.g., Cu, Ni) High strength materials σyσy >E/150) polymers More Ductile Brittle Ductile-to-brittle transition temperature Charpy V-Notch (CVN) Impact Test

ENGR-45_Lec-19_Failure-1.ppt 30 Bruce Mayer, PE Engineering-45: Materials of Engineering Design Criteria: Stay Above DBTT  Problem: DBTT ~ Room Temperature Fabricate-OK; CRACK in Cold Water Pre-WWII: The Titanic WWII: Liberty ships 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.)

ENGR-45_Lec-19_Failure-1.ppt 31 Bruce Mayer, PE Engineering-45: Materials of Engineering WhiteBoard Work  None Today