Presentation on theme: "FRACTURE Fracture is the separation, or fragmentation, of a solid body into two or more parts under the action of stress. Process of fracture- with two."— Presentation transcript:
1FRACTUREFracture is the separation, or fragmentation, of a solid body into two or more parts under the action of stress.Process of fracture- with two components-CRACK INITIATION CRACK PROPAGATIONFRACTUREDUCTILE BRITTLE
2Fracture Behavior of Bulk Crystalline Materials Fundamentals of FractureDuctile FractureBrittle FractureCrack Initiation and PropagationFracture MechanicsFracture ToughnessDesign
3Fundamentals 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 energyStems from the open bonds on the outer atomsGrain boundaries also contain a surface energy due to the large number of open bondsTwo steps in the process of fracture:Crack initiationPropagation
4Fundamentals of Fracture Simple fracture may occur by one of two methods, ductile or brittleDependent upon the plastic deformation of the materialProperties which influence the plastic deformation of a materialModulus of elasticityCrystal structure
5Fundamentals of Fracture (a) Highly ductile fracture(b) Moderately ductile fracture with neckingCalled a cup-and -cone fractureMost common form of ductile fracture(c) Brittle fractureNo plastic deformation occurring
6Fundamentals of Fracture (a) Highly ductile fracture(b) Moderately ductile fracture with neckingCalled a cup-and -cone fractureMost common form of ductile fracture(c) Brittle fractureNo plastic deformation occurring
7Ductile FractureInvolves 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 appliedThe fracture process usually consists of several stages
8Ductile Fracture(a) Initial necking(b) Cavity formation(c) Cavities form a crack(d) Crack propagation(e) Final shearoccurs at an angle of 45°, where shear stress is at a maximum
9Brittle FractureExhibits little or no plastic deformation and low energy absorption before failure.Crack propagation spontaneous and rapidOccurs perpendicular to the direction of the applied stress, forming an almost flat fracture surfaceDeemed unstable as it will continue to grow without the aid of additional stressesCrack propagation across grain boundaries is known as transgranular, while propagation along grain boundaries is termed intergranular
10Dimple size depends largely on the number of inclusion sites. Ductile fractureA pure and inclusion free metal can elongate under tension to give approx. 100% RA and a point fracture.The central fracture surface consists of numerous cup-like depressions generally called dimples.Dimple size depends largely on the number of inclusion sites.(a) Stages in ductile fracture from inclusions(b) Fracture toughness v/s thickness
11Cleavage patterns in HS steel fracture (x12000) Dimples in a ductile fracture of mild steel (x5000)Intergranular fracture in low alloy steel (x1500)Fatigue striations in Nimonic 80A (x7000)(A.Strang)
12(a) Yield and cohesive stress curves (b) Slow notch bend test(c) Effect of temperature on the Izod value of mild steel
13Cohesive stress-strain curves, B, N, and F. If the two curves intersect at Y, brittle fracture occurs preceded by plastic deformation, which decreases as the cohesive strength curve becomes lower with respect to the yield stress-strain curve.Orowan has shown that if the yield stress is denoted by Y, the strength for brittle fracture by B (both Y and B depend on the plastic strain), and the initial value of Y (for strain = 0) by Y0The following are the relationships:The material is brittle if B < Y0;The material is ductile but notch-brittle if Y0 < B < 3Y0The material is not notch-brittle if 3Y < B.
14Brittle fractureBrittle fracture is characterised by the very small amount of work absorbed and by a crystalline appearance of the surfaces of fracture, often with a chevron pattern pointing to the origin of fracture, due to the formation of discontinuous cleavage cracks which join up
15It can occur at a low stress of MPa with great suddenness; the velocity of crack propagation is probably not far from that of sound in the material in this type of fracture plastic deformation is very small, and the crack need not open up considerably in order to propagate, as is necessary with a ductile failure.
16The work required to propagate a crack is given by Griffith`s formula:σ = tensile stress required to propagatea crack of length c γ = surface energy of fracture faces E = Young`s modulusOrowan modified the Griffith theory to includea plastic strain energy factor, p
17Initiation and propagation portions of fatigue life
18Location of local stresses near a crack tip in cylindrical coordinates
19Mode 1:Opening or tensile mode (the crack faces are pulled apart)Mode 2:Sliding or in-plane shear (the crack surfaces slide over each other)Mode 3:Tearing or anti-plane shear (the crack surfaces move parallel to the leading edge of the crack and relative to each other)
20Most alloys contain second phases which lose cohesion with the matrix or fracture and the voids so formed grow as dislocations flow into them.Coalescence of the voids forms a continuous fracture surface followed by failure of the remaining annulus of material usually on plane at 45° to the tension axis.The central fracture surface consists of numerous cup-like depressions generally called dimples.The shape of the dimples is strongly influenced by the direction of major stresses-circular in pure tension and parabolic under shear
21Behaviour described Terms used Crystallographic mode Appearance of FractureStrain to FractureShearFibrousDuctileCleavageGranularBrittleRef: M.Gensamer
22Stress intensity factor for (a) Center-cracked plate loaded in tension,(b) Edge-cracked plate loaded in tension,(c) Double-edge-cracked plate loaded in tension(d) Cracked beam in pure bending
27TYPICAL FATIGUE STRESS CYCLES (a) REVERSED (b) REPEATED (c ) IRREGULAR OR RANDOM
28Atomistic Simulation of Brittle Fracture Image of simulated brittle fractureMode I fracture
29Crack Initiation and Propagation Cracks usually initiate at some point of stress concentrationCommon areas include scratches, fillets, threads, and dentsPropagation 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 specimenStage II: the crack growth rate increases and changes direction, moving perpendicular to the applied stress
31Crack Initiation and Propagation Double-ended crack simulations
32Fracture MechanicsUses fracture analysis to determine the critical stress at which a crack will propagate and eventually failThe stress at which fracture occurs in a material is termed fracture strengthFor a brittle elastic solid this strength is estimated to be around E/10, E being the modulus of elasticityThis strength is a function of the cohesive forces between the atomsExperimental values lie between 10 and 1000 times below this valueThese values are a due to very small flaws occurring throughout the material referred to as stress raisers
33Fracture MechanicsIf 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:Fracture will occur when the stress level exceeds this maximum value .
34The ratio σm/ σ0 is known as the stress concentration factor, Kt : Fracture MechanicsThe ratio σm/ σ0 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
35Griffith Theory of Brittle Fracture The critical stress required for crack propagation in a brittle material is given by:E = modulus of elasticitygs= specific surface energya = half the length of an internal crackApplies only in cases where there is no plastic deformation present.
36Fracture ToughnessStresses 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
37Yielding near crack tip. FRACTURE TOUGHNESSYielding near crack tip.
38Plane Strain Fracture Toughness Kc depends on the thickness of plate in question up to a certain point when it becomes constantThis constant value is known as the plane strain fracture toughness denoted by:The I subscript corresponds to a mode I crack displacementKIc values are used most often because they represent the worst case scenarioBrittle materials have low KIc values, giving to catastrophic failureductile materials usually have much larger KIc valuesKIc depends on temperature, strain rate, and microstructureIncreases as grain size decreases
39Fracture 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 beOnce two of them are determined, the third will be fixedFor example, if the stress level and plane strain fracture toughness are fixed, then the maximum allowable flaw size must be:
40Ductile FractureInvolves 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 appliedThe fracture process usually consists of several stages
41Fracture MechanicsIf 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:Fracture will occur when the stress level exceeds this maximum value .