Fracture Behavior of Bulk Crystalline Materials z Fundamentals

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

Fundamentals of Fracture z A separation of an object into two or more pieces in response to active stresses far below the melting temperature of the material. z Atoms on the surface of a material give rise to a surface energy y. Stems from the open bonds on the outer atoms y. Grain boundary surface energy xlink to grain boundary surface energy section (fract 3. ppt) z Two steps in the process of fracture: y. Crack initiation y. Propagation

Fundamentals of Fracture z Simple fracture may occur by one of two methods, ductile or brittle y. Dependent upon the plastic deformation of the material x. Properties which influence the plastic deformation of a material • Modulus of elasticity • Crystal structure z Related links: y. The Dislocation Process x. Link to dislocation emission processes (Rice paper? ? ) y. Ductile-to-Brittle Trasition x. Link to ductile-brittle transition (fract 2. ppt)

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

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

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

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

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

Brittle Fracture

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

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

Crack Initiation and Propagation

Crack Initiation and Propagation z. Image 1 [110](110) crack zon student simulations fracture page zmode I fracture zanimated gif zhttp: //www. mse. vt. edu/~farkas/st_projec ts/home. html z. Crack propagation simulated in the VT Cave

Crack Initiation and Propagation z. Double-ended crack simulations

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

Fracture Mechanics z 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 x rt 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) x z Fracture will occur when the stress level exceeds this maximum value sm.

Fracture Mechanics z The ratio sm/s 0 is known as the stress concentration factor, Kt : y. It is the degree to which an external stress is amplified at the tip of a small crack

Griffith Theory of Brittle Fracture z The critical stress required for crack propagation in a brittle material is given by: x E = modulus of elasticity x gs= specific surface energy • link to fract 3. ppt on grain boundary surface energy x a = half the length of an internal crack z Applies only in cases where there is no plastic deformation present.

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

Plane Strain Fracture Toughness z Kc depends on the thickness of plate in question up to a certain point when it becomes constant y. This constant value is known as the plane strain fracture toughness denoted by: x. The I subscript corresponds to a mode I crack displacement x. 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 x. KIc depends on temperature, strain rate, and microstructure • Increases as grain size decreases

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