Fracture Behavior of Bulk Crystalline Materials

1. Fracture Behavior of Bulk Crystalline Materials • Fundamentals of Fracture • Ductile Fracture • Brittle Fracture • Crack Initiation and Propagation • Fracture Mechanics • Fracture Toughness • Design

2. Fundamentals of Fracture • A separation of an object into two or more pieces in response to active stresses far below the melting temperature of the material. • Atoms on the surface of a material give rise to a surface energy • Stems from the open bonds on the outer atoms • Grain boundary surface energy • link to grain boundary surface energy section (fract3.ppt) • Two steps in the process of fracture: • Crack initiation • Propagation

3. Fundamentals of Fracture • Simple fracture may occur by one of two methods, ductile or brittle • Dependent upon the plastic deformation of the material • Properties which influence the plastic deformation of a material • Modulus of elasticity • Crystal structure • Related links: • The Dislocation Process • Link to dislocation emission processes (Rice paper??) • Ductile-to-Brittle Trasition • Link to ductile-brittle transition (fract2.ppt)

4. Fundamentals of Fracture • (a) Highly ductile fracture • (b) Moderately ductile fracture with necking • Called a cup-and -cone fracture • Most common form of ductile fracture • (c) Brittle fracture • No plastic deformation occurring

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

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

7. Atomistic Simulation of Ductile Fracture • Link to Ductile fracture model / movie Mode I fracture

8. Brittle Fracture • Exhibits little or no plastic deformation and low energy absorption before failure. • Crack propagation spontaneous and rapid • Occurs perpendicular to the direction of the applied stress, forming an almost flat fracture surface • Deemed unstable as it will continue to grow without the aid of additional stresses • Crack propagation across grain boundaries is known astransgranular, while propagation along grain boundaries is termed intergranular

9. Brittle Fracture

10. Atomistic Simulation of Brittle Fracture • Link or movie of simulated brittle fracture... Mode I fracture

11. Crack Initiation and Propagation • Cracks usually initiate at some point of stress concentration • Common areas include scratches, fillets, threads, and dents • Propagation occurs in two stages: • Stage 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 • Stage II the crack growth rate increases and changes direction, moving perpendicular to the applied stress

12. Crack Initiation and Propagation

13. Crack Initiation and Propagation • Image 1 [110](110) crack • on student simulations fracture page • mode I fracture • animated gif • http://www.mse.vt.edu/~farkas/st_projects/home.html • Crack propagation simulated in the VT Cave

14. Crack Initiation and Propagation • Double-ended crack simulations

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

16. Fracture Mechanics • If 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: • so is the nominal applied tensile stress • rt is the radius of curvature of the crack tip • 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 sm.

17. Fracture Mechanics • The ratio sm/s0 is known as the stress concentration factor, Kt : • It is the degree to which an external stress is amplified at the tip of a small crack

18. Griffith Theory of Brittle Fracture • The critical stress required for crack propagation in a brittle material is given by: • E = modulus of elasticity • gs= specific surface energy • link to fract3.ppt on grain boundary surface energy • a = half the length of an internal crack • Applies only in cases where there is no plastic deformation present.

19. Fracture Toughness • Stresses 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 sc, known as fracture toughness given by: • Y is a dimensionless parameter that depends on both the specimen and crack geometries. • Carries the unusual units of

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

21. Fracture Toughness in Design • There are three crucial factors which must be considered in designing for fracture: • The fracture toughness (Kc or plane strain Kic) • the imposed stress (s) • and the flaw size (a) • It must be determined first what the limits and constraints on the variables will be • Once two of them are determined, the third will be fixed • For example, if the stress level and plane strain fracture toughness are fixed, then the maximum allowable flaw size must be: Next section