2 Part of the top of an Aloha Airlines jet peeled of during the flight
3 Liberty Ship failures involved both brittle fractures and fatigue fractures. Of 2700 ships built, 400 suffered hull and deck fractures. 90 were considered serious and in 20 ships fracture was essentially total with 10 ships breaking in half without warning.
5 Outline Fracture of Materials Types of Fracture Brittle Fracture Ductile FractureBrittle to Ductile TransitionFracture MechanicsStress ConcentrationLEFMK & GKcAppendix - Griffith Theory
6 FractureFracture: separation of a body into pieces due to stress, at temperatures below the melting point.Steps in fracture:Crack formationCrack propagationDepending on the ability of material to undergo plasticdeformation before the fracture two fracture modes can be defined - ductile or brittle
7 Ductile fracture - most metals (not too cold): Extensive plastic deformation ahead of crackCrack is “stable”: resists further extension unless applied stress is increasedBrittle fracture - ceramics, ice, cold metals:Relatively little plastic deformationCrack is “unstable”: propagates rapidly without increase in applied stressDuctile fracture is preferred in most applications
8 Brittle vs. Ductile Fracture Ductile materials - extensive plastic deformation andenergy absorption (“toughness”) before fractureBrittle materials - little plastic deformation and lowenergy absorption before fracture
9 Brittle vs. Ductile Fracture Brittle fracture; (b) Shearing fracture in single crystal(c) Completely ductile (d) Ductile fracture
10 Ductile Fracture Necking, (b) Cavity Formation, (c) Cavity coalescence to form a crack,
12 (Cap-and-cone fracture in Al) Ductile Fracture(Cap-and-cone fracture in Al)
13 Ductile FractureScanning Electron Microscopy: Fractographic studies at high resolution. Spherical “dimples” correspond to micro-cavities that initiate crack formation.
14 Brittle Fracture No appreciable plastic deformation Crack propagation is very fastCrack propagates nearly perpendicular to the direction of the applied stressCrack often propagates by cleavage – breaking of atomic bonds along specific crystallographic planes (cleavage planes)
15 Brittle FractureBrittle fracture in a mild steel
16 Brittle FractureTransgranular fracture: Fracture cracks pass through grains. Fracture surface have faceted texture because of different orientation of cleavage planes in grains.Intergranular fracture: Fracture crack propagation is along grain boundaries (grain boundaries are weakened or embrittled by impurities segregation etc.)
18 Ductile-to-Brittle Transition Ductile-to-Brittle Transition: As temperature decreases a ductile material can become brittleAlloying usually increases the ductile-to-brittle transition temperature.FCC metals remain ductile down to very low temperatures.For ceramics, this type of transition occurs at much higher temperatures than for metals.
19 Ductile-to-Brittle Transition DBTT: Ductile-Brittle Transition Temperature
22 Stress Concentration m 2 (a/)1/2 For a long crack oriented perpendicular to the applied stress the maximum stress near the crack is:m 2 (a/)1/2(1)where σ is the applied external stress, a is the half-length of the crack, and ρ the 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).
23 Stress Concentration Factor The ratio of the maximum stress and the nominal applied tensile stress is denoted as the stress concentration factor, Kt, where Kt can be calculated by Equation 1. The stress concentration factor is a simple measure of the degree to which an external stress is amplified at the tip of a small crack.
24 Stress ConcentrationThe stress distribution at the crack tip in a thin plate for an elastic solid is given by:(2)
25 Stress Concentration K: Stress Intensity Factor (3) Unit of K: psiin, MN/(m3/2), or MPam
26 Stress ConcentrationSubstitute K into Equation (3):(4)
28 Energy Release Rate G = - dU/dA Energy Release Rate: In 1956, Irwin defined an energy release rate, G, which is a measure of the energy available for an increment of crack extension:G = - dU/dASince G is obtained from the derivative of a potential, it is also called the crack extension force or crack driving force
29 Energy Release Rate Griffith Approach: G = 2a/E Where is the nominal stress, a is half-length of crack, E is Young’s Modulus
30 Relationship between K and G Mode IPlain Stress:G = KI2/EPlain Strain:G = KI2(1-2)/E
35 Fracture ToughnessKc: If we assume a material fails locally at some combination of stresses and strains, then crack extension must occur at a critical K value. This Kc value, which is a measure of fracture toughness, is a material constant that is independent of the size and geometry of the cracked body.
36 Fracture Toughness Measurement MEASURE STRENGTH WITH A CRACK OF KNOWN LENGTHSHARP CRACKLINEAR ELASTIC?SMALL PROCESS ZONE RULESASTM STANDARDS: E-399
38 SUMMARY – Cont’d Stress Concentration Stress distribution in front of the crack tip Stress concentration factorLinear Elastic Fracture MechanicsK: Stress Intensity FactorG: Energy Release RateRelationship between K & GCrack tip plasticityFracture Toughness
39 Appendix - Griffith Theory for Brittle Fracture For defect-free material:sth ~ E/10 is orders of magnitude higher than usually observedWhere E – Young’s modulusg – specific surface energya0 – lattice parametersth – theoretical strength of the material
40 Energy criterion for brittle fracture (Griffith Theory) Energy criterion: when rate of change of the release of elastic energy with respect to crack size rate at which energy is consumed to create new surfaces, fracture occursOnset:Where s – Griffith’s stress (the critical stress)gs – surface energy/per unit area
41 Griffith EquationGriffith equation is only for glasses & ceramics – brittle fracture, no plastic deformation occurs prior to fractureMetals and polymers plastic deformation occurs before fracture modified Griffith equation (Orowan equation)