1Introduction to Materials Science, Chapter 8, FailureUniversity of Tennessee, Dept. of Materials Science and Engineering1FailureShip-cyclic loadingfrom waves.Computer chip-cyclicthermal loading.Introduction to Materials Science, Chapter 8, FailureUniversity of Tennessee, Dept. of Materials Science and Engineering2How do Materials Break?Chapter Outline: Failure Ductile vs. brittle fracturePrinciples of fracture mechanics9 Stress concentration Impact fracture testing Fatigue (cyclic stresses)9 Cyclic stresses, the S—N curve9 Crack initiation and propagation9 Factors that affect fatigue behavior Creep (time dependent deformation)9 Stress and temperature effects9Alloys for high-temperature useNot tested: 8.10 Crack propagation rate8.15 Data extrapolation methods2Introduction to Materials Science, Chapter 8, FailureUniversity of Tennessee, Dept. of Materials Science and Engineering3• Stress-strain behavior (Room T):σεE/10E/1000.1perfect mat’l-no flawscarefully produced glass fibertypical ceramictypical strengthened metaltypical polymerTS << TSengineeringmaterialsperfectmaterials• DaVinci (500 yrs ago!) observed...--the longer the wire, thesmaller the load to fail it.• Reasons:--flaws cause premature failure.--Larger samples are more flawed!IDEAL VS REAL MATERIALSIntroduction to Materials Science, Chapter 8, FailureUniversity of Tennessee, Dept. of Materials Science and Engineering4Fracture: separation of a body into pieces due to stress, at temperatures below the melting point. Steps in fracture: ¾ crack formation ¾ crack propagation FractureDepending on the ability of material to undergo plastic deformation before the fracture two fracture modes can be defined - ductile or brittle• Ductile fracture - most metals (not too cold): ¾ Extensive plastic deformation ahead of crack¾ Crack is “stable”: resists further extension unless applied stress is increased• Brittle fracture - ceramics, ice, cold metals: ¾ Relatively little plastic deformation¾ Crack is “unstable”: propagates rapidly without increase in applied stressDuctile fracture is preferred in most applications3Introduction to Materials Science, Chapter 8, FailureUniversity of Tennessee, Dept. of Materials Science and Engineering5Brittle vs. Ductile Fracture• Ductile materials - extensive plastic deformation and energy absorption (“toughness”) before fracture• Brittle materials - little plastic deformation and low energy absorption before fractureIntroduction to Materials Science, Chapter 8, FailureUniversity of Tennessee, Dept. of Materials Science and Engineering6Brittle vs. Ductile FractureA. Very ductile, soft metals (e.g. Pb, Au) at room temperature, other metals, polymers, glasses at high temperature.B. Moderately ductile fracture, typical for ductile metalsC. Brittle fracture, cold metals, ceramics.AB C4Introduction to Materials Science, Chapter 8, FailureUniversity of Tennessee, Dept. of Materials Science and Engineering7Ductile Fracture (Dislocation Mediated)(a) Necking, (b) Cavity Formation, (c) Cavity coalescence to form a crack, (d) Crack propagation, (e) FractureCrack grows 90o to applied stress 45O-maximum shear stressIntroduction to Materials Science, Chapter 8, FailureUniversity of Tennessee, Dept. of Materials Science and Engineering8Ductile FractureTypical Cup-and-Cone fracture in ductile AlScanning Electron Microscopy: Fractographic studies at high resolution. Spherical “dimples” correspond to micro-cavities that initiate crack formation.5Introduction to Materials Science, Chapter 8, FailureUniversity of Tennessee, Dept. of Materials Science and Engineering9¾ No appreciable plastic deformation¾ Crack propagation is very fast¾ Crack propagates nearly perpendicular to the direction of the applied stress¾ Crack often propagates by cleavage - breaking of atomic bonds along specific crystallographic planes (cleavage planes). Brittle Fracture (Limited Dislocation Mobility)Brittle fracture in a mild steelIntroduction to Materials Science, Chapter 8, FailureUniversity of Tennessee, Dept. of Materials Science and Engineering10A. Transgranular fracture: Fracture cracks pass through grains. Fracture surface have faceted texture because of different orientation of cleavage planes in grains.B. Intergranular fracture: Fracture crack propagation is along grain boundaries (grain boundaries are weakened or embrittled by impurities segregation etc.)ABBrittle Fracture6Introduction to Materials Science, Chapter 8, FailureUniversity of Tennessee, Dept. of Materials Science and Engineering11Fracture strength of a brittle solid is related to the cohesive forces between atoms. One can estimate that the theoretical cohesive strength of a brittle material should be ~ E/10. But experimental fracture strength is normally E/100 - E/10,000.This much lower fracture strength is explained by the effect of stress concentration at microscopic flaws. The applied stress is amplified at the tips of micro-cracks, voids, notches, surface scratches, corners, etc. that are called stress raisers. The magnitude of this amplification depends on micro-crack orientations, geometry and dimensions. Stress ConcentrationFigure by N. Bernstein &D. Hess, NRLIntroduction to Materials Science, Chapter 8, FailureUniversity of Tennessee, Dept. of Materials Science and Engineering12Stress Concentrationwhere σ0is the applied external stress, a is the half-lengthof the crack, and ρtthe radius of curvature of the crack tip. (note that a is half-length of the internal flaw, but the full length for a surface flaw).The stress concentration factor is: 2/1t0ma2ρσ≈σFor a long crack oriented perpendicular to the applied stress the maximum stress near the crack tip is:2/1t0mta2Kρ≈σσ=7Introduction to Materials Science, Chapter 8, FailureUniversity of Tennessee, Dept. of Materials Science and Engineering13Simulation courtesyof Farid Abraham. Used with permission from International Business Machines Corporation.• Tensile loading (horizontal dir.) of a FCC metal with notches in the top and bottom surface.• Over 1 billion atoms modeled in 3D block.• Note the large increase in disl. density.SIMULATION: DISLOCATION MOTION/GENERATIONIntroduction to Materials Science, Chapter 8, FailureUniversity of Tennessee, Dept. of Materials Science and Engineering14ENGINEERING FRACTURE DESIGN• Avoid sharp