Chapter 9 Failure of Materials

Failure of Materials Why study materials failure? - design of component @ structure needs the engineer to minimize (prevent) failure. - important to understand the concept of 3 failure modes; 1. Fracture. 2. Fatigue. 3. Creep. Topics covered in this chapter… Fundamental concept - flaws @ crack (defects). - modes of failure. - characteristic & mechanisms. - fracture mechanics. Testing techniques Failure of materials… - failure of engineering materials is undesirable. - several cause of failure: -- improper materials selection, processing & design. -- defects (i.e: internal/external flaws/cracks). -- economic losses. -- interference with availability of products & services. need an appropriate preventive measurement to against failure. - produce & prevent failure. • Ductile fracture: -- one piece -- large deformation Failure of Materials mode mechanism testing technique Fracture Ductile fracture Impact test Brittle fracture Fatigue Initial crack Fatigue test Crack grow Creep test • Brittle fracture: -- many pieces -- small deformations Creep Other examples of failure Computer chip- cyclic thermal loading. Hip implant- cyclic loading from walking. Ship-cyclic loading from waves. Adapted from Fig. 22.30(b), Callister 7e. (Fig. 22.30(b) is courtesy of National Semiconductor Corporation.) Adapted from chapter-opening photograph, Chapter 9, Callister & Rethwisch 3e. (by Neil Boenzi, The New York Times.) Adapted from Fig. 22.26(b), Callister 7e.

Failure of Materials mode of failure: Fracture Fracture of materials results in separation of stressed solid into two or more parts. ductile fracture ductile fracture brittle fracture accompanied by significant plastic deformation & slow crack propagation. - common at low strain rate & high temp. - three steps : 1. Specimen forms neck & cavities within neck. 2. Cavities form crack & crack propagates towards surface, perpendicular to stress. 3. Direction of crack changes to 45o resulting in cup-cone fracture. little @ no significant plastic deformation before fracture & high crack propagation. - Catastrophic (rapid crack propagation). - common at high strain rates & low temp. - three stages: 1. Plastic deformation concentrates dislocation along slip planes. 2. Microcracks nucleate due to shear stress where dislocations are blocked. 3. Crack propagates to fracture. characteristic of fracture SEM micrograph At low operating temp., ductile to brittle transition (DBT) takes place Fracture behavior Very ductile Moderately ductile Brittle brittle fracture Schematic diagram SEM micrograph %AR or %EL Large Moderate Small Ductile fracture is usually more desirable than brittle fracture! Ductile: Warning before fracture Brittle: No warning

mode of failure: Fracture Failure of Materials mode of failure: Fracture Moderately ductile fracture ductile fracture necking s void nucleation shearing at surface fracture void growth & linkage 100 mm Fracture surface of tire cord wire loaded in tension. Courtesy of F. Roehrig, CC Technologies, Dublin, OH. Used with permission. SEM micrograph evolution to failure brittle fracture surfaces Intergranular (between grains) Intragranular (within grains) 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.) V-shaped “chevron” 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.) 160 mm brittle fracture 4 mm 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. 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.) 3 mm SEM micrograph origin of crack 1 mm

mode of failure: Fracture Failure of Materials mode of failure: Fracture brittle fracture (in ceramics) ductile fracture - characteristic of fracture behavior: -- origin point. -- initial region (mirror) is flat & smooth. -- after reaches critical velocity crack branches (mist & hackle). SEM micrograph ductile fracture (in thermoplastic polymer) characteristic of fracture behavior: -- craze formation prior to cracking. -- during crazing, plastic deformation of spherulites. -- and formation of micro voids and fibrillar bridges. brittle fracture aligned chains SEM micrograph fibrillar bridges microvoids crack

mode of failure: Fracture Failure of Materials mode of failure: Fracture concept of fracture mechanics - engineering materials don't reach theoretical strength. - flaws produce stress concentrations that cause premature failure. Flaws are stress concentrators Stress concentration at crack tip Engineering Fracture Design - avoid sharp corners. t , r fillet radius w h o s max smax Stress Conc. Factor, K t = s0 2.5 2.0 increasing w/h Results from crack propagation. Griffith Crack Crack Propagation - cracks propagate due to sharpness of crack tip. 1.5 where t = radius of curvature so = applied stress sm = stress at crack tip brittle 1.0 r/h deformed region 0.5 1.0 ductile sharper fillet radius

mode of failure: Fracture Failure of Materials mode of failure: Fracture concept of fracture mechanics - engineering materials don't reach theoretical strength. - flaws produce stress concentrations that cause premature failure. Crack Propagation TS << TS engineering materials perfect s e E/10 E/100 0.1 perfect mat’l-no flaws carefully produced glass fiber typical ceramic typical strengthened metal typical polymer Stress-strain curves (Room T) perfect & engineering materials - crack propagates if above critical stress. i.e., sm > sc or Kt > Kc where E = modulus of elasticity s = specific surface energy a = one half length of internal crack Kc = c/so Design Against Crack Growth - crack growth condition: K ≥ Kc = - largest, most stressed cracks grow first! -- Result 1: Max. flaw size dictates design stress. -- Result 2: Design stress dictates max. flaw size. s amax no fracture amax s no fracture

Design Example: Aircraft Wing Failure of Materials mode of failure: Fracture concept of fracture mechanics - engineering materials don't reach theoretical strength. - flaws produce stress concentrations that cause premature failure. Design Example: Aircraft Wing Fracture Toughness, KIC for selected materials • Material has Kc = 26 MPa-m0.5 Graphite/ Ceramics/ Semicond Metals/ Alloys Composites/ fibers Polymers 5 K Ic (MPa·m 0.5 ) 1 Mg alloys Al alloys Ti alloys Steels Si crystal Glass - soda Concrete Si carbide PC 6 0.7 2 4 3 10 <100> <111> Diamond PVC PP Polyester PS PET C-C (|| fibers) 0.6 7 100 Al oxide Si nitride C/C ( fibers) Al/Al oxide(sf) Al oxid/SiC(w) Al oxid/ZrO (p) Si nitr/SiC(w) Glass/SiC(w) Y O /ZrO • Two designs to consider... Design A -- largest flaw is 9 mm -- failure stress = 112 MPa Design B -- use same material -- largest flaw is 4 mm -- failure stress = ? • Use... • Key point: Y and Kc are the same in both designs. 9 mm 112 MPa 4 mm -- Result: Answer: • Reducing flaw size pays off! 8

mode of failure: Fracture Failure of Materials mode of failure: Fracture testing technique: Impact test aim: to investigate the energy absorbed & fracture of materials during impact loading at various temperature. Important information from impact test… 1. Fracture (brittle @ ductile). 2. Brittleness (impact energy @ % shear). 3. Ductility (impact energy @ % shear). 4. Toughness (energy absorbed). 5. Ductile-to-Brittle Transition (DBT) temperature. Pre-WWII: The Titanic - classify into 3: 1. Charpy impact test. 2. Izod impact test. 3. Drop weight impact test. fracture behavior can be shown in impact energy vs temperature curves. 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.) BCC metals (e.g., iron at T < 914°C) Impact Energy Temperature High strength materials (s y > E/150) & polymers DBT temperature FCC metals (e.g., Cu, Ni) more brittle more ductile final height initial height (Charpy) WWII: Liberty ships Design Strategy: Stay above the DBT! 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.) Adapted from Fig. 9.18(b), Callister & Rethwisch 3e. (Fig. 9.18(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.) Sinking of Titanic: Titanic was made up of steel which has DBT temperature 32oC. On the day of sinking, sea temperature was –2oC which made the the structure highly brittle and susceptible to more damage.

mode of failure: Fatigue Failure of Materials mode of failure: Fatigue Key points: Fatigue... - failure under cyclic loading. can cause part failure, even though smax < sc. causes ~ 90% of mechanical engineering failures. metals often fail at much lower stress at cyclic loading compared to static loading. crack nucleates at region of stress concentration & propagates due to cyclic loading. failure occurs when cross sectional area of the metal too small to withstand applied load. Fatigue fractured surface of keyed shaft - stress varies with time. -- key parameters are: 1. stress amplitude, S (@ a). 2. mean stress, sm. 3. frequency, f (will convert to no. of cycle, N). Fracture started here Stress amplitude, S = stress to cause failure Number of cycle, N = 1/f Final rupture - fatigue behavior can be shown in SN curves. Important point from fatigue test… 1. Fatigue limit. 2. Fatigue strength. 3. Fatigue life. testing technique: Fatigue test s max min time m S Mean stress Stress amplitude tension on bottom compression on top counter motor flex coupling specimen bearing Stress range Stress range

mode of failure: Fatigue Failure of Materials mode of failure: Fatigue Fatigue Design Parameters Sometimes, the fatigue limit is zero! -- fatigue occurs at any time. Improving Fatigue Life - Fatigue limit, Sfat: -- no fatigue if S < Sfat 1. Impose a compressive surface stress (to suppress surface cracks from growing) example: SN curves for typical steel Adapted from Fig. 9.25(a), Callister & Rethwisch 3e. Sfat N = Cycles to failure 10 3 5 7 9 unsafe safe S = stress amplitude S = stress amplitude --Method 1: shot peening shot unsafe safe 10 3 10 5 10 7 10 9 put surface into compression N = Cycles to failure Adapted from Fig. 9.25(b), Callister & Rethwisch 3e. --Method 2: carburizing C-rich gas example: SN curves for typical polymers • Fatigue limit: - PMMA, PP, PE 2. Remove stress concentrators. • No fatigue limit: - PET, Nylon (dry) bad better Adapted from Fig. 9.32, Callister & Rethwisch 3e.

Failure of Materials T(20 + log tr) = L mode of failure: Creep Creep is progressive deformation under constant stress. - Occurs at elevated temperature, T > 0.4 Tm -- important in high temperature applications. Creep failure along grain boundaries. applied stress g.b. cavities creep calculation… Time to rupture, tr Adapted from Figs. 9.36, Callister & Rethwisch 3e. Data from creep test… 1. creep strain,  2. temperature, T 3. time, t s,e t s T = temperature tr = time to failure (rupture) L = function of applied stress example: elastic primary secondary tertiary Estimate rupture time for S-590 Iron, T = 800°C & s = 20 ksi testing technique: Creep test Creep test determines the effect of temperature & stress on creep rate. Metals are tested at constant stress at different temperature & constant temperature with different stress. 100 20 Stress, ksi 10 data for - creep behavior can be shown in -t curves. S-590 Iron Important information from -t curve… 1 12 20 24 28 16 Primary creep: creep rate (slope) decreases with time due to strain hardening. Secondary creep: creep rate is constant due to simultaneous strain hardening and recovery process. -- steady-state. Tertiary creep: creep rate (slope) increases with time leading to necking & fracture. L(10 3 K-log hr) 24x103 T(20 + log tr) = L 1073K Ans: tr = 233 hr Adapted from Fig. 9.35, Callister & Rethwisch 3e.

SUMMARY • 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. 13