Failure And Fracture Design Strength And Safety Factors
Failure and Fracture failure of engineering materials is an undesirable occurrence!!– can lead to loss of human life– economic lossesOutline prevention is through good design and materials selection Failure - Introduction Safety factor Types of failure- Ductile fractureExcessivewear onstabilizerjackscrew- Brittle fractureAlaska MD-80 crash (1999) Fractography Principles of fracture mechanics Stress concentration and, Griffith theoryDeath 88 peoplefailure of an O-ringseal (polymer)Challenger (1986)Dr. M. MedrajMech. Eng. Dept. - Concordia UniversityMECH 321 Lecture 8/1Mech. Eng. Dept. - Concordia UniversityDr. M. MedrajMECH 321 Lecture 8/2Design Strength and Safety FactorsFailure and Fracture Uncertainties occur in magnitudes of design loads due toinaccuracies in load calculations and . inmechanical propertiesSo, Failure sometimes takes place!!!. Design allowances are made to avoid potential failure using adesign stress dWhy does it occur?What actually happens during fracture? For static loading and ductile materials, the calculated stresslevel c and design factor, N’ are usedHow can we prevent it? d N' cwhere y d and N' 1Engineer should anticipate & plan for possible failure, and iffailure does occur find out why and prevent re-occurrence. A safe working stress may be assigned w based on the yieldstress: w Dr. M. MedrajMech. Eng. Dept. - Concordia UniversityMECH 321 Lecture 8/3Dr. M. Medraj ywhere N is the .NMech. Eng. Dept. - Concordia UniversityMECH 321 Lecture 8/4
Types of FailureExample: Failure of a Pipe Most fundamental types of failure are ductile and brittle Also have impact, fatigue and creep rupture Fracture involves crack initiation and propagation under anapplied stress Cracks may exist but they are and do not propagateunder the particular loading conditions Ductile: warning before fracture Brittle: no warning Ductile fracture is .! Ductile failure:- one piece- large deformation- . Brittle failure:- many pieces- small deformation- . Ductile failure: as a crack propagates, substantial plastic deformation occurswith absorption of energy (energy of fracture) Highly ductile materials deform plastically under load to the fracture point:– metals: gold and lead at room temperatureVery ductileModeratelyductileMech. Eng. Dept. - Concordia UniversityDr. M. MedrajBrittleMECH 321 Lecture 8/5– polymers and glasses at high temperatureMech. Eng. Dept. - Concordia UniversityDr. M. MedrajFracture ModesMECH 321 Lecture 8/6Moderately Ductile Failure Evolution to failure:Cup & coneneckingBrittle void growthand linkagevoidnucleationshearingat surfacefracture50 mResulting fracturesurfaces (steel)100 mParticles serve asvoid nucleationsites.Dr. M. MedrajMech. Eng. Dept. - Concordia UniversityMECH 321 Lecture 8/7Dr. M. MedrajMech. Eng. Dept. - Concordia UniversityMECH 321 Lecture 8/8
Ductile “Cup and Cone” Fracture Brittle FractureCup and cone ductile fracture is common andincludes:– due to local plastic instability– microvoid formation (fracture initiation)– microvoid coalescence– final shear failure forming shear lipsFormation of classical dimples on fracturesurface:– equiaxed dimples– elongated in shear region No deformation priorto crack initiation Crack initiates at a defect or flaw Fracture propagatesperpendicular to load application Fracture surface hascharacteristic pattern– steel plates contain chevronswhich point back to fractureorigin– alternatively, have radial (fanlike) ridges emanating fromfracture origin– or very smooth surface as inglasses or ceramics(a) Equiaxed dimples(b) Elongated due to shearDr. M. MedrajMech. Eng. Dept. - Concordia UniversityMECH 321 Lecture 8/9Dr. M. MedrajBrittle FractureIntergranular intergranular or alonggrain boundaries due toweakening orembrittlement of grainboundaries ( grains)4 mm304 S. Steel (metal)1 mmPolypropylene (polymer)Dr. M. MedrajMech. Eng. Dept. - Concordia UniversityApprox. 2XMech. Eng. Dept. - Concordia UniversityMECH 321 Lecture 8/10FractugraphyTransgranularBrittle fracture mode is bybreaking of atomic bondsalong particularcrystallographic planes cleavage andtransgranular as itpasses through thegrains of the material( . grains)Origin of the crackSEM Fractograph of ductile castiron shows a transgranularfracture surface.160 m316 S. Steel (metal)3 mSEM Fractograph of anintergranular fracture surface.Al2O3 (ceramic)MECH 321 Lecture 8/11Dr. M. MedrajMech. Eng. Dept. - Concordia UniversityMECH 321 Lecture 8/12
Stress ConcentrationsPrinciples of Fracture Mechanics Quantitative study of failure is called fracture mechanics Fracture mechanics is the relationship between materialsproperties, stress, crack-producing flaws and mechanismsof crack propagation The aim is: “design to prevent structural failure” Theoretical cohesive strength of abrittle, elastic material is E/10 . E/100 toE/10,000Quantify relationships between: material properties Griffith (in 1920s) proposed thatthis difference is due tomicroscopic flaws amplifying thelocal stress and producing astress concentration stress level presence of cracks/defects in material types of crack-propagating mechanismsIntention is to allow better design, only works well if we fracture and the above inter-relationships and material’s limitations.Mech. Eng. Dept. - Concordia UniversityDr. M. Medraj Fracture strength is a function ofcohesive forces holding atomstogether.MECH 321 Lecture 8/13Local increment in stress is a stress raiser ( .)Mech. Eng. Dept. - Concordia UniversityDr. M. MedrajStress ConcentrationsFlaws are Stress Concentrators!Assume an elliptical crack of length, 2a, the local stress is:Maximum stressoccurs at the tip m 1/ 2 a o 1 2 t where o is the nominal applied stress and t is the radius of curvature of the crack tip oWhere t is the radius of thecrack tip and a is the length ofa surface crack or half thelength of an internal crack.Dr. M. Medraj max o 2 a 1 2a t t1/ 2 Stress conc. factor:1/ 2Mech. Eng. Dept. - Concordia UniversityKt max / o Large Kt promotes failure: stress concentration factor is Kt m/ o: a K t 2 t Stress distrib. in front of a hole:Elliptical hole in a plate: If (a/ t ) is very large – the crack islong and thin, therefore: a m 2 o t MECH 321 Lecture 8/14NOTSOBADMECH 321 Lecture 8/15Dr. M. MedrajKt 3BAD!Kt 3Mech. Eng. Dept. - Concordia UniversityMECH 321 Lecture 8/16
Engineering Fracture DesignTheoretical Stress ConcentrationsAvoid sharp corners!Stress Conc. Factor, ow maxr hfilletradius max o2.52.0Stress concentrationscan also apply tocorners and holes aswell as .defects.increasing w/h1.51.0Dr. M. MedrajKt 0r/h0.51.0sharper fillet radiusMech. Eng. Dept. - Concordia UniversityMECH 321 Lecture 8/17Stress concentrationshave much moresignificance in .materials as noplastic deformationcan occur.Dr. M. MedrajGriffith Theory of Brittle FractureDr. M. MedrajMech. Eng. Dept. - Concordia UniversityMECH 321 Lecture 8/19MECH 321 Lecture 8/18Griffith Theory of Brittle FractureIf the change in elastic strain energy dueto crack extension is higher than theenergy required to create new cracksurfaces, crack propagation will occurGriffith proposed that there is a population of defects in allbrittle materials of various sizes, shapes and orientations. Whenan applied stress creates a concentrated stress at one of thesedefects which is higher than the cohesive strength then thedefect or crack propagates and fracture occurs. During crack propagation elastic strain energy is released. Fracture creates new surfaces which raise the surfaceenergy. Griffith performed balance between two energies andderived a critical stress c for propagation of an ellipticalcrack.Mech. Eng. Dept. - Concordia University 2 E s c a 1/ 2(Griffith Equation)where,E elastic modulus s specific surface energy (energy to break bonds/unit area)a one half of the length of an elliptical internal crack (2a)Dr. M. MedrajMech. Eng. Dept. - Concordia UniversityMECH 321 Lecture 8/20
Ductile behaviour In materials, energy of fracture involvesboth generation of new surfaces ( s) and plasticdeformation ( p ) particularly at the crack tip Therefore Griffith’s equation becomes: 2 E s p a 1/ 2 c (Irwin, 1940s):Next Time For ductile materials where p s: 2 E p a Continue Fracture Mechanics1/ 2 c Critical strain energy release rate:Gc 2( s p) GC 2 aECrack extension occurs when 2a/E GcDr. M. MedrajA plastic zone develops at the tip. Asthe load increases, the plastic zoneincreases in size until the crackgrows and the elastically strainedmaterial behind the crack tipunloads. This loading and unloadingcycle leads tothe dissipation of energy as heat.Mech. Eng. Dept. - Concordia UniversityMECH 321 Lecture 8/21Dr. M. MedrajMech. Eng. Dept. - Concordia UniversityMECH 321 Lecture 8/22
Fracture surface has characteristic pattern - steel plates contain chevrons which point back to fracture origin - alternatively, have radial ( fan-like) ridges emanating from fracture origin - or very smooth surface as in glasses or ceramics Approx. 2X Origin of the crack Dr. M. Medraj MECH 321 Lecture 8/10 Brittle Fracture Transgranular
A.2 ASTM fracture toughness values 76 A.3 HDPE fracture toughness results by razor cut depth 77 A.4 PC fracture toughness results by razor cut depth 78 A.5 Fracture toughness values, with 4-point bend fixture and toughness tool. . 79 A.6 Fracture toughness values by fracture surface, .020" RC 80 A.7 Fracture toughness values by fracture surface .
Fracture Liaison/ investigation, treatment and follow-up- prevents further fracture Glasgow FLS 2000-2010 Patients with fragility fracture assessed 50,000 Hip fracture rates -7.3% England hip fracture rates 17% Effective Secondary Prevention of Fragility Fractures: Clinical Standards for Fracture Liaison Services: National Osteoporosis .
Fracture control/Fracture Propagation in Pipelines . Fracture control is an integral part of the design of a pipeline, and is required to minimise both the likelihood of failures occurring (fracture initiation control) and to prevent or arrest long running brittle or ductile fractures (fracture propagation control).
Fracture is defined as the separation of a material into pieces due to an applied stress. Based on the ability of materials to undergo plastic deformation before the fracture, two types of fracture can be observed: ductile and brittle fracture.1,2 In ductile fracture, materials have extensive plastic
the Brittle Fracture Problem Fracture is the separation of a solid body into two or more pieces under the action of stress. Fracture can be classified into two broad categories: ductile fracture and brittle fracture. As shown in the Fig. 2 comparison, ductile fractures are characterized by extensive plastic deformation prior to and during crack
6.4 Fracture of zinc 166 6.5 River lines on calcite 171 6.6 Interpretation of interference patterns on fracture surfaces 175 6.6.1 Interference at blisters and wedges 176 6.6.2 Interference at fracture surfaces of polymers that have crazed 178 6.6.3 Transient fracture surface features 180 6.7 Block fracture of gallium arsenide 180
on the fracture increases, the contact area between the two fracture surfaces also increases, increasing the sti -ness of the fracture. Fracture specific sti ness depends on the elastic properties of the rock and depends criti-cally on the amount and distribution of contact area in a fracture that arises from two rough surfaces in contact
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