Crack Initiation and Crack Initiation and Propagation in Ductile and Propagation in Ductile and

Brittle MaterialsBrittle Materials

IntroductionIntroductionWhat is fracture?What is fracture? Separation by applied stress Separation by applied stress

Two different types of fractureTwo different types of fracture-Ductile-Ductile-Brittle-Brittle

Why study fracture mechanics?Why study fracture mechanics?Reduction of riskReduction of risk

Safety of publicSafety of publicReduction of costReduction of cost

Repairs, replacement Repairs, replacement

Griffith Theory of Brittle FractureGriffith Theory of Brittle Fracture

whereU : the total potential energy of the system U0: the elastic energy of the uncracked plate. Ua: the decrease in the elastic energy caused by introducing the crack in the plate. Ug: the increase in the elastic-surface energy caused by the formation of the crack surfaces.

Fig. 1 Fractograph of ductile cast iron showing a trans-granular fracture surface

Fig. 2 Fractograph of an inter-granular fracture surface

Strain Energy ModelStrain Energy Model

whereE = modulus of elasticity gs= specific surface energy a = one half the length of an internal crack

Model for calculationModel for calculation

whereG: the strain energy release rate. gp: plastic deformation energy associated with crack extension. gs: the specific surface energy

Ductile FractureDuctile Fracture

Stages in ductile fractureStages in ductile fracture InitiationInitiationNeckingNeckingMicrovoids formMicrovoids formMicrovoids enlarge to form crackMicrovoids enlarge to form crackCrack spreads laterallyCrack spreads laterallyRapid crack propagation with 45 degree Rapid crack propagation with 45 degree

angleangleFinal shearingFinal shearing

Fig. 4 Rough, irregular dimpled surface

Fig. 5 Image depicts microvoids

Stress intensity factorStress intensity factor• Magnitude of stress around crack tip

where s = remote stress applied to component (not to be confused with the local stresses, sij a = crack length f (a/w) = correction factor that depends on specimen and crack geometry

The energy of fracture The energy of fracture

wheredt: the energy of fracture necessary for the formation of a new fracture surface area. G: the energy released into the crack tip per unit area of the crack (rate of elastic strain energy release). d: the crack growth increment.

Energy release rate (plane Strain)Energy release rate (plane Strain)

whereG: the energy release rate. n: Poisson's Ratio. K: the stress intensity factor. E: the modulus of elasticity.

Energy release rate (plane Stress)Energy release rate (plane Stress)

G=K2/E G=K2/E

wherewhereG: the energy release rate. G: the energy release rate. K: the stress intensity factor. K: the stress intensity factor. E: the modulus of elasticity. E: the modulus of elasticity.

Modes of crackingModes of cracking

Fig. 7 Three modes of cracking.

Final Equation after combination of Final Equation after combination of energy release rate and mode of energy release rate and mode of

crackingcracking

Fig. 8 Cracked Body

P: the potential energy of the external forces. F: the generalized force per unit thickness. D: the corresponding load-point displacement

Crack Speed and Kinetic EnergyCrack Speed and Kinetic Energy

whereEkin: the kinetic energy. G: the energy release rate. R: the force of crack resistance

The assumptions taken for the model are:crack propagation takes place under constant stress the elastic energy release rate does not depend upon crack speed the crack growth resistance R is constant

Crack Growth using Energy Crack Growth using Energy TheoriesTheories

å/Vs is defined in the graph to be growth rate of the average crack

SummarySummaryDuctileDuctile BrittleBrittle

deformationdeformation extensive extensive little little

crack propagationcrack propagation slow, needs stressslow, needs stress fast fast

type of materialstype of materials most metals (not too most metals (not too cold) cold)

ceramics, ice, cold ceramics, ice, cold metals metals

warningwarning permanent elongation permanent elongation none none

strain energystrain energy higher higher lowerlower

fractured surfacefractured surface roughrough smoother smoother

neckingnecking yes yes nono