Fracture Behavior of Bulk Crystalline Materials zFundamentals of Fracture yDuctile Fracture yBrittle Fracture yCrack Initiation and Propagation zFracture Mechanics yFracture Toughness yDesign

Fundamentals of Fracture zA separation of an object into two or more pieces in response to active stresses far below the melting temperature of the material. zAtoms on the surface of a material give rise to a surface energy yStems from the open bonds on the outer atoms yGrain boundary surface energyGrain boundary surface energy xlink to grain boundary surface energy section (fract3.ppt) zTwo steps in the process of fracture: yCrack initiation yPropagation

Fundamentals of Fracture zSimple fracture may occur by one of two methods, ductile or brittle yDependent upon the plastic deformation of the material xProperties which influence the plastic deformation of a material Modulus of elasticity Crystal structure zRelated links: yThe Dislocation ProcessThe Dislocation Process xLink to dislocation emission processes (Rice paper??) yDuctile-to-Brittle TrasitionDuctile-to-Brittle Trasition xLink to ductile-brittle transition (fract2.ppt)

Fundamentals of Fracture z(a) Highly ductile fracture z(b) Moderately ductile fracture with necking yCalled a cup-and -cone fracture yMost common form of ductile fracture z(c) Brittle fracture yNo plastic deformation occurring

Ductile Fracture zInvolves a substantial amount of plastic deformation and energy absorption before failure. yCrack propagation occurs very slowly as the length the crack grows. yOften termed a stable crack, in that it will not grow further unless additional stress is applied zThe fracture process usually consists of several stages:

Ductile Fracture z(a) Initial necking z(b) Cavity formation z(c) Cavities form a crack z(d) Crack propagation z(e) Final shear  occurs at an angle of 45 , where shear stress is at a maximum

Atomistic Simulation of Ductile Fracture zLink to Ductile fracture model / movie Mode I fracture

Brittle Fracture zExhibits little or no plastic deformation and low energy absorption before failure. yCrack propagation spontaneous and rapid xOccurs perpendicular to the direction of the applied stress, forming an almost flat fracture surface yDeemed unstable as it will continue to grow without the aid of additional stresses zCrack propagation across grain boundaries is known as transgranular, while propagation along grain boundaries is termed intergranular

Brittle Fracture

Atomistic Simulation of Brittle Fracture zLink or movie of simulated brittle fracture... Mode I fracture

Crack Initiation and Propagation zCracks usually initiate at some point of stress concentration yCommon areas include scratches, fillets, threads, and dents zPropagation occurs in two stages: yStage I propagates very slowly along crystallographic planes of high shear stress and may constitute either a large or small fraction of the fatigue life of a specimen yStage II the crack growth rate increases and changes direction, moving perpendicular to the applied stress

Crack Initiation and Propagation

zImage 1 [110](110) crack zon student simulations fracture page zmode I fracture zanimated gif zhttp:// ts/home.html zCrack propagation simulated in the VT CaveCrack propagation simulated in the VT Cave

Crack Initiation and Propagation zDouble-ended crack simulationsDouble-ended crack simulations

Fracture Mechanics zUses fracture analysis to determine the critical stress at which a crack will propagate and eventually fail zThe stress at which fracture occurs in a material is termed fracture strength yFor a brittle elastic solid this strength is estimated to be around E/10, E being the modulus of elasticity yThis strength is a function of the cohesive forces between the atoms yExperimental values lie between 10 and 1000 times below this value xThese values are a due to very small flaws occurring throughout the material referred to as stress raisers

Fracture Mechanics zIf we assume that the crack is elliptical in shape and it’s longer axis perpendicular to the applied stress, the maximum stress at the crack tip is:   o is the nominal applied tensile stress   t is the radius of curvature of the crack tip x a is the length of a surface crack (becomes a/2 for an internal crack)  Fracture will occur when the stress level exceeds this maximum value  m.

Fracture Mechanics  The ratio  m /  0 is known as the stress concentration factor, K t : yIt is the degree to which an external stress is amplified at the tip of a small crack

Griffith Theory of Brittle Fracture zThe critical stress required for crack propagation in a brittle material is given by: x E = modulus of elasticity   s = specific surface energyspecific surface energy link to fract3.ppt on grain boundary surface energy x a = half the length of an internal crack zApplies only in cases where there is no plastic deformation present.

Fracture Toughness zStresses near the crack tip of a material can also be characterized by the stress intensity factor, K,  A critical value of K exists, similar to the value  c, known as fracture toughness given by: x Y is a dimensionless parameter that depends on both the specimen and crack geometries. xCarries the unusual units of

Plane Strain Fracture Toughness zK c depends on the thickness of plate in question up to a certain point when it becomes constant yThis constant value is known as the plane strain fracture toughness denoted by: xThe I subscript corresponds to a mode I crack displacementmode I xK Ic values are used most often because they represent the worst case scenario Brittle materials have low K Ic values, giving to catastrophic failure ductile materials usually have much larger K Ic values xK Ic depends on temperature, strain rate, and microstructure Increases as grain size decreases

Fracture Toughness in Design zThere are three crucial factors which must be considered in designing for fracture: yThe fracture toughness (K c or plane strain K ic )  the imposed stress (  ) yand the flaw size (a) zIt must be determined first what the limits and constraints on the variables will be yOnce two of them are determined, the third will be fixed yFor example, if the stress level and plane strain fracture toughness are fixed, then the maximum allowable flaw size must be: Next section